>> x = np.ma.array([[1,2 ], [3, 4]], mask=[0]*4)\n>>> x.mask\narray([[False, False],\n [False, False]])\n>>> x.shrink_mask()\nmasked_array(\n data=[[1, 2],\n [3, 4]],\n mask=False,\n fill_value=999999)\n>>> x.mask\nFalse\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.shrink_mask.htmlnumpy.ma.MaskedArray.unshare_mask\n==================================\n\n method\n\n ma.MaskedArray.unshare_mask()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3623-L3639)\n \nCopy the mask and set the [`sharedmask`](../maskedarray.baseclass#numpy.ma.MaskedArray.sharedmask \"numpy.ma.MaskedArray.sharedmask\") flag to `False`.\n\n Whether the mask is shared between masked arrays can be seen from the [`sharedmask`](../maskedarray.baseclass#numpy.ma.MaskedArray.sharedmask \"numpy.ma.MaskedArray.sharedmask\") property. [`unshare_mask`](#numpy.ma.MaskedArray.unshare_mask \"numpy.ma.MaskedArray.unshare_mask\") ensures the mask is not shared. A copy of the mask is only made if it was shared.\n\n See also\n\n [`sharedmask`](../maskedarray.baseclass#numpy.ma.MaskedArray.sharedmask \"numpy.ma.MaskedArray.sharedmask\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.unshare_mask.htmlnumpy.ma.asarray\n================\n\n ma.asarray(*a*, *dtype=None*, *order=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7958-L8004)\n \nConvert the input to a masked array of the given data-type.\n\n No copy is performed if the input is already an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"). If `a` is a subclass of [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\"), a base class [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\") is returned.\n\n Parameters \n \n**a**array_like\n\nInput data, in any form that can be converted to a masked array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists, ndarrays and masked arrays.\n\n \n**dtype**dtype, optional\n\nBy default, the data-type is inferred from the input data.\n\n \n**order**{‘C’, ‘F’}, optional\n\nWhether to use row-major (‘C’) or column-major (‘FORTRAN’) memory representation. Default is ‘C’.\n\n Returns \n \n**out**MaskedArray\n\nMasked array interpretation of `a`.\n\n See also\n\n [`asanyarray`](numpy.asanyarray#numpy.asanyarray \"numpy.asanyarray\")\n\nSimilar to [`asarray`](numpy.asarray#numpy.asarray \"numpy.asarray\"), but conserves subclasses.\n\n #### Examples\n\n \n```\n>>> x = np.arange(10.).reshape(2, 5)\n>>> x\narray([[0., 1., 2., 3., 4.],\n [5., 6., 7., 8., 9.]])\n>>> np.ma.asarray(x)\nmasked_array(\n data=[[0., 1., 2., 3., 4.],\n [5., 6., 7., 8., 9.]],\n mask=False,\n fill_value=1e+20)\n>>> type(np.ma.asarray(x))\n<class 'numpy.ma.core.MaskedArray'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.asarray.htmlnumpy.ma.asanyarray\n===================\n\n ma.asanyarray(*a*, *dtype=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L8007-L8053)\n \nConvert the input to a masked array, conserving subclasses.\n\n If `a` is a subclass of [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\"), its class is conserved. No copy is performed if the input is already an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\").\n\n Parameters \n \n**a**array_like\n\nInput data, in any form that can be converted to an array.\n\n \n**dtype**dtype, optional\n\nBy default, the data-type is inferred from the input data.\n\n \n**order**{‘C’, ‘F’}, optional\n\nWhether to use row-major (‘C’) or column-major (‘FORTRAN’) memory representation. Default is ‘C’.\n\n Returns \n \n**out**MaskedArray\n\nMaskedArray interpretation of `a`.\n\n See also\n\n [`asarray`](numpy.asarray#numpy.asarray \"numpy.asarray\")\n\nSimilar to [`asanyarray`](numpy.asanyarray#numpy.asanyarray \"numpy.asanyarray\"), but does not conserve subclass.\n\n #### Examples\n\n \n```\n>>> x = np.arange(10.).reshape(2, 5)\n>>> x\narray([[0., 1., 2., 3., 4.],\n [5., 6., 7., 8., 9.]])\n>>> np.ma.asanyarray(x)\nmasked_array(\n data=[[0., 1., 2., 3., 4.],\n [5., 6., 7., 8., 9.]],\n mask=False,\n fill_value=1e+20)\n>>> type(np.ma.asanyarray(x))\n<class 'numpy.ma.core.MaskedArray'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.asanyarray.htmlnumpy.ma.fix_invalid\n=====================\n\n ma.fix_invalid(*a*, *mask=False*, *copy=True*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L718-L774)\n \nReturn input with invalid data masked and replaced by a fill value.\n\n Invalid data means values of [`nan`](../constants#numpy.nan \"numpy.nan\"), [`inf`](../constants#numpy.inf \"numpy.inf\"), etc.\n\n Parameters \n \n**a**array_like\n\nInput array, a (subclass of) ndarray.\n\n \n**mask**sequence, optional\n\nMask. Must be convertible to an array of booleans with the same shape as `data`. True indicates a masked (i.e. invalid) data.\n\n \n**copy**bool, optional\n\nWhether to use a copy of `a` (True) or to fix `a` in place (False). Default is True.\n\n \n**fill_value**scalar, optional\n\nValue used for fixing invalid data. Default is None, in which case the `a.fill_value` is used.\n\n Returns \n \n**b**MaskedArray\n\nThe input array with invalid entries fixed.\n\n #### Notes\n\n A copy is performed by default.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([1., -1, np.nan, np.inf], mask=[1] + [0]*3)\n>>> x\nmasked_array(data=[--, -1.0, nan, inf],\n mask=[ True, False, False, False],\n fill_value=1e+20)\n>>> np.ma.fix_invalid(x)\nmasked_array(data=[--, -1.0, --, --],\n mask=[ True, False, True, True],\n fill_value=1e+20)\n\n```\n \n```\n>>> fixed = np.ma.fix_invalid(x)\n>>> fixed.data\narray([ 1.e+00, -1.e+00, 1.e+20, 1.e+20])\n>>> x.data\narray([ 1., -1., nan, inf])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.fix_invalid.htmlnumpy.ma.masked_equal\n======================\n\n ma.masked_equal(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2073-L2100)\n \nMask an array where equal to a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x == value). For floating point arrays, consider using `masked_values(x, value)`.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n [`masked_values`](numpy.ma.masked_values#numpy.ma.masked_values \"numpy.ma.masked_values\")\n\nMask using floating point equality.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_equal(a, 2)\nmasked_array(data=[0, 1, --, 3],\n mask=[False, False, True, False],\n fill_value=2)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_equal.htmlnumpy.ma.masked_greater\n========================\n\n ma.masked_greater(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L1943-L1966)\n \nMask an array where greater than a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x > value).\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_greater(a, 2)\nmasked_array(data=[0, 1, 2, --],\n mask=[False, False, False, True],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_greater.htmlnumpy.ma.masked_greater_equal\n===============================\n\n ma.masked_greater_equal(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L1969-L1992)\n \nMask an array where greater than or equal to a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x >= value).\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_greater_equal(a, 2)\nmasked_array(data=[0, 1, --, --],\n mask=[False, False, True, True],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_greater_equal.htmlnumpy.ma.masked_inside\n=======================\n\n ma.masked_inside(*x*, *v1*, *v2*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2103-L2140)\n \nMask an array inside a given interval.\n\n Shortcut to `masked_where`, where `condition` is True for `x` inside the interval [v1,v2] (v1 <= x <= v2). The boundaries `v1` and `v2` can be given in either order.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Notes\n\n The array `x` is prefilled with its filling value.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> x = [0.31, 1.2, 0.01, 0.2, -0.4, -1.1]\n>>> ma.masked_inside(x, -0.3, 0.3)\nmasked_array(data=[0.31, 1.2, --, --, -0.4, -1.1],\n mask=[False, False, True, True, False, False],\n fill_value=1e+20)\n\n```\n The order of `v1` and `v2` doesn’t matter.\n\n \n```\n>>> ma.masked_inside(x, 0.3, -0.3)\nmasked_array(data=[0.31, 1.2, --, --, -0.4, -1.1],\n mask=[False, False, True, True, False, False],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_inside.htmlnumpy.ma.masked_invalid\n========================\n\n ma.masked_invalid(*a*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2331-L2370)\n \nMask an array where invalid values occur (NaNs or infs).\n\n This function is a shortcut to `masked_where`, with `condition` = ~(np.isfinite(a)). Any pre-existing mask is conserved. Only applies to arrays with a dtype where NaNs or infs make sense (i.e. floating point types), but accepts any array_like object.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(5, dtype=float)\n>>> a[2] = np.NaN\n>>> a[3] = np.PINF\n>>> a\narray([ 0., 1., nan, inf, 4.])\n>>> ma.masked_invalid(a)\nmasked_array(data=[0.0, 1.0, --, --, 4.0],\n mask=[False, False, True, True, False],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_invalid.htmlnumpy.ma.masked_less\n=====================\n\n ma.masked_less(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L1995-L2018)\n \nMask an array where less than a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x < value).\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_less(a, 2)\nmasked_array(data=[--, --, 2, 3],\n mask=[ True, True, False, False],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_less.htmlnumpy.ma.masked_less_equal\n============================\n\n ma.masked_less_equal(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2021-L2044)\n \nMask an array where less than or equal to a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x <= value).\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_less_equal(a, 2)\nmasked_array(data=[--, --, --, 3],\n mask=[ True, True, True, False],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_less_equal.htmlnumpy.ma.masked_not_equal\n===========================\n\n ma.masked_not_equal(*x*, *value*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2047-L2070)\n \nMask an array where `not` equal to a given value.\n\n This function is a shortcut to `masked_where`, with `condition` = (x != value).\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_not_equal(a, 2)\nmasked_array(data=[--, --, 2, --],\n mask=[ True, True, False, True],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_not_equal.htmlnumpy.ma.masked_object\n=======================\n\n ma.masked_object(*x*, *value*, *copy=True*, *shrink=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2183-L2248)\n \nMask the array `x` where the data are exactly equal to value.\n\n This function is similar to [`masked_values`](numpy.ma.masked_values#numpy.ma.masked_values \"numpy.ma.masked_values\"), but only suitable for object arrays: for floating point, use [`masked_values`](numpy.ma.masked_values#numpy.ma.masked_values \"numpy.ma.masked_values\") instead.\n\n Parameters \n \n**x**array_like\n\nArray to mask\n\n \n**value**object\n\nComparison value\n\n \n**copy**{True, False}, optional\n\nWhether to return a copy of `x`.\n\n \n**shrink**{True, False}, optional\n\nWhether to collapse a mask full of False to nomask\n\n Returns \n \n**result**MaskedArray\n\nThe result of masking `x` where equal to `value`.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n [`masked_equal`](numpy.ma.masked_equal#numpy.ma.masked_equal \"numpy.ma.masked_equal\")\n\nMask where equal to a given value (integers).\n\n [`masked_values`](numpy.ma.masked_values#numpy.ma.masked_values \"numpy.ma.masked_values\")\n\nMask using floating point equality.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> food = np.array(['green_eggs', 'ham'], dtype=object)\n>>> # don't eat spoiled food\n>>> eat = ma.masked_object(food, 'green_eggs')\n>>> eat\nmasked_array(data=[--, 'ham'],\n mask=[ True, False],\n fill_value='green_eggs',\n dtype=object)\n>>> # plain ol` ham is boring\n>>> fresh_food = np.array(['cheese', 'ham', 'pineapple'], dtype=object)\n>>> eat = ma.masked_object(fresh_food, 'green_eggs')\n>>> eat\nmasked_array(data=['cheese', 'ham', 'pineapple'],\n mask=False,\n fill_value='green_eggs',\n dtype=object)\n\n```\n Note that `mask` is set to `nomask` if possible.\n\n \n```\n>>> eat\nmasked_array(data=['cheese', 'ham', 'pineapple'],\n mask=False,\n fill_value='green_eggs',\n dtype=object)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_object.htmlnumpy.ma.masked_outside\n========================\n\n ma.masked_outside(*x*, *v1*, *v2*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2143-L2180)\n \nMask an array outside a given interval.\n\n Shortcut to `masked_where`, where `condition` is True for `x` outside the interval [v1,v2] (x < v1)|(x > v2). The boundaries `v1` and `v2` can be given in either order.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n #### Notes\n\n The array `x` is prefilled with its filling value.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> x = [0.31, 1.2, 0.01, 0.2, -0.4, -1.1]\n>>> ma.masked_outside(x, -0.3, 0.3)\nmasked_array(data=[--, --, 0.01, 0.2, --, --],\n mask=[ True, True, False, False, True, True],\n fill_value=1e+20)\n\n```\n The order of `v1` and `v2` doesn’t matter.\n\n \n```\n>>> ma.masked_outside(x, 0.3, -0.3)\nmasked_array(data=[--, --, 0.01, 0.2, --, --],\n mask=[ True, True, False, False, True, True],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_outside.htmlnumpy.ma.masked_values\n=======================\n\n ma.masked_values(*x*, *value*, *rtol=1e-05*, *atol=1e-08*, *copy=True*, *shrink=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2251-L2328)\n \nMask using floating point equality.\n\n Return a MaskedArray, masked where the data in array `x` are approximately equal to `value`, determined using [`isclose`](numpy.isclose#numpy.isclose \"numpy.isclose\"). The default tolerances for [`masked_values`](#numpy.ma.masked_values \"numpy.ma.masked_values\") are the same as those for [`isclose`](numpy.isclose#numpy.isclose \"numpy.isclose\").\n\n For integer types, exact equality is used, in the same way as [`masked_equal`](numpy.ma.masked_equal#numpy.ma.masked_equal \"numpy.ma.masked_equal\").\n\n The fill_value is set to `value` and the mask is set to `nomask` if possible.\n\n Parameters \n \n**x**array_like\n\nArray to mask.\n\n \n**value**float\n\nMasking value.\n\n \n**rtol, atol**float, optional\n\nTolerance parameters passed on to [`isclose`](numpy.isclose#numpy.isclose \"numpy.isclose\")\n\n \n**copy**bool, optional\n\nWhether to return a copy of `x`.\n\n \n**shrink**bool, optional\n\nWhether to collapse a mask full of False to `nomask`.\n\n Returns \n \n**result**MaskedArray\n\nThe result of masking `x` where approximately equal to `value`.\n\n See also\n\n [`masked_where`](numpy.ma.masked_where#numpy.ma.masked_where \"numpy.ma.masked_where\")\n\nMask where a condition is met.\n\n [`masked_equal`](numpy.ma.masked_equal#numpy.ma.masked_equal \"numpy.ma.masked_equal\")\n\nMask where equal to a given value (integers).\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> x = np.array([1, 1.1, 2, 1.1, 3])\n>>> ma.masked_values(x, 1.1)\nmasked_array(data=[1.0, --, 2.0, --, 3.0],\n mask=[False, True, False, True, False],\n fill_value=1.1)\n\n```\n Note that `mask` is set to `nomask` if possible.\n\n \n```\n>>> ma.masked_values(x, 1.5)\nmasked_array(data=[1. , 1.1, 2. , 1.1, 3. ],\n mask=False,\n fill_value=1.5)\n\n```\n For integers, the fill value will be different in general to the result of `masked_equal`.\n\n \n```\n>>> x = np.arange(5)\n>>> x\narray([0, 1, 2, 3, 4])\n>>> ma.masked_values(x, 2)\nmasked_array(data=[0, 1, --, 3, 4],\n mask=[False, False, True, False, False],\n fill_value=2)\n>>> ma.masked_equal(x, 2)\nmasked_array(data=[0, 1, --, 3, 4],\n mask=[False, False, True, False, False],\n fill_value=2)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_values.htmlnumpy.ma.masked_where\n======================\n\n ma.masked_where(*condition*, *a*, *copy=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L1821-L1940)\n \nMask an array where a condition is met.\n\n Return `a` as an array masked where `condition` is True. Any masked values of `a` or `condition` are also masked in the output.\n\n Parameters \n \n**condition**array_like\n\nMasking condition. When `condition` tests floating point values for equality, consider using `masked_values` instead.\n\n \n**a**array_like\n\nArray to mask.\n\n \n**copy**bool\n\nIf True (default) make a copy of `a` in the result. If False modify `a` in place and return a view.\n\n Returns \n \n**result**MaskedArray\n\nThe result of masking `a` where `condition` is True.\n\n See also\n\n [`masked_values`](numpy.ma.masked_values#numpy.ma.masked_values \"numpy.ma.masked_values\")\n\nMask using floating point equality.\n\n [`masked_equal`](numpy.ma.masked_equal#numpy.ma.masked_equal \"numpy.ma.masked_equal\")\n\nMask where equal to a given value.\n\n [`masked_not_equal`](numpy.ma.masked_not_equal#numpy.ma.masked_not_equal \"numpy.ma.masked_not_equal\")\n\nMask where `not` equal to a given value.\n\n [`masked_less_equal`](numpy.ma.masked_less_equal#numpy.ma.masked_less_equal \"numpy.ma.masked_less_equal\")\n\nMask where less than or equal to a given value.\n\n [`masked_greater_equal`](numpy.ma.masked_greater_equal#numpy.ma.masked_greater_equal \"numpy.ma.masked_greater_equal\")\n\nMask where greater than or equal to a given value.\n\n [`masked_less`](numpy.ma.masked_less#numpy.ma.masked_less \"numpy.ma.masked_less\")\n\nMask where less than a given value.\n\n [`masked_greater`](numpy.ma.masked_greater#numpy.ma.masked_greater \"numpy.ma.masked_greater\")\n\nMask where greater than a given value.\n\n [`masked_inside`](numpy.ma.masked_inside#numpy.ma.masked_inside \"numpy.ma.masked_inside\")\n\nMask inside a given interval.\n\n [`masked_outside`](numpy.ma.masked_outside#numpy.ma.masked_outside \"numpy.ma.masked_outside\")\n\nMask outside a given interval.\n\n [`masked_invalid`](numpy.ma.masked_invalid#numpy.ma.masked_invalid \"numpy.ma.masked_invalid\")\n\nMask invalid values (NaNs or infs).\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(4)\n>>> a\narray([0, 1, 2, 3])\n>>> ma.masked_where(a <= 2, a)\nmasked_array(data=[--, --, --, 3],\n mask=[ True, True, True, False],\n fill_value=999999)\n\n```\n Mask array `b` conditional on `a`.\n\n \n```\n>>> b = ['a', 'b', 'c', 'd']\n>>> ma.masked_where(a == 2, b)\nmasked_array(data=['a', 'b', --, 'd'],\n mask=[False, False, True, False],\n fill_value='N/A',\n dtype='<U1')\n\n```\n Effect of the [`copy`](numpy.copy#numpy.copy \"numpy.copy\") argument.\n\n \n```\n>>> c = ma.masked_where(a <= 2, a)\n>>> c\nmasked_array(data=[--, --, --, 3],\n mask=[ True, True, True, False],\n fill_value=999999)\n>>> c[0] = 99\n>>> c\nmasked_array(data=[99, --, --, 3],\n mask=[False, True, True, False],\n fill_value=999999)\n>>> a\narray([0, 1, 2, 3])\n>>> c = ma.masked_where(a <= 2, a, copy=False)\n>>> c[0] = 99\n>>> c\nmasked_array(data=[99, --, --, 3],\n mask=[False, True, True, False],\n fill_value=999999)\n>>> a\narray([99, 1, 2, 3])\n\n```\n When `condition` or `a` contain masked values.\n\n \n```\n>>> a = np.arange(4)\n>>> a = ma.masked_where(a == 2, a)\n>>> a\nmasked_array(data=[0, 1, --, 3],\n mask=[False, False, True, False],\n fill_value=999999)\n>>> b = np.arange(4)\n>>> b = ma.masked_where(b == 0, b)\n>>> b\nmasked_array(data=[--, 1, 2, 3],\n mask=[ True, False, False, False],\n fill_value=999999)\n>>> ma.masked_where(a == 3, b)\nmasked_array(data=[--, 1, --, --],\n mask=[ True, False, True, True],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.masked_where.htmlnumpy.ma.compress_cols\n=======================\n\n ma.compress_cols(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L944-L959)\n \nSuppress whole columns of a 2-D array that contain masked values.\n\n This is equivalent to `np.ma.compress_rowcols(a, 1)`, see [`compress_rowcols`](numpy.ma.compress_rowcols#numpy.ma.compress_rowcols \"numpy.ma.compress_rowcols\") for details.\n\n See also\n\n [`compress_rowcols`](numpy.ma.compress_rowcols#numpy.ma.compress_rowcols \"numpy.ma.compress_rowcols\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.compress_cols.htmlnumpy.ma.compress_rowcols\n==========================\n\n ma.compress_rowcols(*x*, *axis=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L871-L923)\n \nSuppress the rows and/or columns of a 2-D array that contain masked values.\n\n The suppression behavior is selected with the `axis` parameter.\n\n * If axis is None, both rows and columns are suppressed.\n* If axis is 0, only rows are suppressed.\n* If axis is 1 or -1, only columns are suppressed.\n\n Parameters \n \n**x**array_like, MaskedArray\n\nThe array to operate on. If not a MaskedArray instance (or if no array elements are masked), `x` is interpreted as a MaskedArray with `mask` set to [`nomask`](../maskedarray.baseclass#numpy.ma.nomask \"numpy.ma.nomask\"). Must be a 2D array.\n\n \n**axis**int, optional\n\nAxis along which to perform the operation. Default is None.\n\n Returns \n \n**compressed_array**ndarray\n\nThe compressed array.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(9).reshape(3, 3), mask=[[1, 0, 0],\n... [1, 0, 0],\n... [0, 0, 0]])\n>>> x\nmasked_array(\n data=[[--, 1, 2],\n [--, 4, 5],\n [6, 7, 8]],\n mask=[[ True, False, False],\n [ True, False, False],\n [False, False, False]],\n fill_value=999999)\n\n```\n \n```\n>>> np.ma.compress_rowcols(x)\narray([[7, 8]])\n>>> np.ma.compress_rowcols(x, 0)\narray([[6, 7, 8]])\n>>> np.ma.compress_rowcols(x, 1)\narray([[1, 2],\n [4, 5],\n [7, 8]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.compress_rowcols.htmlnumpy.ma.compress_rows\n=======================\n\n ma.compress_rows(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L926-L941)\n \nSuppress whole rows of a 2-D array that contain masked values.\n\n This is equivalent to `np.ma.compress_rowcols(a, 0)`, see [`compress_rowcols`](numpy.ma.compress_rowcols#numpy.ma.compress_rowcols \"numpy.ma.compress_rowcols\") for details.\n\n See also\n\n [`compress_rowcols`](numpy.ma.compress_rowcols#numpy.ma.compress_rowcols \"numpy.ma.compress_rowcols\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.compress_rows.htmlnumpy.ma.compressed\n===================\n\n ma.compressed(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6962-L6974)\n \nReturn all the non-masked data as a 1-D array.\n\n This function is equivalent to calling the “compressed” method of a [`ma.MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\"), see [`ma.MaskedArray.compressed`](numpy.ma.maskedarray.compressed#numpy.ma.MaskedArray.compressed \"numpy.ma.MaskedArray.compressed\") for details.\n\n See also\n\n [`ma.MaskedArray.compressed`](numpy.ma.maskedarray.compressed#numpy.ma.MaskedArray.compressed \"numpy.ma.MaskedArray.compressed\")\n\nEquivalent method.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.compressed.htmlnumpy.ma.filled\n===============\n\n ma.filled(*a*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L580-L634)\n \nReturn input as an array with masked data replaced by a fill value.\n\n If `a` is not a [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\"), `a` itself is returned. If `a` is a [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\") and `fill_value` is None, `fill_value` is set to `a.fill_value`.\n\n Parameters \n \n**a**MaskedArray or array_like\n\nAn input object.\n\n \n**fill_value**array_like, optional.\n\nCan be scalar or non-scalar. If non-scalar, the resulting filled array should be broadcastable over input array. Default is None.\n\n Returns \n \n**a**ndarray\n\nThe filled array.\n\n See also\n\n [`compressed`](numpy.ma.compressed#numpy.ma.compressed \"numpy.ma.compressed\")\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(9).reshape(3, 3), mask=[[1, 0, 0],\n... [1, 0, 0],\n... [0, 0, 0]])\n>>> x.filled()\narray([[999999, 1, 2],\n [999999, 4, 5],\n [ 6, 7, 8]])\n>>> x.filled(fill_value=333)\narray([[333, 1, 2],\n [333, 4, 5],\n [ 6, 7, 8]])\n>>> x.filled(fill_value=np.arange(3))\narray([[0, 1, 2],\n [0, 4, 5],\n [6, 7, 8]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.filled.htmlnumpy.ma.MaskedArray.compressed\n===============================\n\n method\n\n ma.MaskedArray.compressed()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3856-L3881)\n \nReturn all the non-masked data as a 1-D array.\n\n Returns \n \n**data**ndarray\n\nA new [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") holding the non-masked data is returned.\n\n #### Notes\n\n The result is **not** a MaskedArray!\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(5), mask=[0]*2 + [1]*3)\n>>> x.compressed()\narray([0, 1])\n>>> type(x.compressed())\n<class 'numpy.ndarray'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.compressed.htmlnumpy.ma.MaskedArray.filled\n===========================\n\n method\n\n ma.MaskedArray.filled(*fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3776-L3854)\n \nReturn a copy of self, with masked values filled with a given value. **However**, if there are no masked values to fill, self will be returned instead as an ndarray.\n\n Parameters \n \n**fill_value**array_like, optional\n\nThe value to use for invalid entries. Can be scalar or non-scalar. If non-scalar, the resulting ndarray must be broadcastable over input array. Default is None, in which case, the [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") attribute of the array is used instead.\n\n Returns \n \n**filled_array**ndarray\n\nA copy of `self` with invalid entries replaced by *fill_value* (be it the function argument or the attribute of `self`), or `self` itself as an ndarray if there are no invalid entries to be replaced.\n\n #### Notes\n\n The result is **not** a MaskedArray!\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([1,2,3,4,5], mask=[0,0,1,0,1], fill_value=-999)\n>>> x.filled()\narray([ 1, 2, -999, 4, -999])\n>>> x.filled(fill_value=1000)\narray([ 1, 2, 1000, 4, 1000])\n>>> type(x.filled())\n<class 'numpy.ndarray'```\n Subclassing is preserved. This means that if, e.g., the data part of the masked array is a recarray, [`filled`](#numpy.ma.MaskedArray.filled \"numpy.ma.MaskedArray.filled\") returns a recarray:\n\n \n```\n>>> x = np.array([(-1, 2), (-3, 4)], dtype='i8,i8').view(np.recarray)\n>>> m = np.ma.array(x, mask=[(True, False), (False, True)])\n>>> m.filled()\nrec.array([(999999, 2), ( -3, 999999)],\n dtype=[('f0', '<i8'), ('f1', '<i8')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.filled.htmlnumpy.ma.MaskedArray.tofile\n===========================\n\n method\n\n ma.MaskedArray.tofile(*fid*, *sep=''*, *format='%s'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6154-L6167)\n \nSave a masked array to a file in binary format.\n\n Warning\n\n This function is not implemented yet.\n\n Raises \n NotImplementedError\n\nWhen [`tofile`](#numpy.ma.MaskedArray.tofile \"numpy.ma.MaskedArray.tofile\") is called.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.tofile.htmlnumpy.ma.MaskedArray.tolist\n===========================\n\n method\n\n ma.MaskedArray.tolist(*fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6048-L6097)\n \nReturn the data portion of the masked array as a hierarchical Python list.\n\n Data items are converted to the nearest compatible Python type. Masked values are converted to [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\"). If [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") is None, the corresponding entries in the output list will be `None`.\n\n Parameters \n \n**fill_value**scalar, optional\n\nThe value to use for invalid entries. Default is None.\n\n Returns \n \n**result**list\n\nThe Python list representation of the masked array.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3], [4,5,6], [7,8,9]], mask=[0] + [1,0]*4)\n>>> x.tolist()\n[[1, None, 3], [None, 5, None], [7, None, 9]]\n>>> x.tolist(-999)\n[[1, -999, 3], [-999, 5, -999], [7, -999, 9]]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.tolist.htmlnumpy.ma.MaskedArray.torecords\n==============================\n\n method\n\n ma.MaskedArray.torecords()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6169-L6226)\n \nTransforms a masked array into a flexible-type array.\n\n The flexible type array that is returned will have two fields:\n\n * the `_data` field stores the `_data` part of the array.\n* the `_mask` field stores the `_mask` part of the array.\n\n Parameters \n **None**\n Returns \n \n**record**ndarray\n\nA new flexible-type [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") with two fields: the first element containing a value, the second element containing the corresponding mask boolean. The returned record shape matches self.shape.\n\n #### Notes\n\n A side-effect of transforming a masked array into a flexible [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") is that meta information (`fill_value`, …) will be lost.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.toflex()\narray([[(1, False), (2, True), (3, False)],\n [(4, True), (5, False), (6, True)],\n [(7, False), (8, True), (9, False)]],\n dtype=[('_data', '<i8'), ('_mask', '?')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.torecords.htmlnumpy.ma.MaskedArray.tobytes\n============================\n\n method\n\n ma.MaskedArray.tobytes(*fill_value=None*, *order='C'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6114-L6152)\n \nReturn the array data as a string containing the raw bytes in the array.\n\n The array is filled with a fill value before the string conversion.\n\n New in version 1.9.0.\n\n Parameters \n \n**fill_value**scalar, optional\n\nValue used to fill in the masked values. Default is None, in which case `MaskedArray.fill_value` is used.\n\n \n**order**{‘C’,’F’,’A’}, optional\n\nOrder of the data item in the copy. Default is ‘C’.\n\n * ‘C’ – C order (row major).\n* ‘F’ – Fortran order (column major).\n* ‘A’ – Any, current order of array.\n* None – Same as ‘A’.\n\n See also\n\n [`numpy.ndarray.tobytes`](numpy.ndarray.tobytes#numpy.ndarray.tobytes \"numpy.ndarray.tobytes\")\n\n[`tolist`](numpy.ma.maskedarray.tolist#numpy.ma.MaskedArray.tolist \"numpy.ma.MaskedArray.tolist\"), [`tofile`](numpy.ma.maskedarray.tofile#numpy.ma.MaskedArray.tofile \"numpy.ma.MaskedArray.tofile\")\n\n #### Notes\n\n As for [`ndarray.tobytes`](numpy.ndarray.tobytes#numpy.ndarray.tobytes \"numpy.ndarray.tobytes\"), information about the shape, dtype, etc., but also about [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\"), will be lost.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.array([[1, 2], [3, 4]]), mask=[[0, 1], [1, 0]])\n>>> x.tobytes()\nb'\\x01\\x00\\x00\\x00\\x00\\x00\\x00\\x00?B\\x0f\\x00\\x00\\x00\\x00\\x00?B\\x0f\\x00\\x00\\x00\\x00\\x00\\x04\\x00\\x00\\x00\\x00\\x00\\x00\\x00'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.tobytes.htmlnumpy.ma.common_fill_value\n============================\n\n ma.common_fill_value(*a*, *b*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L548-L577)\n \nReturn the common filling value of two masked arrays, if any.\n\n If `a.fill_value == b.fill_value`, return the fill value, otherwise return None.\n\n Parameters \n \n**a, b**MaskedArray\n\nThe masked arrays for which to compare fill values.\n\n Returns \n \n**fill_value**scalar or None\n\nThe common fill value, or None.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([0, 1.], fill_value=3)\n>>> y = np.ma.array([0, 1.], fill_value=3)\n>>> np.ma.common_fill_value(x, y)\n3.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.common_fill_value.htmlnumpy.ma.default_fill_value\n=============================\n\n ma.default_fill_value(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L223-L275)\n \nReturn the default fill value for the argument object.\n\n The default filling value depends on the datatype of the input array or the type of the input scalar:\n\n \n\n| datatype | default |\n| --- | --- |\n| bool | True |\n| int | 999999 |\n| float | 1.e20 |\n| complex | 1.e20+0j |\n| object | ‘?’ |\n| string | ‘N/A’ |\n\n For structured types, a structured scalar is returned, with each field the default fill value for its type.\n\n For subarray types, the fill value is an array of the same size containing the default scalar fill value.\n\n Parameters \n \n**obj**ndarray, dtype or scalar\n\nThe array data-type or scalar for which the default fill value is returned.\n\n Returns \n \n**fill_value**scalar\n\nThe default fill value.\n\n #### Examples\n\n \n```\n>>> np.ma.default_fill_value(1)\n999999\n>>> np.ma.default_fill_value(np.array([1.1, 2., np.pi]))\n1e+20\n>>> np.ma.default_fill_value(np.dtype(complex))\n(1e+20+0j)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.default_fill_value.htmlnumpy.ma.maximum_fill_value\n=============================\n\n ma.maximum_fill_value(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L343-L391)\n \nReturn the minimum value that can be represented by the dtype of an object.\n\n This function is useful for calculating a fill value suitable for taking the maximum of an array with a given dtype.\n\n Parameters \n \n**obj**ndarray, dtype or scalar\n\nAn object that can be queried for it’s numeric type.\n\n Returns \n \n**val**scalar\n\nThe minimum representable value.\n\n Raises \n TypeError\n\nIf `obj` isn’t a suitable numeric type.\n\n See also\n\n [`minimum_fill_value`](numpy.ma.minimum_fill_value#numpy.ma.minimum_fill_value \"numpy.ma.minimum_fill_value\")\n\nThe inverse function.\n\n [`set_fill_value`](numpy.ma.set_fill_value#numpy.ma.set_fill_value \"numpy.ma.set_fill_value\")\n\nSet the filling value of a masked array.\n\n [`MaskedArray.fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\")\n\nReturn current fill value.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.int8()\n>>> ma.maximum_fill_value(a)\n-128\n>>> a = np.int32()\n>>> ma.maximum_fill_value(a)\n-2147483648\n\n```\n An array of numeric data can also be passed.\n\n \n```\n>>> a = np.array([1, 2, 3], dtype=np.int8)\n>>> ma.maximum_fill_value(a)\n-128\n>>> a = np.array([1, 2, 3], dtype=np.float32)\n>>> ma.maximum_fill_value(a)\n-inf\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.maximum_fill_value.htmlnumpy.ma.minimum_fill_value\n=============================\n\n ma.minimum_fill_value(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L292-L340)\n \nReturn the maximum value that can be represented by the dtype of an object.\n\n This function is useful for calculating a fill value suitable for taking the minimum of an array with a given dtype.\n\n Parameters \n \n**obj**ndarray, dtype or scalar\n\nAn object that can be queried for it’s numeric type.\n\n Returns \n \n**val**scalar\n\nThe maximum representable value.\n\n Raises \n TypeError\n\nIf `obj` isn’t a suitable numeric type.\n\n See also\n\n [`maximum_fill_value`](numpy.ma.maximum_fill_value#numpy.ma.maximum_fill_value \"numpy.ma.maximum_fill_value\")\n\nThe inverse function.\n\n [`set_fill_value`](numpy.ma.set_fill_value#numpy.ma.set_fill_value \"numpy.ma.set_fill_value\")\n\nSet the filling value of a masked array.\n\n [`MaskedArray.fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\")\n\nReturn current fill value.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.int8()\n>>> ma.minimum_fill_value(a)\n127\n>>> a = np.int32()\n>>> ma.minimum_fill_value(a)\n2147483647\n\n```\n An array of numeric data can also be passed.\n\n \n```\n>>> a = np.array([1, 2, 3], dtype=np.int8)\n>>> ma.minimum_fill_value(a)\n127\n>>> a = np.array([1, 2, 3], dtype=np.float32)\n>>> ma.minimum_fill_value(a)\ninf\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.minimum_fill_value.htmlnumpy.ma.set_fill_value\n=========================\n\n ma.set_fill_value(*a*, *fill_value*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L470-L532)\n \nSet the filling value of a, if a is a masked array.\n\n This function changes the fill value of the masked array `a` in place. If `a` is not a masked array, the function returns silently, without doing anything.\n\n Parameters \n \n**a**array_like\n\nInput array.\n\n \n**fill_value**dtype\n\nFilling value. A consistency test is performed to make sure the value is compatible with the dtype of `a`.\n\n Returns \n None\n\nNothing returned by this function.\n\n See also\n\n [`maximum_fill_value`](numpy.ma.maximum_fill_value#numpy.ma.maximum_fill_value \"numpy.ma.maximum_fill_value\")\n\nReturn the default fill value for a dtype.\n\n [`MaskedArray.fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\")\n\nReturn current fill value.\n\n [`MaskedArray.set_fill_value`](numpy.ma.maskedarray.set_fill_value#numpy.ma.MaskedArray.set_fill_value \"numpy.ma.MaskedArray.set_fill_value\")\n\nEquivalent method.\n\n #### Examples\n\n \n```\n>>> import numpy.ma as ma\n>>> a = np.arange(5)\n>>> a\narray([0, 1, 2, 3, 4])\n>>> a = ma.masked_where(a < 3, a)\n>>> a\nmasked_array(data=[--, --, --, 3, 4],\n mask=[ True, True, True, False, False],\n fill_value=999999)\n>>> ma.set_fill_value(a, -999)\n>>> a\nmasked_array(data=[--, --, --, 3, 4],\n mask=[ True, True, True, False, False],\n fill_value=-999)\n\n```\n Nothing happens if `a` is not a masked array.\n\n \n```\n>>> a = list(range(5))\n>>> a\n[0, 1, 2, 3, 4]\n>>> ma.set_fill_value(a, 100)\n>>> a\n[0, 1, 2, 3, 4]\n>>> a = np.arange(5)\n>>> a\narray([0, 1, 2, 3, 4])\n>>> ma.set_fill_value(a, 100)\n>>> a\narray([0, 1, 2, 3, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.set_fill_value.htmlnumpy.ma.MaskedArray.get_fill_value\n=====================================\n\n method\n\n ma.MaskedArray.get_fill_value()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3712-L3751)\n \nThe filling value of the masked array is a scalar. When setting, None will set to a default based on the data type.\n\n #### Examples\n\n \n```\n>>> for dt in [np.int32, np.int64, np.float64, np.complex128]:\n... np.ma.array([0, 1], dtype=dt).get_fill_value()\n...\n999999\n999999\n1e+20\n(1e+20+0j)\n\n```\n \n```\n>>> x = np.ma.array([0, 1.], fill_value=-np.inf)\n>>> x.fill_value\n-inf\n>>> x.fill_value = np.pi\n>>> x.fill_value\n3.1415926535897931 # may vary\n\n```\n Reset to default:\n\n \n```\n>>> x.fill_value = None\n>>> x.fill_value\n1e+20\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.get_fill_value.htmlnumpy.ma.MaskedArray.set_fill_value\n=====================================\n\n method\n\n ma.MaskedArray.set_fill_value(*value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3753-L3770)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.set_fill_value.htmlnumpy.ma.anom\n=============\n\n ma.anom(*self*, *axis=None*, *dtype=None*)*=<numpy.ma.core._frommethod object>*\n \nCompute the anomalies (deviations from the arithmetic mean) along the given axis.\n\n Returns an array of anomalies, with the same shape as the input and where the arithmetic mean is computed along the given axis.\n\n Parameters \n \n**axis**int, optional\n\nAxis over which the anomalies are taken. The default is to use the mean of the flattened array as reference.\n\n \n**dtype**dtype, optional\n\n Type to use in computing the variance. For arrays of integer type\n\nthe default is float32; for arrays of float types it is the same as the array type.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nCompute the mean of the array.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1,2,3])\n>>> a.anom()\nmasked_array(data=[-1., 0., 1.],\n mask=False,\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.anom.htmlnumpy.ma.anomalies\n==================\n\n ma.anomalies(*self*, *axis=None*, *dtype=None*)*=<numpy.ma.core._frommethod object>*\n \nCompute the anomalies (deviations from the arithmetic mean) along the given axis.\n\n Returns an array of anomalies, with the same shape as the input and where the arithmetic mean is computed along the given axis.\n\n Parameters \n \n**axis**int, optional\n\nAxis over which the anomalies are taken. The default is to use the mean of the flattened array as reference.\n\n \n**dtype**dtype, optional\n\n Type to use in computing the variance. For arrays of integer type\n\nthe default is float32; for arrays of float types it is the same as the array type.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nCompute the mean of the array.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1,2,3])\n>>> a.anom()\nmasked_array(data=[-1., 0., 1.],\n mask=False,\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.anomalies.htmlnumpy.ma.average\n================\n\n ma.average(*a*, *axis=None*, *weights=None*, *returned=False*, ***, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L528-L657)\n \nReturn the weighted average of array over the given axis.\n\n Parameters \n \n**a**array_like\n\nData to be averaged. Masked entries are not taken into account in the computation.\n\n \n**axis**int, optional\n\nAxis along which to average `a`. If None, averaging is done over the flattened array.\n\n \n**weights**array_like, optional\n\nThe importance that each element has in the computation of the average. The weights array can either be 1-D (in which case its length must be the size of `a` along the given axis) or of the same shape as `a`. If `weights=None`, then all data in `a` are assumed to have a weight equal to one. The 1-D calculation is:\n\n \n```\navg = sum(a * weights) / sum(weights)\n\n```\n The only constraint on `weights` is that `sum(weights)` must not be 0.\n\n \n**returned**bool, optional\n\nFlag indicating whether a tuple `(result, sum of weights)` should be returned as output (True), or just the result (False). Default is False.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. *Note:* `keepdims` will not work with instances of [`numpy.matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") or other classes whose methods do not support `keepdims`.\n\n New in version 1.23.0.\n\n Returns \n \n**average, [sum_of_weights]**(tuple of) scalar or MaskedArray\n\nThe average along the specified axis. When returned is `True`, return a tuple with the average as the first element and the sum of the weights as the second element. The return type is `np.float64` if `a` is of integer type and floats smaller than [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"), or the input data-type, otherwise. If returned, `sum_of_weights` is always [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\").\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1., 2., 3., 4.], mask=[False, False, True, True])\n>>> np.ma.average(a, weights=[3, 1, 0, 0])\n1.25\n\n```\n \n```\n>>> x = np.ma.arange(6.).reshape(3, 2)\n>>> x\nmasked_array(\n data=[[0., 1.],\n [2., 3.],\n [4., 5.]],\n mask=False,\n fill_value=1e+20)\n>>> avg, sumweights = np.ma.average(x, axis=0, weights=[1, 2, 3],\n... returned=True)\n>>> avg\nmasked_array(data=[2.6666666666666665, 3.6666666666666665],\n mask=[False, False],\n fill_value=1e+20)\n\n```\n With `keepdims=True`, the following result has shape (3, 1).\n\n \n```\n>>> np.ma.average(x, axis=1, keepdims=True)\nmasked_array(\n data=[[0.5],\n [2.5],\n [4.5]],\n mask=False,\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.average.htmlnumpy.ma.conjugate\n==================\n\n ma.conjugate(*x*, */*, *out=None*, ***, *where=True*, *casting='same_kind'*, *order='K'*, *dtype=None*, *subok=True*[, *signature*, *extobj*])*=<numpy.ma.core._MaskedUnaryOperation object>*\n \nReturn the complex conjugate, element-wise.\n\n The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.\n\n Parameters \n \n**x**array_like\n\nInput value.\n\n \n**out**ndarray, None, or tuple of ndarray and None, optional\n\nA location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.\n\n \n**where**array_like, optional\n\nThis condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized.\n\n ****kwargs**\n\nFor other keyword-only arguments, see the [ufunc docs](../ufuncs#ufuncs-kwargs).\n\n Returns \n \n**y**ndarray\n\nThe complex conjugate of `x`, with same dtype as `y`. This is a scalar if `x` is a scalar.\n\n #### Notes\n\n [`conj`](numpy.conj#numpy.conj \"numpy.conj\") is an alias for [`conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\"):\n\n \n```\n>>> np.conj is np.conjugate\nTrue\n\n```\n #### Examples\n\n \n```\n>>> np.conjugate(1+2j)\n(1-2j)\n\n```\n \n```\n>>> x = np.eye(2) + 1j * np.eye(2)\n>>> np.conjugate(x)\narray([[ 1.-1.j, 0.-0.j],\n [ 0.-0.j, 1.-1.j]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.conjugate.htmlnumpy.ma.corrcoef\n=================\n\n ma.corrcoef(*x*, *y=None*, *rowvar=True*, *bias=<no value>*, *allow_masked=True*, *ddof=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L1407-L1491)\n \nReturn Pearson product-moment correlation coefficients.\n\n Except for the handling of missing data this function does the same as [`numpy.corrcoef`](numpy.corrcoef#numpy.corrcoef \"numpy.corrcoef\"). For more details and examples, see [`numpy.corrcoef`](numpy.corrcoef#numpy.corrcoef \"numpy.corrcoef\").\n\n Parameters \n \n**x**array_like\n\nA 1-D or 2-D array containing multiple variables and observations. Each row of `x` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below.\n\n \n**y**array_like, optional\n\nAn additional set of variables and observations. `y` has the same shape as `x`.\n\n \n**rowvar**bool, optional\n\nIf `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.\n\n \n**bias**_NoValue, optional\n\nHas no effect, do not use.\n\n Deprecated since version 1.10.0.\n\n \n**allow_masked**bool, optional\n\nIf True, masked values are propagated pair-wise: if a value is masked in `x`, the corresponding value is masked in `y`. If False, raises an exception. Because `bias` is deprecated, this argument needs to be treated as keyword only to avoid a warning.\n\n \n**ddof**_NoValue, optional\n\nHas no effect, do not use.\n\n Deprecated since version 1.10.0.\n\n See also\n\n [`numpy.corrcoef`](numpy.corrcoef#numpy.corrcoef \"numpy.corrcoef\")\n\nEquivalent function in top-level NumPy module.\n\n [`cov`](numpy.cov#numpy.cov \"numpy.cov\")\n\nEstimate the covariance matrix.\n\n #### Notes\n\n This function accepts but discards arguments `bias` and `ddof`. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.corrcoef.htmlnumpy.ma.cov\n============\n\n ma.cov(*x*, *y=None*, *rowvar=True*, *bias=False*, *allow_masked=True*, *ddof=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L1334-L1404)\n \nEstimate the covariance matrix.\n\n Except for the handling of missing data this function does the same as [`numpy.cov`](numpy.cov#numpy.cov \"numpy.cov\"). For more details and examples, see [`numpy.cov`](numpy.cov#numpy.cov \"numpy.cov\").\n\n By default, masked values are recognized as such. If `x` and `y` have the same shape, a common mask is allocated: if `x[i,j]` is masked, then `y[i,j]` will also be masked. Setting `allow_masked` to False will raise an exception if values are missing in either of the input arrays.\n\n Parameters \n \n**x**array_like\n\nA 1-D or 2-D array containing multiple variables and observations. Each row of `x` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below.\n\n \n**y**array_like, optional\n\nAn additional set of variables and observations. `y` has the same shape as `x`.\n\n \n**rowvar**bool, optional\n\nIf `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.\n\n \n**bias**bool, optional\n\nDefault normalization (False) is by `(N-1)`, where `N` is the number of observations given (unbiased estimate). If `bias` is True, then normalization is by `N`. This keyword can be overridden by the keyword `ddof` in numpy versions >= 1.5.\n\n \n**allow_masked**bool, optional\n\nIf True, masked values are propagated pair-wise: if a value is masked in `x`, the corresponding value is masked in `y`. If False, raises a `ValueError` exception when some values are missing.\n\n \n**ddof**{None, int}, optional\n\nIf not `None` normalization is by `(N - ddof)`, where `N` is the number of observations; this overrides the value implied by `bias`. The default value is `None`.\n\n New in version 1.5.\n\n Raises \n ValueError\n\nRaised if some values are missing and `allow_masked` is False.\n\n See also\n\n [`numpy.cov`](numpy.cov#numpy.cov \"numpy.cov\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.cov.htmlnumpy.ma.cumsum\n===============\n\n ma.cumsum(*self*, *axis=None*, *dtype=None*, *out=None*)*=<numpy.ma.core._frommethod object>*\n \nReturn the cumulative sum of the array elements over the given axis.\n\n Masked values are set to 0 internally during the computation. However, their position is saved, and the result will be masked at the same locations.\n\n Refer to [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\") for full documentation.\n\n See also\n\n [`numpy.ndarray.cumsum`](numpy.ndarray.cumsum#numpy.ndarray.cumsum \"numpy.ndarray.cumsum\")\n\ncorresponding function for ndarrays\n\n [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\nequivalent function\n\n #### Notes\n\n The mask is lost if `out` is not a valid [`ma.MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\") !\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n #### Examples\n\n \n```\n>>> marr = np.ma.array(np.arange(10), mask=[0,0,0,1,1,1,0,0,0,0])\n>>> marr.cumsum()\nmasked_array(data=[0, 1, 3, --, --, --, 9, 16, 24, 33],\n mask=[False, False, False, True, True, True, False, False,\n False, False],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.cumsum.htmlnumpy.ma.cumprod\n================\n\n ma.cumprod(*self*, *axis=None*, *dtype=None*, *out=None*)*=<numpy.ma.core._frommethod object>*\n \nReturn the cumulative product of the array elements over the given axis.\n\n Masked values are set to 1 internally during the computation. However, their position is saved, and the result will be masked at the same locations.\n\n Refer to [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\") for full documentation.\n\n See also\n\n [`numpy.ndarray.cumprod`](numpy.ndarray.cumprod#numpy.ndarray.cumprod \"numpy.ndarray.cumprod\")\n\ncorresponding function for ndarrays\n\n [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\")\n\nequivalent function\n\n #### Notes\n\n The mask is lost if `out` is not a valid MaskedArray !\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.cumprod.htmlnumpy.ma.mean\n=============\n\n ma.mean(*self*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)*=<numpy.ma.core._frommethod object>*\n \nReturns the average of the array elements along given axis.\n\n Masked entries are ignored, and result elements which are not finite will be masked.\n\n Refer to [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\") for full documentation.\n\n See also\n\n [`numpy.ndarray.mean`](numpy.ndarray.mean#numpy.ndarray.mean \"numpy.ndarray.mean\")\n\ncorresponding function for ndarrays\n\n [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nEquivalent function\n\n [`numpy.ma.average`](numpy.ma.average#numpy.ma.average \"numpy.ma.average\")\n\nWeighted average.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1,2,3], mask=[False, False, True])\n>>> a\nmasked_array(data=[1, 2, --],\n mask=[False, False, True],\n fill_value=999999)\n>>> a.mean()\n1.5\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.mean.htmlnumpy.ma.median\n===============\n\n ma.median(*a*, *axis=None*, *out=None*, *overwrite_input=False*, *keepdims=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L660-L740)\n \nCompute the median along the specified axis.\n\n Returns the median of the array elements.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array.\n\n \n**axis**int, optional\n\nAxis along which the medians are computed. The default (None) is to compute the median along a flattened version of the array.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow use of memory of input array (a) for calculations. The input array will be modified by the call to median. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. Note that, if `overwrite_input` is True, and the input is not already an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), an error will be raised.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.\n\n New in version 1.10.0.\n\n Returns \n \n**median**ndarray\n\nA new array holding the result is returned unless out is specified, in which case a reference to out is returned. Return data-type is [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\") for integers and floats smaller than [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"), or the input data-type, otherwise.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n #### Notes\n\n Given a vector `V` with `N` non masked values, the median of `V` is the middle value of a sorted copy of `V` (`Vs`) - i.e. `Vs[(N-1)/2]`, when `N` is odd, or `{Vs[N/2 - 1] + Vs[N/2]}/2` when `N` is even.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(8), mask=[0]*4 + [1]*4)\n>>> np.ma.median(x)\n1.5\n\n```\n \n```\n>>> x = np.ma.array(np.arange(10).reshape(2, 5), mask=[0]*6 + [1]*4)\n>>> np.ma.median(x)\n2.5\n>>> np.ma.median(x, axis=-1, overwrite_input=True)\nmasked_array(data=[2.0, 5.0],\n mask=[False, False],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.median.htmlnumpy.ma.power\n==============\n\n ma.power(*a*, *b*, *third=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6867-L6916)\n \nReturns element-wise base array raised to power from second array.\n\n This is the masked array version of [`numpy.power`](numpy.power#numpy.power \"numpy.power\"). For details see [`numpy.power`](numpy.power#numpy.power \"numpy.power\").\n\n See also\n\n [`numpy.power`](numpy.power#numpy.power \"numpy.power\")\n #### Notes\n\n The *out* argument to [`numpy.power`](numpy.power#numpy.power \"numpy.power\") is not supported, `third` has to be None.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.power.htmlnumpy.ma.prod\n=============\n\n ma.prod(*self*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)*=<numpy.ma.core._frommethod object>*\n \nReturn the product of the array elements over the given axis.\n\n Masked elements are set to 1 internally for computation.\n\n Refer to [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\") for full documentation.\n\n See also\n\n [`numpy.ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\")\n\ncorresponding function for ndarrays\n\n [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\")\n\nequivalent function\n\n #### Notes\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.prod.htmlnumpy.ma.std\n============\n\n ma.std(*self*, *axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*)*=<numpy.ma.core._frommethod object>*\n \nReturns the standard deviation of the array elements along given axis.\n\n Masked entries are ignored.\n\n Refer to [`numpy.std`](numpy.std#numpy.std \"numpy.std\") for full documentation.\n\n See also\n\n [`numpy.ndarray.std`](numpy.ndarray.std#numpy.ndarray.std \"numpy.ndarray.std\")\n\ncorresponding function for ndarrays\n\n [`numpy.std`](numpy.std#numpy.std \"numpy.std\")\n\nEquivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.std.htmlnumpy.ma.sum\n============\n\n ma.sum(*self*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)*=<numpy.ma.core._frommethod object>*\n \nReturn the sum of the array elements over the given axis.\n\n Masked elements are set to 0 internally.\n\n Refer to [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\") for full documentation.\n\n See also\n\n [`numpy.ndarray.sum`](numpy.ndarray.sum#numpy.ndarray.sum \"numpy.ndarray.sum\")\n\ncorresponding function for ndarrays\n\n [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\")\n\nequivalent function\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.sum()\n25\n>>> x.sum(axis=1)\nmasked_array(data=[4, 5, 16],\n mask=[False, False, False],\n fill_value=999999)\n>>> x.sum(axis=0)\nmasked_array(data=[8, 5, 12],\n mask=[False, False, False],\n fill_value=999999)\n>>> print(type(x.sum(axis=0, dtype=np.int64)[0]))\n<class 'numpy.int64'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.sum.htmlnumpy.ma.var\n============\n\n ma.var(*self*, *axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*)*=<numpy.ma.core._frommethod object>*\n \nCompute the variance along the specified axis.\n\n Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**None or int or tuple of ints, optional\n\nAxis or axes along which the variance is computed. The default is to compute the variance of the flattened array.\n\n New in version 1.7.0.\n\n If this is a tuple of ints, a variance is performed over multiple axes, instead of a single axis or all the axes as before.\n\n \n**dtype**data-type, optional\n\nType to use in computing the variance. For arrays of integer type the default is [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"); for arrays of float types it is the same as the array type.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.\n\n \n**ddof**int, optional\n\n“Delta Degrees of Freedom”: the divisor used in the calculation is `N - ddof`, where `N` represents the number of elements. By default `ddof` is zero.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.\n\n If the default value is passed, then `keepdims` will not be passed through to the [`var`](numpy.var#numpy.var \"numpy.var\") method of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), however any non-default value will be. If the sub-class’ method does not implement `keepdims` any exceptions will be raised.\n\n \n**where**array_like of bool, optional\n\nElements to include in the variance. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.20.0.\n\n Returns \n \n**variance**ndarray, see dtype parameter above\n\nIf `out=None`, returns a new array containing the variance; otherwise, a reference to the output array is returned.\n\n See also\n\n \n[`std`](numpy.std#numpy.std \"numpy.std\"), [`mean`](numpy.mean#numpy.mean \"numpy.mean\"), [`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\"), [`nanstd`](numpy.nanstd#numpy.nanstd \"numpy.nanstd\"), [`nanvar`](numpy.nanvar#numpy.nanvar \"numpy.nanvar\")\n\n[Output type determination](../../user/basics.ufuncs#ufuncs-output-type)\n #### Notes\n\n The variance is the average of the squared deviations from the mean, i.e., `var = mean(x)`, where `x = abs(a - a.mean())**2`.\n\n The mean is typically calculated as `x.sum() / N`, where `N = len(x)`. If, however, `ddof` is specified, the divisor `N - ddof` is used instead. In standard statistical practice, `ddof=1` provides an unbiased estimator of the variance of a hypothetical infinite population. `ddof=0` provides a maximum likelihood estimate of the variance for normally distributed variables.\n\n Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.\n\n For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for [`float32`](../arrays.scalars#numpy.float32 \"numpy.float32\") (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> np.var(a)\n1.25\n>>> np.var(a, axis=0)\narray([1., 1.])\n>>> np.var(a, axis=1)\narray([0.25, 0.25])\n\n```\n In single precision, var() can be inaccurate:\n\n \n```\n>>> a = np.zeros((2, 512*512), dtype=np.float32)\n>>> a[0, :] = 1.0\n>>> a[1, :] = 0.1\n>>> np.var(a)\n0.20250003\n\n```\n Computing the variance in float64 is more accurate:\n\n \n```\n>>> np.var(a, dtype=np.float64)\n0.20249999932944759 # may vary\n>>> ((1-0.55)**2 + (0.1-0.55)**2)/2\n0.2025\n\n```\n Specifying a where argument:\n\n \n```\n>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])\n>>> np.var(a)\n6.833333333333333 # may vary\n>>> np.var(a, where=[[True], [True], [False]])\n4.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.var.htmlnumpy.ma.MaskedArray.anom\n=========================\n\n method\n\n ma.MaskedArray.anom(*axis=None*, *dtype=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5306-L5341)\n \nCompute the anomalies (deviations from the arithmetic mean) along the given axis.\n\n Returns an array of anomalies, with the same shape as the input and where the arithmetic mean is computed along the given axis.\n\n Parameters \n \n**axis**int, optional\n\nAxis over which the anomalies are taken. The default is to use the mean of the flattened array as reference.\n\n \n**dtype**dtype, optional\n\n Type to use in computing the variance. For arrays of integer type\n\nthe default is float32; for arrays of float types it is the same as the array type.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nCompute the mean of the array.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1,2,3])\n>>> a.anom()\nmasked_array(data=[-1., 0., 1.],\n mask=False,\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.anom.htmlnumpy.ma.MaskedArray.cumprod\n============================\n\n method\n\n ma.MaskedArray.cumprod(*axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5228-L5257)\n \nReturn the cumulative product of the array elements over the given axis.\n\n Masked values are set to 1 internally during the computation. However, their position is saved, and the result will be masked at the same locations.\n\n Refer to [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\") for full documentation.\n\n See also\n\n [`numpy.ndarray.cumprod`](numpy.ndarray.cumprod#numpy.ndarray.cumprod \"numpy.ndarray.cumprod\")\n\ncorresponding function for ndarrays\n\n [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\")\n\nequivalent function\n\n #### Notes\n\n The mask is lost if `out` is not a valid MaskedArray !\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.cumprod.htmlnumpy.ma.MaskedArray.cumsum\n===========================\n\n method\n\n ma.MaskedArray.cumsum(*axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5145-L5184)\n \nReturn the cumulative sum of the array elements over the given axis.\n\n Masked values are set to 0 internally during the computation. However, their position is saved, and the result will be masked at the same locations.\n\n Refer to [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\") for full documentation.\n\n See also\n\n [`numpy.ndarray.cumsum`](numpy.ndarray.cumsum#numpy.ndarray.cumsum \"numpy.ndarray.cumsum\")\n\ncorresponding function for ndarrays\n\n [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\nequivalent function\n\n #### Notes\n\n The mask is lost if `out` is not a valid [`ma.MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\") !\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n #### Examples\n\n \n```\n>>> marr = np.ma.array(np.arange(10), mask=[0,0,0,1,1,1,0,0,0,0])\n>>> marr.cumsum()\nmasked_array(data=[0, 1, 3, --, --, --, 9, 16, 24, 33],\n mask=[False, False, False, True, True, True, False, False,\n False, False],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.cumsum.htmlnumpy.ma.MaskedArray.mean\n=========================\n\n method\n\n ma.MaskedArray.mean(*axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5259-L5304)\n \nReturns the average of the array elements along given axis.\n\n Masked entries are ignored, and result elements which are not finite will be masked.\n\n Refer to [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\") for full documentation.\n\n See also\n\n [`numpy.ndarray.mean`](numpy.ndarray.mean#numpy.ndarray.mean \"numpy.ndarray.mean\")\n\ncorresponding function for ndarrays\n\n [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nEquivalent function\n\n [`numpy.ma.average`](numpy.ma.average#numpy.ma.average \"numpy.ma.average\")\n\nWeighted average.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1,2,3], mask=[False, False, True])\n>>> a\nmasked_array(data=[1, 2, --],\n mask=[False, False, True],\n fill_value=999999)\n>>> a.mean()\n1.5\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.mean.htmlnumpy.ma.MaskedArray.prod\n=========================\n\n method\n\n ma.MaskedArray.prod(*axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5186-L5225)\n \nReturn the product of the array elements over the given axis.\n\n Masked elements are set to 1 internally for computation.\n\n Refer to [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\") for full documentation.\n\n See also\n\n [`numpy.ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\")\n\ncorresponding function for ndarrays\n\n [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\")\n\nequivalent function\n\n #### Notes\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.prod.htmlnumpy.ma.MaskedArray.std\n========================\n\n method\n\n ma.MaskedArray.std(*axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5407-L5429)\n \nReturns the standard deviation of the array elements along given axis.\n\n Masked entries are ignored.\n\n Refer to [`numpy.std`](numpy.std#numpy.std \"numpy.std\") for full documentation.\n\n See also\n\n [`numpy.ndarray.std`](numpy.ndarray.std#numpy.ndarray.std \"numpy.ndarray.std\")\n\ncorresponding function for ndarrays\n\n [`numpy.std`](numpy.std#numpy.std \"numpy.std\")\n\nEquivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.std.htmlnumpy.ma.MaskedArray.sum\n========================\n\n method\n\n ma.MaskedArray.sum(*axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5083-L5143)\n \nReturn the sum of the array elements over the given axis.\n\n Masked elements are set to 0 internally.\n\n Refer to [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\") for full documentation.\n\n See also\n\n [`numpy.ndarray.sum`](numpy.ndarray.sum#numpy.ndarray.sum \"numpy.ndarray.sum\")\n\ncorresponding function for ndarrays\n\n [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\")\n\nequivalent function\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.sum()\n25\n>>> x.sum(axis=1)\nmasked_array(data=[4, 5, 16],\n mask=[False, False, False],\n fill_value=999999)\n>>> x.sum(axis=0)\nmasked_array(data=[8, 5, 12],\n mask=[False, False, False],\n fill_value=999999)\n>>> print(type(x.sum(axis=0, dtype=np.int64)[0]))\n<class 'numpy.int64'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.sum.htmlnumpy.ma.MaskedArray.var\n========================\n\n method\n\n ma.MaskedArray.var(*axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5343-L5404)\n \nCompute the variance along the specified axis.\n\n Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**None or int or tuple of ints, optional\n\nAxis or axes along which the variance is computed. The default is to compute the variance of the flattened array.\n\n New in version 1.7.0.\n\n If this is a tuple of ints, a variance is performed over multiple axes, instead of a single axis or all the axes as before.\n\n \n**dtype**data-type, optional\n\nType to use in computing the variance. For arrays of integer type the default is [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"); for arrays of float types it is the same as the array type.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.\n\n \n**ddof**int, optional\n\n“Delta Degrees of Freedom”: the divisor used in the calculation is `N - ddof`, where `N` represents the number of elements. By default `ddof` is zero.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.\n\n If the default value is passed, then `keepdims` will not be passed through to the [`var`](numpy.var#numpy.var \"numpy.var\") method of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), however any non-default value will be. If the sub-class’ method does not implement `keepdims` any exceptions will be raised.\n\n \n**where**array_like of bool, optional\n\nElements to include in the variance. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.20.0.\n\n Returns \n \n**variance**ndarray, see dtype parameter above\n\nIf `out=None`, returns a new array containing the variance; otherwise, a reference to the output array is returned.\n\n See also\n\n \n[`std`](numpy.std#numpy.std \"numpy.std\"), [`mean`](numpy.mean#numpy.mean \"numpy.mean\"), [`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\"), [`nanstd`](numpy.nanstd#numpy.nanstd \"numpy.nanstd\"), [`nanvar`](numpy.nanvar#numpy.nanvar \"numpy.nanvar\")\n\n[Output type determination](../../user/basics.ufuncs#ufuncs-output-type)\n #### Notes\n\n The variance is the average of the squared deviations from the mean, i.e., `var = mean(x)`, where `x = abs(a - a.mean())**2`.\n\n The mean is typically calculated as `x.sum() / N`, where `N = len(x)`. If, however, `ddof` is specified, the divisor `N - ddof` is used instead. In standard statistical practice, `ddof=1` provides an unbiased estimator of the variance of a hypothetical infinite population. `ddof=0` provides a maximum likelihood estimate of the variance for normally distributed variables.\n\n Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.\n\n For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for [`float32`](../arrays.scalars#numpy.float32 \"numpy.float32\") (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> np.var(a)\n1.25\n>>> np.var(a, axis=0)\narray([1., 1.])\n>>> np.var(a, axis=1)\narray([0.25, 0.25])\n\n```\n In single precision, var() can be inaccurate:\n\n \n```\n>>> a = np.zeros((2, 512*512), dtype=np.float32)\n>>> a[0, :] = 1.0\n>>> a[1, :] = 0.1\n>>> np.var(a)\n0.20250003\n\n```\n Computing the variance in float64 is more accurate:\n\n \n```\n>>> np.var(a, dtype=np.float64)\n0.20249999932944759 # may vary\n>>> ((1-0.55)**2 + (0.1-0.55)**2)/2\n0.2025\n\n```\n Specifying a where argument:\n\n \n```\n>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])\n>>> np.var(a)\n6.833333333333333 # may vary\n>>> np.var(a, where=[[True], [True], [False]])\n4.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.var.htmlnumpy.ma.argmax\n===============\n\n ma.argmax(*self*, *axis=None*, *fill_value=None*, *out=None*)*=<numpy.ma.core._frommethod object>*\n \nReturns array of indices of the maximum values along the given axis. Masked values are treated as if they had the value fill_value.\n\n Parameters \n \n**axis**{None, integer}\n\nIf None, the index is into the flattened array, otherwise along the specified axis\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, the output of maximum_fill_value(self._data) is used instead.\n\n \n**out**{None, array}, optional\n\nArray into which the result can be placed. Its type is preserved and it must be of the right shape to hold the output.\n\n Returns \n \n**index_array**{integer_array}\n\n #### Examples\n\n \n```\n>>> a = np.arange(6).reshape(2,3)\n>>> a.argmax()\n5\n>>> a.argmax(0)\narray([1, 1, 1])\n>>> a.argmax(1)\narray([2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.argmax.htmlnumpy.ma.argmin\n===============\n\n ma.argmin(*self*, *axis=None*, *fill_value=None*, *out=None*)*=<numpy.ma.core._frommethod object>*\n \nReturn array of indices to the minimum values along the given axis.\n\n Parameters \n \n**axis**{None, integer}\n\nIf None, the index is into the flattened array, otherwise along the specified axis\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, the output of minimum_fill_value(self._data) is used instead.\n\n \n**out**{None, array}, optional\n\nArray into which the result can be placed. Its type is preserved and it must be of the right shape to hold the output.\n\n Returns \n ndarray or scalar\n\nIf multi-dimension input, returns a new ndarray of indices to the minimum values along the given axis. Otherwise, returns a scalar of index to the minimum values along the given axis.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(4), mask=[1,1,0,0])\n>>> x.shape = (2,2)\n>>> x\nmasked_array(\n data=[[--, --],\n [2, 3]],\n mask=[[ True, True],\n [False, False]],\n fill_value=999999)\n>>> x.argmin(axis=0, fill_value=-1)\narray([0, 0])\n>>> x.argmin(axis=0, fill_value=9)\narray([1, 1])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.argmin.htmlnumpy.ma.max\n============\n\n ma.max(*obj*, *axis=None*, *out=None*, *fill_value=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6760-L6769)\n \nReturn the maximum along a given axis.\n\n Parameters \n \n**axis**None or int or tuple of ints, optional\n\nAxis along which to operate. By default, `axis` is None and the flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before.\n\n \n**out**array_like, optional\n\nAlternative output array in which to place the result. Must be of the same shape and buffer length as the expected output.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, use the output of maximum_fill_value().\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**amax**array_like\n\nNew array holding the result. If `out` was specified, `out` is returned.\n\n See also\n\n [`ma.maximum_fill_value`](numpy.ma.maximum_fill_value#numpy.ma.maximum_fill_value \"numpy.ma.maximum_fill_value\")\n\nReturns the maximum filling value for a given datatype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.max.htmlnumpy.ma.min\n============\n\n ma.min(*obj*, *axis=None*, *out=None*, *fill_value=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6748-L6757)\n \nReturn the minimum along a given axis.\n\n Parameters \n \n**axis**None or int or tuple of ints, optional\n\nAxis along which to operate. By default, `axis` is None and the flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before.\n\n \n**out**array_like, optional\n\nAlternative output array in which to place the result. Must be of the same shape and buffer length as the expected output.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, use the output of [`minimum_fill_value`](numpy.ma.minimum_fill_value#numpy.ma.minimum_fill_value \"numpy.ma.minimum_fill_value\").\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**amin**array_like\n\nNew array holding the result. If `out` was specified, `out` is returned.\n\n See also\n\n [`ma.minimum_fill_value`](numpy.ma.minimum_fill_value#numpy.ma.minimum_fill_value \"numpy.ma.minimum_fill_value\")\n\nReturns the minimum filling value for a given datatype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.min.htmlnumpy.ma.ptp\n============\n\n ma.ptp(*obj*, *axis=None*, *out=None*, *fill_value=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6773-L6781)\n \nReturn (maximum - minimum) along the given dimension (i.e. peak-to-peak value).\n\n Warning\n\n [`ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\") preserves the data type of the array. This means the return value for an input of signed integers with n bits (e.g. `np.int8`, `np.int16`, etc) is also a signed integer with n bits. In that case, peak-to-peak values greater than `2**(n-1)-1` will be returned as negative values. An example with a work-around is shown below.\n\n Parameters \n \n**axis**{None, int}, optional\n\nAxis along which to find the peaks. If None (default) the flattened array is used.\n\n \n**out**{None, array_like}, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**ptp**ndarray.\n\nA new array holding the result, unless `out` was specified, in which case a reference to `out` is returned.\n\n #### Examples\n\n \n```\n>>> x = np.ma.MaskedArray([[4, 9, 2, 10],\n... [6, 9, 7, 12]])\n\n```\n \n```\n>>> x.ptp(axis=1)\nmasked_array(data=[8, 6],\n mask=False,\n fill_value=999999)\n\n```\n \n```\n>>> x.ptp(axis=0)\nmasked_array(data=[2, 0, 5, 2],\n mask=False,\n fill_value=999999)\n\n```\n \n```\n>>> x.ptp()\n10\n\n```\n This example shows that a negative value can be returned when the input is an array of signed integers.\n\n \n```\n>>> y = np.ma.MaskedArray([[1, 127],\n... [0, 127],\n... [-1, 127],\n... [-2, 127]], dtype=np.int8)\n>>> y.ptp(axis=1)\nmasked_array(data=[ 126, 127, -128, -127],\n mask=False,\n fill_value=999999,\n dtype=int8)\n\n```\n A work-around is to use the `view()` method to view the result as unsigned integers with the same bit width:\n\n \n```\n>>> y.ptp(axis=1).view(np.uint8)\nmasked_array(data=[126, 127, 128, 129],\n mask=False,\n fill_value=999999,\n dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.ptp.htmlnumpy.ma.diff\n=============\n\n ma.diff(**args*, ***kwargs*)*=<numpy.ma.core._convert2ma object>*\n \nCalculate the n-th discrete difference along the given axis.\n\n The first difference is given by `out[i] = a[i+1] - a[i]` along the given axis, higher differences are calculated by using [`diff`](numpy.diff#numpy.diff \"numpy.diff\") recursively.\n\n Parameters \n \n**a**array_like\n\nInput array\n\n \n**n**int, optional\n\nThe number of times values are differenced. If zero, the input is returned as-is.\n\n \n**axis**int, optional\n\nThe axis along which the difference is taken, default is the last axis.\n\n \n**prepend, append**array_like, optional\n\nValues to prepend or append to `a` along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match `a` except along axis.\n\n New in version 1.16.0.\n\n Returns \n \n**diff**MaskedArray\n\nThe n-th differences. The shape of the output is the same as `a` except along `axis` where the dimension is smaller by `n`. The type of the output is the same as the type of the difference between any two elements of `a`. This is the same as the type of `a` in most cases. A notable exception is [`datetime64`](../arrays.scalars#numpy.datetime64 \"numpy.datetime64\"), which results in a [`timedelta64`](../arrays.scalars#numpy.timedelta64 \"numpy.timedelta64\") output array.\n\n See also\n\n \n[`gradient`](numpy.gradient#numpy.gradient \"numpy.gradient\"), [`ediff1d`](numpy.ediff1d#numpy.ediff1d \"numpy.ediff1d\"), [`cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\n #### Notes\n\n Type is preserved for boolean arrays, so the result will contain `False` when consecutive elements are the same and `True` when they differ.\n\n For unsigned integer arrays, the results will also be unsigned. This should not be surprising, as the result is consistent with calculating the difference directly:\n\n \n```\n>>> u8_arr = np.array([1, 0], dtype=np.uint8)\n>>> np.diff(u8_arr)\narray([255], dtype=uint8)\n>>> u8_arr[1,...] - u8_arr[0,...]\n255\n\n```\n If this is not desirable, then the array should be cast to a larger integer type first:\n\n \n```\n>>> i16_arr = u8_arr.astype(np.int16)\n>>> np.diff(i16_arr)\narray([-1], dtype=int16)\n\n```\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 4, 7, 0])\n>>> np.diff(x)\narray([ 1, 2, 3, -7])\n>>> np.diff(x, n=2)\narray([ 1, 1, -10])\n\n```\n \n```\n>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])\n>>> np.diff(x)\narray([[2, 3, 4],\n [5, 1, 2]])\n>>> np.diff(x, axis=0)\narray([[-1, 2, 0, -2]])\n\n```\n \n```\n>>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)\n>>> np.diff(x)\narray([1, 1], dtype='timedelta64[D]')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.diff.htmlnumpy.ma.MaskedArray.argmax\n===========================\n\n method\n\n ma.MaskedArray.argmax(*axis=None*, *fill_value=None*, *out=None*, ***, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5583-L5620)\n \nReturns array of indices of the maximum values along the given axis. Masked values are treated as if they had the value fill_value.\n\n Parameters \n \n**axis**{None, integer}\n\nIf None, the index is into the flattened array, otherwise along the specified axis\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, the output of maximum_fill_value(self._data) is used instead.\n\n \n**out**{None, array}, optional\n\nArray into which the result can be placed. Its type is preserved and it must be of the right shape to hold the output.\n\n Returns \n \n**index_array**{integer_array}\n\n #### Examples\n\n \n```\n>>> a = np.arange(6).reshape(2,3)\n>>> a.argmax()\n5\n>>> a.argmax(0)\narray([1, 1, 1])\n>>> a.argmax(1)\narray([2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.argmax.htmlnumpy.ma.MaskedArray.argmin\n===========================\n\n method\n\n ma.MaskedArray.argmin(*axis=None*, *fill_value=None*, *out=None*, ***, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5536-L5581)\n \nReturn array of indices to the minimum values along the given axis.\n\n Parameters \n \n**axis**{None, integer}\n\nIf None, the index is into the flattened array, otherwise along the specified axis\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, the output of minimum_fill_value(self._data) is used instead.\n\n \n**out**{None, array}, optional\n\nArray into which the result can be placed. Its type is preserved and it must be of the right shape to hold the output.\n\n Returns \n ndarray or scalar\n\nIf multi-dimension input, returns a new ndarray of indices to the minimum values along the given axis. Otherwise, returns a scalar of index to the minimum values along the given axis.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array(np.arange(4), mask=[1,1,0,0])\n>>> x.shape = (2,2)\n>>> x\nmasked_array(\n data=[[--, --],\n [2, 3]],\n mask=[[ True, True],\n [False, False]],\n fill_value=999999)\n>>> x.argmin(axis=0, fill_value=-1)\narray([0, 0])\n>>> x.argmin(axis=0, fill_value=9)\narray([1, 1])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.argmin.htmlnumpy.ma.MaskedArray.max\n========================\n\n method\n\n ma.MaskedArray.max(*axis=None*, *out=None*, *fill_value=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5842-L5910)\n \nReturn the maximum along a given axis.\n\n Parameters \n \n**axis**None or int or tuple of ints, optional\n\nAxis along which to operate. By default, `axis` is None and the flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before.\n\n \n**out**array_like, optional\n\nAlternative output array in which to place the result. Must be of the same shape and buffer length as the expected output.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, use the output of maximum_fill_value().\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**amax**array_like\n\nNew array holding the result. If `out` was specified, `out` is returned.\n\n See also\n\n [`ma.maximum_fill_value`](numpy.ma.maximum_fill_value#numpy.ma.maximum_fill_value \"numpy.ma.maximum_fill_value\")\n\nReturns the maximum filling value for a given datatype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.max.htmlnumpy.ma.MaskedArray.min\n========================\n\n method\n\n ma.MaskedArray.min(*axis=None*, *out=None*, *fill_value=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5705-L5772)\n \nReturn the minimum along a given axis.\n\n Parameters \n \n**axis**None or int or tuple of ints, optional\n\nAxis along which to operate. By default, `axis` is None and the flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before.\n\n \n**out**array_like, optional\n\nAlternative output array in which to place the result. Must be of the same shape and buffer length as the expected output.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values. If None, use the output of `minimum_fill_value`.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**amin**array_like\n\nNew array holding the result. If `out` was specified, `out` is returned.\n\n See also\n\n [`ma.minimum_fill_value`](numpy.ma.minimum_fill_value#numpy.ma.minimum_fill_value \"numpy.ma.minimum_fill_value\")\n\nReturns the minimum filling value for a given datatype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.min.htmlnumpy.ma.MaskedArray.ptp\n========================\n\n method\n\n ma.MaskedArray.ptp(*axis=None*, *out=None*, *fill_value=None*, *keepdims=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5912-L5998)\n \nReturn (maximum - minimum) along the given dimension (i.e. peak-to-peak value).\n\n Warning\n\n [`ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\") preserves the data type of the array. This means the return value for an input of signed integers with n bits (e.g. `np.int8`, `np.int16`, etc) is also a signed integer with n bits. In that case, peak-to-peak values greater than `2**(n-1)-1` will be returned as negative values. An example with a work-around is shown below.\n\n Parameters \n \n**axis**{None, int}, optional\n\nAxis along which to find the peaks. If None (default) the flattened array is used.\n\n \n**out**{None, array_like}, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary.\n\n \n**fill_value**scalar or None, optional\n\nValue used to fill in the masked values.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n Returns \n \n**ptp**ndarray.\n\nA new array holding the result, unless `out` was specified, in which case a reference to `out` is returned.\n\n #### Examples\n\n \n```\n>>> x = np.ma.MaskedArray([[4, 9, 2, 10],\n... [6, 9, 7, 12]])\n\n```\n \n```\n>>> x.ptp(axis=1)\nmasked_array(data=[8, 6],\n mask=False,\n fill_value=999999)\n\n```\n \n```\n>>> x.ptp(axis=0)\nmasked_array(data=[2, 0, 5, 2],\n mask=False,\n fill_value=999999)\n\n```\n \n```\n>>> x.ptp()\n10\n\n```\n This example shows that a negative value can be returned when the input is an array of signed integers.\n\n \n```\n>>> y = np.ma.MaskedArray([[1, 127],\n... [0, 127],\n... [-1, 127],\n... [-2, 127]], dtype=np.int8)\n>>> y.ptp(axis=1)\nmasked_array(data=[ 126, 127, -128, -127],\n mask=False,\n fill_value=999999,\n dtype=int8)\n\n```\n A work-around is to use the `view()` method to view the result as unsigned integers with the same bit width:\n\n \n```\n>>> y.ptp(axis=1).view(np.uint8)\nmasked_array(data=[126, 127, 128, 129],\n mask=False,\n fill_value=999999,\n dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.ptp.htmlnumpy.ma.argsort\n================\n\n ma.argsort(*a*, *axis=<no value>*, *kind=None*, *order=None*, *endwith=True*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6921-L6933)\n \nReturn an ndarray of indices that sort the array along the specified axis. Masked values are filled beforehand to `fill_value`.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. If None, the default, the flattened array is used.\n\n Changed in version 1.13.0: Previously, the default was documented to be -1, but that was in error. At some future date, the default will change to -1, as originally intended. Until then, the axis should be given explicitly when `arr.ndim > 1`, to avoid a FutureWarning.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nThe sorting algorithm used.\n\n \n**order**list, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified.\n\n \n**endwith**{True, False}, optional\n\nWhether missing values (if any) should be treated as the largest values (True) or the smallest values (False) When the array contains unmasked values at the same extremes of the datatype, the ordering of these values and the masked values is undefined.\n\n \n**fill_value**scalar or None, optional\n\nValue used internally for the masked values. If `fill_value` is not None, it supersedes `endwith`.\n\n Returns \n \n**index_array**ndarray, int\n\nArray of indices that sort `a` along the specified axis. In other words, `a[index_array]` yields a sorted `a`.\n\n See also\n\n [`ma.MaskedArray.sort`](numpy.ma.maskedarray.sort#numpy.ma.MaskedArray.sort \"numpy.ma.MaskedArray.sort\")\n\nDescribes sorting algorithms used.\n\n [`lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort with multiple keys.\n\n [`numpy.ndarray.sort`](numpy.ndarray.sort#numpy.ndarray.sort \"numpy.ndarray.sort\")\n\nInplace sort.\n\n #### Notes\n\n See [`sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([3,2,1], mask=[False, False, True])\n>>> a\nmasked_array(data=[3, 2, --],\n mask=[False, False, True],\n fill_value=999999)\n>>> a.argsort()\narray([1, 0, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.argsort.htmlnumpy.ma.sort\n=============\n\n ma.sort(*a*, *axis=- 1*, *kind=None*, *order=None*, *endwith=True*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6936-L6959)\n \nReturn a sorted copy of the masked array.\n\n Equivalent to creating a copy of the array and applying the MaskedArray `sort()` method.\n\n Refer to `MaskedArray.sort` for the full documentation\n\n See also\n\n [`MaskedArray.sort`](numpy.ma.maskedarray.sort#numpy.ma.MaskedArray.sort \"numpy.ma.MaskedArray.sort\")\n\nequivalent method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.sort.htmlnumpy.ma.MaskedArray.argsort\n============================\n\n method\n\n ma.MaskedArray.argsort(*axis=<no value>*, *kind=None*, *order=None*, *endwith=True*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5456-L5534)\n \nReturn an ndarray of indices that sort the array along the specified axis. Masked values are filled beforehand to [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\").\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. If None, the default, the flattened array is used.\n\n Changed in version 1.13.0: Previously, the default was documented to be -1, but that was in error. At some future date, the default will change to -1, as originally intended. Until then, the axis should be given explicitly when `arr.ndim > 1`, to avoid a FutureWarning.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nThe sorting algorithm used.\n\n \n**order**list, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified.\n\n \n**endwith**{True, False}, optional\n\nWhether missing values (if any) should be treated as the largest values (True) or the smallest values (False) When the array contains unmasked values at the same extremes of the datatype, the ordering of these values and the masked values is undefined.\n\n \n**fill_value**scalar or None, optional\n\nValue used internally for the masked values. If `fill_value` is not None, it supersedes `endwith`.\n\n Returns \n \n**index_array**ndarray, int\n\nArray of indices that sort `a` along the specified axis. In other words, `a[index_array]` yields a sorted `a`.\n\n See also\n\n [`ma.MaskedArray.sort`](numpy.ma.maskedarray.sort#numpy.ma.MaskedArray.sort \"numpy.ma.MaskedArray.sort\")\n\nDescribes sorting algorithms used.\n\n [`lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort with multiple keys.\n\n [`numpy.ndarray.sort`](numpy.ndarray.sort#numpy.ndarray.sort \"numpy.ndarray.sort\")\n\nInplace sort.\n\n #### Notes\n\n See [`sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([3,2,1], mask=[False, False, True])\n>>> a\nmasked_array(data=[3, 2, --],\n mask=[False, False, True],\n fill_value=999999)\n>>> a.argsort()\narray([1, 0, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.argsort.htmlnumpy.ma.MaskedArray.sort\n=========================\n\n method\n\n ma.MaskedArray.sort(*axis=- 1*, *kind=None*, *order=None*, *endwith=True*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5622-L5703)\n \nSort the array, in-place\n\n Parameters \n \n**a**array_like\n\nArray to be sorted.\n\n \n**axis**int, optional\n\nAxis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nThe sorting algorithm used.\n\n \n**order**list, optional\n\nWhen `a` is a structured array, this argument specifies which fields to compare first, second, and so on. This list does not need to include all of the fields.\n\n \n**endwith**{True, False}, optional\n\nWhether missing values (if any) should be treated as the largest values (True) or the smallest values (False) When the array contains unmasked values sorting at the same extremes of the datatype, the ordering of these values and the masked values is undefined.\n\n \n**fill_value**scalar or None, optional\n\nValue used internally for the masked values. If `fill_value` is not None, it supersedes `endwith`.\n\n Returns \n \n**sorted_array**ndarray\n\nArray of the same type and shape as `a`.\n\n See also\n\n [`numpy.ndarray.sort`](numpy.ndarray.sort#numpy.ndarray.sort \"numpy.ndarray.sort\")\n\nMethod to sort an array in-place.\n\n [`argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nIndirect sort.\n\n [`lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort on multiple keys.\n\n [`searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nFind elements in a sorted array.\n\n #### Notes\n\n See `sort` for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1, 2, 5, 4, 3],mask=[0, 1, 0, 1, 0])\n>>> # Default\n>>> a.sort()\n>>> a\nmasked_array(data=[1, 3, 5, --, --],\n mask=[False, False, False, True, True],\n fill_value=999999)\n\n```\n \n```\n>>> a = np.ma.array([1, 2, 5, 4, 3],mask=[0, 1, 0, 1, 0])\n>>> # Put missing values in the front\n>>> a.sort(endwith=False)\n>>> a\nmasked_array(data=[--, --, 1, 3, 5],\n mask=[ True, True, False, False, False],\n fill_value=999999)\n\n```\n \n```\n>>> a = np.ma.array([1, 2, 5, 4, 3],mask=[0, 1, 0, 1, 0])\n>>> # fill_value takes over endwith\n>>> a.sort(endwith=False, fill_value=3)\n>>> a\nmasked_array(data=[1, --, --, 3, 5],\n mask=[False, True, True, False, False],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.sort.htmlnumpy.ma.diag\n=============\n\n ma.diag(*v*, *k=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7037-L7052)\n \nExtract a diagonal or construct a diagonal array.\n\n This function is the equivalent of [`numpy.diag`](numpy.diag#numpy.diag \"numpy.diag\") that takes masked values into account, see [`numpy.diag`](numpy.diag#numpy.diag \"numpy.diag\") for details.\n\n See also\n\n [`numpy.diag`](numpy.diag#numpy.diag \"numpy.diag\")\n\nEquivalent function for ndarrays.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.diag.htmlnumpy.ma.dot\n============\n\n ma.dot(*a*, *b*, *strict=False*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7597-L7676)\n \nReturn the dot product of two arrays.\n\n This function is the equivalent of [`numpy.dot`](numpy.dot#numpy.dot \"numpy.dot\") that takes masked values into account. Note that `strict` and `out` are in different position than in the method version. In order to maintain compatibility with the corresponding method, it is recommended that the optional arguments be treated as keyword only. At some point that may be mandatory.\n\n Note\n\n Works only with 2-D arrays at the moment.\n\n Parameters \n \n**a, b**masked_array_like\n\nInputs arrays.\n\n \n**strict**bool, optional\n\nWhether masked data are propagated (True) or set to 0 (False) for the computation. Default is False. Propagating the mask means that if a masked value appears in a row or column, the whole row or column is considered masked.\n\n \n**out**masked_array, optional\n\nOutput argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a,b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.\n\n New in version 1.10.2.\n\n See also\n\n [`numpy.dot`](numpy.dot#numpy.dot \"numpy.dot\")\n\nEquivalent function for ndarrays.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([[1, 2, 3], [4, 5, 6]], mask=[[1, 0, 0], [0, 0, 0]])\n>>> b = np.ma.array([[1, 2], [3, 4], [5, 6]], mask=[[1, 0], [0, 0], [0, 0]])\n>>> np.ma.dot(a, b)\nmasked_array(\n data=[[21, 26],\n [45, 64]],\n mask=[[False, False],\n [False, False]],\n fill_value=999999)\n>>> np.ma.dot(a, b, strict=True)\nmasked_array(\n data=[[--, --],\n [--, 64]],\n mask=[[ True, True],\n [ True, False]],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.dot.htmlnumpy.ma.identity\n=================\n\n ma.identity(*n*, *dtype=None*)*=<numpy.ma.core._convert2ma object>*\n \nReturn the identity array.\n\n The identity array is a square array with ones on the main diagonal.\n\n Parameters \n \n**n**int\n\nNumber of rows (and columns) in `n` x `n` output.\n\n \n**dtype**data-type, optional\n\nData-type of the output. Defaults to `float`.\n\n \n**like**array_like, optional\n\nReference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as `like` supports the `__array_function__` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument.\n\n New in version 1.20.0.\n\n Returns \n \n**out**MaskedArray\n\n`n` x `n` array with its main diagonal set to one, and all other elements 0.\n\n #### Examples\n\n \n```\n>>> np.identity(3)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.identity.htmlnumpy.ma.inner\n==============\n\n ma.inner(*a*, *b*, */*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7679-L7693)\n \nInner product of two arrays.\n\n Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes.\n\n Parameters \n \n**a, b**array_like\n\nIf `a` and `b` are nonscalar, their last dimensions must match.\n\n Returns \n \n**out**ndarray\n\nIf `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. `out.shape = (*a.shape[:-1], *b.shape[:-1])`\n\n Raises \n ValueError\n\nIf both `a` and `b` are nonscalar and their last dimensions have different sizes.\n\n See also\n\n [`tensordot`](numpy.tensordot#numpy.tensordot \"numpy.tensordot\")\n\nSum products over arbitrary axes.\n\n [`dot`](numpy.dot#numpy.dot \"numpy.dot\")\n\nGeneralised matrix product, using second last dimension of `b`.\n\n [`einsum`](numpy.einsum#numpy.einsum \"numpy.einsum\")\n\nEinstein summation convention.\n\n #### Notes\n\n Masked values are replaced by 0.\n\n For vectors (1-D arrays) it computes the ordinary inner-product:\n\n \n```\nnp.inner(a, b) = sum(a[:]*b[:])\n\n```\n More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`:\n\n \n```\nnp.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))\n\n```\n or explicitly:\n\n \n```\nnp.inner(a, b)[i0,...,ir-2,j0,...,js-2]\n = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])\n\n```\n In addition `a` or `b` may be scalars, in which case:\n\n \n```\nnp.inner(a,b) = a*b\n\n```\n #### Examples\n\n Ordinary inner product for vectors:\n\n \n```\n>>> a = np.array([1,2,3])\n>>> b = np.array([0,1,0])\n>>> np.inner(a, b)\n2\n\n```\n Some multidimensional examples:\n\n \n```\n>>> a = np.arange(24).reshape((2,3,4))\n>>> b = np.arange(4)\n>>> c = np.inner(a, b)\n>>> c.shape\n(2, 3)\n>>> c\narray([[ 14, 38, 62],\n [ 86, 110, 134]])\n\n```\n \n```\n>>> a = np.arange(2).reshape((1,1,2))\n>>> b = np.arange(6).reshape((3,2))\n>>> c = np.inner(a, b)\n>>> c.shape\n(1, 1, 3)\n>>> c\narray([[[1, 3, 5]]])\n\n```\n An example where `b` is a scalar:\n\n \n```\n>>> np.inner(np.eye(2), 7)\narray([[7., 0.],\n [0., 7.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.inner.htmlnumpy.ma.innerproduct\n=====================\n\n ma.innerproduct(*a*, *b*, */*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7679-L7693)\n \nInner product of two arrays.\n\n Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes.\n\n Parameters \n \n**a, b**array_like\n\nIf `a` and `b` are nonscalar, their last dimensions must match.\n\n Returns \n \n**out**ndarray\n\nIf `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. `out.shape = (*a.shape[:-1], *b.shape[:-1])`\n\n Raises \n ValueError\n\nIf both `a` and `b` are nonscalar and their last dimensions have different sizes.\n\n See also\n\n [`tensordot`](numpy.tensordot#numpy.tensordot \"numpy.tensordot\")\n\nSum products over arbitrary axes.\n\n [`dot`](numpy.dot#numpy.dot \"numpy.dot\")\n\nGeneralised matrix product, using second last dimension of `b`.\n\n [`einsum`](numpy.einsum#numpy.einsum \"numpy.einsum\")\n\nEinstein summation convention.\n\n #### Notes\n\n Masked values are replaced by 0.\n\n For vectors (1-D arrays) it computes the ordinary inner-product:\n\n \n```\nnp.inner(a, b) = sum(a[:]*b[:])\n\n```\n More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`:\n\n \n```\nnp.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))\n\n```\n or explicitly:\n\n \n```\nnp.inner(a, b)[i0,...,ir-2,j0,...,js-2]\n = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])\n\n```\n In addition `a` or `b` may be scalars, in which case:\n\n \n```\nnp.inner(a,b) = a*b\n\n```\n #### Examples\n\n Ordinary inner product for vectors:\n\n \n```\n>>> a = np.array([1,2,3])\n>>> b = np.array([0,1,0])\n>>> np.inner(a, b)\n2\n\n```\n Some multidimensional examples:\n\n \n```\n>>> a = np.arange(24).reshape((2,3,4))\n>>> b = np.arange(4)\n>>> c = np.inner(a, b)\n>>> c.shape\n(2, 3)\n>>> c\narray([[ 14, 38, 62],\n [ 86, 110, 134]])\n\n```\n \n```\n>>> a = np.arange(2).reshape((1,1,2))\n>>> b = np.arange(6).reshape((3,2))\n>>> c = np.inner(a, b)\n>>> c.shape\n(1, 1, 3)\n>>> c\narray([[[1, 3, 5]]])\n\n```\n An example where `b` is a scalar:\n\n \n```\n>>> np.inner(np.eye(2), 7)\narray([[7., 0.],\n [0., 7.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.innerproduct.htmlnumpy.ma.outer\n==============\n\n ma.outer(*a*, *b*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7699-L7711)\n \nCompute the outer product of two vectors.\n\n Given two vectors, `a = [a0, a1, ..., aM]` and `b = [b0, b1, ..., bN]`, the outer product [[1]](#r863504129d6e-1) is:\n\n \n```\n[[a0*b0 a0*b1 ... a0*bN ]\n [a1*b0 .\n [ ... .\n [aM*b0 aM*bN ]]\n\n```\n Parameters \n \n**a**(M,) array_like\n\nFirst input vector. Input is flattened if not already 1-dimensional.\n\n \n**b**(N,) array_like\n\nSecond input vector. Input is flattened if not already 1-dimensional.\n\n \n**out**(M, N) ndarray, optional\n\nA location where the result is stored\n\n New in version 1.9.0.\n\n Returns \n \n**out**(M, N) ndarray\n\n`out[i, j] = a[i] * b[j]`\n\n See also\n\n [`inner`](numpy.inner#numpy.inner \"numpy.inner\")\n[`einsum`](numpy.einsum#numpy.einsum \"numpy.einsum\")\n\n`einsum('i,j->ij', a.ravel(), b.ravel())` is the equivalent.\n\n [`ufunc.outer`](numpy.ufunc.outer#numpy.ufunc.outer \"numpy.ufunc.outer\")\n\nA generalization to dimensions other than 1D and other operations. `np.multiply.outer(a.ravel(), b.ravel())` is the equivalent.\n\n [`tensordot`](numpy.tensordot#numpy.tensordot \"numpy.tensordot\")\n\n`np.tensordot(a.ravel(), b.ravel(), axes=((), ()))` is the equivalent.\n\n #### Notes\n\n Masked values are replaced by 0.\n\n #### References\n\n [1](#id1) \n: <NAME> and <NAME>, *Matrix Computations*, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8.\n\n #### Examples\n\n Make a (*very* coarse) grid for computing a Mandelbrot set:\n\n \n```\n>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))\n>>> rl\narray([[-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.]])\n>>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))\n>>> im\narray([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],\n [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],\n [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],\n [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])\n>>> grid = rl + im\n>>> grid\narray([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j],\n [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j],\n [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j],\n [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j],\n [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])\n\n```\n An example using a “vector” of letters:\n\n \n```\n>>> x = np.array(['a', 'b', 'c'], dtype=object)\n>>> np.outer(x, [1, 2, 3])\narray([['a', 'aa', 'aaa'],\n ['b', 'bb', 'bbb'],\n ['c', 'cc', 'ccc']], dtype=object)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.outer.htmlnumpy.ma.outerproduct\n=====================\n\n ma.outerproduct(*a*, *b*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7699-L7711)\n \nCompute the outer product of two vectors.\n\n Given two vectors, `a = [a0, a1, ..., aM]` and `b = [b0, b1, ..., bN]`, the outer product [[1]](#rf0d57dd5badd-1) is:\n\n \n```\n[[a0*b0 a0*b1 ... a0*bN ]\n [a1*b0 .\n [ ... .\n [aM*b0 aM*bN ]]\n\n```\n Parameters \n \n**a**(M,) array_like\n\nFirst input vector. Input is flattened if not already 1-dimensional.\n\n \n**b**(N,) array_like\n\nSecond input vector. Input is flattened if not already 1-dimensional.\n\n \n**out**(M, N) ndarray, optional\n\nA location where the result is stored\n\n New in version 1.9.0.\n\n Returns \n \n**out**(M, N) ndarray\n\n`out[i, j] = a[i] * b[j]`\n\n See also\n\n [`inner`](numpy.inner#numpy.inner \"numpy.inner\")\n[`einsum`](numpy.einsum#numpy.einsum \"numpy.einsum\")\n\n`einsum('i,j->ij', a.ravel(), b.ravel())` is the equivalent.\n\n [`ufunc.outer`](numpy.ufunc.outer#numpy.ufunc.outer \"numpy.ufunc.outer\")\n\nA generalization to dimensions other than 1D and other operations. `np.multiply.outer(a.ravel(), b.ravel())` is the equivalent.\n\n [`tensordot`](numpy.tensordot#numpy.tensordot \"numpy.tensordot\")\n\n`np.tensordot(a.ravel(), b.ravel(), axes=((), ()))` is the equivalent.\n\n #### Notes\n\n Masked values are replaced by 0.\n\n #### References\n\n [1](#id1) \n: <NAME> and <NAME>, *Matrix Computations*, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8.\n\n #### Examples\n\n Make a (*very* coarse) grid for computing a Mandelbrot set:\n\n \n```\n>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))\n>>> rl\narray([[-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.],\n [-2., -1., 0., 1., 2.]])\n>>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))\n>>> im\narray([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],\n [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],\n [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],\n [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])\n>>> grid = rl + im\n>>> grid\narray([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j],\n [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j],\n [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j],\n [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j],\n [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])\n\n```\n An example using a “vector” of letters:\n\n \n```\n>>> x = np.array(['a', 'b', 'c'], dtype=object)\n>>> np.outer(x, [1, 2, 3])\narray([['a', 'aa', 'aaa'],\n ['b', 'bb', 'bbb'],\n ['c', 'cc', 'ccc']], dtype=object)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.outerproduct.htmlnumpy.ma.trace\n==============\n\n ma.trace(*self*, *offset=0*, *axis1=0*, *axis2=1*, *dtype=None*, *out=None) a.trace(offset=0*, *axis1=0*, *axis2=1*, *dtype=None*, *out=None*)*=<numpy.ma.core._frommethod object>*\n Return the sum along diagonals of the array.\n\n Refer to [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\") for full documentation.\n\n See also\n\n [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.trace.htmlnumpy.ma.MaskedArray.trace\n==========================\n\n method\n\n ma.MaskedArray.trace(*offset=0*, *axis1=0*, *axis2=1*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5029-L5041)\n \nReturn the sum along diagonals of the array.\n\n Refer to [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\") for full documentation.\n\n See also\n\n [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.trace.htmlnumpy.ma.vander\n===============\n\n ma.vander(*x*, *n=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L1975-L1984)\n \nGenerate a Vandermonde matrix.\n\n The columns of the output matrix are powers of the input vector. The order of the powers is determined by the `increasing` boolean argument. Specifically, when `increasing` is False, the `i`-th output column is the input vector raised element-wise to the power of `N - i - 1`. Such a matrix with a geometric progression in each row is named for Alexandre- <NAME>.\n\n Parameters \n \n**x**array_like\n\n1-D input array.\n\n \n**N**int, optional\n\nNumber of columns in the output. If `N` is not specified, a square array is returned (`N = len(x)`).\n\n \n**increasing**bool, optional\n\nOrder of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed.\n\n New in version 1.9.0.\n\n Returns \n \n**out**ndarray\n\nVandermonde matrix. If `increasing` is False, the first column is `x^(N-1)`, the second `x^(N-2)` and so forth. If `increasing` is True, the columns are `x^0, x^1, ..., x^(N-1)`.\n\n See also\n\n [`polynomial.polynomial.polyvander`](numpy.polynomial.polynomial.polyvander#numpy.polynomial.polynomial.polyvander \"numpy.polynomial.polynomial.polyvander\")\n #### Notes\n\n Masked values in the input array result in rows of zeros.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3, 5])\n>>> N = 3\n>>> np.vander(x, N)\narray([[ 1, 1, 1],\n [ 4, 2, 1],\n [ 9, 3, 1],\n [25, 5, 1]])\n\n```\n \n```\n>>> np.column_stack([x**(N-1-i) for i in range(N)])\narray([[ 1, 1, 1],\n [ 4, 2, 1],\n [ 9, 3, 1],\n [25, 5, 1]])\n\n```\n \n```\n>>> x = np.array([1, 2, 3, 5])\n>>> np.vander(x)\narray([[ 1, 1, 1, 1],\n [ 8, 4, 2, 1],\n [ 27, 9, 3, 1],\n [125, 25, 5, 1]])\n>>> np.vander(x, increasing=True)\narray([[ 1, 1, 1, 1],\n [ 1, 2, 4, 8],\n [ 1, 3, 9, 27],\n [ 1, 5, 25, 125]])\n\n```\n The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector:\n\n \n```\n>>> np.linalg.det(np.vander(x))\n48.000000000000043 # may vary\n>>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)\n48\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.vander.htmlnumpy.ma.polyfit\n================\n\n ma.polyfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*, *cov=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L1989-L2021)\n \nLeast squares polynomial fit.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Fit a polynomial `p(x) = p[0] * x**deg + ... + p[deg]` of degree `deg` to points `(x, y)`. Returns a vector of coefficients `p` that minimises the squared error in the order `deg`, `deg-1`, … `0`.\n\n The [`Polynomial.fit`](numpy.polynomial.polynomial.polynomial.fit#numpy.polynomial.polynomial.Polynomial.fit \"numpy.polynomial.polynomial.Polynomial.fit\") class method is recommended for new code as it is more stable numerically. See the documentation of the method for more information.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int\n\nDegree of the fitting polynomial\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n \n**cov**bool or str, optional\n\nIf given and not `False`, return not just the estimate but also its covariance matrix. By default, the covariance are scaled by chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed to be unreliable except in a relative sense and everything is scaled such that the reduced chi2 is unity. This scaling is omitted if `cov='unscaled'`, as is relevant for the case that the weights are w = 1/sigma, with sigma known to be a reliable estimate of the uncertainty.\n\n Returns \n \n**p**ndarray, shape (deg + 1,) or (deg + 1, K)\n\nPolynomial coefficients, highest power first. If `y` was 2-D, the coefficients for `k`-th data set are in `p[:,k]`.\n\n residuals, rank, singular_values, rcond\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the effective rank of the scaled Vandermonde\n\ncoefficient matrix\n* singular_values – singular values of the scaled Vandermonde\n\ncoefficient matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n**V**ndarray, shape (M,M) or (M,M,K)\n\nPresent only if `full == False` and `cov == True`. The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-D array, then the covariance matrix for the `k`-th data set are in `V[:,:,k]`\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`.\n\n The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\nCompute polynomial values.\n\n [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n Any masked values in x is propagated in y, and vice-versa.\n\n The solution minimizes the squared error\n\n \\[E = \\sum_{j=0}^k |p(x_j) - y_j|^2\\] in the equations:\n\n \n```\nx[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]\nx[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]\n...\nx[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]\n\n```\n The coefficient matrix of the coefficients `p` is a Vandermonde matrix.\n\n [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\") issues a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") when the least-squares fit is badly conditioned. This implies that the best fit is not well-defined due to numerical error. The results may be improved by lowering the polynomial degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious: including contributions from the small singular values can add numerical noise to the result.\n\n Note that fitting polynomial coefficients is inherently badly conditioned when the degree of the polynomial is large or the interval of sample points is badly centered. The quality of the fit should always be checked in these cases. When polynomial fits are not satisfactory, splines may be a good alternative.\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting 2 \nWikipedia, “Polynomial interpolation”, <https://en.wikipedia.org/wiki/Polynomial_interpolation #### Examples\n\n \n```\n>>> import warnings\n>>> x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])\n>>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])\n>>> z = np.polyfit(x, y, 3)\n>>> z\narray([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) # may vary\n\n```\n It is convenient to use [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\") objects for dealing with polynomials:\n\n \n```\n>>> p = np.poly1d(z)\n>>> p(0.5)\n0.6143849206349179 # may vary\n>>> p(3.5)\n-0.34732142857143039 # may vary\n>>> p(10)\n22.579365079365115 # may vary\n\n```\n High-order polynomials may oscillate wildly:\n\n \n```\n>>> with warnings.catch_warnings():\n... warnings.simplefilter('ignore', np.RankWarning)\n... p30 = np.poly1d(np.polyfit(x, y, 30))\n...\n>>> p30(4)\n-0.80000000000000204 # may vary\n>>> p30(5)\n-0.99999999999999445 # may vary\n>>> p30(4.5)\n-0.10547061179440398 # may vary\n\n```\n Illustration:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> xp = np.linspace(-2, 6, 100)\n>>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')\n>>> plt.ylim(-2,2)\n(-2, 2)\n>>> plt.show()\n\n```\n ![../../_images/numpy-ma-polyfit-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.polyfit.htmlnumpy.ma.around\n===============\n\n ma.around*=<numpy.ma.core._MaskedUnaryOperation object>*\n \nRound an array to the given number of decimals.\n\n See also\n\n [`around`](numpy.around#numpy.around \"numpy.around\")\n\nequivalent function; see for details.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.around.htmlnumpy.ma.clip\n=============\n\n ma.clip(**args*, ***kwargs*)*=<numpy.ma.core._convert2ma object>*\n \nClip (limit) the values in an array.\n\n Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of `[0, 1]` is specified, values smaller than 0 become 0, and values larger than 1 become 1.\n\n Equivalent to but faster than `np.minimum(a_max, np.maximum(a, a_min))`.\n\n No check is performed to ensure `a_min < a_max`.\n\n Parameters \n \n**a**array_like\n\nArray containing elements to clip.\n\n \n**a_min, a_max**array_like or None\n\nMinimum and maximum value. If `None`, clipping is not performed on the corresponding edge. Only one of `a_min` and `a_max` may be `None`. Both are broadcast against `a`.\n\n \n**out**ndarray, optional\n\nThe results will be placed in this array. It may be the input array for in-place clipping. `out` must be of the right shape to hold the output. Its type is preserved.\n\n ****kwargs**\n\nFor other keyword-only arguments, see the [ufunc docs](../ufuncs#ufuncs-kwargs).\n\n New in version 1.17.0.\n\n Returns \n \n**clipped_array**MaskedArray\n\nAn array with the elements of `a`, but where values < `a_min` are replaced with `a_min`, and those > `a_max` with `a_max`.\n\n See also\n\n [Output type determination](../../user/basics.ufuncs#ufuncs-output-type)\n #### Notes\n\n When `a_min` is greater than `a_max`, [`clip`](numpy.clip#numpy.clip \"numpy.clip\") returns an array in which all values are equal to `a_max`, as shown in the second example.\n\n #### Examples\n\n \n```\n>>> a = np.arange(10)\n>>> a\narray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n>>> np.clip(a, 1, 8)\narray([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])\n>>> np.clip(a, 8, 1)\narray([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n>>> np.clip(a, 3, 6, out=a)\narray([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])\n>>> a\narray([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])\n>>> a = np.arange(10)\n>>> a\narray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n>>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)\narray([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.clip.htmlnumpy.ma.round\n==============\n\n ma.round(*a*, *decimals=0*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7469-L7499)\n \nReturn a copy of a, rounded to ‘decimals’ places.\n\n When ‘decimals’ is negative, it specifies the number of positions to the left of the decimal point. The real and imaginary parts of complex numbers are rounded separately. Nothing is done if the array is not of float type and ‘decimals’ is greater than or equal to 0.\n\n Parameters \n \n**decimals**int\n\nNumber of decimals to round to. May be negative.\n\n \n**out**array_like\n\nExisting array to use for output. If not given, returns a default copy of a.\n\n #### Notes\n\n If out is given and does not have a mask attribute, the mask of a is lost!\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.round.htmlnumpy.ma.MaskedArray.clip\n=========================\n\n method\n\n ma.MaskedArray.clip(*min=None*, *max=None*, *out=None*, ***kwargs*)\n \nReturn an array whose values are limited to `[min, max]`. One of max or min must be given.\n\n Refer to [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\") for full documentation.\n\n See also\n\n [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.clip.htmlnumpy.ma.MaskedArray.round\n==========================\n\n method\n\n ma.MaskedArray.round(*decimals=0*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5431-L5454)\n \nReturn each element rounded to the given number of decimals.\n\n Refer to [`numpy.around`](numpy.around#numpy.around \"numpy.around\") for full documentation.\n\n See also\n\n [`numpy.ndarray.round`](numpy.ndarray.round#numpy.ndarray.round \"numpy.ndarray.round\")\n\ncorresponding function for ndarrays\n\n [`numpy.around`](numpy.around#numpy.around \"numpy.around\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.round.htmlnumpy.ma.allequal\n=================\n\n ma.allequal(*a*, *b*, *fill_value=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7792-L7847)\n \nReturn True if all entries of a and b are equal, using fill_value as a truth value where either or both are masked.\n\n Parameters \n \n**a, b**array_like\n\nInput arrays to compare.\n\n \n**fill_value**bool, optional\n\nWhether masked values in a or b are considered equal (True) or not (False).\n\n Returns \n \n**y**bool\n\nReturns True if the two arrays are equal within the given tolerance, False otherwise. If either array contains NaN, then False is returned.\n\n See also\n\n \n[`all`](numpy.all#numpy.all \"numpy.all\"), [`any`](numpy.any#numpy.any \"numpy.any\")\n\n[`numpy.ma.allclose`](numpy.ma.allclose#numpy.ma.allclose \"numpy.ma.allclose\")\n #### Examples\n\n \n```\n>>> a = np.ma.array([1e10, 1e-7, 42.0], mask=[0, 0, 1])\n>>> a\nmasked_array(data=[10000000000.0, 1e-07, --],\n mask=[False, False, True],\n fill_value=1e+20)\n\n```\n \n```\n>>> b = np.array([1e10, 1e-7, -42.0])\n>>> b\narray([ 1.00000000e+10, 1.00000000e-07, -4.20000000e+01])\n>>> np.ma.allequal(a, b, fill_value=False)\nFalse\n>>> np.ma.allequal(a, b)\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.allequal.htmlnumpy.ma.allclose\n=================\n\n ma.allclose(*a*, *b*, *masked_equal=True*, *rtol=1e-05*, *atol=1e-08*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7850-L7955)\n \nReturns True if two arrays are element-wise equal within a tolerance.\n\n This function is equivalent to [`allclose`](numpy.allclose#numpy.allclose \"numpy.allclose\") except that masked values are treated as equal (default) or unequal, depending on the [`masked_equal`](numpy.ma.masked_equal#numpy.ma.masked_equal \"numpy.ma.masked_equal\") argument.\n\n Parameters \n \n**a, b**array_like\n\nInput arrays to compare.\n\n \n**masked_equal**bool, optional\n\nWhether masked values in `a` and `b` are considered equal (True) or not (False). They are considered equal by default.\n\n \n**rtol**float, optional\n\nRelative tolerance. The relative difference is equal to `rtol * b`. Default is 1e-5.\n\n \n**atol**float, optional\n\nAbsolute tolerance. The absolute difference is equal to `atol`. Default is 1e-8.\n\n Returns \n \n**y**bool\n\nReturns True if the two arrays are equal within the given tolerance, False otherwise. If either array contains NaN, then False is returned.\n\n See also\n\n \n[`all`](numpy.all#numpy.all \"numpy.all\"), [`any`](numpy.any#numpy.any \"numpy.any\")\n\n[`numpy.allclose`](numpy.allclose#numpy.allclose \"numpy.allclose\")\n\nthe non-masked [`allclose`](numpy.allclose#numpy.allclose \"numpy.allclose\").\n\n #### Notes\n\n If the following equation is element-wise True, then [`allclose`](numpy.allclose#numpy.allclose \"numpy.allclose\") returns True:\n\n \n```\nabsolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))\n\n```\n Return True if all elements of `a` and `b` are equal subject to given tolerances.\n\n #### Examples\n\n \n```\n>>> a = np.ma.array([1e10, 1e-7, 42.0], mask=[0, 0, 1])\n>>> a\nmasked_array(data=[10000000000.0, 1e-07, --],\n mask=[False, False, True],\n fill_value=1e+20)\n>>> b = np.ma.array([1e10, 1e-8, -42.0], mask=[0, 0, 1])\n>>> np.ma.allclose(a, b)\nFalse\n\n```\n \n```\n>>> a = np.ma.array([1e10, 1e-8, 42.0], mask=[0, 0, 1])\n>>> b = np.ma.array([1.00001e10, 1e-9, -42.0], mask=[0, 0, 1])\n>>> np.ma.allclose(a, b)\nTrue\n>>> np.ma.allclose(a, b, masked_equal=False)\nFalse\n\n```\n Masked values are not compared directly.\n\n \n```\n>>> a = np.ma.array([1e10, 1e-8, 42.0], mask=[0, 0, 1])\n>>> b = np.ma.array([1.00001e10, 1e-9, 42.0], mask=[0, 0, 1])\n>>> np.ma.allclose(a, b)\nTrue\n>>> np.ma.allclose(a, b, masked_equal=False)\nFalse\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.allclose.htmlnumpy.ma.apply_along_axis\n===========================\n\n ma.apply_along_axis(*func1d*, *axis*, *arr*, **args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L371-L450)\n \nApply a function to 1-D slices along the given axis.\n\n Execute `func1d(a, *args, **kwargs)` where `func1d` operates on 1-D arrays and `a` is a 1-D slice of `arr` along `axis`.\n\n This is equivalent to (but faster than) the following use of [`ndindex`](numpy.ndindex#numpy.ndindex \"numpy.ndindex\") and [`s_`](numpy.s_#numpy.s_ \"numpy.s_\"), which sets each of `ii`, `jj`, and `kk` to a tuple of indices:\n\n \n```\nNi, Nk = a.shape[:axis], a.shape[axis+1:]\nfor ii in ndindex(Ni):\n for kk in ndindex(Nk):\n f = func1d(arr[ii + s_[:,] + kk])\n Nj = f.shape\n for jj in ndindex(Nj):\n out[ii + jj + kk] = f[jj]\n\n```\n Equivalently, eliminating the inner loop, this can be expressed as:\n\n \n```\nNi, Nk = a.shape[:axis], a.shape[axis+1:]\nfor ii in ndindex(Ni):\n for kk in ndindex(Nk):\n out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])\n\n```\n Parameters \n \n**func1d**function (M,) -> (Nj…)\n\nThis function should accept 1-D arrays. It is applied to 1-D slices of `arr` along the specified axis.\n\n \n**axis**integer\n\nAxis along which `arr` is sliced.\n\n \n**arr**ndarray (Ni…, M, Nk…)\n\nInput array.\n\n \n**args**any\n\nAdditional arguments to `func1d`.\n\n \n**kwargs**any\n\nAdditional named arguments to `func1d`.\n\n New in version 1.9.0.\n\n Returns \n \n**out**ndarray (Ni…, Nj…, Nk…)\n\nThe output array. The shape of `out` is identical to the shape of `arr`, except along the `axis` dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of `func1d`. So if `func1d` returns a scalar `out` will have one fewer dimensions than `arr`.\n\n See also\n\n [`apply_over_axes`](numpy.apply_over_axes#numpy.apply_over_axes \"numpy.apply_over_axes\")\n\nApply a function repeatedly over multiple axes.\n\n #### Examples\n\n \n```\n>>> def my_func(a):\n... \"\"\"Average first and last element of a 1-D array\"\"\"\n... return (a[0] + a[-1]) * 0.5\n>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])\n>>> np.apply_along_axis(my_func, 0, b)\narray([4., 5., 6.])\n>>> np.apply_along_axis(my_func, 1, b)\narray([2., 5., 8.])\n\n```\n For a function that returns a 1D array, the number of dimensions in `outarr` is the same as `arr`.\n\n \n```\n>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])\n>>> np.apply_along_axis(sorted, 1, b)\narray([[1, 7, 8],\n [3, 4, 9],\n [2, 5, 6]])\n\n```\n For a function that returns a higher dimensional array, those dimensions are inserted in place of the `axis` dimension.\n\n \n```\n>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])\n>>> np.apply_along_axis(np.diag, -1, b)\narray([[[1, 0, 0],\n [0, 2, 0],\n [0, 0, 3]],\n [[4, 0, 0],\n [0, 5, 0],\n [0, 0, 6]],\n [[7, 0, 0],\n [0, 8, 0],\n [0, 0, 9]]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.apply_along_axis.htmlnumpy.ma.apply_over_axes\n==========================\n\n ma.apply_over_axes(*func*, *a*, *axes*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L454-L476)\n \nApply a function repeatedly over multiple axes.\n\n `func` is called as `res = func(a, axis)`, where `axis` is the first element of `axes`. The result `res` of the function call must have either the same dimensions as `a` or one less dimension. If `res` has one less dimension than `a`, a dimension is inserted before `axis`. The call to `func` is then repeated for each axis in `axes`, with `res` as the first argument.\n\n Parameters \n \n**func**function\n\nThis function must take two arguments, `func(a, axis)`.\n\n \n**a**array_like\n\nInput array.\n\n \n**axes**array_like\n\nAxes over which `func` is applied; the elements must be integers.\n\n Returns \n \n**apply_over_axis**ndarray\n\nThe output array. The number of dimensions is the same as `a`, but the shape can be different. This depends on whether `func` changes the shape of its output with respect to its input.\n\n See also\n\n [`apply_along_axis`](numpy.apply_along_axis#numpy.apply_along_axis \"numpy.apply_along_axis\")\n\nApply a function to 1-D slices of an array along the given axis.\n\n #### Examples\n\n \n```\n>>> a = np.ma.arange(24).reshape(2,3,4)\n>>> a[:,0,1] = np.ma.masked\n>>> a[:,1,:] = np.ma.masked\n>>> a\nmasked_array(\n data=[[[0, --, 2, 3],\n [--, --, --, --],\n [8, 9, 10, 11]],\n [[12, --, 14, 15],\n [--, --, --, --],\n [20, 21, 22, 23]]],\n mask=[[[False, True, False, False],\n [ True, True, True, True],\n [False, False, False, False]],\n [[False, True, False, False],\n [ True, True, True, True],\n [False, False, False, False]]],\n fill_value=999999)\n>>> np.ma.apply_over_axes(np.ma.sum, a, [0,2])\nmasked_array(\n data=[[[46],\n [--],\n [124]]],\n mask=[[[False],\n [ True],\n [False]]],\n fill_value=999999)\n\n```\n Tuple axis arguments to ufuncs are equivalent:\n\n \n```\n>>> np.ma.sum(a, axis=(0,2)).reshape((1,-1,1))\nmasked_array(\n data=[[[46],\n [--],\n [124]]],\n mask=[[[False],\n [ True],\n [False]]],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.apply_over_axes.htmlnumpy.ma.arange\n===============\n\n ma.arange([*start*, ]*stop*, [*step*, ]*dtype=None*, ***, *like=None*)*=<numpy.ma.core._convert2ma object>*\n \nReturn evenly spaced values within a given interval.\n\n `arange` can be called with a varying number of positional arguments:\n\n * `arange(stop)`: Values are generated within the half-open interval `[0, stop)` (in other words, the interval including `start` but excluding `stop`).\n* `arange(start, stop)`: Values are generated within the half-open interval `[start, stop)`.\n* `arange(start, stop, step)` Values are generated within the half-open interval `[start, stop)`, with spacing between values given by `step`.\n\n For integer arguments the function is roughly equivalent to the Python built-in [`range`](https://docs.python.org/3/library/stdtypes.html#range \"(in Python v3.10)\"), but returns an ndarray rather than a `range` instance.\n\n When using a non-integer step, such as 0.1, it is often better to use [`numpy.linspace`](numpy.linspace#numpy.linspace \"numpy.linspace\").\n\n See the Warning sections below for more information.\n\n Parameters \n \n**start**integer or real, optional\n\nStart of interval. The interval includes this value. The default start value is 0.\n\n \n**stop**integer or real\n\nEnd of interval. The interval does not include this value, except in some cases where `step` is not an integer and floating point round-off affects the length of `out`.\n\n \n**step**integer or real, optional\n\nSpacing between values. For any output `out`, this is the distance between two adjacent values, `out[i+1] - out[i]`. The default step size is 1. If `step` is specified as a position argument, `start` must also be given.\n\n \n**dtype**dtype, optional\n\nThe type of the output array. If [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") is not given, infer the data type from the other input arguments.\n\n \n**like**array_like, optional\n\nReference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as `like` supports the `__array_function__` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument.\n\n New in version 1.20.0.\n\n Returns \n \n**arange**MaskedArray\n\nArray of evenly spaced values.\n\n For floating point arguments, the length of the result is `ceil((stop - start)/step)`. Because of floating point overflow, this rule may result in the last element of `out` being greater than `stop`.\n\n Warning\n\n The length of the output might not be numerically stable.\n\n Another stability issue is due to the internal implementation of [`numpy.arange`](numpy.arange#numpy.arange \"numpy.arange\"). The actual step value used to populate the array is `dtype(start + step) - dtype(start)` and not `step`. Precision loss can occur here, due to casting or due to using floating points when `start` is much larger than `step`. This can lead to unexpected behaviour. For example:\n\n \n```\n>>> np.arange(0, 5, 0.5, dtype=int)\narray([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n>>> np.arange(-3, 3, 0.5, dtype=int)\narray([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8])\n\n```\n In such cases, the use of [`numpy.linspace`](numpy.linspace#numpy.linspace \"numpy.linspace\") should be preferred.\n\n The built-in [`range`](https://docs.python.org/3/library/stdtypes.html#range \"(in Python v3.10)\") generates [Python built-in integers that have arbitrary size](https://docs.python.org/3/c-api/long.html \"(in Python v3.10)\"), while [`numpy.arange`](numpy.arange#numpy.arange \"numpy.arange\") produces [`numpy.int32`](../arrays.scalars#numpy.int32 \"numpy.int32\") or [`numpy.int64`](../arrays.scalars#numpy.int64 \"numpy.int64\") numbers. This may result in incorrect results for large integer values:\n\n \n```\n>>> power = 40\n>>> modulo = 10000\n>>> x1 = [(n ** power) % modulo for n in range(8)]\n>>> x2 = [(n ** power) % modulo for n in np.arange(8)]\n>>> print(x1)\n[0, 1, 7776, 8801, 6176, 625, 6576, 4001] # correct\n>>> print(x2)\n[0, 1, 7776, 7185, 0, 5969, 4816, 3361] # incorrect\n\n```\n See also\n\n [`numpy.linspace`](numpy.linspace#numpy.linspace \"numpy.linspace\")\n\nEvenly spaced numbers with careful handling of endpoints.\n\n [`numpy.ogrid`](numpy.ogrid#numpy.ogrid \"numpy.ogrid\")\n\nArrays of evenly spaced numbers in N-dimensions.\n\n [`numpy.mgrid`](numpy.mgrid#numpy.mgrid \"numpy.mgrid\")\n\nGrid-shaped arrays of evenly spaced numbers in N-dimensions.\n\n #### Examples\n\n \n```\n>>> np.arange(3)\narray([0, 1, 2])\n>>> np.arange(3.0)\narray([ 0., 1., 2.])\n>>> np.arange(3,7)\narray([3, 4, 5, 6])\n>>> np.arange(3,7,2)\narray([3, 5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.arange.htmlnumpy.ma.choose\n===============\n\n ma.choose(*indices*, *choices*, *out=None*, *mode='raise'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L7394-L7466)\n \nUse an index array to construct a new array from a list of choices.\n\n Given an array of integers and a list of n choice arrays, this method will create a new array that merges each of the choice arrays. Where a value in `index` is i, the new array will have the value that choices[i] contains in the same place.\n\n Parameters \n \n**indices**ndarray of ints\n\nThis array must contain integers in `[0, n-1]`, where n is the number of choices.\n\n \n**choices**sequence of arrays\n\nChoice arrays. The index array and all of the choices should be broadcastable to the same shape.\n\n \n**out**array, optional\n\nIf provided, the result will be inserted into this array. It should be of the appropriate shape and [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\").\n\n \n**mode**{‘raise’, ‘wrap’, ‘clip’}, optional\n\nSpecifies how out-of-bounds indices will behave.\n\n * ‘raise’ : raise an error\n* ‘wrap’ : wrap around\n* ‘clip’ : clip to the range\n\n Returns \n \n**merged_array**array\n\n See also\n\n [`choose`](numpy.choose#numpy.choose \"numpy.choose\")\n\nequivalent function\n\n #### Examples\n\n \n```\n>>> choice = np.array([[1,1,1], [2,2,2], [3,3,3]])\n>>> a = np.array([2, 1, 0])\n>>> np.ma.choose(a, choice)\nmasked_array(data=[3, 2, 1],\n mask=False,\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.choose.htmlnumpy.ma.ediff1d\n================\n\n ma.ediff1d(*arr*, *to_end=None*, *to_begin=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/extras.py#L1067-L1093)\n \nCompute the differences between consecutive elements of an array.\n\n This function is the equivalent of [`numpy.ediff1d`](numpy.ediff1d#numpy.ediff1d \"numpy.ediff1d\") that takes masked values into account, see [`numpy.ediff1d`](numpy.ediff1d#numpy.ediff1d \"numpy.ediff1d\") for details.\n\n See also\n\n [`numpy.ediff1d`](numpy.ediff1d#numpy.ediff1d \"numpy.ediff1d\")\n\nEquivalent function for ndarrays.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.ediff1d.htmlnumpy.ma.indices\n================\n\n ma.indices(*dimensions*, *dtype=<class 'int'>*, *sparse=False*)*=<numpy.ma.core._convert2ma object>*\n \nReturn an array representing the indices of a grid.\n\n Compute an array where the subarrays contain index values 0, 1, … varying only along the corresponding axis.\n\n Parameters \n \n**dimensions**sequence of ints\n\nThe shape of the grid.\n\n \n**dtype**dtype, optional\n\nData type of the result.\n\n \n**sparse**boolean, optional\n\nReturn a sparse representation of the grid instead of a dense representation. Default is False.\n\n New in version 1.17.\n\n Returns \n \n**grid**one MaskedArray or tuple of MaskedArrays\n\n If sparse is False:\n\nReturns one array of grid indices, `grid.shape = (len(dimensions),) + tuple(dimensions)`.\n\n If sparse is True:\n\nReturns a tuple of arrays, with `grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)` with dimensions[i] in the ith place\n\n See also\n\n \n[`mgrid`](numpy.mgrid#numpy.mgrid \"numpy.mgrid\"), [`ogrid`](numpy.ogrid#numpy.ogrid \"numpy.ogrid\"), [`meshgrid`](numpy.meshgrid#numpy.meshgrid \"numpy.meshgrid\")\n\n #### Notes\n\n The output shape in the dense case is obtained by prepending the number of dimensions in front of the tuple of dimensions, i.e. if `dimensions` is a tuple `(r0, ..., rN-1)` of length `N`, the output shape is `(N, r0, ..., rN-1)`.\n\n The subarrays `grid[k]` contains the N-D array of indices along the `k-th` axis. Explicitly:\n\n \n```\ngrid[k, i0, i1, ..., iN-1] = ik\n\n```\n #### Examples\n\n \n```\n>>> grid = np.indices((2, 3))\n>>> grid.shape\n(2, 2, 3)\n>>> grid[0] # row indices\narray([[0, 0, 0],\n [1, 1, 1]])\n>>> grid[1] # column indices\narray([[0, 1, 2],\n [0, 1, 2]])\n\n```\n The indices can be used as an index into an array.\n\n \n```\n>>> x = np.arange(20).reshape(5, 4)\n>>> row, col = np.indices((2, 3))\n>>> x[row, col]\narray([[0, 1, 2],\n [4, 5, 6]])\n\n```\n Note that it would be more straightforward in the above example to extract the required elements directly with `x[:2, :3]`.\n\n If sparse is set to true, the grid will be returned in a sparse representation.\n\n \n```\n>>> i, j = np.indices((2, 3), sparse=True)\n>>> i.shape\n(2, 1)\n>>> j.shape\n(1, 3)\n>>> i # row indices\narray([[0],\n [1]])\n>>> j # column indices\narray([[0, 1, 2]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.indices.htmlnumpy.unwrap\n============\n\n numpy.unwrap(*p*, *discont=None*, *axis=- 1*, ***, *period=6.283185307179586*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1658-L1751)\n \nUnwrap by taking the complement of large deltas with respect to the period.\n\n This unwraps a signal `p` by changing elements which have an absolute difference from their predecessor of more than `max(discont, period/2)` to their `period`-complementary values.\n\n For the default case where `period` is \\(2\\pi\\) and `discont` is \\(\\pi\\), this unwraps a radian phase `p` such that adjacent differences are never greater than \\(\\pi\\) by adding \\(2k\\pi\\) for some integer \\(k\\).\n\n Parameters \n \n**p**array_like\n\nInput array.\n\n \n**discont**float, optional\n\nMaximum discontinuity between values, default is `period/2`. Values below `period/2` are treated as if they were `period/2`. To have an effect different from the default, `discont` should be larger than `period/2`.\n\n \n**axis**int, optional\n\nAxis along which unwrap will operate, default is the last axis.\n\n \n**period**float, optional\n\nSize of the range over which the input wraps. By default, it is `2 pi`.\n\n New in version 1.21.0.\n\n Returns \n \n**out**ndarray\n\nOutput array.\n\n See also\n\n \n[`rad2deg`](numpy.rad2deg#numpy.rad2deg \"numpy.rad2deg\"), [`deg2rad`](numpy.deg2rad#numpy.deg2rad \"numpy.deg2rad\")\n\n #### Notes\n\n If the discontinuity in `p` is smaller than `period/2`, but larger than `discont`, no unwrapping is done because taking the complement would only make the discontinuity larger.\n\n #### Examples\n\n \n```\n>>> phase = np.linspace(0, np.pi, num=5)\n>>> phase[3:] += np.pi\n>>> phase\narray([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) # may vary\n>>> np.unwrap(phase)\narray([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) # may vary\n>>> np.unwrap([0, 1, 2, -1, 0], period=4)\narray([0, 1, 2, 3, 4])\n>>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6)\narray([1, 2, 3, 4, 5, 6, 7, 8, 9])\n>>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4)\narray([2, 3, 4, 5, 6, 7, 8, 9])\n>>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180\n>>> np.unwrap(phase_deg, period=360)\narray([-180., -140., -100., -60., -20., 20., 60., 100., 140.,\n 180., 220., 260., 300., 340., 380., 420., 460., 500.,\n 540.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.unwrap.htmlnumpy.round_\n=============\n\n numpy.round_(*a*, *decimals=0*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/fromnumeric.py#L3722-L3731)\n \nRound an array to the given number of decimals.\n\n See also\n\n [`around`](numpy.around#numpy.around \"numpy.around\")\n\nequivalent function; see for details.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.round_.htmlnumpy.fix\n=========\n\n numpy.fix(*x*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/ufunclike.py#L73-L124)\n \nRound to nearest integer towards zero.\n\n Round an array of floats element-wise to nearest integer towards zero. The rounded values are returned as floats.\n\n Parameters \n \n**x**array_like\n\nAn array of floats to be rounded\n\n \n**out**ndarray, optional\n\nA location into which the result is stored. If provided, it must have a shape that the input broadcasts to. If not provided or None, a freshly-allocated array is returned.\n\n Returns \n \n**out**ndarray of floats\n\nA float array with the same dimensions as the input. If second argument is not supplied then a float array is returned with the rounded values.\n\n If a second argument is supplied the result is stored there. The return value `out` is then a reference to that array.\n\n See also\n\n \n[`rint`](numpy.rint#numpy.rint \"numpy.rint\"), [`trunc`](numpy.trunc#numpy.trunc \"numpy.trunc\"), [`floor`](numpy.floor#numpy.floor \"numpy.floor\"), [`ceil`](numpy.ceil#numpy.ceil \"numpy.ceil\")\n\n[`around`](numpy.around#numpy.around \"numpy.around\")\n\nRound to given number of decimals\n\n #### Examples\n\n \n```\n>>> np.fix(3.14)\n3.0\n>>> np.fix(3)\n3.0\n>>> np.fix([2.1, 2.9, -2.1, -2.9])\narray([ 2., 2., -2., -2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.fix.htmlnumpy.nanprod\n=============\n\n numpy.nanprod(*a*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*, *initial=<no value>*, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L732-L807)\n \nReturn the product of array elements over a given axis treating Not a Numbers (NaNs) as ones.\n\n One is returned for slices that are all-NaN or empty.\n\n New in version 1.10.0.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose product is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the product is computed. The default is to compute the product of the flattened array.\n\n \n**dtype**data-type, optional\n\nThe type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. The default is `None`. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details. The casting of NaN to integer can yield unexpected results.\n\n \n**keepdims**bool, optional\n\nIf True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`.\n\n \n**initial**scalar, optional\n\nThe starting value for this product. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n \n**where**array_like of bool, optional\n\nElements to include in the product. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**nanprod**ndarray\n\nA new array holding the result is returned unless `out` is specified, in which case it is returned.\n\n See also\n\n [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\")\n\nProduct across array propagating NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShow which elements are NaN.\n\n #### Examples\n\n \n```\n>>> np.nanprod(1)\n1\n>>> np.nanprod([1])\n1\n>>> np.nanprod([1, np.nan])\n1.0\n>>> a = np.array([[1, 2], [3, np.nan]])\n>>> np.nanprod(a)\n6.0\n>>> np.nanprod(a, axis=0)\narray([3., 2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanprod.htmlnumpy.nansum\n============\n\n numpy.nansum(*a*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*, *initial=<no value>*, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L623-L724)\n \nReturn the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.\n\n In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or empty. In later versions zero is returned.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose sum is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the sum is computed. The default is to compute the sum of the flattened array.\n\n \n**dtype**data-type, optional\n\nThe type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.\n\n New in version 1.8.0.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. The default is `None`. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details. The casting of NaN to integer can yield unexpected results.\n\n New in version 1.8.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If the value is anything but the default, then `keepdims` will be passed through to the [`mean`](numpy.mean#numpy.mean \"numpy.mean\") or [`sum`](numpy.sum#numpy.sum \"numpy.sum\") methods of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"). If the sub-classes methods does not implement `keepdims` any exceptions will be raised.\n\n New in version 1.8.0.\n\n \n**initial**scalar, optional\n\nStarting value for the sum. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n \n**where**array_like of bool, optional\n\nElements to include in the sum. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**nansum**ndarray.\n\nA new array holding the result is returned unless `out` is specified, in which it is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array.\n\n See also\n\n [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\")\n\nSum across array propagating NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShow which elements are NaN.\n\n [`isfinite`](numpy.isfinite#numpy.isfinite \"numpy.isfinite\")\n\nShow which elements are not NaN or +/-inf.\n\n #### Notes\n\n If both positive and negative infinity are present, the sum will be Not A Number (NaN).\n\n #### Examples\n\n \n```\n>>> np.nansum(1)\n1\n>>> np.nansum([1])\n1\n>>> np.nansum([1, np.nan])\n1.0\n>>> a = np.array([[1, 1], [1, np.nan]])\n>>> np.nansum(a)\n3.0\n>>> np.nansum(a, axis=0)\narray([2., 1.])\n>>> np.nansum([1, np.nan, np.inf])\ninf\n>>> np.nansum([1, np.nan, np.NINF])\n-inf\n>>> from numpy.testing import suppress_warnings\n>>> with suppress_warnings() as sup:\n... sup.filter(RuntimeWarning)\n... np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present\nnan\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nansum.htmlnumpy.nancumprod\n================\n\n numpy.nancumprod(*a*, *axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L884-L944)\n \nReturn the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones.\n\n Ones are returned for slices that are all-NaN or empty.\n\n New in version 1.12.0.\n\n Parameters \n \n**a**array_like\n\nInput array.\n\n \n**axis**int, optional\n\nAxis along which the cumulative product is computed. By default the input is flattened.\n\n \n**dtype**dtype, optional\n\nType of the returned array, as well as of the accumulator in which the elements are multiplied. If *dtype* is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary.\n\n Returns \n \n**nancumprod**ndarray\n\nA new array holding the result is returned unless `out` is specified, in which case it is returned.\n\n See also\n\n [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\")\n\nCumulative product across array propagating NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShow which elements are NaN.\n\n #### Examples\n\n \n```\n>>> np.nancumprod(1)\narray([1])\n>>> np.nancumprod([1])\narray([1])\n>>> np.nancumprod([1, np.nan])\narray([1., 1.])\n>>> a = np.array([[1, 2], [3, np.nan]])\n>>> np.nancumprod(a)\narray([1., 2., 6., 6.])\n>>> np.nancumprod(a, axis=0)\narray([[1., 2.],\n [3., 2.]])\n>>> np.nancumprod(a, axis=1)\narray([[1., 2.],\n [3., 3.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nancumprod.htmlnumpy.nancumsum\n===============\n\n numpy.nancumsum(*a*, *axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L814-L877)\n \nReturn the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros.\n\n Zeros are returned for slices that are all-NaN or empty.\n\n New in version 1.12.0.\n\n Parameters \n \n**a**array_like\n\nInput array.\n\n \n**axis**int, optional\n\nAxis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.\n\n \n**dtype**dtype, optional\n\nType of the returned array and of the accumulator in which the elements are summed. If [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details.\n\n Returns \n \n**nancumsum**ndarray.\n\nA new array holding the result is returned unless `out` is specified, in which it is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array.\n\n See also\n\n [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\nCumulative sum across array propagating NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShow which elements are NaN.\n\n #### Examples\n\n \n```\n>>> np.nancumsum(1)\narray([1])\n>>> np.nancumsum([1])\narray([1])\n>>> np.nancumsum([1, np.nan])\narray([1., 1.])\n>>> a = np.array([[1, 2], [3, np.nan]])\n>>> np.nancumsum(a)\narray([1., 3., 6., 6.])\n>>> np.nancumsum(a, axis=0)\narray([[1., 2.],\n [4., 2.]])\n>>> np.nancumsum(a, axis=1)\narray([[1., 3.],\n [3., 3.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nancumsum.htmlnumpy.ediff1d\n=============\n\n numpy.ediff1d(*ary*, *to_end=None*, *to_begin=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L37-L122)\n \nThe differences between consecutive elements of an array.\n\n Parameters \n \n**ary**array_like\n\nIf necessary, will be flattened before the differences are taken.\n\n \n**to_end**array_like, optional\n\nNumber(s) to append at the end of the returned differences.\n\n \n**to_begin**array_like, optional\n\nNumber(s) to prepend at the beginning of the returned differences.\n\n Returns \n \n**ediff1d**ndarray\n\nThe differences. Loosely, this is `ary.flat[1:] - ary.flat[:-1]`.\n\n See also\n\n \n[`diff`](numpy.diff#numpy.diff \"numpy.diff\"), [`gradient`](numpy.gradient#numpy.gradient \"numpy.gradient\")\n\n #### Notes\n\n When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 4, 7, 0])\n>>> np.ediff1d(x)\narray([ 1, 2, 3, -7])\n\n```\n \n```\n>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))\narray([-99, 1, 2, ..., -7, 88, 99])\n\n```\n The returned array is always 1D.\n\n \n```\n>>> y = [[1, 2, 4], [1, 6, 24]]\n>>> np.ediff1d(y)\narray([ 1, 2, -3, 5, 18])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ediff1d.htmlnumpy.gradient\n==============\n\n numpy.gradient(*f*, **varargs*, *axis=None*, *edge_order=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L969-L1312)\n \nReturn the gradient of an N-dimensional array.\n\n The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.\n\n Parameters \n \n**f**array_like\n\nAn N-dimensional array containing samples of a scalar function.\n\n \n**varargs**list of scalar or array, optional\n\nSpacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using:\n\n 1. single scalar to specify a sample distance for all dimensions.\n2. N scalars to specify a constant sample distance for each dimension. i.e. `dx`, `dy`, `dz`, …\n3. N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension\n4. Any combination of N scalars/arrays with the meaning of 2. and 3.\n\n If `axis` is given, the number of varargs must equal the number of axes. Default: 1.\n\n \n**edge_order**{1, 2}, optional\n\nGradient is calculated using N-th order accurate differences at the boundaries. Default: 1.\n\n New in version 1.9.1.\n\n \n**axis**None or int or tuple of ints, optional\n\nGradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis.\n\n New in version 1.11.0.\n\n Returns \n \n**gradient**ndarray or list of ndarray\n\nA list of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.\n\n #### Notes\n\n Assuming that \\(f\\in C^{3}\\) (i.e., \\(f\\) has at least 3 continuous derivatives) and let \\(h_{*}\\) be a non-homogeneous stepsize, we minimize the “consistency error” \\(\\eta_{i}\\) between the true gradient and its estimate from a linear combination of the neighboring grid-points:\n\n \\[\\eta_{i} = f_{i}^{\\left(1\\right)} - \\left[ \\alpha f\\left(x_{i}\\right) + \\beta f\\left(x_{i} + h_{d}\\right) + \\gamma f\\left(x_{i}-h_{s}\\right) \\right]\\] By substituting \\(f(x_{i} + h_{d})\\) and \\(f(x_{i} - h_{s})\\) with their Taylor series expansion, this translates into solving the following the linear system:\n\n \\[\\begin{split}\\left\\{ \\begin{array}{r} \\alpha+\\beta+\\gamma=0 \\\\ \\beta h_{d}-\\gamma h_{s}=1 \\\\ \\beta h_{d}^{2}+\\gamma h_{s}^{2}=0 \\end{array} \\right.\\end{split}\\] The resulting approximation of \\(f_{i}^{(1)}\\) is the following:\n\n \\[\\hat f_{i}^{(1)} = \\frac{ h_{s}^{2}f\\left(x_{i} + h_{d}\\right) + \\left(h_{d}^{2} - h_{s}^{2}\\right)f\\left(x_{i}\\right) - h_{d}^{2}f\\left(x_{i}-h_{s}\\right)} { h_{s}h_{d}\\left(h_{d} + h_{s}\\right)} + \\mathcal{O}\\left(\\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\\right)\\] It is worth noting that if \\(h_{s}=h_{d}\\) (i.e., data are evenly spaced) we find the standard second order approximation:\n\n \\[\\hat f_{i}^{(1)}= \\frac{f\\left(x_{i+1}\\right) - f\\left(x_{i-1}\\right)}{2h} + \\mathcal{O}\\left(h^{2}\\right)\\] With a similar procedure the forward/backward approximations used for boundaries can be derived.\n\n #### References\n\n 1 \n<NAME>., <NAME>., <NAME>. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer.\n\n 2 \n<NAME>. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer.\n\n 3 \n<NAME>. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699-706. [PDF](http://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf).\n\n #### Examples\n\n \n```\n>>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float)\n>>> np.gradient(f)\narray([1. , 1.5, 2.5, 3.5, 4.5, 5. ])\n>>> np.gradient(f, 2)\narray([0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ])\n\n```\n Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing:\n\n \n```\n>>> x = np.arange(f.size)\n>>> np.gradient(f, x)\narray([1. , 1.5, 2.5, 3.5, 4.5, 5. ])\n\n```\n Or a non uniform one:\n\n \n```\n>>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float)\n>>> np.gradient(f, x)\narray([1. , 3. , 3.5, 6.7, 6.9, 2.5])\n\n```\n For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction:\n\n \n```\n>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float))\n[array([[ 2., 2., -1.],\n [ 2., 2., -1.]]), array([[1. , 2.5, 4. ],\n [1. , 1. , 1. ]])]\n\n```\n In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1\n\n \n```\n>>> dx = 2.\n>>> y = [1., 1.5, 3.5]\n>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y)\n[array([[ 1. , 1. , -0.5],\n [ 1. , 1. , -0.5]]), array([[2. , 2. , 2. ],\n [2. , 1.7, 0.5]])]\n\n```\n It is possible to specify how boundaries are treated using `edge_order`\n\n \n```\n>>> x = np.array([0, 1, 2, 3, 4])\n>>> f = x**2\n>>> np.gradient(f, edge_order=1)\narray([1., 2., 4., 6., 7.])\n>>> np.gradient(f, edge_order=2)\narray([0., 2., 4., 6., 8.])\n\n```\n The `axis` keyword can be used to specify a subset of axes of which the gradient is calculated\n\n \n```\n>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0)\narray([[ 2., 2., -1.],\n [ 2., 2., -1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.gradient.htmlnumpy.trapz\n===========\n\n numpy.trapz(*y*, *x=None*, *dx=1.0*, *axis=- 1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L4727-L4838)\n \nIntegrate along the given axis using the composite trapezoidal rule.\n\n If `x` is provided, the integration happens in sequence along its elements - they are not sorted.\n\n Integrate `y` (`x`) along each 1d slice on the given axis, compute \\(\\int y(x) dx\\). When `x` is specified, this integrates along the parametric curve, computing \\(\\int_t y(t) dt = \\int_t y(t) \\left.\\frac{dx}{dt}\\right|_{x=x(t)} dt\\).\n\n Parameters \n \n**y**array_like\n\nInput array to integrate.\n\n \n**x**array_like, optional\n\nThe sample points corresponding to the `y` values. If `x` is None, the sample points are assumed to be evenly spaced `dx` apart. The default is None.\n\n \n**dx**scalar, optional\n\nThe spacing between sample points when `x` is None. The default is 1.\n\n \n**axis**int, optional\n\nThe axis along which to integrate.\n\n Returns \n \n**trapz**float or ndarray\n\nDefinite integral of `y` = n-dimensional array as approximated along a single axis by the trapezoidal rule. If `y` is a 1-dimensional array, then the result is a float. If `n` is greater than 1, then the result is an `n`-1 dimensional array.\n\n See also\n\n \n[`sum`](numpy.sum#numpy.sum \"numpy.sum\"), [`cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\n #### Notes\n\n Image [[2]](#r7aa6c77779c0-2) illustrates trapezoidal rule – y-axis locations of points will be taken from `y` array, by default x-axis distances between points will be 1.0, alternatively they can be provided with `x` array or with `dx` scalar. Return value will be equal to combined area under the red lines.\n\n #### References\n\n 1 \nWikipedia page: <https://en.wikipedia.org/wiki/Trapezoidal_rule [2](#id1) \nIllustration image: <https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png #### Examples\n\n \n```\n>>> np.trapz([1,2,3])\n4.0\n>>> np.trapz([1,2,3], x=[4,6,8])\n8.0\n>>> np.trapz([1,2,3], dx=2)\n8.0\n\n```\n Using a decreasing `x` corresponds to integrating in reverse:\n\n \n```\n>>> np.trapz([1,2,3], x=[8,6,4])\n-8.0\n\n```\n More generally `x` is used to integrate along a parametric curve. This finds the area of a circle, noting we repeat the sample which closes the curve:\n\n \n```\n>>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True)\n>>> np.trapz(np.cos(theta), x=np.sin(theta))\n3.141571941375841\n\n```\n \n```\n>>> a = np.arange(6).reshape(2, 3)\n>>> a\narray([[0, 1, 2],\n [3, 4, 5]])\n>>> np.trapz(a, axis=0)\narray([1.5, 2.5, 3.5])\n>>> np.trapz(a, axis=1)\narray([2., 8.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.trapz.htmlnumpy.sinc\n==========\n\n numpy.sinc(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L3560-L3638)\n \nReturn the normalized sinc function.\n\n The sinc function is equal to \\(\\sin(\\pi x)/(\\pi x)\\) for any argument \\(x\\ne 0\\). `sinc(0)` takes the limit value 1, making `sinc` not only everywhere continuous but also infinitely differentiable.\n\n Note\n\n Note the normalization factor of `pi` used in the definition. This is the most commonly used definition in signal processing. Use `sinc(x / np.pi)` to obtain the unnormalized sinc function \\(\\sin(x)/x\\) that is more common in mathematics.\n\n Parameters \n \n**x**ndarray\n\nArray (possibly multi-dimensional) of values for which to calculate `sinc(x)`.\n\n Returns \n \n**out**ndarray\n\n`sinc(x)`, which has the same shape as the input.\n\n #### Notes\n\n The name sinc is short for “sine cardinal” or “sinus cardinalis”.\n\n The sinc function is used in various signal processing applications, including in anti-aliasing, in the construction of a Lanczos resampling filter, and in interpolation.\n\n For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Sinc Function.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/SincFunction.html 2 \nWikipedia, “Sinc function”, <https://en.wikipedia.org/wiki/Sinc_function #### Examples\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-4, 4, 41)\n>>> np.sinc(x)\n array([-3.89804309e-17, -4.92362781e-02, -8.40918587e-02, # may vary\n -8.90384387e-02, -5.84680802e-02, 3.89804309e-17,\n 6.68206631e-02, 1.16434881e-01, 1.26137788e-01,\n 8.50444803e-02, -3.89804309e-17, -1.03943254e-01,\n -1.89206682e-01, -2.16236208e-01, -1.55914881e-01,\n 3.89804309e-17, 2.33872321e-01, 5.04551152e-01,\n 7.56826729e-01, 9.35489284e-01, 1.00000000e+00,\n 9.35489284e-01, 7.56826729e-01, 5.04551152e-01,\n 2.33872321e-01, 3.89804309e-17, -1.55914881e-01,\n -2.16236208e-01, -1.89206682e-01, -1.03943254e-01,\n -3.89804309e-17, 8.50444803e-02, 1.26137788e-01,\n 1.16434881e-01, 6.68206631e-02, 3.89804309e-17,\n -5.84680802e-02, -8.90384387e-02, -8.40918587e-02,\n -4.92362781e-02, -3.89804309e-17])\n\n```\n \n```\n>>> plt.plot(x, np.sinc(x))\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Sinc Function\")\nText(0.5, 1.0, 'Sinc Function')\n>>> plt.ylabel(\"Amplitude\")\nText(0, 0.5, 'Amplitude')\n>>> plt.xlabel(\"X\")\nText(0.5, 0, 'X')\n>>> plt.show()\n\n```\n ![../../_images/numpy-sinc-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.sinc.htmlnumpy.angle\n===========\n\n numpy.angle(*z*, *deg=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1601-L1651)\n \nReturn the angle of the complex argument.\n\n Parameters \n \n**z**array_like\n\nA complex number or sequence of complex numbers.\n\n \n**deg**bool, optional\n\nReturn angle in degrees if True, radians if False (default).\n\n Returns \n \n**angle**ndarray or scalar\n\nThe counterclockwise angle from the positive real axis on the complex plane in the range `(-pi, pi]`, with dtype as numpy.float64.\n\n Changed in version 1.16.0: This function works on subclasses of ndarray like [`ma.array`](numpy.ma.array#numpy.ma.array \"numpy.ma.array\").\n\n See also\n\n [`arctan2`](numpy.arctan2#numpy.arctan2 \"numpy.arctan2\")\n[`absolute`](numpy.absolute#numpy.absolute \"numpy.absolute\")\n #### Notes\n\n Although the angle of the complex number 0 is undefined, `numpy.angle(0)` returns the value 0.\n\n #### Examples\n\n \n```\n>>> np.angle([1.0, 1.0j, 1+1j]) # in radians\narray([ 0. , 1.57079633, 0.78539816]) # may vary\n>>> np.angle(1+1j, deg=True) # in degrees\n45.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.angle.htmlnumpy.nanmax\n============\n\n numpy.nanmax(*a*, *axis=None*, *out=None*, *keepdims=<no value>*, *initial=<no value>*, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L369-L494)\n \nReturn the maximum of an array or maximum along an axis, ignoring any NaNs. When all-NaN slices are encountered a `RuntimeWarning` is raised and NaN is returned for that slice.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose maximum is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the maximum is computed. The default is to compute the maximum of the flattened array.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. The default is `None`; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details.\n\n New in version 1.8.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If the value is anything but the default, then `keepdims` will be passed through to the [`max`](https://docs.python.org/3/library/functions.html#max \"(in Python v3.10)\") method of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"). If the sub-classes methods does not implement `keepdims` any exceptions will be raised.\n\n New in version 1.8.0.\n\n \n**initial**scalar, optional\n\nThe minimum value of an output element. Must be present to allow computation on empty slice. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n \n**where**array_like of bool, optional\n\nElements to compare for the maximum. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**nanmax**ndarray\n\nAn array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned.\n\n See also\n\n [`nanmin`](numpy.nanmin#numpy.nanmin \"numpy.nanmin\")\n\nThe minimum value of an array along a given axis, ignoring any NaNs.\n\n [`amax`](numpy.amax#numpy.amax \"numpy.amax\")\n\nThe maximum value of an array along a given axis, propagating any NaNs.\n\n [`fmax`](numpy.fmax#numpy.fmax \"numpy.fmax\")\n\nElement-wise maximum of two arrays, ignoring any NaNs.\n\n [`maximum`](numpy.maximum#numpy.maximum \"numpy.maximum\")\n\nElement-wise maximum of two arrays, propagating any NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShows which elements are Not a Number (NaN).\n\n [`isfinite`](numpy.isfinite#numpy.isfinite \"numpy.isfinite\")\n\nShows which elements are neither NaN nor infinity.\n\n \n[`amin`](numpy.amin#numpy.amin \"numpy.amin\"), [`fmin`](numpy.fmin#numpy.fmin \"numpy.fmin\"), [`minimum`](numpy.minimum#numpy.minimum \"numpy.minimum\")\n\n #### Notes\n\n NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number.\n\n If the input has a integer type the function is equivalent to np.max.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, np.nan]])\n>>> np.nanmax(a)\n3.0\n>>> np.nanmax(a, axis=0)\narray([3., 2.])\n>>> np.nanmax(a, axis=1)\narray([2., 3.])\n\n```\n When positive infinity and negative infinity are present:\n\n \n```\n>>> np.nanmax([1, 2, np.nan, np.NINF])\n2.0\n>>> np.nanmax([1, 2, np.nan, np.inf])\ninf\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanmax.htmlnumpy.nanmin\n============\n\n numpy.nanmin(*a*, *axis=None*, *out=None*, *keepdims=<no value>*, *initial=<no value>*, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L236-L361)\n \nReturn minimum of an array or minimum along an axis, ignoring any NaNs. When all-NaN slices are encountered a `RuntimeWarning` is raised and Nan is returned for that slice.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose minimum is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the minimum is computed. The default is to compute the minimum of the flattened array.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. The default is `None`; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details.\n\n New in version 1.8.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If the value is anything but the default, then `keepdims` will be passed through to the [`min`](https://docs.python.org/3/library/functions.html#min \"(in Python v3.10)\") method of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"). If the sub-classes methods does not implement `keepdims` any exceptions will be raised.\n\n New in version 1.8.0.\n\n \n**initial**scalar, optional\n\nThe maximum value of an output element. Must be present to allow computation on empty slice. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n \n**where**array_like of bool, optional\n\nElements to compare for the minimum. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**nanmin**ndarray\n\nAn array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned.\n\n See also\n\n [`nanmax`](numpy.nanmax#numpy.nanmax \"numpy.nanmax\")\n\nThe maximum value of an array along a given axis, ignoring any NaNs.\n\n [`amin`](numpy.amin#numpy.amin \"numpy.amin\")\n\nThe minimum value of an array along a given axis, propagating any NaNs.\n\n [`fmin`](numpy.fmin#numpy.fmin \"numpy.fmin\")\n\nElement-wise minimum of two arrays, ignoring any NaNs.\n\n [`minimum`](numpy.minimum#numpy.minimum \"numpy.minimum\")\n\nElement-wise minimum of two arrays, propagating any NaNs.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShows which elements are Not a Number (NaN).\n\n [`isfinite`](numpy.isfinite#numpy.isfinite \"numpy.isfinite\")\n\nShows which elements are neither NaN nor infinity.\n\n \n[`amax`](numpy.amax#numpy.amax \"numpy.amax\"), [`fmax`](numpy.fmax#numpy.fmax \"numpy.fmax\"), [`maximum`](numpy.maximum#numpy.maximum \"numpy.maximum\")\n\n #### Notes\n\n NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number.\n\n If the input has a integer type the function is equivalent to np.min.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, np.nan]])\n>>> np.nanmin(a)\n1.0\n>>> np.nanmin(a, axis=0)\narray([1., 2.])\n>>> np.nanmin(a, axis=1)\narray([1., 3.])\n\n```\n When positive infinity and negative infinity are present:\n\n \n```\n>>> np.nanmin([1, 2, np.nan, np.inf])\n1.0\n>>> np.nanmin([1, 2, np.nan, np.NINF])\n-inf\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanmin.htmlnumpy.convolve\n==============\n\n numpy.convolve(*a*, *v*, *mode='full'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/numeric.py#L754-L850)\n \nReturns the discrete, linear convolution of two one-dimensional sequences.\n\n The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [[1]](#r95849f33d2b1-1). In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions.\n\n If `v` is longer than `a`, the arrays are swapped before computation.\n\n Parameters \n \n**a**(N,) array_like\n\nFirst one-dimensional input array.\n\n \n**v**(M,) array_like\n\nSecond one-dimensional input array.\n\n \n**mode**{‘full’, ‘valid’, ‘same’}, optional\n\n ‘full’:\n\nBy default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen.\n\n ‘same’:\n\nMode ‘same’ returns output of length `max(M, N)`. Boundary effects are still visible.\n\n ‘valid’:\n\nMode ‘valid’ returns output of length `max(M, N) - min(M, N) + 1`. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect.\n\n Returns \n \n**out**ndarray\n\nDiscrete, linear convolution of `a` and `v`.\n\n See also\n\n [`scipy.signal.fftconvolve`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.fftconvolve.html#scipy.signal.fftconvolve \"(in SciPy v1.8.1)\")\n\nConvolve two arrays using the Fast Fourier Transform.\n\n [`scipy.linalg.toeplitz`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.toeplitz.html#scipy.linalg.toeplitz \"(in SciPy v1.8.1)\")\n\nUsed to construct the convolution operator.\n\n [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\")\n\nPolynomial multiplication. Same output as convolve, but also accepts poly1d objects as input.\n\n #### Notes\n\n The discrete convolution operation is defined as\n\n \\[(a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m}\\] It can be shown that a convolution \\(x(t) * y(t)\\) in time/space is equivalent to the multiplication \\(X(f) Y(f)\\) in the Fourier domain, after appropriate padding (padding is necessary to prevent circular convolution). Since multiplication is more efficient (faster) than convolution, the function [`scipy.signal.fftconvolve`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.fftconvolve.html#scipy.signal.fftconvolve \"(in SciPy v1.8.1)\") exploits the FFT to calculate the convolution of large data-sets.\n\n #### References\n\n [1](#id1) \nWikipedia, “Convolution”, <https://en.wikipedia.org/wiki/Convolution #### Examples\n\n Note how the convolution operator flips the second array before “sliding” the two across one another:\n\n \n```\n>>> np.convolve([1, 2, 3], [0, 1, 0.5])\narray([0. , 1. , 2.5, 4. , 1.5])\n\n```\n Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account:\n\n \n```\n>>> np.convolve([1,2,3],[0,1,0.5], 'same')\narray([1. , 2.5, 4. ])\n\n```\n The two arrays are of the same length, so there is only one position where they completely overlap:\n\n \n```\n>>> np.convolve([1,2,3],[0,1,0.5], 'valid')\narray([2.5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.convolve.htmlnumpy.nan_to_num\n==================\n\n numpy.nan_to_num(*x*, *copy=True*, *nan=0.0*, *posinf=None*, *neginf=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/type_check.py#L404-L521)\n \nReplace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the [`nan`](../constants#numpy.nan \"numpy.nan\"), `posinf` and/or `neginf` keywords.\n\n If `x` is inexact, NaN is replaced by zero or by the user defined value in [`nan`](../constants#numpy.nan \"numpy.nan\") keyword, infinity is replaced by the largest finite floating point values representable by `x.dtype` or by the user defined value in `posinf` keyword and -infinity is replaced by the most negative finite floating point values representable by `x.dtype` or by the user defined value in `neginf` keyword.\n\n For complex dtypes, the above is applied to each of the real and imaginary components of `x` separately.\n\n If `x` is not inexact, then no replacements are made.\n\n Parameters \n \n**x**scalar or array_like\n\nInput data.\n\n \n**copy**bool, optional\n\nWhether to create a copy of `x` (True) or to replace values in-place (False). The in-place operation only occurs if casting to an array does not require a copy. Default is True.\n\n New in version 1.13.\n\n \n**nan**int, float, optional\n\nValue to be used to fill NaN values. If no value is passed then NaN values will be replaced with 0.0.\n\n New in version 1.17.\n\n \n**posinf**int, float, optional\n\nValue to be used to fill positive infinity values. If no value is passed then positive infinity values will be replaced with a very large number.\n\n New in version 1.17.\n\n \n**neginf**int, float, optional\n\nValue to be used to fill negative infinity values. If no value is passed then negative infinity values will be replaced with a very small (or negative) number.\n\n New in version 1.17.\n\n Returns \n \n**out**ndarray\n\n`x`, with the non-finite values replaced. If [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False, this may be `x` itself.\n\n See also\n\n [`isinf`](numpy.isinf#numpy.isinf \"numpy.isinf\")\n\nShows which elements are positive or negative infinity.\n\n [`isneginf`](numpy.isneginf#numpy.isneginf \"numpy.isneginf\")\n\nShows which elements are negative infinity.\n\n [`isposinf`](numpy.isposinf#numpy.isposinf \"numpy.isposinf\")\n\nShows which elements are positive infinity.\n\n [`isnan`](numpy.isnan#numpy.isnan \"numpy.isnan\")\n\nShows which elements are Not a Number (NaN).\n\n [`isfinite`](numpy.isfinite#numpy.isfinite \"numpy.isfinite\")\n\nShows which elements are finite (not NaN, not infinity)\n\n #### Notes\n\n NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity.\n\n #### Examples\n\n \n```\n>>> np.nan_to_num(np.inf)\n1.7976931348623157e+308\n>>> np.nan_to_num(-np.inf)\n-1.7976931348623157e+308\n>>> np.nan_to_num(np.nan)\n0.0\n>>> x = np.array([np.inf, -np.inf, np.nan, -128, 128])\n>>> np.nan_to_num(x)\narray([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary\n -1.28000000e+002, 1.28000000e+002])\n>>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333)\narray([ 3.3333333e+07, 3.3333333e+07, -9.9990000e+03,\n -1.2800000e+02, 1.2800000e+02])\n>>> y = np.array([complex(np.inf, np.nan), np.nan, complex(np.nan, np.inf)])\narray([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary\n -1.28000000e+002, 1.28000000e+002])\n>>> np.nan_to_num(y)\narray([ 1.79769313e+308 +0.00000000e+000j, # may vary\n 0.00000000e+000 +0.00000000e+000j,\n 0.00000000e+000 +1.79769313e+308j])\n>>> np.nan_to_num(y, nan=111111, posinf=222222)\narray([222222.+111111.j, 111111. +0.j, 111111.+222222.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nan_to_num.htmlnumpy.real_if_close\n=====================\n\n numpy.real_if_close(*a*, *tol=100*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/type_check.py#L529-L583)\n \nIf input is complex with all imaginary parts close to zero, return real parts.\n\n “Close to zero” is defined as `tol` * (machine epsilon of the type for `a`).\n\n Parameters \n \n**a**array_like\n\nInput array.\n\n \n**tol**float\n\nTolerance in machine epsilons for the complex part of the elements in the array.\n\n Returns \n \n**out**ndarray\n\nIf `a` is real, the type of `a` is used for the output. If `a` has complex elements, the returned type is float.\n\n See also\n\n \n[`real`](numpy.real#numpy.real \"numpy.real\"), [`imag`](numpy.imag#numpy.imag \"numpy.imag\"), [`angle`](numpy.angle#numpy.angle \"numpy.angle\")\n\n #### Notes\n\n Machine epsilon varies from machine to machine and between data types but Python floats on most platforms have a machine epsilon equal to 2.2204460492503131e-16. You can use ‘np.finfo(float).eps’ to print out the machine epsilon for floats.\n\n #### Examples\n\n \n```\n>>> np.finfo(float).eps\n2.2204460492503131e-16 # may vary\n\n```\n \n```\n>>> np.real_if_close([2.1 + 4e-14j, 5.2 + 3e-15j], tol=1000)\narray([2.1, 5.2])\n>>> np.real_if_close([2.1 + 4e-13j, 5.2 + 3e-15j], tol=1000)\narray([2.1+4.e-13j, 5.2 + 3e-15j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.real_if_close.htmlnumpy.interp\n============\n\n numpy.interp(*x*, *xp*, *fp*, *left=None*, *right=None*, *period=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1456-L1594)\n \nOne-dimensional linear interpolation for monotonically increasing sample points.\n\n Returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (`xp`, `fp`), evaluated at `x`.\n\n Parameters \n \n**x**array_like\n\nThe x-coordinates at which to evaluate the interpolated values.\n\n \n**xp**1-D sequence of floats\n\nThe x-coordinates of the data points, must be increasing if argument `period` is not specified. Otherwise, `xp` is internally sorted after normalizing the periodic boundaries with `xp = xp % period`.\n\n \n**fp**1-D sequence of float or complex\n\nThe y-coordinates of the data points, same length as `xp`.\n\n \n**left**optional float or complex corresponding to fp\n\nValue to return for `x < xp[0]`, default is `fp[0]`.\n\n \n**right**optional float or complex corresponding to fp\n\nValue to return for `x > xp[-1]`, default is `fp[-1]`.\n\n \n**period**None or float, optional\n\nA period for the x-coordinates. This parameter allows the proper interpolation of angular x-coordinates. Parameters `left` and `right` are ignored if `period` is specified.\n\n New in version 1.10.0.\n\n Returns \n \n**y**float or complex (corresponding to fp) or ndarray\n\nThe interpolated values, same shape as `x`.\n\n Raises \n ValueError\n\nIf `xp` and `fp` have different length If `xp` or `fp` are not 1-D sequences If `period == 0`\n\n Warning\n\n The x-coordinate sequence is expected to be increasing, but this is not explicitly enforced. However, if the sequence `xp` is non-increasing, interpolation results are meaningless.\n\n Note that, since NaN is unsortable, `xp` also cannot contain NaNs.\n\n A simple check for `xp` being strictly increasing is:\n\n \n```\nnp.all(np.diff(xp) > 0)\n\n```\n See also\n\n [`scipy.interpolate`](https://docs.scipy.org/doc/scipy/reference/interpolate.html#module-scipy.interpolate \"(in SciPy v1.8.1)\")\n #### Examples\n\n \n```\n>>> xp = [1, 2, 3]\n>>> fp = [3, 2, 0]\n>>> np.interp(2.5, xp, fp)\n1.0\n>>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)\narray([3. , 3. , 2.5 , 0.56, 0. ])\n>>> UNDEF = -99.0\n>>> np.interp(3.14, xp, fp, right=UNDEF)\n-99.0\n\n```\n Plot an interpolant to the sine function:\n\n \n```\n>>> x = np.linspace(0, 2*np.pi, 10)\n>>> y = np.sin(x)\n>>> xvals = np.linspace(0, 2*np.pi, 50)\n>>> yinterp = np.interp(xvals, x, y)\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'o')\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.plot(xvals, yinterp, '-x')\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.show()\n\n```\n ![../../_images/numpy-interp-1_00_00.png] Interpolation with periodic x-coordinates:\n\n \n```\n>>> x = [-180, -170, -185, 185, -10, -5, 0, 365]\n>>> xp = [190, -190, 350, -350]\n>>> fp = [5, 10, 3, 4]\n>>> np.interp(x, xp, fp, period=360)\narray([7.5 , 5. , 8.75, 6.25, 3. , 3.25, 3.5 , 3.75])\n\n```\n Complex interpolation:\n\n \n```\n>>> x = [1.5, 4.0]\n>>> xp = [2,3,5]\n>>> fp = [1.0j, 0, 2+3j]\n>>> np.interp(x, xp, fp)\narray([0.+1.j , 1.+1.5j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.interp.htmlnumpy.setbufsize\n================\n\n numpy.setbufsize(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_ufunc_config.py#L181-L203)\n \nSet the size of the buffer used in ufuncs.\n\n Parameters \n \n**size**int\n\nSize of buffer.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.setbufsize.htmlnumpy.getbufsize\n================\n\n numpy.getbufsize()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_ufunc_config.py#L206-L217)\n \nReturn the size of the buffer used in ufuncs.\n\n Returns \n \n**getbufsize**int\n\nSize of ufunc buffer in bytes.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.getbufsize.htmlnumpy.may_share_memory\n========================\n\n numpy.may_share_memory(*a*, *b*, */*, *max_work=None*)\n \nDetermine if two arrays might share memory\n\n A return of True does not necessarily mean that the two arrays share any element. It just means that they *might*.\n\n Only the memory bounds of a and b are checked by default.\n\n Parameters \n \n**a, b**ndarray\n\nInput arrays\n\n \n**max_work**int, optional\n\nEffort to spend on solving the overlap problem. See [`shares_memory`](numpy.shares_memory#numpy.shares_memory \"numpy.shares_memory\") for details. Default for `may_share_memory` is to do a bounds check.\n\n Returns \n \n**out**bool\n\n See also\n\n [`shares_memory`](numpy.shares_memory#numpy.shares_memory \"numpy.shares_memory\")\n #### Examples\n\n \n```\n>>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))\nFalse\n>>> x = np.zeros([3, 4])\n>>> np.may_share_memory(x[:,0], x[:,1])\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.may_share_memory.htmlnumpy.byte_bounds\n==================\n\n numpy.byte_bounds(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/utils.py#L227-L276)\n \nReturns pointers to the end-points of an array.\n\n Parameters \n \n**a**ndarray\n\nInput array. It must conform to the Python-side of the array interface.\n\n Returns \n \n**(low, high)**tuple of 2 integers\n\nThe first integer is the first byte of the array, the second integer is just past the last byte of the array. If `a` is not contiguous it will not use every byte between the (`low`, `high`) values.\n\n #### Examples\n\n \n```\n>>> I = np.eye(2, dtype='f'); I.dtype\ndtype('float32')\n>>> low, high = np.byte_bounds(I)\n>>> high - low == I.size*I.itemsize\nTrue\n>>> I = np.eye(2); I.dtype\ndtype('float64')\n>>> low, high = np.byte_bounds(I)\n>>> high - low == I.size*I.itemsize\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.byte_bounds.htmlnumpy.lib.NumpyVersion\n======================\n\n *class*numpy.lib.NumpyVersion(*vstring*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/_version.py#L14-L155)\n \nParse and compare numpy version strings.\n\n NumPy has the following versioning scheme (numbers given are examples; they can be > 9 in principle):\n\n * Released version: ‘1.8.0’, ‘1.8.1’, etc.\n* Alpha: ‘1.8.0a1’, ‘1.8.0a2’, etc.\n* Beta: ‘1.8.0b1’, ‘1.8.0b2’, etc.\n* Release candidates: ‘1.8.0rc1’, ‘1.8.0rc2’, etc.\n* Development versions: ‘1.8.0.dev-f1234afa’ (git commit hash appended)\n* Development versions after a1: ‘1.8.0a1.dev-f1234afa’,\n\n‘1.8.0b2.dev-f1234afa’, ‘1.8.1rc1.dev-f1234afa’, etc.\n* Development versions (no git hash available): ‘1.8.0.dev-Unknown’\n\n Comparing needs to be done against a valid version string or other [`NumpyVersion`](#numpy.lib.NumpyVersion \"numpy.lib.NumpyVersion\") instance. Note that all development versions of the same (pre-)release compare equal.\n\n New in version 1.9.0.\n\n Parameters \n \n**vstring**str\n\nNumPy version string (`np.__version__`).\n\n #### Examples\n\n \n```\n>>> from numpy.lib import NumpyVersion\n>>> if NumpyVersion(np.__version__) < '1.7.0':\n... print('skip')\n>>> # skip\n\n```\n \n```\n>>> NumpyVersion('1.7') # raises ValueError, add \".0\"\nTraceback (most recent call last):\n ...\nValueError: Not a valid numpy version string\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.NumpyVersion.htmlnumpy.get_include\n==================\n\n numpy.get_include()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/utils.py#L19-L45)\n \nReturn the directory that contains the NumPy *.h header files.\n\n Extension modules that need to compile against NumPy should use this function to locate the appropriate include directory.\n\n #### Notes\n\n When using `distutils`, for example in `setup.py`:\n\n \n```\nimport numpy as np\n...\nExtension('extension_name', ...\n include_dirs=[np.get_include()])\n...\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.get_include.htmlnumpy.show_config\n==================\n\n numpy.show_config()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/__config__.py#L28-L119)\n \nShow libraries in the system on which NumPy was built.\n\n Print information about various resources (libraries, library directories, include directories, etc.) in the system on which NumPy was built.\n\n See also\n\n [`get_include`](numpy.get_include#numpy.get_include \"numpy.get_include\")\n\nReturns the directory containing NumPy C header files.\n\n #### Notes\n\n 1. Classes specifying the information to be printed are defined in the `numpy.distutils.system_info` module.\n\n Information may include:\n\n\t* `language`: language used to write the libraries (mostly C or f77)\n\t* `libraries`: names of libraries found in the system\n\t* `library_dirs`: directories containing the libraries\n\t* `include_dirs`: directories containing library header files\n\t* `src_dirs`: directories containing library source files\n\t* `define_macros`: preprocessor macros used by `distutils.setup`\n\t* `baseline`: minimum CPU features required\n\t* `found`: dispatched features supported in the system\n\t* `not found`: dispatched features that are not supported in the system\n2. NumPy BLAS/LAPACK Installation Notes\n\n Installing a numpy wheel (`pip install numpy` or force it via `pip install numpy --only-binary :numpy: numpy`) includes an OpenBLAS implementation of the BLAS and LAPACK linear algebra APIs. In this case, `library_dirs` reports the original build time configuration as compiled with gcc/gfortran; at run time the OpenBLAS library is in `site-packages/numpy.libs/` (linux), or `site-packages/numpy/.dylibs/` (macOS), or `site-packages/numpy/.libs/` (windows).\n\n Installing numpy from source (`pip install numpy --no-binary numpy`) searches for BLAS and LAPACK dynamic link libraries at build time as influenced by environment variables NPY_BLAS_LIBS, NPY_CBLAS_LIBS, and NPY_LAPACK_LIBS; or NPY_BLAS_ORDER and NPY_LAPACK_ORDER; or the optional file `~/.numpy-site.cfg`. NumPy remembers those locations and expects to load the same libraries at run-time. In NumPy 1.21+ on macOS, ‘accelerate’ (Apple’s Accelerate BLAS library) is in the default build-time search order after ‘openblas’.\n\n #### Examples\n\n \n```\n>>> import numpy as np\n>>> np.show_config()\nblas_opt_info:\n language = c\n define_macros = [('HAVE_CBLAS', None)]\n libraries = ['openblas', 'openblas']\n library_dirs = ['/usr/local/lib']\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.show_config.htmlnumpy.deprecate\n===============\n\n numpy.deprecate(**args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/utils.py#L143-L193)\n \nIssues a DeprecationWarning, adds warning to `old_name`’s docstring, rebinds `old_name.__name__` and returns the new function object.\n\n This function may also be used as a decorator.\n\n Parameters \n \n**func**function\n\nThe function to be deprecated.\n\n \n**old_name**str, optional\n\nThe name of the function to be deprecated. Default is None, in which case the name of `func` is used.\n\n \n**new_name**str, optional\n\nThe new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead.\n\n \n**message**str, optional\n\nAdditional explanation of the deprecation. Displayed in the docstring after the warning.\n\n Returns \n \n**old_func**function\n\nThe deprecated function.\n\n #### Examples\n\n Note that `olduint` returns a value after printing Deprecation Warning:\n\n \n```\n>>> olduint = np.deprecate(np.uint)\nDeprecationWarning: `uint64` is deprecated! # may vary\n>>> olduint(6)\n6\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.deprecate.htmlnumpy.deprecate_with_doc\n==========================\n\n numpy.deprecate_with_doc(*msg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/utils.py#L196-L220)\n \nDeprecates a function and includes the deprecation in its docstring.\n\n This function is used as a decorator. It returns an object that can be used to issue a DeprecationWarning, by passing the to-be decorated function as argument, this adds warning to the to-be decorated function’s docstring and returns the new function object.\n\n Parameters \n \n**msg**str\n\nAdditional explanation of the deprecation. Displayed in the docstring after the warning.\n\n Returns \n \n**obj**object\n\n See also\n\n [`deprecate`](numpy.deprecate#numpy.deprecate \"numpy.deprecate\")\n\nDecorate a function such that it issues a `DeprecationWarning`\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.deprecate_with_doc.htmlnumpy.broadcast_shapes\n=======================\n\n numpy.broadcast_shapes(**args*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/stride_tricks.py#L433-L473)\n \nBroadcast the input shapes into a single shape.\n\n [Learn more about broadcasting here](../../user/basics.broadcasting#basics-broadcasting).\n\n New in version 1.20.0.\n\n Parameters \n \n**`*args`**tuples of ints, or ints\n\nThe shapes to be broadcast against each other.\n\n Returns \n tuple\n\nBroadcasted shape.\n\n Raises \n ValueError\n\nIf the shapes are not compatible and cannot be broadcast according to NumPy’s broadcasting rules.\n\n See also\n\n [`broadcast`](numpy.broadcast#numpy.broadcast \"numpy.broadcast\")\n[`broadcast_arrays`](numpy.broadcast_arrays#numpy.broadcast_arrays \"numpy.broadcast_arrays\")\n[`broadcast_to`](numpy.broadcast_to#numpy.broadcast_to \"numpy.broadcast_to\")\n #### Examples\n\n \n```\n>>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))\n(3, 2)\n\n```\n \n```\n>>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))\n(5, 6, 7)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast_shapes.htmlnumpy.who\n=========\n\n numpy.who(*vardict=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/utils.py#L284-L376)\n \nPrint the NumPy arrays in the given dictionary.\n\n If there is no dictionary passed in or `vardict` is None then returns NumPy arrays in the globals() dictionary (all NumPy arrays in the namespace).\n\n Parameters \n \n**vardict**dict, optional\n\nA dictionary possibly containing ndarrays. Default is globals().\n\n Returns \n \n**out**None\n\nReturns ‘None’.\n\n #### Notes\n\n Prints out the name, shape, bytes and type of all of the ndarrays present in `vardict`.\n\n #### Examples\n\n \n```\n>>> a = np.arange(10)\n>>> b = np.ones(20)\n>>> np.who()\nName Shape Bytes Type\n===========================================================\na 10 80 int64\nb 20 160 float64\nUpper bound on total bytes = 240\n\n```\n \n```\n>>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str',\n... 'idx':5}\n>>> np.who(d)\nName Shape Bytes Type\n===========================================================\nx 2 16 float64\ny 3 24 float64\nUpper bound on total bytes = 40\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.who.htmlnumpy.disp\n==========\n\n numpy.disp(*mesg*, *device=None*, *linefeed=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1956-L1995)\n \nDisplay a message on a device.\n\n Parameters \n \n**mesg**str\n\nMessage to display.\n\n \n**device**object\n\nDevice to write message. If None, defaults to `sys.stdout` which is very similar to `print`. `device` needs to have `write()` and `flush()` methods.\n\n \n**linefeed**bool, optional\n\nOption whether to print a line feed or not. Defaults to True.\n\n Raises \n AttributeError\n\nIf `device` does not have a `write()` or `flush()` method.\n\n #### Examples\n\n Besides `sys.stdout`, a file-like object can also be used as it has both required methods:\n\n \n```\n>>> from io import StringIO\n>>> buf = StringIO()\n>>> np.disp(u'\"Display\" in a file', device=buf)\n>>> buf.getvalue()\n'\"Display\" in a file\\n'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.disp.htmlnumpy.AxisError\n===============\n\n *exception*numpy.AxisError(*axis*, *ndim=None*, *msg_prefix=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/__init__.py)\n \nAxis supplied was invalid.\n\n This is raised whenever an `axis` parameter is specified that is larger than the number of array dimensions. For compatibility with code written against older numpy versions, which raised a mixture of `ValueError` and `IndexError` for this situation, this exception subclasses both to ensure that `except ValueError` and `except IndexError` statements continue to catch [`AxisError`](#numpy.AxisError \"numpy.AxisError\").\n\n New in version 1.13.\n\n Parameters \n \n**axis**int or str\n\nThe out of bounds axis or a custom exception message. If an axis is provided, then `ndim` should be specified as well.\n\n \n**ndim**int, optional\n\nThe number of array dimensions.\n\n \n**msg_prefix**str, optional\n\nA prefix for the exception message.\n\n #### Examples\n\n \n```\n>>> array_1d = np.arange(10)\n>>> np.cumsum(array_1d, axis=1)\nTraceback (most recent call last):\n ...\nnumpy.AxisError: axis 1 is out of bounds for array of dimension 1\n\n```\n Negative axes are preserved:\n\n \n```\n>>> np.cumsum(array_1d, axis=-2)\nTraceback (most recent call last):\n ...\nnumpy.AxisError: axis -2 is out of bounds for array of dimension 1\n\n```\n The class constructor generally takes the axis and arrays’ dimensionality as arguments:\n\n \n```\n>>> print(np.AxisError(2, 1, msg_prefix='error'))\nerror: axis 2 is out of bounds for array of dimension 1\n\n```\n Alternatively, a custom exception message can be passed:\n\n \n```\n>>> print(np.AxisError('Custom error message'))\nCustom error message\n\n```\n Attributes \n \n**axis**int, optional\n\nThe out of bounds axis or `None` if a custom exception message was provided. This should be the axis as passed by the user, before any normalization to resolve negative indices.\n\n New in version 1.22.\n\n \n**ndim**int, optional\n\nThe number of array dimensions or `None` if a custom exception message was provided.\n\n New in version 1.22.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.AxisError.htmlUsing the Convenience Classes\n=============================\n\n The convenience classes provided by the polynomial package are:\n\n \n\n| Name | Provides |\n| --- | --- |\n| Polynomial | Power series |\n| Chebyshev | Chebyshev series |\n| Legendre | Legendre series |\n| Laguerre | Laguerre series |\n| Hermite | Hermite series |\n| HermiteE | HermiteE series |\n\n The series in this context are finite sums of the corresponding polynomial basis functions multiplied by coefficients. For instance, a power series looks like\n\n \\[p(x) = 1 + 2x + 3x^2\\] and has coefficients \\([1, 2, 3]\\). The Chebyshev series with the same coefficients looks like\n\n \\[p(x) = 1 T_0(x) + 2 T_1(x) + 3 T_2(x)\\] and more generally\n\n \\[p(x) = \\sum_{i=0}^n c_i T_i(x)\\] where in this case the \\(T_n\\) are the Chebyshev functions of degree \\(n\\), but could just as easily be the basis functions of any of the other classes. The convention for all the classes is that the coefficient \\(c[i]\\) goes with the basis function of degree i.\n\n All of the classes are immutable and have the same methods, and especially they implement the Python numeric operators +, -, *, //, %, divmod, **, ==, and !=. The last two can be a bit problematic due to floating point roundoff errors. We now give a quick demonstration of the various operations using NumPy version 1.7.0.\n\n Basics\n------\n\n First we need a polynomial class and a polynomial instance to play with. The classes can be imported directly from the polynomial package or from the module of the relevant type. Here we import from the package and use the conventional Polynomial class because of its familiarity:\n\n \n```\n>>> from numpy.polynomial import Polynomial as P\n>>> p = P([1,2,3])\n>>> p\nPolynomial([1., 2., 3.], domain=[-1, 1], window=[-1, 1])\n\n```\n Note that there are three parts to the long version of the printout. The first is the coefficients, the second is the domain, and the third is the window:\n\n \n```\n>>> p.coef\narray([1., 2., 3.])\n>>> p.domain\narray([-1, 1])\n>>> p.window\narray([-1, 1])\n\n```\n Printing a polynomial yields the polynomial expression in a more familiar format:\n\n \n```\n>>> print(p)\n1.0 + 2.0·x¹ + 3.0·x²\n\n```\n Note that the string representation of polynomials uses Unicode characters by default (except on Windows) to express powers and subscripts. An ASCII-based representation is also available (default on Windows). The polynomial string format can be toggled at the package-level with the [`set_default_printstyle`](generated/numpy.polynomial.set_default_printstyle#numpy.polynomial.set_default_printstyle \"numpy.polynomial.set_default_printstyle\") function:\n\n \n```\n>>> np.polynomial.set_default_printstyle('ascii')\n>>> print(p)\n1.0 + 2.0 x**1 + 3.0 x**2\n\n```\n or controlled for individual polynomial instances with string formatting:\n\n \n```\n>>> print(f\"{p:unicode}\")\n1.0 + 2.0·x¹ + 3.0·x²\n\n```\n We will deal with the domain and window when we get to fitting, for the moment we ignore them and run through the basic algebraic and arithmetic operations.\n\n Addition and Subtraction:\n\n \n```\n>>> p + p\nPolynomial([2., 4., 6.], domain=[-1., 1.], window=[-1., 1.])\n>>> p - p\nPolynomial([0.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Multiplication:\n\n \n```\n>>> p * p\nPolynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Powers:\n\n \n```\n>>> p**2\nPolynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Division:\n\n Floor division, ‘//’, is the division operator for the polynomial classes, polynomials are treated like integers in this regard. For Python versions < 3.x the ‘/’ operator maps to ‘//’, as it does for Python, for later versions the ‘/’ will only work for division by scalars. At some point it will be deprecated:\n\n \n```\n>>> p // P([-1, 1])\nPolynomial([5., 3.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Remainder:\n\n \n```\n>>> p % P([-1, 1])\nPolynomial([6.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Divmod:\n\n \n```\n>>> quo, rem = divmod(p, P([-1, 1]))\n>>> quo\nPolynomial([5., 3.], domain=[-1., 1.], window=[-1., 1.])\n>>> rem\nPolynomial([6.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Evaluation:\n\n \n```\n>>> x = np.arange(5)\n>>> p(x)\narray([ 1., 6., 17., 34., 57.])\n>>> x = np.arange(6).reshape(3,2)\n>>> p(x)\narray([[ 1., 6.],\n [17., 34.],\n [57., 86.]])\n\n```\n Substitution:\n\n Substitute a polynomial for x and expand the result. Here we substitute p in itself leading to a new polynomial of degree 4 after expansion. If the polynomials are regarded as functions this is composition of functions:\n\n \n```\n>>> p(p)\nPolynomial([ 6., 16., 36., 36., 27.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Roots:\n\n \n```\n>>> p.roots()\narray([-0.33333333-0.47140452j, -0.33333333+0.47140452j])\n\n```\n It isn’t always convenient to explicitly use Polynomial instances, so tuples, lists, arrays, and scalars are automatically cast in the arithmetic operations:\n\n \n```\n>>> p + [1, 2, 3]\nPolynomial([2., 4., 6.], domain=[-1., 1.], window=[-1., 1.])\n>>> [1, 2, 3] * p\nPolynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.])\n>>> p / 2\nPolynomial([0.5, 1. , 1.5], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Polynomials that differ in domain, window, or class can’t be mixed in arithmetic:\n\n \n```\n>>> from numpy.polynomial import Chebyshev as T\n>>> p + P([1], domain=[0,1])\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\n File \"<string>\", line 213, in __add__\nTypeError: Domains differ\n>>> p + P([1], window=[0,1])\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\n File \"<string>\", line 215, in __add__\nTypeError: Windows differ\n>>> p + T([1])\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\n File \"<string>\", line 211, in __add__\nTypeError: Polynomial types differ\n\n```\n But different types can be used for substitution. In fact, this is how conversion of Polynomial classes among themselves is done for type, domain, and window casting:\n\n \n```\n>>> p(T([0, 1]))\nChebyshev([2.5, 2. , 1.5], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Which gives the polynomial `p` in Chebyshev form. This works because \\(T_1(x) = x\\) and substituting \\(x\\) for \\(x\\) doesn’t change the original polynomial. However, all the multiplications and divisions will be done using Chebyshev series, hence the type of the result.\n\n It is intended that all polynomial instances are immutable, therefore augmented operations (`+=`, `-=`, etc.) and any other functionality that would violate the immutablity of a polynomial instance are intentionally unimplemented.\n\n Calculus\n--------\n\n Polynomial instances can be integrated and differentiated.:\n\n \n```\n>>> from numpy.polynomial import Polynomial as P\n>>> p = P([2, 6])\n>>> p.integ()\nPolynomial([0., 2., 3.], domain=[-1., 1.], window=[-1., 1.])\n>>> p.integ(2)\nPolynomial([0., 0., 1., 1.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n The first example integrates `p` once, the second example integrates it twice. By default, the lower bound of the integration and the integration constant are 0, but both can be specified.:\n\n \n```\n>>> p.integ(lbnd=-1)\nPolynomial([-1., 2., 3.], domain=[-1., 1.], window=[-1., 1.])\n>>> p.integ(lbnd=-1, k=1)\nPolynomial([0., 2., 3.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n In the first case the lower bound of the integration is set to -1 and the integration constant is 0. In the second the constant of integration is set to 1 as well. Differentiation is simpler since the only option is the number of times the polynomial is differentiated:\n\n \n```\n>>> p = P([1, 2, 3])\n>>> p.deriv(1)\nPolynomial([2., 6.], domain=[-1., 1.], window=[-1., 1.])\n>>> p.deriv(2)\nPolynomial([6.], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Other Polynomial Constructors\n-----------------------------\n\n Constructing polynomials by specifying coefficients is just one way of obtaining a polynomial instance, they may also be created by specifying their roots, by conversion from other polynomial types, and by least squares fits. Fitting is discussed in its own section, the other methods are demonstrated below:\n\n \n```\n>>> from numpy.polynomial import Polynomial as P\n>>> from numpy.polynomial import Chebyshev as T\n>>> p = P.fromroots([1, 2, 3])\n>>> p\nPolynomial([-6., 11., -6., 1.], domain=[-1., 1.], window=[-1., 1.])\n>>> p.convert(kind=T)\nChebyshev([-9. , 11.75, -3. , 0.25], domain=[-1., 1.], window=[-1., 1.])\n\n```\n The convert method can also convert domain and window:\n\n \n```\n>>> p.convert(kind=T, domain=[0, 1])\nChebyshev([-2.4375 , 2.96875, -0.5625 , 0.03125], domain=[0., 1.], window=[-1., 1.])\n>>> p.convert(kind=P, domain=[0, 1])\nPolynomial([-1.875, 2.875, -1.125, 0.125], domain=[0., 1.], window=[-1., 1.])\n\n```\n In numpy versions >= 1.7.0 the `basis` and `cast` class methods are also available. The cast method works like the convert method while the basis method returns the basis polynomial of given degree:\n\n \n```\n>>> P.basis(3)\nPolynomial([0., 0., 0., 1.], domain=[-1., 1.], window=[-1., 1.])\n>>> T.cast(p)\nChebyshev([-9. , 11.75, -3. , 0.25], domain=[-1., 1.], window=[-1., 1.])\n\n```\n Conversions between types can be useful, but it is *not* recommended for routine use. The loss of numerical precision in passing from a Chebyshev series of degree 50 to a Polynomial series of the same degree can make the results of numerical evaluation essentially random.\n\n Fitting\n-------\n\n Fitting is the reason that the `domain` and `window` attributes are part of the convenience classes. To illustrate the problem, the values of the Chebyshev polynomials up to degree 5 are plotted below.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from numpy.polynomial import Chebyshev as T\n>>> x = np.linspace(-1, 1, 100)\n>>> for i in range(6):\n... ax = plt.plot(x, T.basis(i)(x), lw=2, label=f\"$T_{i}$\")\n...\n>>> plt.legend(loc=\"upper left\")\n>>> plt.show()\n\n```\n ![../_images/routines-polynomials-classes-1.png] In the range -1 <= `x` <= 1 they are nice, equiripple functions lying between +/- 1. The same plots over the range -2 <= `x` <= 2 look very different:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from numpy.polynomial import Chebyshev as T\n>>> x = np.linspace(-2, 2, 100)\n>>> for i in range(6):\n... ax = plt.plot(x, T.basis(i)(x), lw=2, label=f\"$T_{i}$\")\n...\n>>> plt.legend(loc=\"lower right\")\n>>> plt.show()\n\n```\n ![../_images/routines-polynomials-classes-2.png] As can be seen, the “good” parts have shrunk to insignificance. In using Chebyshev polynomials for fitting we want to use the region where `x` is between -1 and 1 and that is what the `window` specifies. However, it is unlikely that the data to be fit has all its data points in that interval, so we use `domain` to specify the interval where the data points lie. When the fit is done, the domain is first mapped to the window by a linear transformation and the usual least squares fit is done using the mapped data points. The window and domain of the fit are part of the returned series and are automatically used when computing values, derivatives, and such. If they aren’t specified in the call the fitting routine will use the default window and the smallest domain that holds all the data points. This is illustrated below for a fit to a noisy sine curve.\n\n \n```\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from numpy.polynomial import Chebyshev as T\n>>> np.random.seed(11)\n>>> x = np.linspace(0, 2*np.pi, 20)\n>>> y = np.sin(x) + np.random.normal(scale=.1, size=x.shape)\n>>> p = T.fit(x, y, 5)\n>>> plt.plot(x, y, 'o')\n>>> xx, yy = p.linspace()\n>>> plt.plot(xx, yy, lw=2)\n>>> p.domain\narray([0. , 6.28318531])\n>>> p.window\narray([-1., 1.])\n>>> plt.show()\n\n```\n ![../_images/routines-polynomials-classes-3.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.classes.htmlPower Series (numpy.polynomial.polynomial)\n==========================================\n\n This module provides a number of objects (mostly functions) useful for dealing with polynomials, including a [`Polynomial`](generated/numpy.polynomial.polynomial.polynomial#numpy.polynomial.polynomial.Polynomial \"numpy.polynomial.polynomial.Polynomial\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with polynomial objects is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`Polynomial`](generated/numpy.polynomial.polynomial.polynomial#numpy.polynomial.polynomial.Polynomial \"numpy.polynomial.polynomial.Polynomial\")(coef[, domain, window]) | A power series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`polydomain`](generated/numpy.polynomial.polynomial.polydomain#numpy.polynomial.polynomial.polydomain \"numpy.polynomial.polynomial.polydomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`polyzero`](generated/numpy.polynomial.polynomial.polyzero#numpy.polynomial.polynomial.polyzero \"numpy.polynomial.polynomial.polyzero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`polyone`](generated/numpy.polynomial.polynomial.polyone#numpy.polynomial.polynomial.polyone \"numpy.polynomial.polynomial.polyone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`polyx`](generated/numpy.polynomial.polynomial.polyx#numpy.polynomial.polynomial.polyx \"numpy.polynomial.polynomial.polyx\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`polyadd`](generated/numpy.polynomial.polynomial.polyadd#numpy.polynomial.polynomial.polyadd \"numpy.polynomial.polynomial.polyadd\")(c1, c2) | Add one polynomial to another. |\n| [`polysub`](generated/numpy.polynomial.polynomial.polysub#numpy.polynomial.polynomial.polysub \"numpy.polynomial.polynomial.polysub\")(c1, c2) | Subtract one polynomial from another. |\n| [`polymulx`](generated/numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\")(c) | Multiply a polynomial by x. |\n| [`polymul`](generated/numpy.polynomial.polynomial.polymul#numpy.polynomial.polynomial.polymul \"numpy.polynomial.polynomial.polymul\")(c1, c2) | Multiply one polynomial by another. |\n| [`polydiv`](generated/numpy.polynomial.polynomial.polydiv#numpy.polynomial.polynomial.polydiv \"numpy.polynomial.polynomial.polydiv\")(c1, c2) | Divide one polynomial by another. |\n| [`polypow`](generated/numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")(c, pow[, maxpower]) | Raise a polynomial to a power. |\n| [`polyval`](generated/numpy.polynomial.polynomial.polyval#numpy.polynomial.polynomial.polyval \"numpy.polynomial.polynomial.polyval\")(x, c[, tensor]) | Evaluate a polynomial at points x. |\n| [`polyval2d`](generated/numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\")(x, y, c) | Evaluate a 2-D polynomial at points (x, y). |\n| [`polyval3d`](generated/numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\")(x, y, z, c) | Evaluate a 3-D polynomial at points (x, y, z). |\n| [`polygrid2d`](generated/numpy.polynomial.polynomial.polygrid2d#numpy.polynomial.polynomial.polygrid2d \"numpy.polynomial.polynomial.polygrid2d\")(x, y, c) | Evaluate a 2-D polynomial on the Cartesian product of x and y. |\n| [`polygrid3d`](generated/numpy.polynomial.polynomial.polygrid3d#numpy.polynomial.polynomial.polygrid3d \"numpy.polynomial.polynomial.polygrid3d\")(x, y, z, c) | Evaluate a 3-D polynomial on the Cartesian product of x, y and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`polyder`](generated/numpy.polynomial.polynomial.polyder#numpy.polynomial.polynomial.polyder \"numpy.polynomial.polynomial.polyder\")(c[, m, scl, axis]) | Differentiate a polynomial. |\n| [`polyint`](generated/numpy.polynomial.polynomial.polyint#numpy.polynomial.polynomial.polyint \"numpy.polynomial.polynomial.polyint\")(c[, m, k, lbnd, scl, axis]) | Integrate a polynomial. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`polyfromroots`](generated/numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")(roots) | Generate a monic polynomial with given roots. |\n| [`polyroots`](generated/numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")(c) | Compute the roots of a polynomial. |\n| [`polyvalfromroots`](generated/numpy.polynomial.polynomial.polyvalfromroots#numpy.polynomial.polynomial.polyvalfromroots \"numpy.polynomial.polynomial.polyvalfromroots\")(x, r[, tensor]) | Evaluate a polynomial specified by its roots at points x. |\n| [`polyvander`](generated/numpy.polynomial.polynomial.polyvander#numpy.polynomial.polynomial.polyvander \"numpy.polynomial.polynomial.polyvander\")(x, deg) | Vandermonde matrix of given degree. |\n| [`polyvander2d`](generated/numpy.polynomial.polynomial.polyvander2d#numpy.polynomial.polynomial.polyvander2d \"numpy.polynomial.polynomial.polyvander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`polyvander3d`](generated/numpy.polynomial.polynomial.polyvander3d#numpy.polynomial.polynomial.polyvander3d \"numpy.polynomial.polynomial.polyvander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`polycompanion`](generated/numpy.polynomial.polynomial.polycompanion#numpy.polynomial.polynomial.polycompanion \"numpy.polynomial.polynomial.polycompanion\")(c) | Return the companion matrix of c. |\n| [`polyfit`](generated/numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")(x, y, deg[, rcond, full, w]) | Least-squares fit of a polynomial to data. |\n| [`polytrim`](generated/numpy.polynomial.polynomial.polytrim#numpy.polynomial.polynomial.polytrim \"numpy.polynomial.polynomial.polytrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`polyline`](generated/numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")(off, scl) | Returns an array representing a linear polynomial. |\n\n See Also\n--------\n\n [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.polynomial.htmlChebyshev Series (numpy.polynomial.chebyshev)\n=============================================\n\n This module provides a number of objects (mostly functions) useful for dealing with Chebyshev series, including a [`Chebyshev`](generated/numpy.polynomial.chebyshev.chebyshev#numpy.polynomial.chebyshev.Chebyshev \"numpy.polynomial.chebyshev.Chebyshev\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`Chebyshev`](generated/numpy.polynomial.chebyshev.chebyshev#numpy.polynomial.chebyshev.Chebyshev \"numpy.polynomial.chebyshev.Chebyshev\")(coef[, domain, window]) | A Chebyshev series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`chebdomain`](generated/numpy.polynomial.chebyshev.chebdomain#numpy.polynomial.chebyshev.chebdomain \"numpy.polynomial.chebyshev.chebdomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`chebzero`](generated/numpy.polynomial.chebyshev.chebzero#numpy.polynomial.chebyshev.chebzero \"numpy.polynomial.chebyshev.chebzero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`chebone`](generated/numpy.polynomial.chebyshev.chebone#numpy.polynomial.chebyshev.chebone \"numpy.polynomial.chebyshev.chebone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`chebx`](generated/numpy.polynomial.chebyshev.chebx#numpy.polynomial.chebyshev.chebx \"numpy.polynomial.chebyshev.chebx\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`chebadd`](generated/numpy.polynomial.chebyshev.chebadd#numpy.polynomial.chebyshev.chebadd \"numpy.polynomial.chebyshev.chebadd\")(c1, c2) | Add one Chebyshev series to another. |\n| [`chebsub`](generated/numpy.polynomial.chebyshev.chebsub#numpy.polynomial.chebyshev.chebsub \"numpy.polynomial.chebyshev.chebsub\")(c1, c2) | Subtract one Chebyshev series from another. |\n| [`chebmulx`](generated/numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\")(c) | Multiply a Chebyshev series by x. |\n| [`chebmul`](generated/numpy.polynomial.chebyshev.chebmul#numpy.polynomial.chebyshev.chebmul \"numpy.polynomial.chebyshev.chebmul\")(c1, c2) | Multiply one Chebyshev series by another. |\n| [`chebdiv`](generated/numpy.polynomial.chebyshev.chebdiv#numpy.polynomial.chebyshev.chebdiv \"numpy.polynomial.chebyshev.chebdiv\")(c1, c2) | Divide one Chebyshev series by another. |\n| [`chebpow`](generated/numpy.polynomial.chebyshev.chebpow#numpy.polynomial.chebyshev.chebpow \"numpy.polynomial.chebyshev.chebpow\")(c, pow[, maxpower]) | Raise a Chebyshev series to a power. |\n| [`chebval`](generated/numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\")(x, c[, tensor]) | Evaluate a Chebyshev series at points x. |\n| [`chebval2d`](generated/numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\")(x, y, c) | Evaluate a 2-D Chebyshev series at points (x, y). |\n| [`chebval3d`](generated/numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\")(x, y, z, c) | Evaluate a 3-D Chebyshev series at points (x, y, z). |\n| [`chebgrid2d`](generated/numpy.polynomial.chebyshev.chebgrid2d#numpy.polynomial.chebyshev.chebgrid2d \"numpy.polynomial.chebyshev.chebgrid2d\")(x, y, c) | Evaluate a 2-D Chebyshev series on the Cartesian product of x and y. |\n| [`chebgrid3d`](generated/numpy.polynomial.chebyshev.chebgrid3d#numpy.polynomial.chebyshev.chebgrid3d \"numpy.polynomial.chebyshev.chebgrid3d\")(x, y, z, c) | Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`chebder`](generated/numpy.polynomial.chebyshev.chebder#numpy.polynomial.chebyshev.chebder \"numpy.polynomial.chebyshev.chebder\")(c[, m, scl, axis]) | Differentiate a Chebyshev series. |\n| [`chebint`](generated/numpy.polynomial.chebyshev.chebint#numpy.polynomial.chebyshev.chebint \"numpy.polynomial.chebyshev.chebint\")(c[, m, k, lbnd, scl, axis]) | Integrate a Chebyshev series. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`chebfromroots`](generated/numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")(roots) | Generate a Chebyshev series with given roots. |\n| [`chebroots`](generated/numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")(c) | Compute the roots of a Chebyshev series. |\n| [`chebvander`](generated/numpy.polynomial.chebyshev.chebvander#numpy.polynomial.chebyshev.chebvander \"numpy.polynomial.chebyshev.chebvander\")(x, deg) | Pseudo-Vandermonde matrix of given degree. |\n| [`chebvander2d`](generated/numpy.polynomial.chebyshev.chebvander2d#numpy.polynomial.chebyshev.chebvander2d \"numpy.polynomial.chebyshev.chebvander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`chebvander3d`](generated/numpy.polynomial.chebyshev.chebvander3d#numpy.polynomial.chebyshev.chebvander3d \"numpy.polynomial.chebyshev.chebvander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`chebgauss`](generated/numpy.polynomial.chebyshev.chebgauss#numpy.polynomial.chebyshev.chebgauss \"numpy.polynomial.chebyshev.chebgauss\")(deg) | Gauss-Chebyshev quadrature. |\n| [`chebweight`](generated/numpy.polynomial.chebyshev.chebweight#numpy.polynomial.chebyshev.chebweight \"numpy.polynomial.chebyshev.chebweight\")(x) | The weight function of the Chebyshev polynomials. |\n| [`chebcompanion`](generated/numpy.polynomial.chebyshev.chebcompanion#numpy.polynomial.chebyshev.chebcompanion \"numpy.polynomial.chebyshev.chebcompanion\")(c) | Return the scaled companion matrix of c. |\n| [`chebfit`](generated/numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")(x, y, deg[, rcond, full, w]) | Least squares fit of Chebyshev series to data. |\n| [`chebpts1`](generated/numpy.polynomial.chebyshev.chebpts1#numpy.polynomial.chebyshev.chebpts1 \"numpy.polynomial.chebyshev.chebpts1\")(npts) | Chebyshev points of the first kind. |\n| [`chebpts2`](generated/numpy.polynomial.chebyshev.chebpts2#numpy.polynomial.chebyshev.chebpts2 \"numpy.polynomial.chebyshev.chebpts2\")(npts) | Chebyshev points of the second kind. |\n| [`chebtrim`](generated/numpy.polynomial.chebyshev.chebtrim#numpy.polynomial.chebyshev.chebtrim \"numpy.polynomial.chebyshev.chebtrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`chebline`](generated/numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")(off, scl) | Chebyshev series whose graph is a straight line. |\n| [`cheb2poly`](generated/numpy.polynomial.chebyshev.cheb2poly#numpy.polynomial.chebyshev.cheb2poly \"numpy.polynomial.chebyshev.cheb2poly\")(c) | Convert a Chebyshev series to a polynomial. |\n| [`poly2cheb`](generated/numpy.polynomial.chebyshev.poly2cheb#numpy.polynomial.chebyshev.poly2cheb \"numpy.polynomial.chebyshev.poly2cheb\")(pol) | Convert a polynomial to a Chebyshev series. |\n| [`chebinterpolate`](generated/numpy.polynomial.chebyshev.chebinterpolate#numpy.polynomial.chebyshev.chebinterpolate \"numpy.polynomial.chebyshev.chebinterpolate\")(func, deg[, args]) | Interpolate a function at the Chebyshev points of the first kind. |\n\n See also\n--------\n\n [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")\n\n Notes\n-----\n\n The implementations of multiplication, division, integration, and differentiation use the algebraic identities [[1]](#r3f3efff98d00-1):\n\n \\[\\begin{split}T_n(x) = \\frac{z^n + z^{-n}}{2} \\\\ z\\frac{dx}{dz} = \\frac{z - z^{-1}}{2}.\\end{split}\\] where\n\n \\[x = \\frac{z + z^{-1}}{2}.\\] These identities allow a Chebyshev series to be expressed as a finite, symmetric Laurent series. In this module, this sort of Laurent series is referred to as a “z-series.”\n\n References\n----------\n\n [1](#id1) \n<NAME>, et al., “Combinatorial Trigonometry with Chebyshev Polynomials,” *Journal of Statistical Planning and Inference 14*, 2008 (<https://web.archive.org/web/20080221202153/https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf>, pg. 4)\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.chebyshev.htmlHermite Series, “Physicists” (numpy.polynomial.hermite)\n=======================================================\n\n This module provides a number of objects (mostly functions) useful for dealing with Hermite series, including a [`Hermite`](generated/numpy.polynomial.hermite.hermite#numpy.polynomial.hermite.Hermite \"numpy.polynomial.hermite.Hermite\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`Hermite`](generated/numpy.polynomial.hermite.hermite#numpy.polynomial.hermite.Hermite \"numpy.polynomial.hermite.Hermite\")(coef[, domain, window]) | An Hermite series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`hermdomain`](generated/numpy.polynomial.hermite.hermdomain#numpy.polynomial.hermite.hermdomain \"numpy.polynomial.hermite.hermdomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermzero`](generated/numpy.polynomial.hermite.hermzero#numpy.polynomial.hermite.hermzero \"numpy.polynomial.hermite.hermzero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermone`](generated/numpy.polynomial.hermite.hermone#numpy.polynomial.hermite.hermone \"numpy.polynomial.hermite.hermone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermx`](generated/numpy.polynomial.hermite.hermx#numpy.polynomial.hermite.hermx \"numpy.polynomial.hermite.hermx\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`hermadd`](generated/numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\")(c1, c2) | Add one Hermite series to another. |\n| [`hermsub`](generated/numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\")(c1, c2) | Subtract one Hermite series from another. |\n| [`hermmulx`](generated/numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\")(c) | Multiply a Hermite series by x. |\n| [`hermmul`](generated/numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\")(c1, c2) | Multiply one Hermite series by another. |\n| [`hermdiv`](generated/numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\")(c1, c2) | Divide one Hermite series by another. |\n| [`hermpow`](generated/numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")(c, pow[, maxpower]) | Raise a Hermite series to a power. |\n| [`hermval`](generated/numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\")(x, c[, tensor]) | Evaluate an Hermite series at points x. |\n| [`hermval2d`](generated/numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\")(x, y, c) | Evaluate a 2-D Hermite series at points (x, y). |\n| [`hermval3d`](generated/numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\")(x, y, z, c) | Evaluate a 3-D Hermite series at points (x, y, z). |\n| [`hermgrid2d`](generated/numpy.polynomial.hermite.hermgrid2d#numpy.polynomial.hermite.hermgrid2d \"numpy.polynomial.hermite.hermgrid2d\")(x, y, c) | Evaluate a 2-D Hermite series on the Cartesian product of x and y. |\n| [`hermgrid3d`](generated/numpy.polynomial.hermite.hermgrid3d#numpy.polynomial.hermite.hermgrid3d \"numpy.polynomial.hermite.hermgrid3d\")(x, y, z, c) | Evaluate a 3-D Hermite series on the Cartesian product of x, y, and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`hermder`](generated/numpy.polynomial.hermite.hermder#numpy.polynomial.hermite.hermder \"numpy.polynomial.hermite.hermder\")(c[, m, scl, axis]) | Differentiate a Hermite series. |\n| [`hermint`](generated/numpy.polynomial.hermite.hermint#numpy.polynomial.hermite.hermint \"numpy.polynomial.hermite.hermint\")(c[, m, k, lbnd, scl, axis]) | Integrate a Hermite series. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`hermfromroots`](generated/numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")(roots) | Generate a Hermite series with given roots. |\n| [`hermroots`](generated/numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")(c) | Compute the roots of a Hermite series. |\n| [`hermvander`](generated/numpy.polynomial.hermite.hermvander#numpy.polynomial.hermite.hermvander \"numpy.polynomial.hermite.hermvander\")(x, deg) | Pseudo-Vandermonde matrix of given degree. |\n| [`hermvander2d`](generated/numpy.polynomial.hermite.hermvander2d#numpy.polynomial.hermite.hermvander2d \"numpy.polynomial.hermite.hermvander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`hermvander3d`](generated/numpy.polynomial.hermite.hermvander3d#numpy.polynomial.hermite.hermvander3d \"numpy.polynomial.hermite.hermvander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`hermgauss`](generated/numpy.polynomial.hermite.hermgauss#numpy.polynomial.hermite.hermgauss \"numpy.polynomial.hermite.hermgauss\")(deg) | Gauss-Hermite quadrature. |\n| [`hermweight`](generated/numpy.polynomial.hermite.hermweight#numpy.polynomial.hermite.hermweight \"numpy.polynomial.hermite.hermweight\")(x) | Weight function of the Hermite polynomials. |\n| [`hermcompanion`](generated/numpy.polynomial.hermite.hermcompanion#numpy.polynomial.hermite.hermcompanion \"numpy.polynomial.hermite.hermcompanion\")(c) | Return the scaled companion matrix of c. |\n| [`hermfit`](generated/numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")(x, y, deg[, rcond, full, w]) | Least squares fit of Hermite series to data. |\n| [`hermtrim`](generated/numpy.polynomial.hermite.hermtrim#numpy.polynomial.hermite.hermtrim \"numpy.polynomial.hermite.hermtrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`hermline`](generated/numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")(off, scl) | Hermite series whose graph is a straight line. |\n| [`herm2poly`](generated/numpy.polynomial.hermite.herm2poly#numpy.polynomial.hermite.herm2poly \"numpy.polynomial.hermite.herm2poly\")(c) | Convert a Hermite series to a polynomial. |\n| [`poly2herm`](generated/numpy.polynomial.hermite.poly2herm#numpy.polynomial.hermite.poly2herm \"numpy.polynomial.hermite.poly2herm\")(pol) | Convert a polynomial to a Hermite series. |\n\n See also\n--------\n\n [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.hermite.htmlHermiteE Series, “Probabilists” (numpy.polynomial.hermite_e)\n=============================================================\n\n This module provides a number of objects (mostly functions) useful for dealing with Hermite_e series, including a [`HermiteE`](generated/numpy.polynomial.hermite_e.hermitee#numpy.polynomial.hermite_e.HermiteE \"numpy.polynomial.hermite_e.HermiteE\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`HermiteE`](generated/numpy.polynomial.hermite_e.hermitee#numpy.polynomial.hermite_e.HermiteE \"numpy.polynomial.hermite_e.HermiteE\")(coef[, domain, window]) | An HermiteE series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`hermedomain`](generated/numpy.polynomial.hermite_e.hermedomain#numpy.polynomial.hermite_e.hermedomain \"numpy.polynomial.hermite_e.hermedomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermezero`](generated/numpy.polynomial.hermite_e.hermezero#numpy.polynomial.hermite_e.hermezero \"numpy.polynomial.hermite_e.hermezero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermeone`](generated/numpy.polynomial.hermite_e.hermeone#numpy.polynomial.hermite_e.hermeone \"numpy.polynomial.hermite_e.hermeone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`hermex`](generated/numpy.polynomial.hermite_e.hermex#numpy.polynomial.hermite_e.hermex \"numpy.polynomial.hermite_e.hermex\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`hermeadd`](generated/numpy.polynomial.hermite_e.hermeadd#numpy.polynomial.hermite_e.hermeadd \"numpy.polynomial.hermite_e.hermeadd\")(c1, c2) | Add one Hermite series to another. |\n| [`hermesub`](generated/numpy.polynomial.hermite_e.hermesub#numpy.polynomial.hermite_e.hermesub \"numpy.polynomial.hermite_e.hermesub\")(c1, c2) | Subtract one Hermite series from another. |\n| [`hermemulx`](generated/numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\")(c) | Multiply a Hermite series by x. |\n| [`hermemul`](generated/numpy.polynomial.hermite_e.hermemul#numpy.polynomial.hermite_e.hermemul \"numpy.polynomial.hermite_e.hermemul\")(c1, c2) | Multiply one Hermite series by another. |\n| [`hermediv`](generated/numpy.polynomial.hermite_e.hermediv#numpy.polynomial.hermite_e.hermediv \"numpy.polynomial.hermite_e.hermediv\")(c1, c2) | Divide one Hermite series by another. |\n| [`hermepow`](generated/numpy.polynomial.hermite_e.hermepow#numpy.polynomial.hermite_e.hermepow \"numpy.polynomial.hermite_e.hermepow\")(c, pow[, maxpower]) | Raise a Hermite series to a power. |\n| [`hermeval`](generated/numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\")(x, c[, tensor]) | Evaluate an HermiteE series at points x. |\n| [`hermeval2d`](generated/numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\")(x, y, c) | Evaluate a 2-D HermiteE series at points (x, y). |\n| [`hermeval3d`](generated/numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\")(x, y, z, c) | Evaluate a 3-D Hermite_e series at points (x, y, z). |\n| [`hermegrid2d`](generated/numpy.polynomial.hermite_e.hermegrid2d#numpy.polynomial.hermite_e.hermegrid2d \"numpy.polynomial.hermite_e.hermegrid2d\")(x, y, c) | Evaluate a 2-D HermiteE series on the Cartesian product of x and y. |\n| [`hermegrid3d`](generated/numpy.polynomial.hermite_e.hermegrid3d#numpy.polynomial.hermite_e.hermegrid3d \"numpy.polynomial.hermite_e.hermegrid3d\")(x, y, z, c) | Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`hermeder`](generated/numpy.polynomial.hermite_e.hermeder#numpy.polynomial.hermite_e.hermeder \"numpy.polynomial.hermite_e.hermeder\")(c[, m, scl, axis]) | Differentiate a Hermite_e series. |\n| [`hermeint`](generated/numpy.polynomial.hermite_e.hermeint#numpy.polynomial.hermite_e.hermeint \"numpy.polynomial.hermite_e.hermeint\")(c[, m, k, lbnd, scl, axis]) | Integrate a Hermite_e series. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`hermefromroots`](generated/numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")(roots) | Generate a HermiteE series with given roots. |\n| [`hermeroots`](generated/numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")(c) | Compute the roots of a HermiteE series. |\n| [`hermevander`](generated/numpy.polynomial.hermite_e.hermevander#numpy.polynomial.hermite_e.hermevander \"numpy.polynomial.hermite_e.hermevander\")(x, deg) | Pseudo-Vandermonde matrix of given degree. |\n| [`hermevander2d`](generated/numpy.polynomial.hermite_e.hermevander2d#numpy.polynomial.hermite_e.hermevander2d \"numpy.polynomial.hermite_e.hermevander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`hermevander3d`](generated/numpy.polynomial.hermite_e.hermevander3d#numpy.polynomial.hermite_e.hermevander3d \"numpy.polynomial.hermite_e.hermevander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`hermegauss`](generated/numpy.polynomial.hermite_e.hermegauss#numpy.polynomial.hermite_e.hermegauss \"numpy.polynomial.hermite_e.hermegauss\")(deg) | Gauss-HermiteE quadrature. |\n| [`hermeweight`](generated/numpy.polynomial.hermite_e.hermeweight#numpy.polynomial.hermite_e.hermeweight \"numpy.polynomial.hermite_e.hermeweight\")(x) | Weight function of the Hermite_e polynomials. |\n| [`hermecompanion`](generated/numpy.polynomial.hermite_e.hermecompanion#numpy.polynomial.hermite_e.hermecompanion \"numpy.polynomial.hermite_e.hermecompanion\")(c) | Return the scaled companion matrix of c. |\n| [`hermefit`](generated/numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")(x, y, deg[, rcond, full, w]) | Least squares fit of Hermite series to data. |\n| [`hermetrim`](generated/numpy.polynomial.hermite_e.hermetrim#numpy.polynomial.hermite_e.hermetrim \"numpy.polynomial.hermite_e.hermetrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`hermeline`](generated/numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")(off, scl) | Hermite series whose graph is a straight line. |\n| [`herme2poly`](generated/numpy.polynomial.hermite_e.herme2poly#numpy.polynomial.hermite_e.herme2poly \"numpy.polynomial.hermite_e.herme2poly\")(c) | Convert a Hermite series to a polynomial. |\n| [`poly2herme`](generated/numpy.polynomial.hermite_e.poly2herme#numpy.polynomial.hermite_e.poly2herme \"numpy.polynomial.hermite_e.poly2herme\")(pol) | Convert a polynomial to a Hermite series. |\n\n See also\n--------\n\n [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.hermite_e.htmlLaguerre Series (numpy.polynomial.laguerre)\n===========================================\n\n This module provides a number of objects (mostly functions) useful for dealing with Laguerre series, including a [`Laguerre`](generated/numpy.polynomial.laguerre.laguerre#numpy.polynomial.laguerre.Laguerre \"numpy.polynomial.laguerre.Laguerre\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`Laguerre`](generated/numpy.polynomial.laguerre.laguerre#numpy.polynomial.laguerre.Laguerre \"numpy.polynomial.laguerre.Laguerre\")(coef[, domain, window]) | A Laguerre series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`lagdomain`](generated/numpy.polynomial.laguerre.lagdomain#numpy.polynomial.laguerre.lagdomain \"numpy.polynomial.laguerre.lagdomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`lagzero`](generated/numpy.polynomial.laguerre.lagzero#numpy.polynomial.laguerre.lagzero \"numpy.polynomial.laguerre.lagzero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`lagone`](generated/numpy.polynomial.laguerre.lagone#numpy.polynomial.laguerre.lagone \"numpy.polynomial.laguerre.lagone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`lagx`](generated/numpy.polynomial.laguerre.lagx#numpy.polynomial.laguerre.lagx \"numpy.polynomial.laguerre.lagx\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`lagadd`](generated/numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\")(c1, c2) | Add one Laguerre series to another. |\n| [`lagsub`](generated/numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\")(c1, c2) | Subtract one Laguerre series from another. |\n| [`lagmulx`](generated/numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\")(c) | Multiply a Laguerre series by x. |\n| [`lagmul`](generated/numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\")(c1, c2) | Multiply one Laguerre series by another. |\n| [`lagdiv`](generated/numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\")(c1, c2) | Divide one Laguerre series by another. |\n| [`lagpow`](generated/numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")(c, pow[, maxpower]) | Raise a Laguerre series to a power. |\n| [`lagval`](generated/numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\")(x, c[, tensor]) | Evaluate a Laguerre series at points x. |\n| [`lagval2d`](generated/numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\")(x, y, c) | Evaluate a 2-D Laguerre series at points (x, y). |\n| [`lagval3d`](generated/numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\")(x, y, z, c) | Evaluate a 3-D Laguerre series at points (x, y, z). |\n| [`laggrid2d`](generated/numpy.polynomial.laguerre.laggrid2d#numpy.polynomial.laguerre.laggrid2d \"numpy.polynomial.laguerre.laggrid2d\")(x, y, c) | Evaluate a 2-D Laguerre series on the Cartesian product of x and y. |\n| [`laggrid3d`](generated/numpy.polynomial.laguerre.laggrid3d#numpy.polynomial.laguerre.laggrid3d \"numpy.polynomial.laguerre.laggrid3d\")(x, y, z, c) | Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`lagder`](generated/numpy.polynomial.laguerre.lagder#numpy.polynomial.laguerre.lagder \"numpy.polynomial.laguerre.lagder\")(c[, m, scl, axis]) | Differentiate a Laguerre series. |\n| [`lagint`](generated/numpy.polynomial.laguerre.lagint#numpy.polynomial.laguerre.lagint \"numpy.polynomial.laguerre.lagint\")(c[, m, k, lbnd, scl, axis]) | Integrate a Laguerre series. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`lagfromroots`](generated/numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")(roots) | Generate a Laguerre series with given roots. |\n| [`lagroots`](generated/numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")(c) | Compute the roots of a Laguerre series. |\n| [`lagvander`](generated/numpy.polynomial.laguerre.lagvander#numpy.polynomial.laguerre.lagvander \"numpy.polynomial.laguerre.lagvander\")(x, deg) | Pseudo-Vandermonde matrix of given degree. |\n| [`lagvander2d`](generated/numpy.polynomial.laguerre.lagvander2d#numpy.polynomial.laguerre.lagvander2d \"numpy.polynomial.laguerre.lagvander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`lagvander3d`](generated/numpy.polynomial.laguerre.lagvander3d#numpy.polynomial.laguerre.lagvander3d \"numpy.polynomial.laguerre.lagvander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`laggauss`](generated/numpy.polynomial.laguerre.laggauss#numpy.polynomial.laguerre.laggauss \"numpy.polynomial.laguerre.laggauss\")(deg) | Gauss-Laguerre quadrature. |\n| [`lagweight`](generated/numpy.polynomial.laguerre.lagweight#numpy.polynomial.laguerre.lagweight \"numpy.polynomial.laguerre.lagweight\")(x) | Weight function of the Laguerre polynomials. |\n| [`lagcompanion`](generated/numpy.polynomial.laguerre.lagcompanion#numpy.polynomial.laguerre.lagcompanion \"numpy.polynomial.laguerre.lagcompanion\")(c) | Return the companion matrix of c. |\n| [`lagfit`](generated/numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")(x, y, deg[, rcond, full, w]) | Least squares fit of Laguerre series to data. |\n| [`lagtrim`](generated/numpy.polynomial.laguerre.lagtrim#numpy.polynomial.laguerre.lagtrim \"numpy.polynomial.laguerre.lagtrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`lagline`](generated/numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")(off, scl) | Laguerre series whose graph is a straight line. |\n| [`lag2poly`](generated/numpy.polynomial.laguerre.lag2poly#numpy.polynomial.laguerre.lag2poly \"numpy.polynomial.laguerre.lag2poly\")(c) | Convert a Laguerre series to a polynomial. |\n| [`poly2lag`](generated/numpy.polynomial.laguerre.poly2lag#numpy.polynomial.laguerre.poly2lag \"numpy.polynomial.laguerre.poly2lag\")(pol) | Convert a polynomial to a Laguerre series. |\n\n See also\n--------\n\n [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.laguerre.htmlLegendre Series (numpy.polynomial.legendre)\n===========================================\n\n This module provides a number of objects (mostly functions) useful for dealing with Legendre series, including a [`Legendre`](generated/numpy.polynomial.legendre.legendre#numpy.polynomial.legendre.Legendre \"numpy.polynomial.legendre.Legendre\") class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, [`numpy.polynomial`](routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\")).\n\n Classes\n-------\n\n \n\n| | |\n| --- | --- |\n| [`Legendre`](generated/numpy.polynomial.legendre.legendre#numpy.polynomial.legendre.Legendre \"numpy.polynomial.legendre.Legendre\")(coef[, domain, window]) | A Legendre series class. |\n\n Constants\n---------\n\n \n\n| | |\n| --- | --- |\n| [`legdomain`](generated/numpy.polynomial.legendre.legdomain#numpy.polynomial.legendre.legdomain \"numpy.polynomial.legendre.legdomain\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`legzero`](generated/numpy.polynomial.legendre.legzero#numpy.polynomial.legendre.legzero \"numpy.polynomial.legendre.legzero\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`legone`](generated/numpy.polynomial.legendre.legone#numpy.polynomial.legendre.legone \"numpy.polynomial.legendre.legone\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n| [`legx`](generated/numpy.polynomial.legendre.legx#numpy.polynomial.legendre.legx \"numpy.polynomial.legendre.legx\") | An array object represents a multidimensional, homogeneous array of fixed-size items. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`legadd`](generated/numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\")(c1, c2) | Add one Legendre series to another. |\n| [`legsub`](generated/numpy.polynomial.legendre.legsub#numpy.polynomial.legendre.legsub \"numpy.polynomial.legendre.legsub\")(c1, c2) | Subtract one Legendre series from another. |\n| [`legmulx`](generated/numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\")(c) | Multiply a Legendre series by x. |\n| [`legmul`](generated/numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\")(c1, c2) | Multiply one Legendre series by another. |\n| [`legdiv`](generated/numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\")(c1, c2) | Divide one Legendre series by another. |\n| [`legpow`](generated/numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")(c, pow[, maxpower]) | Raise a Legendre series to a power. |\n| [`legval`](generated/numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\")(x, c[, tensor]) | Evaluate a Legendre series at points x. |\n| [`legval2d`](generated/numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\")(x, y, c) | Evaluate a 2-D Legendre series at points (x, y). |\n| [`legval3d`](generated/numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\")(x, y, z, c) | Evaluate a 3-D Legendre series at points (x, y, z). |\n| [`leggrid2d`](generated/numpy.polynomial.legendre.leggrid2d#numpy.polynomial.legendre.leggrid2d \"numpy.polynomial.legendre.leggrid2d\")(x, y, c) | Evaluate a 2-D Legendre series on the Cartesian product of x and y. |\n| [`leggrid3d`](generated/numpy.polynomial.legendre.leggrid3d#numpy.polynomial.legendre.leggrid3d \"numpy.polynomial.legendre.leggrid3d\")(x, y, z, c) | Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`legder`](generated/numpy.polynomial.legendre.legder#numpy.polynomial.legendre.legder \"numpy.polynomial.legendre.legder\")(c[, m, scl, axis]) | Differentiate a Legendre series. |\n| [`legint`](generated/numpy.polynomial.legendre.legint#numpy.polynomial.legendre.legint \"numpy.polynomial.legendre.legint\")(c[, m, k, lbnd, scl, axis]) | Integrate a Legendre series. |\n\n Misc Functions\n--------------\n\n \n\n| | |\n| --- | --- |\n| [`legfromroots`](generated/numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")(roots) | Generate a Legendre series with given roots. |\n| [`legroots`](generated/numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")(c) | Compute the roots of a Legendre series. |\n| [`legvander`](generated/numpy.polynomial.legendre.legvander#numpy.polynomial.legendre.legvander \"numpy.polynomial.legendre.legvander\")(x, deg) | Pseudo-Vandermonde matrix of given degree. |\n| [`legvander2d`](generated/numpy.polynomial.legendre.legvander2d#numpy.polynomial.legendre.legvander2d \"numpy.polynomial.legendre.legvander2d\")(x, y, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`legvander3d`](generated/numpy.polynomial.legendre.legvander3d#numpy.polynomial.legendre.legvander3d \"numpy.polynomial.legendre.legvander3d\")(x, y, z, deg) | Pseudo-Vandermonde matrix of given degrees. |\n| [`leggauss`](generated/numpy.polynomial.legendre.leggauss#numpy.polynomial.legendre.leggauss \"numpy.polynomial.legendre.leggauss\")(deg) | Gauss-Legendre quadrature. |\n| [`legweight`](generated/numpy.polynomial.legendre.legweight#numpy.polynomial.legendre.legweight \"numpy.polynomial.legendre.legweight\")(x) | Weight function of the Legendre polynomials. |\n| [`legcompanion`](generated/numpy.polynomial.legendre.legcompanion#numpy.polynomial.legendre.legcompanion \"numpy.polynomial.legendre.legcompanion\")(c) | Return the scaled companion matrix of c. |\n| [`legfit`](generated/numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")(x, y, deg[, rcond, full, w]) | Least squares fit of Legendre series to data. |\n| [`legtrim`](generated/numpy.polynomial.legendre.legtrim#numpy.polynomial.legendre.legtrim \"numpy.polynomial.legendre.legtrim\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`legline`](generated/numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")(off, scl) | Legendre series whose graph is a straight line. |\n| [`leg2poly`](generated/numpy.polynomial.legendre.leg2poly#numpy.polynomial.legendre.leg2poly \"numpy.polynomial.legendre.leg2poly\")(c) | Convert a Legendre series to a polynomial. |\n| [`poly2leg`](generated/numpy.polynomial.legendre.poly2leg#numpy.polynomial.legendre.poly2leg \"numpy.polynomial.legendre.poly2leg\")(pol) | Convert a polynomial to a Legendre series. |\n\n See also\n--------\n\n numpy.polynomial\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.legendre.htmlPolyutils\n=========\n\n Utility classes and functions for the polynomial modules.\n\n This module provides: error and warning objects; a polynomial base class; and some routines used in both the `polynomial` and `chebyshev` modules.\n\n Warning objects\n---------------\n\n \n\n| | |\n| --- | --- |\n| [`RankWarning`](generated/numpy.polynomial.polyutils.rankwarning#numpy.polynomial.polyutils.RankWarning \"numpy.polynomial.polyutils.RankWarning\") | Issued by chebfit when the design matrix is rank deficient. |\n\n Functions\n---------\n\n \n\n| | |\n| --- | --- |\n| [`as_series`](generated/numpy.polynomial.polyutils.as_series#numpy.polynomial.polyutils.as_series \"numpy.polynomial.polyutils.as_series\")(alist[, trim]) | Return argument as a list of 1-d arrays. |\n| [`trimseq`](generated/numpy.polynomial.polyutils.trimseq#numpy.polynomial.polyutils.trimseq \"numpy.polynomial.polyutils.trimseq\")(seq) | Remove small Poly series coefficients. |\n| [`trimcoef`](generated/numpy.polynomial.polyutils.trimcoef#numpy.polynomial.polyutils.trimcoef \"numpy.polynomial.polyutils.trimcoef\")(c[, tol]) | Remove \"small\" \"trailing\" coefficients from a polynomial. |\n| [`getdomain`](generated/numpy.polynomial.polyutils.getdomain#numpy.polynomial.polyutils.getdomain \"numpy.polynomial.polyutils.getdomain\")(x) | Return a domain suitable for given abscissae. |\n| [`mapdomain`](generated/numpy.polynomial.polyutils.mapdomain#numpy.polynomial.polyutils.mapdomain \"numpy.polynomial.polyutils.mapdomain\")(x, old, new) | Apply linear map to input points. |\n| [`mapparms`](generated/numpy.polynomial.polyutils.mapparms#numpy.polynomial.polyutils.mapparms \"numpy.polynomial.polyutils.mapparms\")(old, new) | Linear map parameters between domains. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.polyutils.htmlPoly1d\n======\n\n Basics\n------\n\n \n\n| | |\n| --- | --- |\n| [`poly1d`](generated/numpy.poly1d#numpy.poly1d \"numpy.poly1d\")(c_or_r[, r, variable]) | A one-dimensional polynomial class. |\n| [`polyval`](generated/numpy.polyval#numpy.polyval \"numpy.polyval\")(p, x) | Evaluate a polynomial at specific values. |\n| [`poly`](generated/numpy.poly#numpy.poly \"numpy.poly\")(seq_of_zeros) | Find the coefficients of a polynomial with the given sequence of roots. |\n| [`roots`](generated/numpy.roots#numpy.roots \"numpy.roots\")(p) | Return the roots of a polynomial with coefficients given in p. |\n\n Fitting\n-------\n\n \n\n| | |\n| --- | --- |\n| [`polyfit`](generated/numpy.polyfit#numpy.polyfit \"numpy.polyfit\")(x, y, deg[, rcond, full, w, cov]) | Least squares polynomial fit. |\n\n Calculus\n--------\n\n \n\n| | |\n| --- | --- |\n| [`polyder`](generated/numpy.polyder#numpy.polyder \"numpy.polyder\")(p[, m]) | Return the derivative of the specified order of a polynomial. |\n| [`polyint`](generated/numpy.polyint#numpy.polyint \"numpy.polyint\")(p[, m, k]) | Return an antiderivative (indefinite integral) of a polynomial. |\n\n Arithmetic\n----------\n\n \n\n| | |\n| --- | --- |\n| [`polyadd`](generated/numpy.polyadd#numpy.polyadd \"numpy.polyadd\")(a1, a2) | Find the sum of two polynomials. |\n| [`polydiv`](generated/numpy.polydiv#numpy.polydiv \"numpy.polydiv\")(u, v) | Returns the quotient and remainder of polynomial division. |\n| [`polymul`](generated/numpy.polymul#numpy.polymul \"numpy.polymul\")(a1, a2) | Find the product of two polynomials. |\n| [`polysub`](generated/numpy.polysub#numpy.polysub \"numpy.polysub\")(a1, a2) | Difference (subtraction) of two polynomials. |\n\n Warnings\n--------\n\n \n\n| | |\n| --- | --- |\n| [`RankWarning`](generated/numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") | Issued by [`polyfit`](generated/numpy.polyfit#numpy.polyfit \"numpy.polyfit\") when the Vandermonde matrix is rank deficient. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.poly1d.htmlConvenience Classes\n===================\n\n The following lists the various constants and methods common to all of the classes representing the various kinds of polynomials. In the following, the term `Poly` represents any one of the convenience classes (e.g. [`Polynomial`](generated/numpy.polynomial.polynomial.polynomial#numpy.polynomial.polynomial.Polynomial \"numpy.polynomial.polynomial.Polynomial\"), [`Chebyshev`](generated/numpy.polynomial.chebyshev.chebyshev#numpy.polynomial.chebyshev.Chebyshev \"numpy.polynomial.chebyshev.Chebyshev\"), [`Hermite`](generated/numpy.polynomial.hermite.hermite#numpy.polynomial.hermite.Hermite \"numpy.polynomial.hermite.Hermite\"), etc.) while the lowercase `p` represents an **instance** of a polynomial class.\n\n Constants\n---------\n\n * `Poly.domain` – Default domain\n* `Poly.window` – Default window\n* `Poly.basis_name` – String used to represent the basis\n* `Poly.maxpower` – Maximum value `n` such that `p**n` is allowed\n* `Poly.nickname` – String used in printing\n\n Creation\n--------\n\n Methods for creating polynomial instances.\n\n * `Poly.basis(degree)` – Basis polynomial of given degree\n* `Poly.identity()` – `p` where `p(x) = x` for all `x`\n* `Poly.fit(x, y, deg)` – `p` of degree `deg` with coefficients determined by the least-squares fit to the data `x`, `y`\n* `Poly.fromroots(roots)` – `p` with specified roots\n* `p.copy()` – Create a copy of `p`\n\n Conversion\n----------\n\n Methods for converting a polynomial instance of one kind to another.\n\n * `p.cast(Poly)` – Convert `p` to instance of kind `Poly`\n* `p.convert(Poly)` – Convert `p` to instance of kind `Poly` or map between `domain` and `window`\n\n Calculus\n--------\n\n * `p.deriv()` – Take the derivative of `p`\n* `p.integ()` – Integrate `p`\n\n Validation\n----------\n\n * `Poly.has_samecoef(p1, p2)` – Check if coefficients match\n* `Poly.has_samedomain(p1, p2)` – Check if domains match\n* `Poly.has_sametype(p1, p2)` – Check if types match\n* `Poly.has_samewindow(p1, p2)` – Check if windows match\n\n Misc\n----\n\n * `p.linspace()` – Return `x, p(x)` at equally-spaced points in `domain`\n* `p.mapparms()` – Return the parameters for the linear mapping between `domain` and `window`.\n* `p.roots()` – Return the roots of `p`.\n* `p.trim()` – Remove trailing coefficients.\n* `p.cutdeg(degree)` – Truncate p to given degree\n* `p.truncate(size)` – Truncate p to given size\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/routines.polynomials.package.htmlnumpy.poly1d\n============\n\n *class*numpy.poly1d(*c_or_r*, *r=False*, *variable=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/__init__.py)\n \nA one-dimensional polynomial class.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n A convenience class, used to encapsulate “natural” operations on polynomials so that said operations may take on their customary form in code (see Examples).\n\n Parameters \n \n**c_or_r**array_like\n\nThe polynomial’s coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial’s roots (values where the polynomial evaluates to 0). For example, `poly1d([1, 2, 3])` returns an object that represents \\(x^2 + 2x + 3\\), whereas `poly1d([1, 2, 3], True)` returns one that represents \\((x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6\\).\n\n \n**r**bool, optional\n\nIf True, `c_or_r` specifies the polynomial’s roots; the default is False.\n\n \n**variable**str, optional\n\nChanges the variable used when printing `p` from `x` to [`variable`](numpy.poly1d.variable#numpy.poly1d.variable \"numpy.poly1d.variable\") (see Examples).\n\n #### Examples\n\n Construct the polynomial \\(x^2 + 2x + 3\\):\n\n \n```\n>>> p = np.poly1d([1, 2, 3])\n>>> print(np.poly1d(p))\n 2\n1 x + 2 x + 3\n\n```\n Evaluate the polynomial at \\(x = 0.5\\):\n\n \n```\n>>> p(0.5)\n4.25\n\n```\n Find the roots:\n\n \n```\n>>> p.r\narray([-1.+1.41421356j, -1.-1.41421356j])\n>>> p(p.r)\narray([ -4.44089210e-16+0.j, -4.44089210e-16+0.j]) # may vary\n\n```\n These numbers in the previous line represent (0, 0) to machine precision\n\n Show the coefficients:\n\n \n```\n>>> p.c\narray([1, 2, 3])\n\n```\n Display the order (the leading zero-coefficients are removed):\n\n \n```\n>>> p.order\n2\n\n```\n Show the coefficient of the k-th power in the polynomial (which is equivalent to `p.c[-(i+1)]`):\n\n \n```\n>>> p[1]\n2\n\n```\n Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder):\n\n \n```\n>>> p * p\npoly1d([ 1, 4, 10, 12, 9])\n\n```\n \n```\n>>> (p**3 + 4) / p\n(poly1d([ 1., 4., 10., 12., 9.]), poly1d([4.]))\n\n```\n `asarray(p)` gives the coefficient array, so polynomials can be used in all functions that accept arrays:\n\n \n```\n>>> p**2 # square of polynomial\npoly1d([ 1, 4, 10, 12, 9])\n\n```\n \n```\n>>> np.square(p) # square of individual coefficients\narray([1, 4, 9])\n\n```\n The variable used in the string representation of `p` can be modified, using the [`variable`](numpy.poly1d.variable#numpy.poly1d.variable \"numpy.poly1d.variable\") parameter:\n\n \n```\n>>> p = np.poly1d([1,2,3], variable='z')\n>>> print(p)\n 2\n1 z + 2 z + 3\n\n```\n Construct a polynomial from its roots:\n\n \n```\n>>> np.poly1d([1, 2], True)\npoly1d([ 1., -3., 2.])\n\n```\n This is the same polynomial as obtained by:\n\n \n```\n>>> np.poly1d([1, -1]) * np.poly1d([1, -2])\npoly1d([ 1, -3, 2])\n\n```\n Attributes \n [`c`](numpy.poly1d.c#numpy.poly1d.c \"numpy.poly1d.c\")\n\nThe polynomial coefficients\n\n [`coef`](numpy.poly1d.coef#numpy.poly1d.coef \"numpy.poly1d.coef\")\n\nThe polynomial coefficients\n\n [`coefficients`](numpy.poly1d.coefficients#numpy.poly1d.coefficients \"numpy.poly1d.coefficients\")\n\nThe polynomial coefficients\n\n [`coeffs`](numpy.poly1d.coeffs#numpy.poly1d.coeffs \"numpy.poly1d.coeffs\")\n\nThe polynomial coefficients\n\n [`o`](numpy.poly1d.o#numpy.poly1d.o \"numpy.poly1d.o\")\n\nThe order or degree of the polynomial\n\n [`order`](numpy.poly1d.order#numpy.poly1d.order \"numpy.poly1d.order\")\n\nThe order or degree of the polynomial\n\n [`r`](numpy.poly1d.r#numpy.poly1d.r \"numpy.poly1d.r\")\n\nThe roots of the polynomial, where self(x) == 0\n\n [`roots`](numpy.roots#numpy.roots \"numpy.roots\")\n\nThe roots of the polynomial, where self(x) == 0\n\n [`variable`](numpy.poly1d.variable#numpy.poly1d.variable \"numpy.poly1d.variable\")\n\nThe name of the polynomial variable\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.poly1d.__call__#numpy.poly1d.__call__ \"numpy.poly1d.__call__\")(val) | Call self as a function. |\n| [`deriv`](numpy.poly1d.deriv#numpy.poly1d.deriv \"numpy.poly1d.deriv\")([m]) | Return a derivative of this polynomial. |\n| [`integ`](numpy.poly1d.integ#numpy.poly1d.integ \"numpy.poly1d.integ\")([m, k]) | Return an antiderivative (indefinite integral) of this polynomial. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.htmlnumpy.polyadd\n=============\n\n numpy.polyadd(*a1*, *a2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L787-L852)\n \nFind the sum of two polynomials.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Returns the polynomial resulting from the sum of two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree.\n\n Parameters \n \n**a1, a2**array_like or poly1d object\n\nInput polynomials.\n\n Returns \n \n**out**ndarray or poly1d object\n\nThe sum of the inputs. If either input is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree.\n\n See also\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nA one-dimensional polynomial class.\n\n \n[`poly`](numpy.poly#numpy.poly \"numpy.poly\"), [`polyadd`](#numpy.polyadd \"numpy.polyadd\"), [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\"), [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\n #### Examples\n\n \n```\n>>> np.polyadd([1, 2], [9, 5, 4])\narray([9, 6, 6])\n\n```\n Using poly1d objects:\n\n \n```\n>>> p1 = np.poly1d([1, 2])\n>>> p2 = np.poly1d([9, 5, 4])\n>>> print(p1)\n1 x + 2\n>>> print(p2)\n 2\n9 x + 5 x + 4\n>>> print(np.polyadd(p1, p2))\n 2\n9 x + 6 x + 6\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polyadd.htmlnumpy.polyval\n=============\n\n numpy.polyval(*p*, *x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L704-L780)\n \nEvaluate a polynomial at specific values.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n If `p` is of length N, this function returns the value:\n\n `p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]`\n\n If `x` is a sequence, then `p(x)` is returned for each element of `x`. If `x` is another polynomial then the composite polynomial `p(x(t))` is returned.\n\n Parameters \n \n**p**array_like or poly1d object\n\n1D array of polynomial coefficients (including coefficients equal to zero) from highest degree to the constant term, or an instance of poly1d.\n\n \n**x**array_like or poly1d object\n\nA number, an array of numbers, or an instance of poly1d, at which to evaluate `p`.\n\n Returns \n \n**values**ndarray or poly1d\n\nIf `x` is a poly1d instance, the result is the composition of the two polynomials, i.e., `x` is “substituted” in `p` and the simplified result is returned. In addition, the type of `x` - array_like or poly1d - governs the type of the output: `x` array_like => `values` array_like, `x` a poly1d object => `values` is also.\n\n See also\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nA polynomial class.\n\n #### Notes\n\n Horner’s scheme [[1]](#r138ee7027ddf-1) is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully.\n\n If `x` is a subtype of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") the return value will be of the same type.\n\n #### References\n\n [1](#id1) \n<NAME>, <NAME>, and <NAME> (Eng. trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand Reinhold Co., 1985, pg. 720.\n\n #### Examples\n\n \n```\n>>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1\n76\n>>> np.polyval([3,0,1], np.poly1d(5))\npoly1d([76])\n>>> np.polyval(np.poly1d([3,0,1]), 5)\n76\n>>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))\npoly1d([76])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polyval.htmlnumpy.polyfit\n=============\n\n numpy.polyfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*, *cov=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L452-L697)\n \nLeast squares polynomial fit.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Fit a polynomial `p(x) = p[0] * x**deg + ... + p[deg]` of degree `deg` to points `(x, y)`. Returns a vector of coefficients `p` that minimises the squared error in the order `deg`, `deg-1`, … `0`.\n\n The [`Polynomial.fit`](numpy.polynomial.polynomial.polynomial.fit#numpy.polynomial.polynomial.Polynomial.fit \"numpy.polynomial.polynomial.Polynomial.fit\") class method is recommended for new code as it is more stable numerically. See the documentation of the method for more information.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int\n\nDegree of the fitting polynomial\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n \n**cov**bool or str, optional\n\nIf given and not `False`, return not just the estimate but also its covariance matrix. By default, the covariance are scaled by chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed to be unreliable except in a relative sense and everything is scaled such that the reduced chi2 is unity. This scaling is omitted if `cov='unscaled'`, as is relevant for the case that the weights are w = 1/sigma, with sigma known to be a reliable estimate of the uncertainty.\n\n Returns \n \n**p**ndarray, shape (deg + 1,) or (deg + 1, K)\n\nPolynomial coefficients, highest power first. If `y` was 2-D, the coefficients for `k`-th data set are in `p[:,k]`.\n\n residuals, rank, singular_values, rcond\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the effective rank of the scaled Vandermonde\n\ncoefficient matrix\n* singular_values – singular values of the scaled Vandermonde\n\ncoefficient matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n**V**ndarray, shape (M,M) or (M,M,K)\n\nPresent only if `full == False` and `cov == True`. The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-D array, then the covariance matrix for the `k`-th data set are in `V[:,:,k]`\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`.\n\n The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\nCompute polynomial values.\n\n [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution minimizes the squared error\n\n \\[E = \\sum_{j=0}^k |p(x_j) - y_j|^2\\] in the equations:\n\n \n```\nx[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]\nx[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]\n...\nx[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]\n\n```\n The coefficient matrix of the coefficients `p` is a Vandermonde matrix.\n\n [`polyfit`](#numpy.polyfit \"numpy.polyfit\") issues a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") when the least-squares fit is badly conditioned. This implies that the best fit is not well-defined due to numerical error. The results may be improved by lowering the polynomial degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious: including contributions from the small singular values can add numerical noise to the result.\n\n Note that fitting polynomial coefficients is inherently badly conditioned when the degree of the polynomial is large or the interval of sample points is badly centered. The quality of the fit should always be checked in these cases. When polynomial fits are not satisfactory, splines may be a good alternative.\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting 2 \nWikipedia, “Polynomial interpolation”, <https://en.wikipedia.org/wiki/Polynomial_interpolation #### Examples\n\n \n```\n>>> import warnings\n>>> x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])\n>>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])\n>>> z = np.polyfit(x, y, 3)\n>>> z\narray([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) # may vary\n\n```\n It is convenient to use [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\") objects for dealing with polynomials:\n\n \n```\n>>> p = np.poly1d(z)\n>>> p(0.5)\n0.6143849206349179 # may vary\n>>> p(3.5)\n-0.34732142857143039 # may vary\n>>> p(10)\n22.579365079365115 # may vary\n\n```\n High-order polynomials may oscillate wildly:\n\n \n```\n>>> with warnings.catch_warnings():\n... warnings.simplefilter('ignore', np.RankWarning)\n... p30 = np.poly1d(np.polyfit(x, y, 30))\n...\n>>> p30(4)\n-0.80000000000000204 # may vary\n>>> p30(5)\n-0.99999999999999445 # may vary\n>>> p30(4.5)\n-0.10547061179440398 # may vary\n\n```\n Illustration:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> xp = np.linspace(-2, 6, 100)\n>>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')\n>>> plt.ylim(-2,2)\n(-2, 2)\n>>> plt.show()\n\n```\n ![../../_images/numpy-polyfit-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polyfit.htmlnumpy.poly\n==========\n\n numpy.poly(*seq_of_zeros*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L44-L164)\n \nFind the coefficients of a polynomial with the given sequence of roots.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Returns the coefficients of the polynomial whose leading coefficient is one for the given sequence of zeros (multiple roots must be included in the sequence as many times as their multiplicity; see Examples). A square matrix (or array, which will be treated as a matrix) can also be given, in which case the coefficients of the characteristic polynomial of the matrix are returned.\n\n Parameters \n \n**seq_of_zeros**array_like, shape (N,) or (N, N)\n\nA sequence of polynomial roots, or a square array or matrix object.\n\n Returns \n \n**c**ndarray\n\n1D array of polynomial coefficients from highest to lowest degree:\n\n `c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]` where c[0] always equals 1.\n\n Raises \n ValueError\n\nIf input is the wrong shape (the input must be a 1-D or square 2-D array).\n\n See also\n\n [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\nCompute polynomial values.\n\n [`roots`](numpy.roots#numpy.roots \"numpy.roots\")\n\nReturn the roots of a polynomial.\n\n [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\")\n\nLeast squares polynomial fit.\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nA one-dimensional polynomial class.\n\n #### Notes\n\n Specifying the roots of a polynomial still leaves one degree of freedom, typically represented by an undetermined leading coefficient. [[1]](#r6c2ffae921d1-1) In the case of this function, that coefficient - the first one in the returned array - is always taken as one. (If for some reason you have one other point, the only automatic way presently to leverage that information is to use `polyfit`.)\n\n The characteristic polynomial, \\(p_a(t)\\), of an `n`-by-`n` matrix **A** is given by\n\n \\(p_a(t) = \\mathrm{det}(t\\, \\mathbf{I} - \\mathbf{A})\\),\n\n where **I** is the `n`-by-`n` identity matrix. [[2]](#r6c2ffae921d1-2)\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, III, “Algebra and Trignometry, Enhanced With Graphing Utilities,” Prentice-Hall, pg. 318, 1996.\n\n [2](#id2) \n<NAME>, “Linear Algebra and Its Applications, 2nd Edition,” Academic Press, pg. 182, 1980.\n\n #### Examples\n\n Given a sequence of a polynomial’s zeros:\n\n \n```\n>>> np.poly((0, 0, 0)) # Multiple root example\narray([1., 0., 0., 0.])\n\n```\n The line above represents z**3 + 0*z**2 + 0*z + 0.\n\n \n```\n>>> np.poly((-1./2, 0, 1./2))\narray([ 1. , 0. , -0.25, 0. ])\n\n```\n The line above represents z**3 - z/4\n\n \n```\n>>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))\narray([ 1. , -0.77086955, 0.08618131, 0. ]) # random\n\n```\n Given a square array object:\n\n \n```\n>>> P = np.array([[0, 1./3], [-1./2, 0]])\n>>> np.poly(P)\narray([1. , 0. , 0.16666667])\n\n```\n Note how in all cases the leading coefficient is always 1.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly.htmlnumpy.polynomial.polynomial.Polynomial\n======================================\n\n *class*numpy.polynomial.polynomial.Polynomial(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1472-L1530)\n \nA power series class.\n\n The Polynomial class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the `ABCPolyBase` documentation.\n\n Parameters \n \n**coef**array_like\n\nPolynomial coefficients in order of increasing degree, i.e., `(1, 2, 3)` give `1 + 2*x + 3*x**2`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [-1, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.polynomial.polynomial.domain#numpy.polynomial.polynomial.Polynomial.domain \"numpy.polynomial.polynomial.Polynomial.domain\") for its use. The default value is [-1, 1].\n\n New in version 1.6.0.\n\n Attributes \n **basis_name**\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.polynomial.polynomial.__call__#numpy.polynomial.polynomial.Polynomial.__call__ \"numpy.polynomial.polynomial.Polynomial.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.polynomial.polynomial.basis#numpy.polynomial.polynomial.Polynomial.basis \"numpy.polynomial.polynomial.Polynomial.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.polynomial.polynomial.cast#numpy.polynomial.polynomial.Polynomial.cast \"numpy.polynomial.polynomial.Polynomial.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.polynomial.polynomial.convert#numpy.polynomial.polynomial.Polynomial.convert \"numpy.polynomial.polynomial.Polynomial.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.polynomial.polynomial.copy#numpy.polynomial.polynomial.Polynomial.copy \"numpy.polynomial.polynomial.Polynomial.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.polynomial.polynomial.cutdeg#numpy.polynomial.polynomial.Polynomial.cutdeg \"numpy.polynomial.polynomial.Polynomial.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.polynomial.polynomial.degree#numpy.polynomial.polynomial.Polynomial.degree \"numpy.polynomial.polynomial.Polynomial.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.polynomial.polynomial.deriv#numpy.polynomial.polynomial.Polynomial.deriv \"numpy.polynomial.polynomial.Polynomial.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.polynomial.polynomial.fit#numpy.polynomial.polynomial.Polynomial.fit \"numpy.polynomial.polynomial.Polynomial.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.polynomial.polynomial.fromroots#numpy.polynomial.polynomial.Polynomial.fromroots \"numpy.polynomial.polynomial.Polynomial.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.polynomial.polynomial.has_samecoef#numpy.polynomial.polynomial.Polynomial.has_samecoef \"numpy.polynomial.polynomial.Polynomial.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.polynomial.polynomial.has_samedomain#numpy.polynomial.polynomial.Polynomial.has_samedomain \"numpy.polynomial.polynomial.Polynomial.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.polynomial.polynomial.has_sametype#numpy.polynomial.polynomial.Polynomial.has_sametype \"numpy.polynomial.polynomial.Polynomial.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.polynomial.polynomial.has_samewindow#numpy.polynomial.polynomial.Polynomial.has_samewindow \"numpy.polynomial.polynomial.Polynomial.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.polynomial.polynomial.identity#numpy.polynomial.polynomial.Polynomial.identity \"numpy.polynomial.polynomial.Polynomial.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.polynomial.polynomial.integ#numpy.polynomial.polynomial.Polynomial.integ \"numpy.polynomial.polynomial.Polynomial.integ\")([m, k, lbnd]) | Integrate. |\n| [`linspace`](numpy.polynomial.polynomial.polynomial.linspace#numpy.polynomial.polynomial.Polynomial.linspace \"numpy.polynomial.polynomial.Polynomial.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.polynomial.polynomial.mapparms#numpy.polynomial.polynomial.Polynomial.mapparms \"numpy.polynomial.polynomial.Polynomial.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.polynomial.polynomial.roots#numpy.polynomial.polynomial.Polynomial.roots \"numpy.polynomial.polynomial.Polynomial.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.polynomial.polynomial.trim#numpy.polynomial.polynomial.Polynomial.trim \"numpy.polynomial.polynomial.Polynomial.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.polynomial.polynomial.truncate#numpy.polynomial.polynomial.Polynomial.truncate \"numpy.polynomial.polynomial.Polynomial.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.htmlnumpy.polynomial.polynomial.Polynomial.fit\n==========================================\n\n method\n\n *classmethod*polynomial.polynomial.Polynomial.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.fit.htmlnumpy.polynomial.polynomial.Polynomial.convert\n==============================================\n\n method\n\n polynomial.polynomial.Polynomial.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.convert.htmlRandom Generator\n================\n\n The [`Generator`](#numpy.random.Generator \"numpy.random.Generator\") provides access to a wide range of distributions, and served as a replacement for [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\"). The main difference between the two is that `Generator` relies on an additional BitGenerator to manage state and generate the random bits, which are then transformed into random values from useful distributions. The default BitGenerator used by `Generator` is [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\"). The BitGenerator can be changed by passing an instantized BitGenerator to `Generator`.\n\n numpy.random.default_rng()\n \nConstruct a new Generator with the default BitGenerator (PCG64).\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional\n\nA seed to initialize the [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance. Additionally, when passed a [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"), it will be wrapped by [`Generator`](#numpy.random.Generator \"numpy.random.Generator\"). If passed a [`Generator`](#numpy.random.Generator \"numpy.random.Generator\"), it will be returned unaltered.\n\n Returns \n Generator\n\nThe initialized generator object.\n\n #### Notes\n\n If `seed` is not a [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") or a [`Generator`](#numpy.random.Generator \"numpy.random.Generator\"), a new [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") is instantiated. This function does not manage a default global instance.\n\n #### Examples\n\n `default_rng` is the recommended constructor for the random number class `Generator`. Here are several ways we can construct a random number generator using `default_rng` and the `Generator` class.\n\n Here we use `default_rng` to generate a random float:\n\n \n```\n>>> import numpy as np\n>>> rng = np.random.default_rng(12345)\n>>> print(rng)\nGenerator(PCG64)\n>>> rfloat = rng.random()\n>>> rfloat\n0.22733602246716966\n>>> type(rfloat)\n<class 'float'```\n Here we use `default_rng` to generate 3 random integers between 0 (inclusive) and 10 (exclusive):\n\n \n```\n>>> import numpy as np\n>>> rng = np.random.default_rng(12345)\n>>> rints = rng.integers(low=0, high=10, size=3)\n>>> rints\narray([6, 2, 7])\n>>> type(rints[0])\n<class 'numpy.int64'```\n Here we specify a seed so that we have reproducible results:\n\n \n```\n>>> import numpy as np\n>>> rng = np.random.default_rng(seed=42)\n>>> print(rng)\nGenerator(PCG64)\n>>> arr1 = rng.random((3, 3))\n>>> arr1\narray([[0.77395605, 0.43887844, 0.85859792],\n [0.69736803, 0.09417735, 0.97562235],\n [0.7611397 , 0.78606431, 0.12811363]])\n\n```\n If we exit and restart our Python interpreter, we’ll see that we generate the same random numbers again:\n\n \n```\n>>> import numpy as np\n>>> rng = np.random.default_rng(seed=42)\n>>> arr2 = rng.random((3, 3))\n>>> arr2\narray([[0.77395605, 0.43887844, 0.85859792],\n [0.69736803, 0.09417735, 0.97562235],\n [0.7611397 , 0.78606431, 0.12811363]])\n\n```\n \n *class*numpy.random.Generator(*bit_generator*)\n \nContainer for the BitGenerators.\n\n `Generator` exposes a number of methods for generating random numbers drawn from a variety of probability distributions. In addition to the distribution-specific arguments, each method takes a keyword argument `size` that defaults to `None`. If `size` is `None`, then a single value is generated and returned. If `size` is an integer, then a 1-D array filled with generated values is returned. If `size` is a tuple, then an array with that shape is filled and returned.\n\n The function [`numpy.random.default_rng`](#numpy.random.default_rng \"numpy.random.default_rng\") will instantiate a [`Generator`](#numpy.random.Generator \"numpy.random.Generator\") with numpy’s default [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\").\n\n **No Compatibility Guarantee**\n\n `Generator` does not provide a version compatibility guarantee. In particular, as better algorithms evolve the bit stream may change.\n\n Parameters \n \n**bit_generator**BitGenerator\n\nBitGenerator to use as the core generator.\n\n See also\n\n [`default_rng`](#numpy.random.default_rng \"numpy.random.default_rng\")\n\nRecommended constructor for [`Generator`](#numpy.random.Generator \"numpy.random.Generator\").\n\n #### Notes\n\n The Python stdlib module [`random`](generated/numpy.random.random#numpy.random.random \"numpy.random.random\") contains pseudo-random number generator with a number of methods that are similar to the ones available in `Generator`. It uses Mersenne Twister, and this bit generator can be accessed using `MT19937`. `Generator`, besides being NumPy-aware, has the advantage that it provides a much larger number of probability distributions to choose from.\n\n #### Examples\n\n \n```\n>>> from numpy.random import Generator, PCG64\n>>> rng = Generator(PCG64())\n>>> rng.standard_normal()\n-0.203 # random\n\n```\n \n Accessing the BitGenerator\n--------------------------\n\n \n\n| | |\n| --- | --- |\n| [`bit_generator`](generated/numpy.random.generator.bit_generator#numpy.random.Generator.bit_generator \"numpy.random.Generator.bit_generator\") | Gets the bit generator instance used by the generator |\n\n Simple random data\n------------------\n\n \n\n| | |\n| --- | --- |\n| [`integers`](generated/numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\")(low[, high, size, dtype, endpoint]) | Return random integers from `low` (inclusive) to `high` (exclusive), or if endpoint=True, `low` (inclusive) to `high` (inclusive). |\n| [`random`](generated/numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\")([size, dtype, out]) | Return random floats in the half-open interval [0.0, 1.0). |\n| [`choice`](generated/numpy.random.generator.choice#numpy.random.Generator.choice \"numpy.random.Generator.choice\")(a[, size, replace, p, axis, shuffle]) | Generates a random sample from a given array |\n| [`bytes`](generated/numpy.random.generator.bytes#numpy.random.Generator.bytes \"numpy.random.Generator.bytes\")(length) | Return random bytes. |\n\n Permutations\n------------\n\n The methods for randomly permuting a sequence are\n\n \n\n| | |\n| --- | --- |\n| [`shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\")(x[, axis]) | Modify an array or sequence in-place by shuffling its contents. |\n| [`permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")(x[, axis]) | Randomly permute a sequence, or return a permuted range. |\n| [`permuted`](generated/numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\")(x[, axis, out]) | Randomly permute `x` along axis `axis`. |\n\n The following table summarizes the behaviors of the methods.\n\n \n\n| method | copy/in-place | axis handling |\n| --- | --- | --- |\n| shuffle | in-place | as if 1d |\n| permutation | copy | as if 1d |\n| permuted | either (use ‘out’ for in-place) | axis independent |\n\n The following subsections provide more details about the differences.\n\n ### In-place vs. copy\n\n The main difference between [`Generator.shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\") and [`Generator.permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\") is that [`Generator.shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\") operates in-place, while [`Generator.permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\") returns a copy.\n\n By default, [`Generator.permuted`](generated/numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\") returns a copy. To operate in-place with [`Generator.permuted`](generated/numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\"), pass the same array as the first argument *and* as the value of the `out` parameter. For example,\n\n \n```\n>>> rng = np.random.default_rng()\n>>> x = np.arange(0, 15).reshape(3, 5)\n>>> x \narray([[ 0, 1, 2, 3, 4],\n [ 5, 6, 7, 8, 9],\n [10, 11, 12, 13, 14]])\n>>> y = rng.permuted(x, axis=1, out=x)\n>>> x \narray([[ 1, 0, 2, 4, 3], # random\n [ 6, 7, 8, 9, 5],\n [10, 14, 11, 13, 12]])\n\n```\n Note that when `out` is given, the return value is `out`:\n\n \n```\n>>> y is x\nTrue\n\n```\n ### Handling the `axis` parameter\n\n An important distinction for these methods is how they handle the `axis` parameter. Both [`Generator.shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\") and [`Generator.permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\") treat the input as a one-dimensional sequence, and the `axis` parameter determines which dimension of the input array to use as the sequence. In the case of a two-dimensional array, `axis=0` will, in effect, rearrange the rows of the array, and `axis=1` will rearrange the columns. For example\n\n \n```\n>>> rng = np.random.default_rng()\n>>> x = np.arange(0, 15).reshape(3, 5)\n>>> x\narray([[ 0, 1, 2, 3, 4],\n [ 5, 6, 7, 8, 9],\n [10, 11, 12, 13, 14]])\n>>> rng.permutation(x, axis=1) \narray([[ 1, 3, 2, 0, 4], # random\n [ 6, 8, 7, 5, 9],\n [11, 13, 12, 10, 14]])\n\n```\n Note that the columns have been rearranged “in bulk”: the values within each column have not changed.\n\n The method [`Generator.permuted`](generated/numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\") treats the `axis` parameter similar to how [`numpy.sort`](../generated/numpy.sort#numpy.sort \"numpy.sort\") treats it. Each slice along the given axis is shuffled independently of the others. Compare the following example of the use of [`Generator.permuted`](generated/numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\") to the above example of [`Generator.permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\"):\n\n \n```\n>>> rng.permuted(x, axis=1) \narray([[ 1, 0, 2, 4, 3], # random\n [ 5, 7, 6, 9, 8],\n [10, 14, 12, 13, 11]])\n\n```\n In this example, the values within each row (i.e. the values along `axis=1`) have been shuffled independently. This is not a “bulk” shuffle of the columns.\n\n ### Shuffling non-NumPy sequences\n\n [`Generator.shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\") works on non-NumPy sequences. That is, if it is given a sequence that is not a NumPy array, it shuffles that sequence in-place. For example,\n\n \n```\n>>> rng = np.random.default_rng()\n>>> a = ['A', 'B', 'C', 'D', 'E']\n>>> rng.shuffle(a) # shuffle the list in-place\n>>> a \n['B', 'D', 'A', 'E', 'C'] # random\n\n```\n Distributions\n-------------\n\n \n\n| | |\n| --- | --- |\n| [`beta`](generated/numpy.random.generator.beta#numpy.random.Generator.beta \"numpy.random.Generator.beta\")(a, b[, size]) | Draw samples from a Beta distribution. |\n| [`binomial`](generated/numpy.random.generator.binomial#numpy.random.Generator.binomial \"numpy.random.Generator.binomial\")(n, p[, size]) | Draw samples from a binomial distribution. |\n| [`chisquare`](generated/numpy.random.generator.chisquare#numpy.random.Generator.chisquare \"numpy.random.Generator.chisquare\")(df[, size]) | Draw samples from a chi-square distribution. |\n| [`dirichlet`](generated/numpy.random.generator.dirichlet#numpy.random.Generator.dirichlet \"numpy.random.Generator.dirichlet\")(alpha[, size]) | Draw samples from the Dirichlet distribution. |\n| [`exponential`](generated/numpy.random.generator.exponential#numpy.random.Generator.exponential \"numpy.random.Generator.exponential\")([scale, size]) | Draw samples from an exponential distribution. |\n| [`f`](generated/numpy.random.generator.f#numpy.random.Generator.f \"numpy.random.Generator.f\")(dfnum, dfden[, size]) | Draw samples from an F distribution. |\n| [`gamma`](generated/numpy.random.generator.gamma#numpy.random.Generator.gamma \"numpy.random.Generator.gamma\")(shape[, scale, size]) | Draw samples from a Gamma distribution. |\n| [`geometric`](generated/numpy.random.generator.geometric#numpy.random.Generator.geometric \"numpy.random.Generator.geometric\")(p[, size]) | Draw samples from the geometric distribution. |\n| [`gumbel`](generated/numpy.random.generator.gumbel#numpy.random.Generator.gumbel \"numpy.random.Generator.gumbel\")([loc, scale, size]) | Draw samples from a Gumbel distribution. |\n| [`hypergeometric`](generated/numpy.random.generator.hypergeometric#numpy.random.Generator.hypergeometric \"numpy.random.Generator.hypergeometric\")(ngood, nbad, nsample[, size]) | Draw samples from a Hypergeometric distribution. |\n| [`laplace`](generated/numpy.random.generator.laplace#numpy.random.Generator.laplace \"numpy.random.Generator.laplace\")([loc, scale, size]) | Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). |\n| [`logistic`](generated/numpy.random.generator.logistic#numpy.random.Generator.logistic \"numpy.random.Generator.logistic\")([loc, scale, size]) | Draw samples from a logistic distribution. |\n| [`lognormal`](generated/numpy.random.generator.lognormal#numpy.random.Generator.lognormal \"numpy.random.Generator.lognormal\")([mean, sigma, size]) | Draw samples from a log-normal distribution. |\n| [`logseries`](generated/numpy.random.generator.logseries#numpy.random.Generator.logseries \"numpy.random.Generator.logseries\")(p[, size]) | Draw samples from a logarithmic series distribution. |\n| [`multinomial`](generated/numpy.random.generator.multinomial#numpy.random.Generator.multinomial \"numpy.random.Generator.multinomial\")(n, pvals[, size]) | Draw samples from a multinomial distribution. |\n| [`multivariate_hypergeometric`](generated/numpy.random.generator.multivariate_hypergeometric#numpy.random.Generator.multivariate_hypergeometric \"numpy.random.Generator.multivariate_hypergeometric\")(colors, nsample) | Generate variates from a multivariate hypergeometric distribution. |\n| [`multivariate_normal`](generated/numpy.random.generator.multivariate_normal#numpy.random.Generator.multivariate_normal \"numpy.random.Generator.multivariate_normal\")(mean, cov[, size, ...]) | Draw random samples from a multivariate normal distribution. |\n| [`negative_binomial`](generated/numpy.random.generator.negative_binomial#numpy.random.Generator.negative_binomial \"numpy.random.Generator.negative_binomial\")(n, p[, size]) | Draw samples from a negative binomial distribution. |\n| [`noncentral_chisquare`](generated/numpy.random.generator.noncentral_chisquare#numpy.random.Generator.noncentral_chisquare \"numpy.random.Generator.noncentral_chisquare\")(df, nonc[, size]) | Draw samples from a noncentral chi-square distribution. |\n| [`noncentral_f`](generated/numpy.random.generator.noncentral_f#numpy.random.Generator.noncentral_f \"numpy.random.Generator.noncentral_f\")(dfnum, dfden, nonc[, size]) | Draw samples from the noncentral F distribution. |\n| [`normal`](generated/numpy.random.generator.normal#numpy.random.Generator.normal \"numpy.random.Generator.normal\")([loc, scale, size]) | Draw random samples from a normal (Gaussian) distribution. |\n| [`pareto`](generated/numpy.random.generator.pareto#numpy.random.Generator.pareto \"numpy.random.Generator.pareto\")(a[, size]) | Draw samples from a Pareto II or Lomax distribution with specified shape. |\n| [`poisson`](generated/numpy.random.generator.poisson#numpy.random.Generator.poisson \"numpy.random.Generator.poisson\")([lam, size]) | Draw samples from a Poisson distribution. |\n| [`power`](generated/numpy.random.generator.power#numpy.random.Generator.power \"numpy.random.Generator.power\")(a[, size]) | Draws samples in [0, 1] from a power distribution with positive exponent a - 1. |\n| [`rayleigh`](generated/numpy.random.generator.rayleigh#numpy.random.Generator.rayleigh \"numpy.random.Generator.rayleigh\")([scale, size]) | Draw samples from a Rayleigh distribution. |\n| [`standard_cauchy`](generated/numpy.random.generator.standard_cauchy#numpy.random.Generator.standard_cauchy \"numpy.random.Generator.standard_cauchy\")([size]) | Draw samples from a standard Cauchy distribution with mode = 0. |\n| [`standard_exponential`](generated/numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\")([size, dtype, method, out]) | Draw samples from the standard exponential distribution. |\n| [`standard_gamma`](generated/numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\")(shape[, size, dtype, out]) | Draw samples from a standard Gamma distribution. |\n| [`standard_normal`](generated/numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")([size, dtype, out]) | Draw samples from a standard Normal distribution (mean=0, stdev=1). |\n| [`standard_t`](generated/numpy.random.generator.standard_t#numpy.random.Generator.standard_t \"numpy.random.Generator.standard_t\")(df[, size]) | Draw samples from a standard Student's t distribution with `df` degrees of freedom. |\n| [`triangular`](generated/numpy.random.generator.triangular#numpy.random.Generator.triangular \"numpy.random.Generator.triangular\")(left, mode, right[, size]) | Draw samples from the triangular distribution over the interval `[left, right]`. |\n| [`uniform`](generated/numpy.random.generator.uniform#numpy.random.Generator.uniform \"numpy.random.Generator.uniform\")([low, high, size]) | Draw samples from a uniform distribution. |\n| [`vonmises`](generated/numpy.random.generator.vonmises#numpy.random.Generator.vonmises \"numpy.random.Generator.vonmises\")(mu, kappa[, size]) | Draw samples from a von Mises distribution. |\n| [`wald`](generated/numpy.random.generator.wald#numpy.random.Generator.wald \"numpy.random.Generator.wald\")(mean, scale[, size]) | Draw samples from a Wald, or inverse Gaussian, distribution. |\n| [`weibull`](generated/numpy.random.generator.weibull#numpy.random.Generator.weibull \"numpy.random.Generator.weibull\")(a[, size]) | Draw samples from a Weibull distribution. |\n| [`zipf`](generated/numpy.random.generator.zipf#numpy.random.Generator.zipf \"numpy.random.Generator.zipf\")(a[, size]) | Draw samples from a Zipf distribution. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generator.htmlLegacy Random Generation\n========================\n\n The [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") provides access to legacy generators. This generator is considered frozen and will have no further improvements. It is guaranteed to produce the same values as the final point release of NumPy v1.16. These all depend on Box-Muller normals or inverse CDF exponentials or gammas. This class should only be used if it is essential to have randoms that are identical to what would have been produced by previous versions of NumPy.\n\n [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") adds additional information to the state which is required when using Box-Muller normals since these are produced in pairs. It is important to use [`RandomState.get_state`](generated/numpy.random.randomstate.get_state#numpy.random.RandomState.get_state \"numpy.random.RandomState.get_state\"), and not the underlying bit generators `state`, when accessing the state so that these extra values are saved.\n\n Although we provide the [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") BitGenerator for use independent of [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\"), note that its default seeding uses [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") rather than the legacy seeding algorithm. [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") will use the legacy seeding algorithm. The methods to use the legacy seeding algorithm are currently private as the main reason to use them is just to implement [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\"). However, one can reset the state of [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") using the state of the [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\"):\n\n \n```\nfrom numpy.random import MT19937\nfrom numpy.random import RandomState\n\nrs = RandomState(12345)\nmt19937 = MT19937()\nmt19937.state = rs.get_state()\nrs2 = RandomState(mt19937)\n\n# Same output\nrs.standard_normal()\nrs2.standard_normal()\n\nrs.random()\nrs2.random()\n\nrs.standard_exponential()\nrs2.standard_exponential()\n\n```\n *class*numpy.random.RandomState(*seed=None*)\n \nContainer for the slow Mersenne Twister pseudo-random number generator. Consider using a different BitGenerator with the Generator container instead.\n\n [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") and [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\") expose a number of methods for generating random numbers drawn from a variety of probability distributions. In addition to the distribution-specific arguments, each method takes a keyword argument `size` that defaults to `None`. If `size` is `None`, then a single value is generated and returned. If `size` is an integer, then a 1-D array filled with generated values is returned. If `size` is a tuple, then an array with that shape is filled and returned.\n\n **Compatibility Guarantee**\n\n A fixed bit generator using a fixed seed and a fixed series of calls to ‘RandomState’ methods using the same parameters will always produce the same results up to roundoff error except when the values were incorrect. [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") is effectively frozen and will only receive updates that are required by changes in the the internals of Numpy. More substantial changes, including algorithmic improvements, are reserved for [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\").\n\n Parameters \n \n**seed**{None, int, array_like, BitGenerator}, optional\n\nRandom seed used to initialize the pseudo-random number generator or an instantized BitGenerator. If an integer or array, used as a seed for the MT19937 BitGenerator. Values can be any integer between 0 and 2**32 - 1 inclusive, an array (or other sequence) of such integers, or `None` (the default). If [`seed`](generated/numpy.random.seed#numpy.random.seed \"numpy.random.seed\") is `None`, then the [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") BitGenerator is initialized by reading data from `/dev/urandom` (or the Windows analogue) if available or seed from the clock otherwise.\n\n See also\n\n [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\")\n[`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\")\n[`numpy.random.BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\")\n #### Notes\n\n The Python stdlib module “random” also contains a Mersenne Twister pseudo-random number generator with a number of methods that are similar to the ones available in [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\"). [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\"), besides being NumPy-aware, has the advantage that it provides a much larger number of probability distributions to choose from.\n\n \n Seeding and State\n-----------------\n\n \n\n| | |\n| --- | --- |\n| [`get_state`](generated/numpy.random.randomstate.get_state#numpy.random.RandomState.get_state \"numpy.random.RandomState.get_state\")() | Return a tuple representing the internal state of the generator. |\n| [`set_state`](generated/numpy.random.randomstate.set_state#numpy.random.RandomState.set_state \"numpy.random.RandomState.set_state\")(state) | Set the internal state of the generator from a tuple. |\n| [`seed`](generated/numpy.random.randomstate.seed#numpy.random.RandomState.seed \"numpy.random.RandomState.seed\")(self[, seed]) | Reseed a legacy MT19937 BitGenerator |\n\n Simple random data\n------------------\n\n \n\n| | |\n| --- | --- |\n| [`rand`](generated/numpy.random.randomstate.rand#numpy.random.RandomState.rand \"numpy.random.RandomState.rand\")(d0, d1, ..., dn) | Random values in a given shape. |\n| [`randn`](generated/numpy.random.randomstate.randn#numpy.random.RandomState.randn \"numpy.random.RandomState.randn\")(d0, d1, ..., dn) | Return a sample (or samples) from the \"standard normal\" distribution. |\n| [`randint`](generated/numpy.random.randomstate.randint#numpy.random.RandomState.randint \"numpy.random.RandomState.randint\")(low[, high, size, dtype]) | Return random integers from `low` (inclusive) to `high` (exclusive). |\n| [`random_integers`](generated/numpy.random.randomstate.random_integers#numpy.random.RandomState.random_integers \"numpy.random.RandomState.random_integers\")(low[, high, size]) | Random integers of type `np.int_` between `low` and `high`, inclusive. |\n| [`random_sample`](generated/numpy.random.randomstate.random_sample#numpy.random.RandomState.random_sample \"numpy.random.RandomState.random_sample\")([size]) | Return random floats in the half-open interval [0.0, 1.0). |\n| [`choice`](generated/numpy.random.randomstate.choice#numpy.random.RandomState.choice \"numpy.random.RandomState.choice\")(a[, size, replace, p]) | Generates a random sample from a given 1-D array |\n| [`bytes`](generated/numpy.random.randomstate.bytes#numpy.random.RandomState.bytes \"numpy.random.RandomState.bytes\")(length) | Return random bytes. |\n\n Permutations\n------------\n\n \n\n| | |\n| --- | --- |\n| [`shuffle`](generated/numpy.random.randomstate.shuffle#numpy.random.RandomState.shuffle \"numpy.random.RandomState.shuffle\")(x) | Modify a sequence in-place by shuffling its contents. |\n| [`permutation`](generated/numpy.random.randomstate.permutation#numpy.random.RandomState.permutation \"numpy.random.RandomState.permutation\")(x) | Randomly permute a sequence, or return a permuted range. |\n\n Distributions\n-------------\n\n \n\n| | |\n| --- | --- |\n| [`beta`](generated/numpy.random.randomstate.beta#numpy.random.RandomState.beta \"numpy.random.RandomState.beta\")(a, b[, size]) | Draw samples from a Beta distribution. |\n| [`binomial`](generated/numpy.random.randomstate.binomial#numpy.random.RandomState.binomial \"numpy.random.RandomState.binomial\")(n, p[, size]) | Draw samples from a binomial distribution. |\n| [`chisquare`](generated/numpy.random.randomstate.chisquare#numpy.random.RandomState.chisquare \"numpy.random.RandomState.chisquare\")(df[, size]) | Draw samples from a chi-square distribution. |\n| [`dirichlet`](generated/numpy.random.randomstate.dirichlet#numpy.random.RandomState.dirichlet \"numpy.random.RandomState.dirichlet\")(alpha[, size]) | Draw samples from the Dirichlet distribution. |\n| [`exponential`](generated/numpy.random.randomstate.exponential#numpy.random.RandomState.exponential \"numpy.random.RandomState.exponential\")([scale, size]) | Draw samples from an exponential distribution. |\n| [`f`](generated/numpy.random.randomstate.f#numpy.random.RandomState.f \"numpy.random.RandomState.f\")(dfnum, dfden[, size]) | Draw samples from an F distribution. |\n| [`gamma`](generated/numpy.random.randomstate.gamma#numpy.random.RandomState.gamma \"numpy.random.RandomState.gamma\")(shape[, scale, size]) | Draw samples from a Gamma distribution. |\n| [`geometric`](generated/numpy.random.randomstate.geometric#numpy.random.RandomState.geometric \"numpy.random.RandomState.geometric\")(p[, size]) | Draw samples from the geometric distribution. |\n| [`gumbel`](generated/numpy.random.randomstate.gumbel#numpy.random.RandomState.gumbel \"numpy.random.RandomState.gumbel\")([loc, scale, size]) | Draw samples from a Gumbel distribution. |\n| [`hypergeometric`](generated/numpy.random.randomstate.hypergeometric#numpy.random.RandomState.hypergeometric \"numpy.random.RandomState.hypergeometric\")(ngood, nbad, nsample[, size]) | Draw samples from a Hypergeometric distribution. |\n| [`laplace`](generated/numpy.random.randomstate.laplace#numpy.random.RandomState.laplace \"numpy.random.RandomState.laplace\")([loc, scale, size]) | Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). |\n| [`logistic`](generated/numpy.random.randomstate.logistic#numpy.random.RandomState.logistic \"numpy.random.RandomState.logistic\")([loc, scale, size]) | Draw samples from a logistic distribution. |\n| [`lognormal`](generated/numpy.random.randomstate.lognormal#numpy.random.RandomState.lognormal \"numpy.random.RandomState.lognormal\")([mean, sigma, size]) | Draw samples from a log-normal distribution. |\n| [`logseries`](generated/numpy.random.randomstate.logseries#numpy.random.RandomState.logseries \"numpy.random.RandomState.logseries\")(p[, size]) | Draw samples from a logarithmic series distribution. |\n| [`multinomial`](generated/numpy.random.randomstate.multinomial#numpy.random.RandomState.multinomial \"numpy.random.RandomState.multinomial\")(n, pvals[, size]) | Draw samples from a multinomial distribution. |\n| [`multivariate_normal`](generated/numpy.random.randomstate.multivariate_normal#numpy.random.RandomState.multivariate_normal \"numpy.random.RandomState.multivariate_normal\")(mean, cov[, size, ...]) | Draw random samples from a multivariate normal distribution. |\n| [`negative_binomial`](generated/numpy.random.randomstate.negative_binomial#numpy.random.RandomState.negative_binomial \"numpy.random.RandomState.negative_binomial\")(n, p[, size]) | Draw samples from a negative binomial distribution. |\n| [`noncentral_chisquare`](generated/numpy.random.randomstate.noncentral_chisquare#numpy.random.RandomState.noncentral_chisquare \"numpy.random.RandomState.noncentral_chisquare\")(df, nonc[, size]) | Draw samples from a noncentral chi-square distribution. |\n| [`noncentral_f`](generated/numpy.random.randomstate.noncentral_f#numpy.random.RandomState.noncentral_f \"numpy.random.RandomState.noncentral_f\")(dfnum, dfden, nonc[, size]) | Draw samples from the noncentral F distribution. |\n| [`normal`](generated/numpy.random.randomstate.normal#numpy.random.RandomState.normal \"numpy.random.RandomState.normal\")([loc, scale, size]) | Draw random samples from a normal (Gaussian) distribution. |\n| [`pareto`](generated/numpy.random.randomstate.pareto#numpy.random.RandomState.pareto \"numpy.random.RandomState.pareto\")(a[, size]) | Draw samples from a Pareto II or Lomax distribution with specified shape. |\n| [`poisson`](generated/numpy.random.randomstate.poisson#numpy.random.RandomState.poisson \"numpy.random.RandomState.poisson\")([lam, size]) | Draw samples from a Poisson distribution. |\n| [`power`](generated/numpy.random.randomstate.power#numpy.random.RandomState.power \"numpy.random.RandomState.power\")(a[, size]) | Draws samples in [0, 1] from a power distribution with positive exponent a - 1. |\n| [`rayleigh`](generated/numpy.random.randomstate.rayleigh#numpy.random.RandomState.rayleigh \"numpy.random.RandomState.rayleigh\")([scale, size]) | Draw samples from a Rayleigh distribution. |\n| [`standard_cauchy`](generated/numpy.random.randomstate.standard_cauchy#numpy.random.RandomState.standard_cauchy \"numpy.random.RandomState.standard_cauchy\")([size]) | Draw samples from a standard Cauchy distribution with mode = 0. |\n| [`standard_exponential`](generated/numpy.random.randomstate.standard_exponential#numpy.random.RandomState.standard_exponential \"numpy.random.RandomState.standard_exponential\")([size]) | Draw samples from the standard exponential distribution. |\n| [`standard_gamma`](generated/numpy.random.randomstate.standard_gamma#numpy.random.RandomState.standard_gamma \"numpy.random.RandomState.standard_gamma\")(shape[, size]) | Draw samples from a standard Gamma distribution. |\n| [`standard_normal`](generated/numpy.random.randomstate.standard_normal#numpy.random.RandomState.standard_normal \"numpy.random.RandomState.standard_normal\")([size]) | Draw samples from a standard Normal distribution (mean=0, stdev=1). |\n| [`standard_t`](generated/numpy.random.randomstate.standard_t#numpy.random.RandomState.standard_t \"numpy.random.RandomState.standard_t\")(df[, size]) | Draw samples from a standard Student's t distribution with `df` degrees of freedom. |\n| [`triangular`](generated/numpy.random.randomstate.triangular#numpy.random.RandomState.triangular \"numpy.random.RandomState.triangular\")(left, mode, right[, size]) | Draw samples from the triangular distribution over the interval `[left, right]`. |\n| [`uniform`](generated/numpy.random.randomstate.uniform#numpy.random.RandomState.uniform \"numpy.random.RandomState.uniform\")([low, high, size]) | Draw samples from a uniform distribution. |\n| [`vonmises`](generated/numpy.random.randomstate.vonmises#numpy.random.RandomState.vonmises \"numpy.random.RandomState.vonmises\")(mu, kappa[, size]) | Draw samples from a von Mises distribution. |\n| [`wald`](generated/numpy.random.randomstate.wald#numpy.random.RandomState.wald \"numpy.random.RandomState.wald\")(mean, scale[, size]) | Draw samples from a Wald, or inverse Gaussian, distribution. |\n| [`weibull`](generated/numpy.random.randomstate.weibull#numpy.random.RandomState.weibull \"numpy.random.RandomState.weibull\")(a[, size]) | Draw samples from a Weibull distribution. |\n| [`zipf`](generated/numpy.random.randomstate.zipf#numpy.random.RandomState.zipf \"numpy.random.RandomState.zipf\")(a[, size]) | Draw samples from a Zipf distribution. |\n\n Functions in numpy.random\n-------------------------\n\n Many of the RandomState methods above are exported as functions in [`numpy.random`](index#module-numpy.random \"numpy.random\") This usage is discouraged, as it is implemented via a global [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") instance which is not advised on two counts:\n\n * It uses global state, which means results will change as the code changes\n* It uses a [`RandomState`](#numpy.random.RandomState \"numpy.random.RandomState\") rather than the more modern [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\").\n\n For backward compatible legacy reasons, we cannot change this. See [Quick Start](index#random-quick-start).\n\n \n\n| | |\n| --- | --- |\n| [`beta`](generated/numpy.random.beta#numpy.random.beta \"numpy.random.beta\")(a, b[, size]) | Draw samples from a Beta distribution. |\n| [`binomial`](generated/numpy.random.binomial#numpy.random.binomial \"numpy.random.binomial\")(n, p[, size]) | Draw samples from a binomial distribution. |\n| [`bytes`](generated/numpy.random.bytes#numpy.random.bytes \"numpy.random.bytes\")(length) | Return random bytes. |\n| [`chisquare`](generated/numpy.random.chisquare#numpy.random.chisquare \"numpy.random.chisquare\")(df[, size]) | Draw samples from a chi-square distribution. |\n| [`choice`](generated/numpy.random.choice#numpy.random.choice \"numpy.random.choice\")(a[, size, replace, p]) | Generates a random sample from a given 1-D array |\n| [`dirichlet`](generated/numpy.random.dirichlet#numpy.random.dirichlet \"numpy.random.dirichlet\")(alpha[, size]) | Draw samples from the Dirichlet distribution. |\n| [`exponential`](generated/numpy.random.exponential#numpy.random.exponential \"numpy.random.exponential\")([scale, size]) | Draw samples from an exponential distribution. |\n| [`f`](generated/numpy.random.f#numpy.random.f \"numpy.random.f\")(dfnum, dfden[, size]) | Draw samples from an F distribution. |\n| [`gamma`](generated/numpy.random.gamma#numpy.random.gamma \"numpy.random.gamma\")(shape[, scale, size]) | Draw samples from a Gamma distribution. |\n| [`geometric`](generated/numpy.random.geometric#numpy.random.geometric \"numpy.random.geometric\")(p[, size]) | Draw samples from the geometric distribution. |\n| [`get_state`](generated/numpy.random.get_state#numpy.random.get_state \"numpy.random.get_state\")() | Return a tuple representing the internal state of the generator. |\n| [`gumbel`](generated/numpy.random.gumbel#numpy.random.gumbel \"numpy.random.gumbel\")([loc, scale, size]) | Draw samples from a Gumbel distribution. |\n| [`hypergeometric`](generated/numpy.random.hypergeometric#numpy.random.hypergeometric \"numpy.random.hypergeometric\")(ngood, nbad, nsample[, size]) | Draw samples from a Hypergeometric distribution. |\n| [`laplace`](generated/numpy.random.laplace#numpy.random.laplace \"numpy.random.laplace\")([loc, scale, size]) | Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). |\n| [`logistic`](generated/numpy.random.logistic#numpy.random.logistic \"numpy.random.logistic\")([loc, scale, size]) | Draw samples from a logistic distribution. |\n| [`lognormal`](generated/numpy.random.lognormal#numpy.random.lognormal \"numpy.random.lognormal\")([mean, sigma, size]) | Draw samples from a log-normal distribution. |\n| [`logseries`](generated/numpy.random.logseries#numpy.random.logseries \"numpy.random.logseries\")(p[, size]) | Draw samples from a logarithmic series distribution. |\n| [`multinomial`](generated/numpy.random.multinomial#numpy.random.multinomial \"numpy.random.multinomial\")(n, pvals[, size]) | Draw samples from a multinomial distribution. |\n| [`multivariate_normal`](generated/numpy.random.multivariate_normal#numpy.random.multivariate_normal \"numpy.random.multivariate_normal\")(mean, cov[, size, ...]) | Draw random samples from a multivariate normal distribution. |\n| [`negative_binomial`](generated/numpy.random.negative_binomial#numpy.random.negative_binomial \"numpy.random.negative_binomial\")(n, p[, size]) | Draw samples from a negative binomial distribution. |\n| [`noncentral_chisquare`](generated/numpy.random.noncentral_chisquare#numpy.random.noncentral_chisquare \"numpy.random.noncentral_chisquare\")(df, nonc[, size]) | Draw samples from a noncentral chi-square distribution. |\n| [`noncentral_f`](generated/numpy.random.noncentral_f#numpy.random.noncentral_f \"numpy.random.noncentral_f\")(dfnum, dfden, nonc[, size]) | Draw samples from the noncentral F distribution. |\n| [`normal`](generated/numpy.random.normal#numpy.random.normal \"numpy.random.normal\")([loc, scale, size]) | Draw random samples from a normal (Gaussian) distribution. |\n| [`pareto`](generated/numpy.random.pareto#numpy.random.pareto \"numpy.random.pareto\")(a[, size]) | Draw samples from a Pareto II or Lomax distribution with specified shape. |\n| [`permutation`](generated/numpy.random.permutation#numpy.random.permutation \"numpy.random.permutation\")(x) | Randomly permute a sequence, or return a permuted range. |\n| [`poisson`](generated/numpy.random.poisson#numpy.random.poisson \"numpy.random.poisson\")([lam, size]) | Draw samples from a Poisson distribution. |\n| [`power`](generated/numpy.random.power#numpy.random.power \"numpy.random.power\")(a[, size]) | Draws samples in [0, 1] from a power distribution with positive exponent a - 1. |\n| [`rand`](generated/numpy.random.rand#numpy.random.rand \"numpy.random.rand\")(d0, d1, ..., dn) | Random values in a given shape. |\n| [`randint`](generated/numpy.random.randint#numpy.random.randint \"numpy.random.randint\")(low[, high, size, dtype]) | Return random integers from `low` (inclusive) to `high` (exclusive). |\n| [`randn`](generated/numpy.random.randn#numpy.random.randn \"numpy.random.randn\")(d0, d1, ..., dn) | Return a sample (or samples) from the \"standard normal\" distribution. |\n| [`random`](generated/numpy.random.random#numpy.random.random \"numpy.random.random\")([size]) | Return random floats in the half-open interval [0.0, 1.0). |\n| [`random_integers`](generated/numpy.random.random_integers#numpy.random.random_integers \"numpy.random.random_integers\")(low[, high, size]) | Random integers of type `np.int_` between `low` and `high`, inclusive. |\n| [`random_sample`](generated/numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\")([size]) | Return random floats in the half-open interval [0.0, 1.0). |\n| [`ranf`](generated/numpy.random.ranf#numpy.random.ranf \"numpy.random.ranf\") | This is an alias of [`random_sample`](generated/numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\"). |\n| [`rayleigh`](generated/numpy.random.rayleigh#numpy.random.rayleigh \"numpy.random.rayleigh\")([scale, size]) | Draw samples from a Rayleigh distribution. |\n| [`sample`](generated/numpy.random.sample#numpy.random.sample \"numpy.random.sample\") | This is an alias of [`random_sample`](generated/numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\"). |\n| [`seed`](generated/numpy.random.seed#numpy.random.seed \"numpy.random.seed\")(self[, seed]) | Reseed a legacy MT19937 BitGenerator |\n| [`set_state`](generated/numpy.random.set_state#numpy.random.set_state \"numpy.random.set_state\")(state) | Set the internal state of the generator from a tuple. |\n| [`shuffle`](generated/numpy.random.shuffle#numpy.random.shuffle \"numpy.random.shuffle\")(x) | Modify a sequence in-place by shuffling its contents. |\n| [`standard_cauchy`](generated/numpy.random.standard_cauchy#numpy.random.standard_cauchy \"numpy.random.standard_cauchy\")([size]) | Draw samples from a standard Cauchy distribution with mode = 0. |\n| [`standard_exponential`](generated/numpy.random.standard_exponential#numpy.random.standard_exponential \"numpy.random.standard_exponential\")([size]) | Draw samples from the standard exponential distribution. |\n| [`standard_gamma`](generated/numpy.random.standard_gamma#numpy.random.standard_gamma \"numpy.random.standard_gamma\")(shape[, size]) | Draw samples from a standard Gamma distribution. |\n| [`standard_normal`](generated/numpy.random.standard_normal#numpy.random.standard_normal \"numpy.random.standard_normal\")([size]) | Draw samples from a standard Normal distribution (mean=0, stdev=1). |\n| [`standard_t`](generated/numpy.random.standard_t#numpy.random.standard_t \"numpy.random.standard_t\")(df[, size]) | Draw samples from a standard Student's t distribution with `df` degrees of freedom. |\n| [`triangular`](generated/numpy.random.triangular#numpy.random.triangular \"numpy.random.triangular\")(left, mode, right[, size]) | Draw samples from the triangular distribution over the interval `[left, right]`. |\n| [`uniform`](generated/numpy.random.uniform#numpy.random.uniform \"numpy.random.uniform\")([low, high, size]) | Draw samples from a uniform distribution. |\n| [`vonmises`](generated/numpy.random.vonmises#numpy.random.vonmises \"numpy.random.vonmises\")(mu, kappa[, size]) | Draw samples from a von Mises distribution. |\n| [`wald`](generated/numpy.random.wald#numpy.random.wald \"numpy.random.wald\")(mean, scale[, size]) | Draw samples from a Wald, or inverse Gaussian, distribution. |\n| [`weibull`](generated/numpy.random.weibull#numpy.random.weibull \"numpy.random.weibull\")(a[, size]) | Draw samples from a Weibull distribution. |\n| [`zipf`](generated/numpy.random.zipf#numpy.random.zipf \"numpy.random.zipf\")(a[, size]) | Draw samples from a Zipf distribution. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/legacy.htmlBit Generators\n==============\n\n The random values produced by [`Generator`](../generator#numpy.random.Generator \"numpy.random.Generator\") originate in a BitGenerator. The BitGenerators do not directly provide random numbers and only contains methods used for seeding, getting or setting the state, jumping or advancing the state, and for accessing low-level wrappers for consumption by code that can efficiently access the functions provided, e.g., [numba](https://numba.pydata.org).\n\n Supported BitGenerators\n-----------------------\n\n The included BitGenerators are:\n\n * PCG-64 - The default. A fast generator that can be advanced by an arbitrary amount. See the documentation for [`advance`](generated/numpy.random.pcg64.advance#numpy.random.PCG64.advance \"numpy.random.PCG64.advance\"). PCG-64 has a period of \\(2^{128}\\). See the [PCG author’s page](http://www.pcg-random.org/) for more details about this class of PRNG.\n* PCG-64 DXSM - An upgraded version of PCG-64 with better statistical properties in parallel contexts. See [Upgrading PCG64 with PCG64DXSM](../upgrading-pcg64#upgrading-pcg64) for more information on these improvements.\n* MT19937 - The standard Python BitGenerator. Adds a [`MT19937.jumped`](generated/numpy.random.mt19937.jumped#numpy.random.MT19937.jumped \"numpy.random.MT19937.jumped\") function that returns a new generator with state as-if \\(2^{128}\\) draws have been made.\n* Philox - A counter-based generator capable of being advanced an arbitrary number of steps or generating independent streams. See the [Random123](https://www.deshawresearch.com/resources_random123.html) page for more details about this class of bit generators.\n* SFC64 - A fast generator based on random invertible mappings. Usually the fastest generator of the four. See the [SFC author’s page](http://pracrand.sourceforge.net/RNG_engines.txt) for (a little) more detail.\n\n \n\n| | |\n| --- | --- |\n| [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\")([seed]) | Base Class for generic BitGenerators, which provide a stream of random bits based on different algorithms. |\n\n * [MT19937](mt19937)\n* [PCG64](pcg64)\n* [PCG64DXSM](pcg64dxsm)\n* [Philox](philox)\n* [SFC64](sfc64)\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/index.htmlUpgrading PCG64 with PCG64DXSM\n==============================\n\n Uses of the [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") in a massively-parallel context have been shown to have statistical weaknesses that were not apparent at the first release in numpy 1.17. Most users will never observe this weakness and are safe to continue to use [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\"). We have introduced a new [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") that will eventually become the new default [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") implementation used by [`default_rng`](generator#numpy.random.default_rng \"numpy.random.default_rng\") in future releases. [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") solves the statistical weakness while preserving the performance and the features of [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\").\n\n Does this affect me?\n--------------------\n\n If you\n\n 1. only use a single [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\") instance,\n2. only use [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\") or the functions in [`numpy.random`](index#module-numpy.random \"numpy.random\"),\n3. only use the [`PCG64.jumped`](bit_generators/generated/numpy.random.pcg64.jumped#numpy.random.PCG64.jumped \"numpy.random.PCG64.jumped\") method to generate parallel streams,\n4. explicitly use a [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") other than [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\"),\n\n then this weakness does not affect you at all. Carry on.\n\n If you use moderate numbers of parallel streams created with [`default_rng`](generator#numpy.random.default_rng \"numpy.random.default_rng\") or [`SeedSequence.spawn`](bit_generators/generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\"), in the 1000s, then the chance of observing this weakness is negligibly small. You can continue to use [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") comfortably.\n\n If you use very large numbers of parallel streams, in the millions, and draw large amounts of numbers from each, then the chance of observing this weakness can become non-negligible, if still small. An example of such a use case would be a very large distributed reinforcement learning problem with millions of long Monte Carlo playouts each generating billions of random number draws. Such use cases should consider using [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") explicitly or another modern [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") like [`SFC64`](bit_generators/sfc64#numpy.random.SFC64 \"numpy.random.SFC64\") or [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\"), but it is unlikely that any old results you may have calculated are invalid. In any case, the weakness is a kind of [Birthday Paradox](https://en.wikipedia.org/wiki/Birthday_problem) collision. That is, a single pair of parallel streams out of the millions, considered together, might fail a stringent set of statistical tests of randomness. The remaining millions of streams would all be perfectly fine, and the effect of the bad pair in the whole calculation is very likely to be swamped by the remaining streams in most applications.\n\n Technical Details\n-----------------\n\n Like many PRNG algorithms, [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") is constructed from a transition function, which advances a 128-bit state, and an output function, that mixes the 128-bit state into a 64-bit integer to be output. One of the guiding design principles of the PCG family of PRNGs is to balance the computational cost (and pseudorandomness strength) between the transition function and the output function. The transition function is a 128-bit linear congruential generator (LCG), which consists of multiplying the 128-bit state with a fixed multiplication constant and then adding a user-chosen increment, in 128-bit modular arithmetic. LCGs are well-analyzed PRNGs with known weaknesses, though 128-bit LCGs are large enough to pass stringent statistical tests on their own, with only the trivial output function. The output function of [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") is intended to patch up some of those known weaknesses by doing “just enough” scrambling of the bits to assist in the statistical properties without adding too much computational cost.\n\n One of these known weaknesses is that advancing the state of the LCG by steps numbering a power of two (`bg.advance(2**N)`) will leave the lower `N` bits identical to the state that was just left. For a single stream drawn from sequentially, this is of little consequence. The remaining \\(128-N\\) bits provide plenty of pseudorandomness that will be mixed in for any practical `N` that can be observed in a single stream, which is why one does not need to worry about this if you only use a single stream in your application. Similarly, the [`PCG64.jumped`](bit_generators/generated/numpy.random.pcg64.jumped#numpy.random.PCG64.jumped \"numpy.random.PCG64.jumped\") method uses a carefully chosen number of steps to avoid creating these collisions. However, once you start creating “randomly-initialized” parallel streams, either using OS entropy by calling [`default_rng`](generator#numpy.random.default_rng \"numpy.random.default_rng\") repeatedly or using [`SeedSequence.spawn`](bit_generators/generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\"), then we need to consider how many lower bits need to “collide” in order to create a bad pair of streams, and then evaluate the probability of creating such a collision. [Empirically](https://github.com/numpy/numpy/issues/16313), it has been determined that if one shares the lower 58 bits of state and shares an increment, then the pair of streams, when interleaved, will fail [PractRand](http://pracrand.sourceforge.net/) in a reasonable amount of time, after drawing a few gigabytes of data. Following the standard Birthday Paradox calculations for a collision of 58 bits, we can see that we can create \\(2^{29}\\), or about half a billion, streams which is when the probability of such a collision becomes high. Half a billion streams is quite high, and the amount of data each stream needs to draw before the statistical correlations become apparent to even the strict `PractRand` tests is in the gigabytes. But this is on the horizon for very large applications like distributed reinforcement learning. There are reasons to expect that even in these applications a collision probably will not have a practical effect in the total result, since the statistical problem is constrained to just the colliding pair.\n\n Now, let us consider the case when the increment is not constrained to be the same. Our implementation of [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") seeds both the state and the increment; that is, two calls to [`default_rng`](generator#numpy.random.default_rng \"numpy.random.default_rng\") (almost certainly) have different states and increments. Upon our first release, we believed that having the seeded increment would provide a certain amount of extra protection, that one would have to be “close” in both the state space and increment space in order to observe correlations (`PractRand` failures) in a pair of streams. If that were true, then the “bottleneck” for collisions would be the 128-bit entropy pool size inside of [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") (and 128-bit collisions are in the “preposterously unlikely” category). Unfortunately, this is not true.\n\n One of the known properties of an LCG is that different increments create *distinct* streams, but with a known relationship. Each LCG has an orbit that traverses all \\(2^{128}\\) different 128-bit states. Two LCGs with different increments are related in that one can “rotate” the orbit of the first LCG (advance it by a number of steps that we can compute from the two increments) such that then both LCGs will always then have the same state, up to an additive constant and maybe an inversion of the bits. If you then iterate both streams in lockstep, then the states will *always* remain related by that same additive constant (and the inversion, if present). Recall that [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") is constructed from both a transition function (the LCG) and an output function. It was expected that the scrambling effect of the output function would have been strong enough to make the distinct streams practically independent (i.e. “passing the `PractRand` tests”) unless the two increments were pathologically related to each other (e.g. 1 and 3). The output function XSL-RR of the then-standard PCG algorithm that we implemented in [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") turns out to be too weak to cover up for the 58-bit collision of the underlying LCG that we described above. For any given pair of increments, the size of the “colliding” space of states is the same, so for this weakness, the extra distinctness provided by the increments does not translate into extra protection from statistical correlations that `PractRand` can detect.\n\n Fortunately, strengthening the output function is able to correct this weakness and *does* turn the extra distinctness provided by differing increments into additional protection from these low-bit collisions. To the [PCG author’s credit](https://github.com/numpy/numpy/issues/13635#issuecomment-506088698), she had developed a stronger output function in response to related discussions during the long birth of the new [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") system. We NumPy developers chose to be “conservative” and use the XSL-RR variant that had undergone a longer period of testing at that time. The DXSM output function adopts a “xorshift-multiply” construction used in strong integer hashes that has much better avalanche properties than the XSL-RR output function. While there are “pathological” pairs of increments that induce “bad” additive constants that relate the two streams, the vast majority of pairs induce “good” additive constants that make the merely-distinct streams of LCG states into practically-independent output streams. Indeed, now the claim we once made about [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") is actually true of [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\"): collisions are possible, but both streams have to simultaneously be both “close” in the 128 bit state space *and* “close” in the 127-bit increment space, so that would be less likely than the negligible chance of colliding in the 128-bit internal [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") pool. The DXSM output function is more computationally intensive than XSL-RR, but some optimizations in the LCG more than make up for the performance hit on most machines, so [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") is a good, safe upgrade. There are, of course, an infinite number of stronger output functions that one could consider, but most will have a greater computational cost, and the DXSM output function has now received many CPU cycles of testing via `PractRand` at this time.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/upgrading-pcg64.htmlParallel Random Number Generation\n=================================\n\n There are three strategies implemented that can be used to produce repeatable pseudo-random numbers across multiple processes (local or distributed).\n\n SeedSequence spawning\n---------------------\n\n [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") [implements an algorithm](http://www.pcg-random.org/posts/developing-a-seed_seq-alternative.html) to process a user-provided seed, typically as an integer of some size, and to convert it into an initial state for a [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). It uses hashing techniques to ensure that low-quality seeds are turned into high quality initial states (at least, with very high probability).\n\n For example, [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") has a state consisting of 624 `uint32` integers. A naive way to take a 32-bit integer seed would be to just set the last element of the state to the 32-bit seed and leave the rest 0s. This is a valid state for [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\"), but not a good one. The Mersenne Twister algorithm [suffers if there are too many 0s](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html). Similarly, two adjacent 32-bit integer seeds (i.e. `12345` and `12346`) would produce very similar streams.\n\n [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") avoids these problems by using successions of integer hashes with good [avalanche properties](https://en.wikipedia.org/wiki/Avalanche_effect) to ensure that flipping any bit in the input has about a 50% chance of flipping any bit in the output. Two input seeds that are very close to each other will produce initial states that are very far from each other (with very high probability). It is also constructed in such a way that you can provide arbitrary-sized integers or lists of integers. [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") will take all of the bits that you provide and mix them together to produce however many bits the consuming [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") needs to initialize itself.\n\n These properties together mean that we can safely mix together the usual user-provided seed with simple incrementing counters to get [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") states that are (to very high probability) independent of each other. We can wrap this together into an API that is easy to use and difficult to misuse.\n\n \n```\nfrom numpy.random import SeedSequence, default_rng\n\nss = SeedSequence(12345)\n\n# Spawn off 10 child SeedSequences to pass to child processes.\nchild_seeds = ss.spawn(10)\nstreams = [default_rng(s) for s in child_seeds]\n\n```\n Child [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") objects can also spawn to make grandchildren, and so on. Each [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") has its position in the tree of spawned [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") objects mixed in with the user-provided seed to generate independent (with very high probability) streams.\n\n \n```\ngrandchildren = child_seeds[0].spawn(4)\ngrand_streams = [default_rng(s) for s in grandchildren]\n\n```\n This feature lets you make local decisions about when and how to split up streams without coordination between processes. You do not have to preallocate space to avoid overlapping or request streams from a common global service. This general “tree-hashing” scheme is [not unique to numpy](https://www.iro.umontreal.ca/~lecuyer/myftp/papers/parallel-rng-imacs.pdf) but not yet widespread. Python has increasingly-flexible mechanisms for parallelization available, and this scheme fits in very well with that kind of use.\n\n Using this scheme, an upper bound on the probability of a collision can be estimated if one knows the number of streams that you derive. [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") hashes its inputs, both the seed and the spawn-tree-path, down to a 128-bit pool by default. The probability that there is a collision in that pool, pessimistically-estimated ([1](#id3)), will be about \\(n^2*2^{-128}\\) where `n` is the number of streams spawned. If a program uses an aggressive million streams, about \\(2^{20}\\), then the probability that at least one pair of them are identical is about \\(2^{-88}\\), which is in solidly-ignorable territory ([2](#id4)).\n\n [1](#id1) \nThe algorithm is carefully designed to eliminate a number of possible ways to collide. For example, if one only does one level of spawning, it is guaranteed that all states will be unique. But it’s easier to estimate the naive upper bound on a napkin and take comfort knowing that the probability is actually lower.\n\n [2](#id2) \nIn this calculation, we can mostly ignore the amount of numbers drawn from each stream. See [Upgrading PCG64 with PCG64DXSM](upgrading-pcg64#upgrading-pcg64) for the technical details about [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\"). The other PRNGs we provide have some extra protection built in that avoids overlaps if the [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") pools differ in the slightest bit. [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") has \\(2^{127}\\) separate cycles determined by the seed in addition to the position in the \\(2^{128}\\) long period for each cycle, so one has to both get on or near the same cycle *and* seed a nearby position in the cycle. [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\") has completely independent cycles determined by the seed. [`SFC64`](bit_generators/sfc64#numpy.random.SFC64 \"numpy.random.SFC64\") incorporates a 64-bit counter so every unique seed is at least \\(2^{64}\\) iterations away from any other seed. And finally, [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") has just an unimaginably huge period. Getting a collision internal to [`SeedSequence`](bit_generators/generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") is the way a failure would be observed.\n\n Independent Streams\n-------------------\n\n [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\") is a counter-based RNG based which generates values by encrypting an incrementing counter using weak cryptographic primitives. The seed determines the key that is used for the encryption. Unique keys create unique, independent streams. [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\") lets you bypass the seeding algorithm to directly set the 128-bit key. Similar, but different, keys will still create independent streams.\n\n \n```\nimport secrets\nfrom numpy.random import Philox\n\n# 128-bit number as a seed\nroot_seed = secrets.getrandbits(128)\nstreams = [Philox(key=root_seed + stream_id) for stream_id in range(10)]\n\n```\n This scheme does require that you avoid reusing stream IDs. This may require coordination between the parallel processes.\n\n Jumping the BitGenerator state\n------------------------------\n\n `jumped` advances the state of the BitGenerator *as-if* a large number of random numbers have been drawn, and returns a new instance with this state. The specific number of draws varies by BitGenerator, and ranges from \\(2^{64}\\) to \\(2^{128}\\). Additionally, the *as-if* draws also depend on the size of the default random number produced by the specific BitGenerator. The BitGenerators that support `jumped`, along with the period of the BitGenerator, the size of the jump and the bits in the default unsigned random are listed below.\n\n \n\n| BitGenerator | Period | Jump Size | Bits per Draw |\n| --- | --- | --- | --- |\n| MT19937 | \\(2^{19937}-1\\) | \\(2^{128}\\) | 32 |\n| PCG64 | \\(2^{128}\\) | \\(~2^{127}\\) ([3](#id8)) | 64 |\n| PCG64DXSM | \\(2^{128}\\) | \\(~2^{127}\\) ([3](#id8)) | 64 |\n| Philox | \\(2^{256}\\) | \\(2^{128}\\) | 64 |\n\n \n3([1](#id6),[2](#id7))\n \nThe jump size is \\((\\phi-1)*2^{128}\\) where \\(\\phi\\) is the golden ratio. As the jumps wrap around the period, the actual distances between neighboring streams will slowly grow smaller than the jump size, but using the golden ratio this way is a classic method of constructing a low-discrepancy sequence that spreads out the states around the period optimally. You will not be able to jump enough to make those distances small enough to overlap in your lifetime.\n\n `jumped` can be used to produce long blocks which should be long enough to not overlap.\n\n \n```\nimport secrets\nfrom numpy.random import PCG64\n\nseed = secrets.getrandbits(128)\nblocked_rng = []\nrng = PCG64(seed)\nfor i in range(10):\n blocked_rng.append(rng.jumped(i))\n\n```\n When using `jumped`, one does have to take care not to jump to a stream that was already used. In the above example, one could not later use `blocked_rng[0].jumped()` as it would overlap with `blocked_rng[1]`. Like with the independent streams, if the main process here wants to split off 10 more streams by jumping, then it needs to start with `range(10, 20)`, otherwise it would recreate the same streams. On the other hand, if you carefully construct the streams, then you are guaranteed to have streams that do not overlap.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/parallel.htmlMultithreaded Generation\n========================\n\n The four core distributions ([`random`](generated/numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\"), [`standard_normal`](generated/numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\"), [`standard_exponential`](generated/numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\"), and [`standard_gamma`](generated/numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\")) all allow existing arrays to be filled using the `out` keyword argument. Existing arrays need to be contiguous and well-behaved (writable and aligned). Under normal circumstances, arrays created using the common constructors such as [`numpy.empty`](../generated/numpy.empty#numpy.empty \"numpy.empty\") will satisfy these requirements.\n\n This example makes use of Python 3 [`concurrent.futures`](https://docs.python.org/3/library/concurrent.futures.html#module-concurrent.futures \"(in Python v3.10)\") to fill an array using multiple threads. Threads are long-lived so that repeated calls do not require any additional overheads from thread creation.\n\n The random numbers generated are reproducible in the sense that the same seed will produce the same outputs, given that the number of threads does not change.\n\n \n```\nfrom numpy.random import default_rng, SeedSequence\nimport multiprocessing\nimport concurrent.futures\nimport numpy as np\n\nclass MultithreadedRNG:\n def __init__(self, n, seed=None, threads=None):\n if threads is None:\n threads = multiprocessing.cpu_count()\n self.threads = threads\n\n seq = SeedSequence(seed)\n self._random_generators = [default_rng(s)\n for s in seq.spawn(threads)]\n\n self.n = n\n self.executor = concurrent.futures.ThreadPoolExecutor(threads)\n self.values = np.empty(n)\n self.step = np.ceil(n / threads).astype(np.int_)\n\n def fill(self):\n def _fill(random_state, out, first, last):\n random_state.standard_normal(out=out[first:last])\n\n futures = {}\n for i in range(self.threads):\n args = (_fill,\n self._random_generators[i],\n self.values,\n i * self.step,\n (i + 1) * self.step)\n futures[self.executor.submit(*args)] = i\n concurrent.futures.wait(futures)\n\n def __del__(self):\n self.executor.shutdown(False)\n\n```\n The multithreaded random number generator can be used to fill an array. The `values` attributes shows the zero-value before the fill and the random value after.\n\n \n```\nIn [2]: mrng = MultithreadedRNG(10000000, seed=12345)\n ...: print(mrng.values[-1])\nOut[2]: 0.0\n\nIn [3]: mrng.fill()\n ...: print(mrng.values[-1])\nOut[3]: 2.4545724517479104\n\n```\n The time required to produce using multiple threads can be compared to the time required to generate using a single thread.\n\n \n```\nIn [4]: print(mrng.threads)\n ...: %timeit mrng.fill()\n\nOut[4]: 4\n ...: 32.8 ms ± 2.71 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n\n```\n The single threaded call directly uses the BitGenerator.\n\n \n```\nIn [5]: values = np.empty(10000000)\n ...: rg = default_rng()\n ...: %timeit rg.standard_normal(out=values)\n\nOut[5]: 99.6 ms ± 222 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n\n```\n The gains are substantial and the scaling is reasonable even for arrays that are only moderately large. The gains are even larger when compared to a call that does not use an existing array due to array creation overhead.\n\n \n```\nIn [6]: rg = default_rng()\n ...: %timeit rg.standard_normal(10000000)\n\nOut[6]: 125 ms ± 309 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n\n```\n Note that if `threads` is not set by the user, it will be determined by `multiprocessing.cpu_count()`.\n\n \n```\nIn [7]: # simulate the behavior for `threads=None`, if the machine had only one thread\n ...: mrng = MultithreadedRNG(10000000, seed=12345, threads=1)\n ...: print(mrng.values[-1])\nOut[7]: 1.1800150052158556\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/multithreading.htmlWhat’s New or Different\n=======================\n\n Warning\n\n The Box-Muller method used to produce NumPy’s normals is no longer available in [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\"). It is not possible to reproduce the exact random values using `Generator` for the normal distribution or any other distribution that relies on the normal such as the [`Generator.gamma`](generated/numpy.random.generator.gamma#numpy.random.Generator.gamma \"numpy.random.Generator.gamma\") or [`Generator.standard_t`](generated/numpy.random.generator.standard_t#numpy.random.Generator.standard_t \"numpy.random.Generator.standard_t\"). If you require bitwise backward compatible streams, use [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\"), i.e., [`RandomState.gamma`](generated/numpy.random.randomstate.gamma#numpy.random.RandomState.gamma \"numpy.random.RandomState.gamma\") or [`RandomState.standard_t`](generated/numpy.random.randomstate.standard_t#numpy.random.RandomState.standard_t \"numpy.random.RandomState.standard_t\").\n\n Quick comparison of legacy [mtrand](legacy#legacy) to the new [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\")\n\n \n\n| | | |\n| --- | --- | --- |\n| Feature | Older Equivalent | Notes |\n| [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\") | [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\") | `Generator` requires a stream source, called a [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") A number of these are provided. `RandomState` uses the Mersenne Twister [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") by default, but can also be instantiated with any BitGenerator. |\n| `random` | `random_sample`, `rand` | Access the values in a BitGenerator, convert them to `float64` in the interval `[0.0.,` `` 1.0)``. In addition to the `size` kwarg, now supports `dtype='d'` or `dtype='f'`, and an `out` kwarg to fill a user- supplied array. Many other distributions are also supported. |\n| `integers` | `randint`, `random_integers` | Use the `endpoint` kwarg to adjust the inclusion or exclusion of the `high` interval endpoint |\n\n And in more detail:\n\n * Simulate from the complex normal distribution (`complex_normal`)\n* The normal, exponential and gamma generators use 256-step Ziggurat methods which are 2-10 times faster than NumPy’s default implementation in [`standard_normal`](generated/numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\"), [`standard_exponential`](generated/numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\") or [`standard_gamma`](generated/numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\").\n\n \n```\nIn [1]: from numpy.random import Generator, PCG64\n\nIn [2]: import numpy.random\n\nIn [3]: rng = Generator(PCG64())\n\nIn [4]: %timeit -n 1 rng.standard_normal(100000)\n ...: %timeit -n 1 numpy.random.standard_normal(100000)\n ...: \n1.11 ms +- 23.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n1.97 ms +- 23.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n\n```\n \n```\nIn [5]: %timeit -n 1 rng.standard_exponential(100000)\n ...: %timeit -n 1 numpy.random.standard_exponential(100000)\n ...: \n603 us +- 11.4 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n1.45 ms +- 15.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n\n```\n \n```\nIn [6]: %timeit -n 1 rng.standard_gamma(3.0, 100000)\n ...: %timeit -n 1 numpy.random.standard_gamma(3.0, 100000)\n ...: \n2.16 ms +- 22.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n4.07 ms +- 15.4 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n\n```\n * [`integers`](generated/numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\") is now the canonical way to generate integer random numbers from a discrete uniform distribution. The `rand` and `randn` methods are only available through the legacy [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\"). This replaces both `randint` and the deprecated `random_integers`.\n* The Box-Muller method used to produce NumPy’s normals is no longer available.\n* All bit generators can produce doubles, uint64s and uint32s via CTypes ([`ctypes`](bit_generators/generated/numpy.random.pcg64.ctypes#numpy.random.PCG64.ctypes \"numpy.random.PCG64.ctypes\")) and CFFI ([`cffi`](bit_generators/generated/numpy.random.pcg64.cffi#numpy.random.PCG64.cffi \"numpy.random.PCG64.cffi\")). This allows these bit generators to be used in numba.\n* The bit generators can be used in downstream projects via Cython.\n* Optional `dtype` argument that accepts `np.float32` or `np.float64` to produce either single or double precision uniform random variables for select distributions\n\n\t+ Uniforms ([`random`](generated/numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\") and [`integers`](generated/numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\"))\n\t+ Normals ([`standard_normal`](generated/numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\"))\n\t+ Standard Gammas ([`standard_gamma`](generated/numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\"))\n\t+ Standard Exponentials ([`standard_exponential`](generated/numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\"))\n\n \n```\nIn [7]: rng = Generator(PCG64(0))\n\nIn [8]: rng.random(3, dtype='d')\nOut[8]: array([0.63696169, 0.26978671, 0.04097352])\n\nIn [9]: rng.random(3, dtype='f')\nOut[9]: array([0.07524014, 0.01652759, 0.17526728], dtype=float32)\n\n```\n * Optional `out` argument that allows existing arrays to be filled for select distributions\n\n\t+ Uniforms ([`random`](generated/numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\"))\n\t+ Normals ([`standard_normal`](generated/numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\"))\n\t+ Standard Gammas ([`standard_gamma`](generated/numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\"))\n\t+ Standard Exponentials ([`standard_exponential`](generated/numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\"))This allows multithreading to fill large arrays in chunks using suitable BitGenerators in parallel.\n\n \n```\nIn [10]: existing = np.zeros(4)\n\nIn [11]: rng.random(out=existing[:2])\nOut[11]: array([0.91275558, 0.60663578])\n\nIn [12]: print(existing)\n[0.91275558 0.60663578 0. 0. ]\n\n```\n * Optional `axis` argument for methods like [`choice`](generated/numpy.random.generator.choice#numpy.random.Generator.choice \"numpy.random.Generator.choice\"), [`permutation`](generated/numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\") and [`shuffle`](generated/numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\") that controls which axis an operation is performed over for multi-dimensional arrays.\n\n \n```\nIn [13]: rng = Generator(PCG64(123456789))\n\nIn [14]: a = np.arange(12).reshape((3, 4))\n\nIn [15]: a\nOut[15]: \narray([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n\nIn [16]: rng.choice(a, axis=1, size=5)\nOut[16]: \narray([[ 3, 0, 2, 3, 1],\n [ 7, 4, 6, 7, 5],\n [11, 8, 10, 11, 9]])\n\nIn [17]: rng.shuffle(a, axis=1) # Shuffle in-place\n\nIn [18]: a\nOut[18]: \narray([[ 3, 1, 2, 0],\n [ 7, 5, 6, 4],\n [11, 9, 10, 8]])\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/new-or-different.htmlPerformance\n===========\n\n Recommendation\n--------------\n\n The recommended generator for general use is [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") or its upgraded variant [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\") for heavily-parallel use cases. They are statistically high quality, full-featured, and fast on most platforms, but somewhat slow when compiled for 32-bit processes. See [Upgrading PCG64 with PCG64DXSM](upgrading-pcg64#upgrading-pcg64) for details on when heavy parallelism would indicate using [`PCG64DXSM`](bit_generators/pcg64dxsm#numpy.random.PCG64DXSM \"numpy.random.PCG64DXSM\").\n\n [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\") is fairly slow, but its statistical properties have very high quality, and it is easy to get an assuredly-independent stream by using unique keys. If that is the style you wish to use for parallel streams, or you are porting from another system that uses that style, then [`Philox`](bit_generators/philox#numpy.random.Philox \"numpy.random.Philox\") is your choice.\n\n [`SFC64`](bit_generators/sfc64#numpy.random.SFC64 \"numpy.random.SFC64\") is statistically high quality and very fast. However, it lacks jumpability. If you are not using that capability and want lots of speed, even on 32-bit processes, this is your choice.\n\n [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") [fails some statistical tests](https://www.iro.umontreal.ca/~lecuyer/myftp/papers/testu01.pdf) and is not especially fast compared to modern PRNGs. For these reasons, we mostly do not recommend using it on its own, only through the legacy [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\") for reproducing old results. That said, it has a very long history as a default in many systems.\n\n Timings\n-------\n\n The timings below are the time in ns to produce 1 random value from a specific distribution. The original [`MT19937`](bit_generators/mt19937#numpy.random.MT19937 \"numpy.random.MT19937\") generator is much slower since it requires 2 32-bit values to equal the output of the faster generators.\n\n Integer performance has a similar ordering.\n\n The pattern is similar for other, more complex generators. The normal performance of the legacy [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\") generator is much lower than the other since it uses the Box-Muller transform rather than the Ziggurat method. The performance gap for Exponentials is also large due to the cost of computing the log function to invert the CDF. The column labeled MT19973 uses the same 32-bit generator as [`RandomState`](legacy#numpy.random.RandomState \"numpy.random.RandomState\") but produces random variates using [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\").\n\n \n\n| | MT19937 | PCG64 | PCG64DXSM | Philox | SFC64 | RandomState |\n| --- | --- | --- | --- | --- | --- | --- |\n| 32-bit Unsigned Ints | 3.3 | 1.9 | 2.0 | 3.3 | 1.8 | 3.1 |\n| 64-bit Unsigned Ints | 5.6 | 3.2 | 2.9 | 4.9 | 2.5 | 5.5 |\n| Uniforms | 5.9 | 3.1 | 2.9 | 5.0 | 2.6 | 6.0 |\n| Normals | 13.9 | 10.8 | 10.5 | 12.0 | 8.3 | 56.8 |\n| Exponentials | 9.1 | 6.0 | 5.8 | 8.1 | 5.4 | 63.9 |\n| Gammas | 37.2 | 30.8 | 28.9 | 34.0 | 27.5 | 77.0 |\n| Binomials | 21.3 | 17.4 | 17.6 | 19.3 | 15.6 | 21.4 |\n| Laplaces | 73.2 | 72.3 | 76.1 | 73.0 | 72.3 | 82.5 |\n| Poissons | 111.7 | 103.4 | 100.5 | 109.4 | 90.7 | 115.2 |\n\n The next table presents the performance in percentage relative to values generated by the legacy generator, `RandomState(MT19937())`. The overall performance was computed using a geometric mean.\n\n \n\n| | MT19937 | PCG64 | PCG64DXSM | Philox | SFC64 |\n| --- | --- | --- | --- | --- | --- |\n| 32-bit Unsigned Ints | 96 | 162 | 160 | 96 | 175 |\n| 64-bit Unsigned Ints | 97 | 171 | 188 | 113 | 218 |\n| Uniforms | 102 | 192 | 206 | 121 | 233 |\n| Normals | 409 | 526 | 541 | 471 | 684 |\n| Exponentials | 701 | 1071 | 1101 | 784 | 1179 |\n| Gammas | 207 | 250 | 266 | 227 | 281 |\n| Binomials | 100 | 123 | 122 | 111 | 138 |\n| Laplaces | 113 | 114 | 108 | 113 | 114 |\n| Poissons | 103 | 111 | 115 | 105 | 127 |\n| Overall | 159 | 219 | 225 | 174 | 251 |\n\n Note\n\n All timings were taken using Linux on an AMD Ryzen 9 3900X processor.\n\n Performance on different Operating Systems\n------------------------------------------\n\n Performance differs across platforms due to compiler and hardware availability (e.g., register width) differences. The default bit generator has been chosen to perform well on 64-bit platforms. Performance on 32-bit operating systems is very different.\n\n The values reported are normalized relative to the speed of MT19937 in each table. A value of 100 indicates that the performance matches the MT19937. Higher values indicate improved performance. These values cannot be compared across tables.\n\n ### 64-bit Linux\n\n \n\n| Distribution | MT19937 | PCG64 | PCG64DXSM | Philox | SFC64 |\n| --- | --- | --- | --- | --- | --- |\n| 32-bit Unsigned Ints | 100 | 168 | 166 | 100 | 182 |\n| 64-bit Unsigned Ints | 100 | 176 | 193 | 116 | 224 |\n| Uniforms | 100 | 188 | 202 | 118 | 228 |\n| Normals | 100 | 128 | 132 | 115 | 167 |\n| Exponentials | 100 | 152 | 157 | 111 | 168 |\n| Overall | 100 | 161 | 168 | 112 | 192 |\n\n ### 64-bit Windows\n\n The relative performance on 64-bit Linux and 64-bit Windows is broadly similar with the notable exception of the Philox generator.\n\n \n\n| Distribution | MT19937 | PCG64 | PCG64DXSM | Philox | SFC64 |\n| --- | --- | --- | --- | --- | --- |\n| 32-bit Unsigned Ints | 100 | 155 | 131 | 29 | 150 |\n| 64-bit Unsigned Ints | 100 | 157 | 143 | 25 | 154 |\n| Uniforms | 100 | 151 | 144 | 24 | 155 |\n| Normals | 100 | 129 | 128 | 37 | 150 |\n| Exponentials | 100 | 150 | 145 | 28 | 159 |\n| **Overall** | 100 | 148 | 138 | 28 | 154 |\n\n ### 32-bit Windows\n\n The performance of 64-bit generators on 32-bit Windows is much lower than on 64-bit operating systems due to register width. MT19937, the generator that has been in NumPy since 2005, operates on 32-bit integers.\n\n \n\n| Distribution | MT19937 | PCG64 | PCG64DXSM | Philox | SFC64 |\n| --- | --- | --- | --- | --- | --- |\n| 32-bit Unsigned Ints | 100 | 24 | 34 | 14 | 57 |\n| 64-bit Unsigned Ints | 100 | 21 | 32 | 14 | 74 |\n| Uniforms | 100 | 21 | 34 | 16 | 73 |\n| Normals | 100 | 36 | 57 | 28 | 101 |\n| Exponentials | 100 | 28 | 44 | 20 | 88 |\n| **Overall** | 100 | 25 | 39 | 18 | 77 |\n\n Note\n\n Linux timings used Ubuntu 20.04 and GCC 9.3.0. Windows timings were made on Windows 10 using Microsoft C/C++ Optimizing Compiler Version 19 (Visual Studio 2019). All timings were produced on an AMD Ryzen 9 3900X processor.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/performance.htmlC API for random\n================\n\n New in version 1.19.0.\n\n Access to various distributions below is available via Cython or C-wrapper libraries like CFFI. All the functions accept a [`bitgen_t`](#c.bitgen_t \"bitgen_t\") as their first argument. To access these from Cython or C, you must link with the `npyrandom` library which is part of the NumPy distribution, located in `numpy/random/lib`.\n\n typebitgen_t \n\n \nThe [`bitgen_t`](#c.bitgen_t \"bitgen_t\") holds the current state of the BitGenerator and pointers to functions that return standard C types while advancing the state.\n\n \n```\nstruct bitgen:\n void *state\n npy_uint64 (*next_uint64)(void *st) nogil\n uint32_t (*next_uint32)(void *st) nogil\n double (*next_double)(void *st) nogil\n npy_uint64 (*next_raw)(void *st) nogil\n\nctypedef bitgen bitgen_t\n\n```\n \n See [Extending](extending) for examples of using these functions.\n\n The functions are named with the following conventions:\n\n * “standard” refers to the reference values for any parameters. For instance “standard_uniform” means a uniform distribution on the interval `0.0` to `1.0`\n* “fill” functions will fill the provided `out` with `cnt` values.\n* The functions without “standard” in their name require additional parameters to describe the distributions.\n* Functions with `inv` in their name are based on the slower inverse method instead of a ziggurat lookup algorithm, which is significantly faster. The non-ziggurat variants are used in corner cases and for legacy compatibility.\n\n doublerandom_standard_uniform([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n voidrandom_standard_uniform_fill([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, double*out) \n\n doublerandom_standard_exponential([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n voidrandom_standard_exponential_fill([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, double*out) \n\n voidrandom_standard_exponential_inv_fill([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, double*out) \n\n doublerandom_standard_normal([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n voidrandom_standard_normal_fill([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")count, double*out) \n\n voidrandom_standard_normal_fill_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")count, float*out) \n\n doublerandom_standard_gamma([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleshape) \n\n floatrandom_standard_uniform_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n voidrandom_standard_uniform_fill_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, float*out) \n\n floatrandom_standard_exponential_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n voidrandom_standard_exponential_fill_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, float*out) \n\n voidrandom_standard_exponential_inv_fill_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")cnt, float*out) \n\n floatrandom_standard_normal_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n floatrandom_standard_gamma_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, floatshape) \n\n doublerandom_normal([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleloc, doublescale) \n\n doublerandom_gamma([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleshape, doublescale) \n\n floatrandom_gamma_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, floatshape, floatscale) \n\n doublerandom_exponential([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublescale) \n\n doublerandom_uniform([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublelower, doublerange) \n\n doublerandom_beta([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublea, doubleb) \n\n doublerandom_chisquare([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubledf) \n\n doublerandom_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubledfnum, doubledfden) \n\n doublerandom_standard_cauchy([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n doublerandom_pareto([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublea) \n\n doublerandom_weibull([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublea) \n\n doublerandom_power([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublea) \n\n doublerandom_laplace([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleloc, doublescale) \n\n doublerandom_gumbel([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleloc, doublescale) \n\n doublerandom_logistic([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleloc, doublescale) \n\n doublerandom_lognormal([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublemean, doublesigma) \n\n doublerandom_rayleigh([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublemode) \n\n doublerandom_standard_t([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubledf) \n\n doublerandom_noncentral_chisquare([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubledf, doublenonc) \n\n doublerandom_noncentral_f([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubledfnum, doubledfden, doublenonc) \n\n doublerandom_wald([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublemean, doublescale) \n\n doublerandom_vonmises([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublemu, doublekappa) \n\n doublerandom_triangular([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doubleleft, doublemode, doubleright) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_poisson([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublelam) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_negative_binomial([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublen, doublep) \n\n typebinomial_t \n\n \n\n```\ntypedef struct s_binomial_t {\n int has_binomial; /* !=0: following parameters initialized for binomial */\n double psave;\n RAND_INT_TYPE nsave;\n double r;\n double q;\n double fm;\n RAND_INT_TYPE m;\n double p1;\n double xm;\n double xl;\n double xr;\n double c;\n double laml;\n double lamr;\n double p2;\n double p3;\n double p4;\n} binomial_t;\n\n```\n \n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_binomial([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublep, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")n, [binomial_t](#c.binomial_t \"binomial_t\")*binomial) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_logseries([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublep) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_geometric_search([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublep) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_geometric_inversion([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublep) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_geometric([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublep) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_zipf([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, doublea) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_hypergeometric([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")good, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")bad, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")sample) \n\n [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")random_interval([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")max) \n\n voidrandom_multinomial([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")n, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")*mnix, double*pix, [npy_intp](../c-api/dtype#c.npy_intp \"npy_intp\")d, [binomial_t](#c.binomial_t \"binomial_t\")*binomial) \n\n intrandom_multivariate_hypergeometric_count([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")total, size_tnum_colors, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")*colors, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")nsample, size_tnum_variates, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")*variates) \n\n voidrandom_multivariate_hypergeometric_marginals([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")total, size_tnum_colors, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")*colors, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")nsample, size_tnum_variates, [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")*variates) \n\n Generate a single integer\n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_positive_int64([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n [npy_int32](../c-api/dtype#c.npy_int32 \"npy_int32\")random_positive_int32([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n [npy_int64](../c-api/dtype#c.npy_int64 \"npy_int64\")random_positive_int([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")random_uint([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state) \n\n Generate random uint64 numbers in closed interval [off, off + rng].\n\n [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")random_bounded_uint64([bitgen_t](#c.bitgen_t \"bitgen_t\")*bitgen_state, [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")off, [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")rng, [npy_uint64](../c-api/dtype#c.npy_uint64 \"npy_uint64\")mask, booluse_masked) \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/c-api.htmlExtending\n=========\n\n The BitGenerators have been designed to be extendable using standard tools for high-performance Python – numba and Cython. The [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\") object can also be used with user-provided BitGenerators as long as these export a small set of required functions.\n\n Numba\n-----\n\n Numba can be used with either CTypes or CFFI. The current iteration of the BitGenerators all export a small set of functions through both interfaces.\n\n This example shows how numba can be used to produce gaussian samples using a pure Python implementation which is then compiled. The random numbers are provided by `ctypes.next_double`.\n\n \n```\nimport numpy as np\nimport numba as nb\n\nfrom numpy.random import PCG64\nfrom timeit import timeit\n\nbit_gen = PCG64()\nnext_d = bit_gen.cffi.next_double\nstate_addr = bit_gen.cffi.state_address\n\ndef normals(n, state):\n out = np.empty(n)\n for i in range((n + 1) // 2):\n x1 = 2.0 * next_d(state) - 1.0\n x2 = 2.0 * next_d(state) - 1.0\n r2 = x1 * x1 + x2 * x2\n while r2 >= 1.0 or r2 == 0.0:\n x1 = 2.0 * next_d(state) - 1.0\n x2 = 2.0 * next_d(state) - 1.0\n r2 = x1 * x1 + x2 * x2\n f = np.sqrt(-2.0 * np.log(r2) / r2)\n out[2 * i] = f * x1\n if 2 * i + 1 < n:\n out[2 * i + 1] = f * x2\n return out\n\n# Compile using Numba\nnormalsj = nb.jit(normals, nopython=True)\n# Must use state address not state with numba\nn = 10000\n\ndef numbacall():\n return normalsj(n, state_addr)\n\nrg = np.random.Generator(PCG64())\n\ndef numpycall():\n return rg.normal(size=n)\n\n# Check that the functions work\nr1 = numbacall()\nr2 = numpycall()\nassert r1.shape == (n,)\nassert r1.shape == r2.shape\n\nt1 = timeit(numbacall, number=1000)\nprint(f'{t1:.2f} secs for {n} PCG64 (Numba/PCG64) gaussian randoms')\nt2 = timeit(numpycall, number=1000)\nprint(f'{t2:.2f} secs for {n} PCG64 (NumPy/PCG64) gaussian randoms')\n\n```\n Both CTypes and CFFI allow the more complicated distributions to be used directly in Numba after compiling the file distributions.c into a `DLL` or `so`. An example showing the use of a more complicated distribution is in the `examples` section below.\n\n Cython\n------\n\n Cython can be used to unpack the `PyCapsule` provided by a BitGenerator. This example uses [`PCG64`](bit_generators/pcg64#numpy.random.PCG64 \"numpy.random.PCG64\") and the example from above. The usual caveats for writing high-performance code using Cython – removing bounds checks and wrap around, providing array alignment information – still apply.\n\n \n```\n#!/usr/bin/env python3\n#cython: language_level=3\n\"\"\"\nThis file shows how the to use a BitGenerator to create a distribution.\n\"\"\"\nimport numpy as np\ncimport numpy as np\ncimport cython\nfrom cpython.pycapsule cimport PyCapsule_IsValid, PyCapsule_GetPointer\nfrom libc.stdint cimport uint16_t, uint64_t\nfrom numpy.random cimport bitgen_t\nfrom numpy.random import PCG64\nfrom numpy.random.c_distributions cimport (\n random_standard_uniform_fill, random_standard_uniform_fill_f)\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef uniforms(Py_ssize_t n):\n \"\"\"\n Create an array of `n` uniformly distributed doubles.\n A 'real' distribution would want to process the values into\n some non-uniform distribution\n \"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef double[::1] random_values\n\n x = PCG64()\n capsule = x.capsule\n # Optional check that the capsule if from a BitGenerator\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n # Cast the pointer\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n random_values = np.empty(n, dtype='float64')\n with x.lock, nogil:\n for i in range(n):\n # Call the function\n random_values[i] = rng.next_double(rng.state)\n randoms = np.asarray(random_values)\n\n return randoms\n\n```\n The BitGenerator can also be directly accessed using the members of the `bitgen_t` struct.\n\n \n```\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef uint10_uniforms(Py_ssize_t n):\n \"\"\"Uniform 10 bit integers stored as 16-bit unsigned integers\"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef uint16_t[::1] random_values\n cdef int bits_remaining\n cdef int width = 10\n cdef uint64_t buff, mask = 0x3FF\n\n x = PCG64()\n capsule = x.capsule\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n random_values = np.empty(n, dtype='uint16')\n # Best practice is to release GIL and acquire the lock\n bits_remaining = 0\n with x.lock, nogil:\n for i in range(n):\n if bits_remaining < width:\n buff = rng.next_uint64(rng.state)\n random_values[i] = buff & mask\n buff >>= width\n\n randoms = np.asarray(random_values)\n return randoms\n\n```\n Cython can be used to directly access the functions in `numpy/random/c_distributions.pxd`. This requires linking with the `npyrandom` library located in `numpy/random/lib`.\n\n \n```\ndef uniforms_ex(bit_generator, Py_ssize_t n, dtype=np.float64):\n \"\"\"\n Create an array of `n` uniformly distributed doubles via a \"fill\" function.\n\n A 'real' distribution would want to process the values into\n some non-uniform distribution\n\n Parameters\n ----------\n bit_generator: BitGenerator instance\n n: int\n Output vector length\n dtype: {str, dtype}, optional\n Desired dtype, either 'd' (or 'float64') or 'f' (or 'float32'). The\n default dtype value is 'd'\n \"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef np.ndarray randoms\n\n capsule = bit_generator.capsule\n # Optional check that the capsule if from a BitGenerator\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n # Cast the pointer\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n\n _dtype = np.dtype(dtype)\n randoms = np.empty(n, dtype=_dtype)\n if _dtype == np.float32:\n with bit_generator.lock:\n random_standard_uniform_fill_f(rng, n, <float*>np.PyArray_DATA(randoms))\n elif _dtype == np.float64:\n with bit_generator.lock:\n random_standard_uniform_fill(rng, n, <double*>np.PyArray_DATA(randoms))\n else:\n raise TypeError('Unsupported dtype %r for random' % _dtype)\n return randoms\n\n```\n See [Extending numpy.random via Cython](examples/cython/index#extending-cython-example) for the complete listings of these examples and a minimal `setup.py` to build the c-extension modules.\n\n CFFI\n----\n\n CFFI can be used to directly access the functions in `include/numpy/random/distributions.h`. Some “massaging” of the header file is required:\n\n \n```\n\"\"\"\nUse cffi to access any of the underlying C functions from distributions.h\n\"\"\"\nimport os\nimport numpy as np\nimport cffi\nfrom .parse import parse_distributions_h\nffi = cffi.FFI()\n\ninc_dir = os.path.join(np.get_include(), 'numpy')\n\n# Basic numpy types\nffi.cdef('''\n typedef intptr_t npy_intp;\n typedef unsigned char npy_bool;\n\n''')\n\nparse_distributions_h(ffi, inc_dir)\n\n```\n Once the header is parsed by `ffi.cdef`, the functions can be accessed directly from the `_generator` shared object, using the [`BitGenerator.cffi`](bit_generators/generated/numpy.random.bitgenerator.cffi#numpy.random.BitGenerator.cffi \"numpy.random.BitGenerator.cffi\") interface.\n\n \n```\n\n# Compare the distributions.h random_standard_normal_fill to\n# Generator.standard_random\nbit_gen = np.random.PCG64()\nrng = np.random.Generator(bit_gen)\nstate = bit_gen.state\n\ninterface = rng.bit_generator.cffi\nn = 100\nvals_cffi = ffi.new('double[%d]' % n)\nlib.random_standard_normal_fill(interface.bit_generator, n, vals_cffi)\n\n# reset the state\nbit_gen.state = state\n\nvals = rng.standard_normal(n)\n\nfor i in range(n):\n assert vals[i] == vals_cffi[i]\n\n```\n New Bit Generators\n------------------\n\n [`Generator`](generator#numpy.random.Generator \"numpy.random.Generator\") can be used with user-provided [`BitGenerator`](bit_generators/generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\")s. The simplest way to write a new BitGenerator is to examine the pyx file of one of the existing BitGenerators. The key structure that must be provided is the `capsule` which contains a `PyCapsule` to a struct pointer of type `bitgen_t`,\n\n \n```\ntypedef struct bitgen {\n void *state;\n uint64_t (*next_uint64)(void *st);\n uint32_t (*next_uint32)(void *st);\n double (*next_double)(void *st);\n uint64_t (*next_raw)(void *st);\n} bitgen_t;\n\n```\n which provides 5 pointers. The first is an opaque pointer to the data structure used by the BitGenerators. The next three are function pointers which return the next 64- and 32-bit unsigned integers, the next random double and the next raw value. This final function is used for testing and so can be set to the next 64-bit unsigned integer function if not needed. Functions inside `Generator` use this structure as in\n\n \n```\nbitgen_state->next_uint64(bitgen_state->state)\n\n```\n Examples\n--------\n\n * [Numba](examples/numba)\n* [CFFI + Numba](examples/numba_cffi)\n* [Cython](examples/cython/index)\n\t+ [setup.py](examples/cython/setup.py)\n\t+ [extending.pyx](examples/cython/extending.pyx)\n\t+ [extending_distributions.pyx](examples/cython/extending_distributions.pyx)\n* [CFFI](examples/cffi)\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/extending.htmlnumpy.random.BitGenerator\n=========================\n\n *class*numpy.random.BitGenerator(*seed=None*)\n \nBase Class for generic BitGenerators, which provide a stream of random bits based on different algorithms. Must be overridden.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to ~`numpy.random.SeedSequence` to derive the initial [`BitGenerator`](#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n See also\n\n [`SeedSequence`](numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\")\n Attributes \n \n**lock**threading.Lock\n\nLock instance that is shared so that the same BitGenerator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`random_raw`](numpy.random.bitgenerator.random_raw#numpy.random.BitGenerator.random_raw \"numpy.random.BitGenerator.random_raw\")(self[, size]) | Return randoms as generated by the underlying BitGenerator |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.BitGenerator.htmlPermuted Congruential Generator (64-bit, PCG64)\n===============================================\n\n *class*numpy.random.PCG64(*seed=None*)\n \nBitGenerator for the PCG-64 pseudo-random number generator.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n #### Notes\n\n PCG-64 is a 128-bit implementation of O’Neill’s permutation congruential generator ([[1]](#r4523891264fe-1), [[2]](#r4523891264fe-2)). PCG-64 has a period of \\(2^{128}\\) and supports advancing an arbitrary number of steps as well as \\(2^{127}\\) streams. The specific member of the PCG family that we use is PCG XSL RR 128/64 as described in the paper ([[2]](#r4523891264fe-2)).\n\n `PCG64` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a `Generator` or similar object that supports low-level access.\n\n Supports the method [`advance`](generated/numpy.random.pcg64.advance#numpy.random.PCG64.advance \"numpy.random.PCG64.advance\") to advance the RNG an arbitrary number of steps. The state of the PCG-64 RNG is represented by 2 128-bit unsigned integers.\n\n **State and Seeding**\n\n The `PCG64` state vector consists of 2 unsigned 128-bit values, which are represented externally as Python ints. One is the state of the PRNG, which is advanced by a linear congruential generator (LCG). The second is a fixed odd increment used in the LCG.\n\n The input seed is processed by [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to generate both values. The increment is not independently settable.\n\n **Parallel Features**\n\n The preferred way to use a BitGenerator in parallel applications is to use the [`SeedSequence.spawn`](generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\") method to obtain entropy values, and to use these to generate new BitGenerators:\n\n \n```\n>>> from numpy.random import Generator, PCG64, SeedSequence\n>>> sg = SeedSequence(1234)\n>>> rg = [Generator(PCG64(s)) for s in sg.spawn(10)]\n\n```\n **Compatibility Guarantee**\n\n `PCG64` makes a guarantee that a fixed seed will always produce the same random integer stream.\n\n #### References\n\n [1](#id1) \n[“PCG, A Family of Better Random Number Generators”](http://www.pcg-random.org/)\n\n \n2([1](#id2),[2](#id3))\n \nO’Neill, <NAME>. [“PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation”](https://www.cs.hmc.edu/tr/hmc-cs-2014-0905.pdf)\n\n \n State\n-----\n\n \n\n| | |\n| --- | --- |\n| [`state`](generated/numpy.random.pcg64.state#numpy.random.PCG64.state \"numpy.random.PCG64.state\") | Get or set the PRNG state |\n\n Parallel generation\n-------------------\n\n \n\n| | |\n| --- | --- |\n| [`advance`](generated/numpy.random.pcg64.advance#numpy.random.PCG64.advance \"numpy.random.PCG64.advance\")(delta) | Advance the underlying RNG as-if delta draws have occurred. |\n| [`jumped`](generated/numpy.random.pcg64.jumped#numpy.random.PCG64.jumped \"numpy.random.PCG64.jumped\")([jumps]) | Returns a new bit generator with the state jumped. |\n\n Extending\n---------\n\n \n\n| | |\n| --- | --- |\n| [`cffi`](generated/numpy.random.pcg64.cffi#numpy.random.PCG64.cffi \"numpy.random.PCG64.cffi\") | CFFI interface |\n| [`ctypes`](generated/numpy.random.pcg64.ctypes#numpy.random.PCG64.ctypes \"numpy.random.PCG64.ctypes\") | ctypes interface |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/pcg64.htmlMersenne Twister (MT19937)\n==========================\n\n *class*numpy.random.MT19937(*seed=None*)\n \nContainer for the Mersenne Twister pseudo-random number generator.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n #### Notes\n\n `MT19937` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers [[1]](#r312276d80bfa-1). These are not directly consumable in Python and must be consumed by a `Generator` or similar object that supports low-level access.\n\n The Python stdlib module “random” also contains a Mersenne Twister pseudo-random number generator.\n\n **State and Seeding**\n\n The `MT19937` state vector consists of a 624-element array of 32-bit unsigned integers plus a single integer value between 0 and 624 that indexes the current position within the main array.\n\n The input seed is processed by [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to fill the whole state. The first element is reset such that only its most significant bit is set.\n\n **Parallel Features**\n\n The preferred way to use a BitGenerator in parallel applications is to use the [`SeedSequence.spawn`](generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\") method to obtain entropy values, and to use these to generate new BitGenerators:\n\n \n```\n>>> from numpy.random import Generator, MT19937, SeedSequence\n>>> sg = SeedSequence(1234)\n>>> rg = [Generator(MT19937(s)) for s in sg.spawn(10)]\n\n```\n Another method is to use [`MT19937.jumped`](generated/numpy.random.mt19937.jumped#numpy.random.MT19937.jumped \"numpy.random.MT19937.jumped\") which advances the state as-if \\(2^{128}\\) random numbers have been generated ([[1]](#r312276d80bfa-1), [[2]](#r312276d80bfa-2)). This allows the original sequence to be split so that distinct segments can be used in each worker process. All generators should be chained to ensure that the segments come from the same sequence.\n\n \n```\n>>> from numpy.random import Generator, MT19937, SeedSequence\n>>> sg = SeedSequence(1234)\n>>> bit_generator = MT19937(sg)\n>>> rg = []\n>>> for _ in range(10):\n... rg.append(Generator(bit_generator))\n... # Chain the BitGenerators\n... bit_generator = bit_generator.jumped()\n\n```\n **Compatibility Guarantee**\n\n `MT19937` makes a guarantee that a fixed seed will always produce the same random integer stream.\n\n #### References\n\n \n1([1](#id1),[2](#id2))\n \n<NAME>, <NAME>, and <NAME>, “A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space”, Sequences and Their Applications - SETA, 290–298, 2008.\n\n [2](#id3) \n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>, “Efficient Jump Ahead for F2-Linear Random Number Generators”, INFORMS JOURNAL ON COMPUTING, Vol. 20, No. 3, Summer 2008, pp. 385-390.\n\n Attributes \n **lock: threading.Lock**\n\nLock instance that is shared so that the same bit git generator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.\n\n \n State\n-----\n\n \n\n| | |\n| --- | --- |\n| [`state`](generated/numpy.random.mt19937.state#numpy.random.MT19937.state \"numpy.random.MT19937.state\") | Get or set the PRNG state |\n\n Parallel generation\n-------------------\n\n \n\n| | |\n| --- | --- |\n| [`jumped`](generated/numpy.random.mt19937.jumped#numpy.random.MT19937.jumped \"numpy.random.MT19937.jumped\")([jumps]) | Returns a new bit generator with the state jumped |\n\n Extending\n---------\n\n \n\n| | |\n| --- | --- |\n| [`cffi`](generated/numpy.random.mt19937.cffi#numpy.random.MT19937.cffi \"numpy.random.MT19937.cffi\") | CFFI interface |\n| [`ctypes`](generated/numpy.random.mt19937.ctypes#numpy.random.MT19937.ctypes \"numpy.random.MT19937.ctypes\") | ctypes interface |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/mt19937.htmlnumpy.random.SeedSequence.spawn\n===============================\n\n method\n\n random.SeedSequence.spawn(*n_children*)\n \nSpawn a number of child `SeedSequence` s by extending the [`spawn_key`](numpy.random.seedsequence.spawn_key#numpy.random.SeedSequence.spawn_key \"numpy.random.SeedSequence.spawn_key\").\n\n Parameters \n \n**n_children**int\n\n Returns \n \n**seqs**list of `SeedSequence` s\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SeedSequence.spawn.htmlnumpy.random.SeedSequence\n=========================\n\n *class*numpy.random.SeedSequence(*entropy=None*, ***, *spawn_key=()*, *pool_size=4*)\n \nSeedSequence mixes sources of entropy in a reproducible way to set the initial state for independent and very probably non-overlapping BitGenerators.\n\n Once the SeedSequence is instantiated, you can call the [`generate_state`](numpy.random.seedsequence.generate_state#numpy.random.SeedSequence.generate_state \"numpy.random.SeedSequence.generate_state\") method to get an appropriately sized seed. Calling [`spawn(n)`](numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\") will create `n` SeedSequences that can be used to seed independent BitGenerators, i.e. for different threads.\n\n Parameters \n \n**entropy**{None, int, sequence[int]}, optional\n\nThe entropy for creating a [`SeedSequence`](#numpy.random.SeedSequence \"numpy.random.SeedSequence\").\n\n \n**spawn_key**{(), sequence[int]}, optional\n\nA third source of entropy, used internally when calling [`SeedSequence.spawn`](numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\")\n\n \n**pool_size**{int}, optional\n\nSize of the pooled entropy to store. Default is 4 to give a 128-bit entropy pool. 8 (for 256 bits) is another reasonable choice if working with larger PRNGs, but there is very little to be gained by selecting another value.\n\n \n**n_children_spawned**{int}, optional\n\nThe number of children already spawned. Only pass this if reconstructing a [`SeedSequence`](#numpy.random.SeedSequence \"numpy.random.SeedSequence\") from a serialized form.\n\n #### Notes\n\n Best practice for achieving reproducible bit streams is to use the default `None` for the initial entropy, and then use [`SeedSequence.entropy`](numpy.random.seedsequence.entropy#numpy.random.SeedSequence.entropy \"numpy.random.SeedSequence.entropy\") to log/pickle the [`entropy`](numpy.random.seedsequence.entropy#numpy.random.SeedSequence.entropy \"numpy.random.SeedSequence.entropy\") for reproducibility:\n\n \n```\n>>> sq1 = np.random.SeedSequence()\n>>> sq1.entropy\n243799254704924441050048792905230269161 # random\n>>> sq2 = np.random.SeedSequence(sq1.entropy)\n>>> np.all(sq1.generate_state(10) == sq2.generate_state(10))\nTrue\n\n```\n Attributes \n **entropy**\n**n_children_spawned**\n**pool**\n**pool_size**\n**spawn_key**\n**state**\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`generate_state`](numpy.random.seedsequence.generate_state#numpy.random.SeedSequence.generate_state \"numpy.random.SeedSequence.generate_state\")(n_words[, dtype]) | Return the requested number of words for PRNG seeding. |\n| [`spawn`](numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\")(n_children) | Spawn a number of child [`SeedSequence`](#numpy.random.SeedSequence \"numpy.random.SeedSequence\") s by extending the [`spawn_key`](numpy.random.seedsequence.spawn_key#numpy.random.SeedSequence.spawn_key \"numpy.random.SeedSequence.spawn_key\"). |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SeedSequence.htmlnumpy.random.RandomState.gamma\n==============================\n\n method\n\n random.RandomState.gamma(*shape*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, [`shape`](../../generated/numpy.shape#numpy.shape \"numpy.shape\") (sometimes designated “k”) and `scale` (sometimes designated “theta”), where both parameters are > 0.\n\n Note\n\n New code should use the `gamma` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**shape**float or array_like of floats\n\nThe shape of the gamma distribution. Must be non-negative.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale of the gamma distribution. Must be non-negative. Default is equal to 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` and `scale` are both scalars. Otherwise, `np.broadcast(shape, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.gamma`](numpy.random.generator.gamma#numpy.random.Generator.gamma \"numpy.random.Generator.gamma\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2)\n>>> s = np.random.gamma(shape, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1)*(np.exp(-bins/scale) / \n... (sps.gamma(shape)*scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.gamma.htmlnumpy.random.RandomState.standard_t\n====================================\n\n method\n\n random.RandomState.standard_t(*df*, *size=None*)\n \nDraw samples from a standard Student’s t distribution with `df` degrees of freedom.\n\n A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution ([`standard_normal`](numpy.random.randomstate.standard_normal#numpy.random.RandomState.standard_normal \"numpy.random.RandomState.standard_normal\")).\n\n Note\n\n New code should use the `standard_t` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard Student’s t distribution.\n\n See also\n\n [`random.Generator.standard_t`](numpy.random.generator.standard_t#numpy.random.Generator.standard_t \"numpy.random.Generator.standard_t\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the t distribution is\n\n \\[P(x, df) = \\frac{\\Gamma(\\frac{df+1}{2})}{\\sqrt{\\pi df} \\Gamma(\\frac{df}{2})}\\Bigl( 1+\\frac{x^2}{df} \\Bigr)^{-(df+1)/2}\\] The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean.\n\n The derivation of the t-distribution was first published in 1908 by <NAME> while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student.\n\n #### References\n\n [1](#id3) \nDalgaard, Peter, “Introductory Statistics With R”, Springer, 2002.\n\n 2 \nWikipedia, “Student’s t-distribution” [https://en.wikipedia.org/wiki/Student’s_t-distribution](https://en.wikipedia.org/wiki/Student's_t-distribution)\n\n #### Examples\n\n From Dalgaard page 83 [[1]](#r89f5270d198b-1), suppose the daily energy intake for 11 women in kilojoules (kJ) is:\n\n \n```\n>>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \\\n... 7515, 8230, 8770])\n\n```\n Does their energy intake deviate systematically from the recommended value of 7725 kJ? Our null hypothesis will be the absence of deviation, and the alternate hypothesis will be the presence of an effect that could be either positive or negative, hence making our test 2-tailed.\n\n Because we are estimating the mean and we have N=11 values in our sample, we have N-1=10 degrees of freedom. We set our significance level to 95% and compute the t statistic using the empirical mean and empirical standard deviation of our intake. We use a ddof of 1 to base the computation of our empirical standard deviation on an unbiased estimate of the variance (note: the final estimate is not unbiased due to the concave nature of the square root).\n\n \n```\n>>> np.mean(intake)\n6753.636363636364\n>>> intake.std(ddof=1)\n1142.1232221373727\n>>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake)))\n>>> t\n-2.8207540608310198\n\n```\n We draw 1000000 samples from Student’s t distribution with the adequate degrees of freedom.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.standard_t(10, size=1000000)\n>>> h = plt.hist(s, bins=100, density=True)\n\n```\n Does our t statistic land in one of the two critical regions found at both tails of the distribution?\n\n \n```\n>>> np.sum(np.abs(t) < np.abs(s)) / float(len(s))\n0.018318 #random < 0.05, statistic is in critical region\n\n```\n The probability value for this 2-tailed test is about 1.83%, which is lower than the 5% pre-determined significance threshold.\n\n Therefore, the probability of observing values as extreme as our intake conditionally on the null hypothesis being true is too low, and we reject the null hypothesis of no deviation.\n\n ![../../../_images/numpy-random-RandomState-standard_t-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.standard_t.htmlnumpy.random.PCG64.ctypes\n=========================\n\n attribute\n\n random.PCG64.ctypes\n \nctypes interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing ctypes wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64.ctypes.htmlnumpy.random.PCG64.cffi\n=======================\n\n attribute\n\n random.PCG64.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64.cffi.htmlnumpy.random.Generator.integers\n===============================\n\n method\n\n random.Generator.integers(*low*, *high=None*, *size=None*, *dtype=np.int64*, *endpoint=False*)\n \nReturn random integers from `low` (inclusive) to `high` (exclusive), or if endpoint=True, `low` (inclusive) to `high` (inclusive). Replaces `RandomState.randint` (with endpoint=False) and `RandomState.random_integers` (with endpoint=True)\n\n Return random integers from the “discrete uniform” distribution of the specified dtype. If `high` is None (the default), then results are from 0 to `low`.\n\n Parameters \n \n**low**int or array-like of ints\n\nLowest (signed) integers to be drawn from the distribution (unless `high=None`, in which case this parameter is 0 and this value is used for `high`).\n\n \n**high**int or array-like of ints, optional\n\nIf provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if `high=None`). If array-like, must contain integer values\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result. Byteorder must be native. The default value is np.int64.\n\n \n**endpoint**bool, optional\n\nIf true, sample from the interval [low, high] instead of the default [low, high) Defaults to False\n\n Returns \n \n**out**int or ndarray of ints\n\n`size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided.\n\n #### Notes\n\n When using broadcasting with uint64 dtypes, the maximum value (2**64) cannot be represented as a standard integer type. The high array (or low if high is None) must have object dtype, e.g., array([2**64]).\n\n #### References\n\n 1 \n<NAME>., “Fast Random Integer Generation in an Interval”, ACM Transactions on Modeling and Computer Simulation 29 (1), 2019, <http://arxiv.org/abs/1805.10941>.\n\n #### Examples\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.integers(2, size=10)\narray([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random\n>>> rng.integers(1, size=10)\narray([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n\n```\n Generate a 2 x 4 array of ints between 0 and 4, inclusive:\n\n \n```\n>>> rng.integers(5, size=(2, 4))\narray([[4, 0, 2, 1],\n [3, 2, 2, 0]]) # random\n\n```\n Generate a 1 x 3 array with 3 different upper bounds\n\n \n```\n>>> rng.integers(1, [3, 5, 10])\narray([2, 2, 9]) # random\n\n```\n Generate a 1 by 3 array with 3 different lower bounds\n\n \n```\n>>> rng.integers([1, 5, 7], 10)\narray([9, 8, 7]) # random\n\n```\n Generate a 2 by 4 array using broadcasting with dtype of uint8\n\n \n```\n>>> rng.integers([1, 3, 5, 7], [[10], [20]], dtype=np.uint8)\narray([[ 8, 6, 9, 7],\n [ 1, 16, 9, 12]], dtype=uint8) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.integers.htmlnumpy.random.Generator.random\n=============================\n\n method\n\n random.Generator.random(*size=None*, *dtype=np.float64*, *out=None*)\n \nReturn random floats in the half-open interval [0.0, 1.0).\n\n Results are from the “continuous uniform” distribution over the stated interval. To sample \\(Unif[a, b), b > a\\) multiply the output of [`random`](../index#module-numpy.random \"numpy.random\") by `(b-a)` and add `a`:\n\n \n```\n(b - a) * random() + a\n\n```\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result, only [`float64`](../../arrays.scalars#numpy.float64 \"numpy.float64\") and [`float32`](../../arrays.scalars#numpy.float32 \"numpy.float32\") are supported. Byteorder must be native. The default value is np.float64.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.\n\n Returns \n \n**out**float or ndarray of floats\n\nArray of random floats of shape `size` (unless `size=None`, in which case a single float is returned).\n\n #### Examples\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.random()\n0.47108547995356098 # random\n>>> type(rng.random())\n<class 'float'>\n>>> rng.random((5,))\narray([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) # random\n\n```\n Three-by-two array of random numbers from [-5, 0):\n\n \n```\n>>> 5 * rng.random((3, 2)) - 5\narray([[-3.99149989, -0.52338984], # random\n [-2.99091858, -0.79479508],\n [-1.23204345, -1.75224494]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.random.htmlnumpy.random.RandomState.random_sample\n=======================================\n\n method\n\n random.RandomState.random_sample(*size=None*)\n \nReturn random floats in the half-open interval [0.0, 1.0).\n\n Results are from the “continuous uniform” distribution over the stated interval. To sample \\(Unif[a, b), b > a\\) multiply the output of [`random_sample`](#numpy.random.RandomState.random_sample \"numpy.random.RandomState.random_sample\") by `(b-a)` and add `a`:\n\n \n```\n(b - a) * random_sample() + a\n\n```\n Note\n\n New code should use the `random` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray of floats\n\nArray of random floats of shape `size` (unless `size=None`, in which case a single float is returned).\n\n See also\n\n [`random.Generator.random`](numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.random_sample()\n0.47108547995356098 # random\n>>> type(np.random.random_sample())\n<class 'float'>\n>>> np.random.random_sample((5,))\narray([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) # random\n\n```\n Three-by-two array of random numbers from [-5, 0):\n\n \n```\n>>> 5 * np.random.random_sample((3, 2)) - 5\narray([[-3.99149989, -0.52338984], # random\n [-2.99091858, -0.79479508],\n [-1.23204345, -1.75224494]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.random_sample.htmlnumpy.random.Generator.choice\n=============================\n\n method\n\n random.Generator.choice(*a*, *size=None*, *replace=True*, *p=None*, *axis=0*, *shuffle=True*)\n \nGenerates a random sample from a given array\n\n Parameters \n \n**a**{array_like, int}\n\nIf an ndarray, a random sample is generated from its elements. If an int, the random sample is generated from np.arange(a).\n\n \n**size**{int, tuple[int]}, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn from the 1-d `a`. If `a` has more than one dimension, the `size` shape will be inserted into the `axis` dimension, so the output `ndim` will be `a.ndim - 1 +\nlen(size)`. Default is None, in which case a single value is returned.\n\n \n**replace**bool, optional\n\nWhether the sample is with or without replacement. Default is True, meaning that a value of `a` can be selected multiple times.\n\n \n**p**1-D array_like, optional\n\nThe probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in `a`.\n\n \n**axis**int, optional\n\nThe axis along which the selection is performed. The default, 0, selects by row.\n\n \n**shuffle**bool, optional\n\nWhether the sample is shuffled when sampling without replacement. Default is True, False provides a speedup.\n\n Returns \n \n**samples**single item or ndarray\n\nThe generated random samples\n\n Raises \n ValueError\n\nIf a is an int and less than zero, if p is not 1-dimensional, if a is array-like with a size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size.\n\n See also\n\n \n[`integers`](numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\"), [`shuffle`](numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\"), [`permutation`](numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")\n\n #### Notes\n\n Setting user-specified probabilities through `p` uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of `p` is 1 / len(a).\n\n #### Examples\n\n Generate a uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.choice(5, 3)\narray([0, 3, 4]) # random\n>>> #This is equivalent to rng.integers(0,5,3)\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> rng.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])\narray([3, 3, 0]) # random\n\n```\n Generate a uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> rng.choice(5, 3, replace=False)\narray([3,1,0]) # random\n>>> #This is equivalent to rng.permutation(np.arange(5))[:3]\n\n```\n Generate a uniform random sample from a 2-D array along the first axis (the default), without replacement:\n\n \n```\n>>> rng.choice([[0, 1, 2], [3, 4, 5], [6, 7, 8]], 2, replace=False)\narray([[3, 4, 5], # random\n [0, 1, 2]])\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> rng.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])\narray([2, 3, 0]) # random\n\n```\n Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:\n\n \n```\n>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']\n>>> rng.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])\narray(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random\n dtype='<U11')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.choice.htmlnumpy.random.Generator.permutation\n==================================\n\n method\n\n random.Generator.permutation(*x*, *axis=0*)\n \nRandomly permute a sequence, or return a permuted range.\n\n Parameters \n \n**x**int or array_like\n\nIf `x` is an integer, randomly permute `np.arange(x)`. If `x` is an array, make a copy and shuffle the elements randomly.\n\n \n**axis**int, optional\n\nThe axis which `x` is shuffled along. Default is 0.\n\n Returns \n \n**out**ndarray\n\nPermuted sequence or array range.\n\n #### Examples\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.permutation(10)\narray([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) # random\n\n```\n \n```\n>>> rng.permutation([1, 4, 9, 12, 15])\narray([15, 1, 9, 4, 12]) # random\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> rng.permutation(arr)\narray([[6, 7, 8], # random\n [0, 1, 2],\n [3, 4, 5]])\n\n```\n \n```\n>>> rng.permutation(\"abc\")\nTraceback (most recent call last):\n ...\nnumpy.AxisError: axis 0 is out of bounds for array of dimension 0\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> rng.permutation(arr, axis=1)\narray([[0, 2, 1], # random\n [3, 5, 4],\n [6, 8, 7]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.permutation.htmlnumpy.random.Generator.shuffle\n==============================\n\n method\n\n random.Generator.shuffle(*x*, *axis=0*)\n \nModify an array or sequence in-place by shuffling its contents.\n\n The order of sub-arrays is changed but their contents remains the same.\n\n Parameters \n \n**x**ndarray or MutableSequence\n\nThe array, list or mutable sequence to be shuffled.\n\n \n**axis**int, optional\n\nThe axis which `x` is shuffled along. Default is 0. It is only supported on [`ndarray`](../../generated/numpy.ndarray#numpy.ndarray \"numpy.ndarray\") objects.\n\n Returns \n None\n See also\n\n [`permuted`](numpy.random.generator.permuted#numpy.random.Generator.permuted \"numpy.random.Generator.permuted\")\n[`permutation`](numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")\n #### Notes\n\n An important distinction between methods `shuffle` and `permuted` is how they both treat the `axis` parameter which can be found at [Handling the axis parameter](../generator#generator-handling-axis-parameter).\n\n #### Examples\n\n \n```\n>>> rng = np.random.default_rng()\n>>> arr = np.arange(10)\n>>> arr\narray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n>>> rng.shuffle(arr)\n>>> arr\narray([2, 0, 7, 5, 1, 4, 8, 9, 3, 6]) # random\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> arr\narray([[0, 1, 2],\n [3, 4, 5],\n [6, 7, 8]])\n>>> rng.shuffle(arr)\n>>> arr\narray([[3, 4, 5], # random\n [6, 7, 8],\n [0, 1, 2]])\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> arr\narray([[0, 1, 2],\n [3, 4, 5],\n [6, 7, 8]])\n>>> rng.shuffle(arr, axis=1)\n>>> arr\narray([[2, 0, 1], # random\n [5, 3, 4],\n [8, 6, 7]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.shuffle.htmlnumpy.RankWarning\n=================\n\n *exception*numpy.RankWarning[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/__init__.py)\n \nIssued by [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\") when the Vandermonde matrix is rank deficient.\n\n For more information, a way to suppress the warning, and an example of [`RankWarning`](#numpy.RankWarning \"numpy.RankWarning\") being issued, see [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.RankWarning.htmlnumpy.in1d\n==========\n\n numpy.in1d(*ar1*, *ar2*, *assume_unique=False*, *invert=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L523-L637)\n \nTest whether each element of a 1-D array is also present in a second array.\n\n Returns a boolean array the same length as `ar1` that is True where an element of `ar1` is in `ar2` and False otherwise.\n\n We recommend using [`isin`](numpy.isin#numpy.isin \"numpy.isin\") instead of [`in1d`](#numpy.in1d \"numpy.in1d\") for new code.\n\n Parameters \n \n**ar1**(M,) array_like\n\nInput array.\n\n \n**ar2**array_like\n\nThe values against which to test each value of `ar1`.\n\n \n**assume_unique**bool, optional\n\nIf True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False.\n\n \n**invert**bool, optional\n\nIf True, the values in the returned array are inverted (that is, False where an element of `ar1` is in `ar2` and True otherwise). Default is False. `np.in1d(a, b, invert=True)` is equivalent to (but is faster than) `np.invert(in1d(a, b))`.\n\n New in version 1.8.0.\n\n Returns \n \n**in1d**(M,) ndarray, bool\n\nThe values `ar1[in1d]` are in `ar2`.\n\n See also\n\n [`isin`](numpy.isin#numpy.isin \"numpy.isin\")\n\nVersion of this function that preserves the shape of ar1.\n\n [`numpy.lib.arraysetops`](numpy.lib.arraysetops#module-numpy.lib.arraysetops \"numpy.lib.arraysetops\")\n\nModule with a number of other functions for performing set operations on arrays.\n\n #### Notes\n\n [`in1d`](#numpy.in1d \"numpy.in1d\") can be considered as an element-wise function version of the python keyword `in`, for 1-D sequences. `in1d(a, b)` is roughly equivalent to `np.array([item in b for item in a])`. However, this idea fails if `ar2` is a set, or similar (non-sequence) container: As `ar2` is converted to an array, in those cases `asarray(ar2)` is an object array rather than the expected array of contained values.\n\n New in version 1.4.0.\n\n #### Examples\n\n \n```\n>>> test = np.array([0, 1, 2, 5, 0])\n>>> states = [0, 2]\n>>> mask = np.in1d(test, states)\n>>> mask\narray([ True, False, True, False, True])\n>>> test[mask]\narray([0, 2, 0])\n>>> mask = np.in1d(test, states, invert=True)\n>>> mask\narray([False, True, False, True, False])\n>>> test[mask]\narray([1, 5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.in1d.htmlnumpy.intersect1d\n=================\n\n numpy.intersect1d(*ar1*, *ar2*, *assume_unique=False*, *return_indices=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L373-L469)\n \nFind the intersection of two arrays.\n\n Return the sorted, unique values that are in both of the input arrays.\n\n Parameters \n \n**ar1, ar2**array_like\n\nInput arrays. Will be flattened if not already 1D.\n\n \n**assume_unique**bool\n\nIf True, the input arrays are both assumed to be unique, which can speed up the calculation. If True but `ar1` or `ar2` are not unique, incorrect results and out-of-bounds indices could result. Default is False.\n\n \n**return_indices**bool\n\nIf True, the indices which correspond to the intersection of the two arrays are returned. The first instance of a value is used if there are multiple. Default is False.\n\n New in version 1.15.0.\n\n Returns \n \n**intersect1d**ndarray\n\nSorted 1D array of common and unique elements.\n\n \n**comm1**ndarray\n\nThe indices of the first occurrences of the common values in `ar1`. Only provided if `return_indices` is True.\n\n \n**comm2**ndarray\n\nThe indices of the first occurrences of the common values in `ar2`. Only provided if `return_indices` is True.\n\n See also\n\n [`numpy.lib.arraysetops`](numpy.lib.arraysetops#module-numpy.lib.arraysetops \"numpy.lib.arraysetops\")\n\nModule with a number of other functions for performing set operations on arrays.\n\n #### Examples\n\n \n```\n>>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])\narray([1, 3])\n\n```\n To intersect more than two arrays, use functools.reduce:\n\n \n```\n>>> from functools import reduce\n>>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))\narray([3])\n\n```\n To return the indices of the values common to the input arrays along with the intersected values:\n\n \n```\n>>> x = np.array([1, 1, 2, 3, 4])\n>>> y = np.array([2, 1, 4, 6])\n>>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True)\n>>> x_ind, y_ind\n(array([0, 2, 4]), array([1, 0, 2]))\n>>> xy, x[x_ind], y[y_ind]\n(array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.intersect1d.htmlnumpy.isin\n==========\n\n numpy.isin(*element*, *test_elements*, *assume_unique=False*, *invert=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L644-L740)\n \nCalculates `element in test_elements`, broadcasting over `element` only. Returns a boolean array of the same shape as `element` that is True where an element of `element` is in `test_elements` and False otherwise.\n\n Parameters \n \n**element**array_like\n\nInput array.\n\n \n**test_elements**array_like\n\nThe values against which to test each value of `element`. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters.\n\n \n**assume_unique**bool, optional\n\nIf True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False.\n\n \n**invert**bool, optional\n\nIf True, the values in the returned array are inverted, as if calculating `element not in test_elements`. Default is False. `np.isin(a, b, invert=True)` is equivalent to (but faster than) `np.invert(np.isin(a, b))`.\n\n Returns \n \n**isin**ndarray, bool\n\nHas the same shape as `element`. The values `element[isin]` are in `test_elements`.\n\n See also\n\n [`in1d`](numpy.in1d#numpy.in1d \"numpy.in1d\")\n\nFlattened version of this function.\n\n [`numpy.lib.arraysetops`](numpy.lib.arraysetops#module-numpy.lib.arraysetops \"numpy.lib.arraysetops\")\n\nModule with a number of other functions for performing set operations on arrays.\n\n #### Notes\n\n [`isin`](#numpy.isin \"numpy.isin\") is an element-wise function version of the python keyword `in`. `isin(a, b)` is roughly equivalent to `np.array([item in b for item in a])` if `a` and `b` are 1-D sequences.\n\n `element` and `test_elements` are converted to arrays if they are not already. If `test_elements` is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in `test_elements`. This is a consequence of the [`array`](numpy.array#numpy.array \"numpy.array\") constructor’s way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior.\n\n New in version 1.13.0.\n\n #### Examples\n\n \n```\n>>> element = 2*np.arange(4).reshape((2, 2))\n>>> element\narray([[0, 2],\n [4, 6]])\n>>> test_elements = [1, 2, 4, 8]\n>>> mask = np.isin(element, test_elements)\n>>> mask\narray([[False, True],\n [ True, False]])\n>>> element[mask]\narray([2, 4])\n\n```\n The indices of the matched values can be obtained with [`nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\"):\n\n \n```\n>>> np.nonzero(mask)\n(array([0, 1]), array([1, 0]))\n\n```\n The test can also be inverted:\n\n \n```\n>>> mask = np.isin(element, test_elements, invert=True)\n>>> mask\narray([[ True, False],\n [False, True]])\n>>> element[mask]\narray([0, 6])\n\n```\n Because of how [`array`](numpy.array#numpy.array \"numpy.array\") handles sets, the following does not work as expected:\n\n \n```\n>>> test_set = {1, 2, 4, 8}\n>>> np.isin(element, test_set)\narray([[False, False],\n [False, False]])\n\n```\n Casting the set to a list gives the expected result:\n\n \n```\n>>> np.isin(element, list(test_set))\narray([[False, True],\n [ True, False]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.isin.htmlnumpy.setdiff1d\n===============\n\n numpy.setdiff1d(*ar1*, *ar2*, *assume_unique=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L788-L830)\n \nFind the set difference of two arrays.\n\n Return the unique values in `ar1` that are not in `ar2`.\n\n Parameters \n \n**ar1**array_like\n\nInput array.\n\n \n**ar2**array_like\n\nInput comparison array.\n\n \n**assume_unique**bool\n\nIf True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False.\n\n Returns \n \n**setdiff1d**ndarray\n\n1D array of values in `ar1` that are not in `ar2`. The result is sorted when `assume_unique=False`, but otherwise only sorted if the input is sorted.\n\n See also\n\n [`numpy.lib.arraysetops`](numpy.lib.arraysetops#module-numpy.lib.arraysetops \"numpy.lib.arraysetops\")\n\nModule with a number of other functions for performing set operations on arrays.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2, 3, 2, 4, 1])\n>>> b = np.array([3, 4, 5, 6])\n>>> np.setdiff1d(a, b)\narray([1, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.setdiff1d.htmlnumpy.setxor1d\n==============\n\n numpy.setxor1d(*ar1*, *ar2*, *assume_unique=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L476-L516)\n \nFind the set exclusive-or of two arrays.\n\n Return the sorted, unique values that are in only one (not both) of the input arrays.\n\n Parameters \n \n**ar1, ar2**array_like\n\nInput arrays.\n\n \n**assume_unique**bool\n\nIf True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False.\n\n Returns \n \n**setxor1d**ndarray\n\nSorted 1D array of unique values that are in only one of the input arrays.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2, 3, 2, 4])\n>>> b = np.array([2, 3, 5, 7, 5])\n>>> np.setxor1d(a,b)\narray([1, 4, 5, 7])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.setxor1d.htmlnumpy.union1d\n=============\n\n numpy.union1d(*ar1*, *ar2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/arraysetops.py#L747-L781)\n \nFind the union of two arrays.\n\n Return the unique, sorted array of values that are in either of the two input arrays.\n\n Parameters \n \n**ar1, ar2**array_like\n\nInput arrays. They are flattened if they are not already 1D.\n\n Returns \n \n**union1d**ndarray\n\nUnique, sorted union of the input arrays.\n\n See also\n\n [`numpy.lib.arraysetops`](numpy.lib.arraysetops#module-numpy.lib.arraysetops \"numpy.lib.arraysetops\")\n\nModule with a number of other functions for performing set operations on arrays.\n\n #### Examples\n\n \n```\n>>> np.union1d([-1, 0, 1], [-2, 0, 2])\narray([-2, -1, 0, 1, 2])\n\n```\n To find the union of more than two arrays, use functools.reduce:\n\n \n```\n>>> from functools import reduce\n>>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))\narray([1, 2, 3, 4, 6])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.union1d.htmlExtending via CFFI\n==================\n\n \n```\n\"\"\"\nUse cffi to access any of the underlying C functions from distributions.h\n\"\"\"\nimport os\nimport numpy as np\nimport cffi\nfrom .parse import parse_distributions_h\nffi = cffi.FFI()\n\ninc_dir = os.path.join(np.get_include(), 'numpy')\n\n# Basic numpy types\nffi.cdef('''\n typedef intptr_t npy_intp;\n typedef unsigned char npy_bool;\n\n''')\n\nparse_distributions_h(ffi, inc_dir)\n\nlib = ffi.dlopen(np.random._generator.__file__)\n\n# Compare the distributions.h random_standard_normal_fill to\n# Generator.standard_random\nbit_gen = np.random.PCG64()\nrng = np.random.Generator(bit_gen)\nstate = bit_gen.state\n\ninterface = rng.bit_generator.cffi\nn = 100\nvals_cffi = ffi.new('double[%d]' % n)\nlib.random_standard_normal_fill(interface.bit_generator, n, vals_cffi)\n\n# reset the state\nbit_gen.state = state\n\nvals = rng.standard_normal(n)\n\nfor i in range(n):\n assert vals[i] == vals_cffi[i]\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/cffi.htmlnumpy.msort\n===========\n\n numpy.msort(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L3645-L3671)\n \nReturn a copy of an array sorted along the first axis.\n\n Parameters \n \n**a**array_like\n\nArray to be sorted.\n\n Returns \n \n**sorted_array**ndarray\n\nArray of the same type and shape as `a`.\n\n See also\n\n [`sort`](numpy.sort#numpy.sort \"numpy.sort\")\n #### Notes\n\n `np.msort(a)` is equivalent to `np.sort(a, axis=0)`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.msort.htmlnumpy.sort_complex\n===================\n\n numpy.sort_complex(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1758-L1792)\n \nSort a complex array using the real part first, then the imaginary part.\n\n Parameters \n \n**a**array_like\n\nInput array\n\n Returns \n \n**out**complex ndarray\n\nAlways returns a sorted complex array.\n\n #### Examples\n\n \n```\n>>> np.sort_complex([5, 3, 6, 2, 1])\narray([1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j])\n\n```\n \n```\n>>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j])\narray([1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.sort_complex.htmlnumpy.nanargmax\n===============\n\n numpy.nanargmax(*a*, *axis=None*, *out=None*, ***, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L561-L615)\n \nReturn the indices of the maximum values in the specified axis ignoring NaNs. For all-NaN slices `ValueError` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and -Infs.\n\n Parameters \n \n**a**array_like\n\nInput data.\n\n \n**axis**int, optional\n\nAxis along which to operate. By default flattened input is used.\n\n \n**out**array, optional\n\nIf provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.\n\n New in version 1.22.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n New in version 1.22.0.\n\n Returns \n \n**index_array**ndarray\n\nAn array of indices or a single index value.\n\n See also\n\n \n[`argmax`](numpy.argmax#numpy.argmax \"numpy.argmax\"), [`nanargmin`](numpy.nanargmin#numpy.nanargmin \"numpy.nanargmin\")\n\n #### Examples\n\n \n```\n>>> a = np.array([[np.nan, 4], [2, 3]])\n>>> np.argmax(a)\n0\n>>> np.nanargmax(a)\n1\n>>> np.nanargmax(a, axis=0)\narray([1, 0])\n>>> np.nanargmax(a, axis=1)\narray([1, 1])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanargmax.htmlnumpy.nanargmin\n===============\n\n numpy.nanargmin(*a*, *axis=None*, *out=None*, ***, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L501-L554)\n \nReturn the indices of the minimum values in the specified axis ignoring NaNs. For all-NaN slices `ValueError` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and Infs.\n\n Parameters \n \n**a**array_like\n\nInput data.\n\n \n**axis**int, optional\n\nAxis along which to operate. By default flattened input is used.\n\n \n**out**array, optional\n\nIf provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.\n\n New in version 1.22.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the array.\n\n New in version 1.22.0.\n\n Returns \n \n**index_array**ndarray\n\nAn array of indices or a single index value.\n\n See also\n\n \n[`argmin`](numpy.argmin#numpy.argmin \"numpy.argmin\"), [`nanargmax`](numpy.nanargmax#numpy.nanargmax \"numpy.nanargmax\")\n\n #### Examples\n\n \n```\n>>> a = np.array([[np.nan, 4], [2, 3]])\n>>> np.argmin(a)\n0\n>>> np.nanargmin(a)\n2\n>>> np.nanargmin(a, axis=0)\narray([1, 1])\n>>> np.nanargmin(a, axis=1)\narray([1, 0])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanargmin.htmlnumpy.argwhere\n==============\n\n numpy.argwhere(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/numeric.py#L577-L624)\n \nFind the indices of array elements that are non-zero, grouped by element.\n\n Parameters \n \n**a**array_like\n\nInput data.\n\n Returns \n \n**index_array**(N, a.ndim) ndarray\n\nIndices of elements that are non-zero. Indices are grouped by element. This array will have shape `(N, a.ndim)` where `N` is the number of non-zero items.\n\n See also\n\n \n[`where`](numpy.where#numpy.where \"numpy.where\"), [`nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\n #### Notes\n\n `np.argwhere(a)` is almost the same as `np.transpose(np.nonzero(a))`, but produces a result of the correct shape for a 0D array.\n\n The output of `argwhere` is not suitable for indexing arrays. For this purpose use `nonzero(a)` instead.\n\n #### Examples\n\n \n```\n>>> x = np.arange(6).reshape(2,3)\n>>> x\narray([[0, 1, 2],\n [3, 4, 5]])\n>>> np.argwhere(x>1)\narray([[0, 2],\n [1, 0],\n [1, 1],\n [1, 2]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.argwhere.htmlnumpy.flatnonzero\n=================\n\n numpy.flatnonzero(*a*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/numeric.py#L631-L669)\n \nReturn indices that are non-zero in the flattened version of a.\n\n This is equivalent to `np.nonzero(np.ravel(a))[0]`.\n\n Parameters \n \n**a**array_like\n\nInput data.\n\n Returns \n \n**res**ndarray\n\nOutput array, containing the indices of the elements of `a.ravel()` that are non-zero.\n\n See also\n\n [`nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nReturn the indices of the non-zero elements of the input array.\n\n [`ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nReturn a 1-D array containing the elements of the input array.\n\n #### Examples\n\n \n```\n>>> x = np.arange(-2, 3)\n>>> x\narray([-2, -1, 0, 1, 2])\n>>> np.flatnonzero(x)\narray([0, 1, 3, 4])\n\n```\n Use the indices of the non-zero elements as an index array to extract these elements:\n\n \n```\n>>> x.ravel()[np.flatnonzero(x)]\narray([-2, -1, 1, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.flatnonzero.htmlnumpy.extract\n=============\n\n numpy.extract(*condition*, *arr*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L1856-L1905)\n \nReturn the elements of an array that satisfy some condition.\n\n This is equivalent to `np.compress(ravel(condition), ravel(arr))`. If `condition` is boolean `np.extract` is equivalent to `arr[condition]`.\n\n Note that [`place`](numpy.place#numpy.place \"numpy.place\") does the exact opposite of [`extract`](#numpy.extract \"numpy.extract\").\n\n Parameters \n \n**condition**array_like\n\nAn array whose nonzero or True entries indicate the elements of `arr` to extract.\n\n \n**arr**array_like\n\nInput array of the same size as `condition`.\n\n Returns \n \n**extract**ndarray\n\nRank 1 array of values from `arr` where `condition` is True.\n\n See also\n\n \n[`take`](numpy.take#numpy.take \"numpy.take\"), [`put`](numpy.put#numpy.put \"numpy.put\"), [`copyto`](numpy.copyto#numpy.copyto \"numpy.copyto\"), [`compress`](numpy.compress#numpy.compress \"numpy.compress\"), [`place`](numpy.place#numpy.place \"numpy.place\")\n\n #### Examples\n\n \n```\n>>> arr = np.arange(12).reshape((3, 4))\n>>> arr\narray([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> condition = np.mod(arr, 3)==0\n>>> condition\narray([[ True, False, False, True],\n [False, False, True, False],\n [False, True, False, False]])\n>>> np.extract(condition, arr)\narray([0, 3, 6, 9])\n\n```\n If `condition` is boolean:\n\n \n```\n>>> arr[condition]\narray([0, 3, 6, 9])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.extract.htmlnumpy.count_nonzero\n====================\n\n numpy.count_nonzero(*a*, *axis=None*, ***, *keepdims=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/numeric.py#L431-L502)\n \nCounts the number of non-zero values in the array `a`.\n\n The word “non-zero” is in reference to the Python 2.x built-in method `__nonzero__()` (renamed `__bool__()` in Python 3.x) of Python objects that tests an object’s “truthfulness”. For example, any number is considered truthful if it is nonzero, whereas any string is considered truthful if it is not the empty string. Thus, this function (recursively) counts how many elements in `a` (and in sub-arrays thereof) have their `__nonzero__()` or `__bool__()` method evaluated to `True`.\n\n Parameters \n \n**a**array_like\n\nThe array for which to count non-zeros.\n\n \n**axis**int or tuple, optional\n\nAxis or tuple of axes along which to count non-zeros. Default is None, meaning that non-zeros will be counted along a flattened version of `a`.\n\n New in version 1.12.0.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes that are counted are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.\n\n New in version 1.19.0.\n\n Returns \n \n**count**int or array of int\n\nNumber of non-zero values in the array along a given axis. Otherwise, the total number of non-zero values in the array is returned.\n\n See also\n\n [`nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nReturn the coordinates of all the non-zero values.\n\n #### Examples\n\n \n```\n>>> np.count_nonzero(np.eye(4))\n4\n>>> a = np.array([[0, 1, 7, 0],\n... [3, 0, 2, 19]])\n>>> np.count_nonzero(a)\n5\n>>> np.count_nonzero(a, axis=0)\narray([1, 1, 2, 1])\n>>> np.count_nonzero(a, axis=1)\narray([2, 3])\n>>> np.count_nonzero(a, axis=1, keepdims=True)\narray([[2],\n [3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.count_nonzero.htmlnumpy.percentile\n================\n\n numpy.percentile(*a*, *q*, *axis=None*, *out=None*, *overwrite_input=False*, *method='linear'*, *keepdims=False*, ***, *interpolation=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L3884-L4167)\n \nCompute the q-th percentile of the data along the specified axis.\n\n Returns the q-th percentile(s) of the array elements.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array.\n\n \n**q**array_like of float\n\nPercentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array.\n\n Changed in version 1.9.0: A tuple of axes is supported\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined.\n\n \n**method**str, optional\n\nThis parameter specifies the method to use for estimating the percentile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [[1]](#r08bde0ebf37b-1) are:\n\n 1. ‘inverted_cdf’\n2. ‘averaged_inverted_cdf’\n3. ‘closest_observation’\n4. ‘interpolated_inverted_cdf’\n5. ‘hazen’\n6. ‘weibull’\n7. ‘linear’ (default)\n8. ‘median_unbiased’\n9. ‘normal_unbiased’\n\n The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default ‘linear’ (7.) option:\n\n * ‘lower’\n* ‘higher’,\n* ‘midpoint’\n* ‘nearest’\n\n Changed in version 1.22.0: This argument was previously called “interpolation” and only offered the “linear” default and last four options.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`.\n\n New in version 1.9.0.\n\n \n**interpolation**str, optional\n\nDeprecated name for the method keyword argument.\n\n Deprecated since version 1.22.0.\n\n Returns \n \n**percentile**scalar or ndarray\n\nIf `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than `float64`, the output data-type is `float64`. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n[`median`](numpy.median#numpy.median \"numpy.median\")\n\nequivalent to `percentile(..., 50)`\n\n [`nanpercentile`](numpy.nanpercentile#numpy.nanpercentile \"numpy.nanpercentile\")\n[`quantile`](numpy.quantile#numpy.quantile \"numpy.quantile\")\n\nequivalent to percentile, except q in the range [0, 1].\n\n #### Notes\n\n Given a vector `V` of length `N`, the q-th percentile of `V` is the value `q/100` of the way from the minimum to the maximum in a sorted copy of `V`. The values and distances of the two nearest neighbors as well as the `method` parameter will determine the percentile if the normalized ranking does not match the location of `q` exactly. This function is the same as the median if `q=50`, the same as the minimum if `q=0` and the same as the maximum if `q=100`.\n\n This optional `method` parameter specifies the method to use when the desired quantile lies between two data points `i < j`. If `g` is the fractional part of the index surrounded by `i` and alpha and beta are correction constants modifying i and j.\n\n Below, ‘q’ is the quantile value, ‘n’ is the sample size and alpha and beta are constants. The following formula gives an interpolation “i + g” of where the quantile would be in the sorted sample. With ‘i’ being the floor and ‘g’ the fractional part of the result.\n\n \\[i + g = (q - alpha) / ( n - alpha - beta + 1 )\\] The different methods then work as follows\n\n inverted_cdf:\n\nmethod 1 of H&F [[1]](#r08bde0ebf37b-1). This method gives discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 ; then take i\n\n averaged_inverted_cdf:\n\nmethod 2 of H&F [[1]](#r08bde0ebf37b-1). This method give discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 ; then average between bounds\n\n closest_observation:\n\nmethod 3 of H&F [[1]](#r08bde0ebf37b-1). This method give discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 and index is odd ; then take j\n* if g = 0 and index is even ; then take i\n\n interpolated_inverted_cdf:\n\nmethod 4 of H&F [[1]](#r08bde0ebf37b-1). This method give continuous results using:\n\n * alpha = 0\n* beta = 1\n\n hazen:\n\nmethod 5 of H&F [[1]](#r08bde0ebf37b-1). This method give continuous results using:\n\n * alpha = 1/2\n* beta = 1/2\n\n weibull:\n\nmethod 6 of H&F [[1]](#r08bde0ebf37b-1). This method give continuous results using:\n\n * alpha = 0\n* beta = 0\n\n linear:\n\nmethod 7 of H&F [[1]](#r08bde0ebf37b-1). This method give continuous results using:\n\n * alpha = 1\n* beta = 1\n\n median_unbiased:\n\nmethod 8 of H&F [[1]](#r08bde0ebf37b-1). This method is probably the best method if the sample distribution function is unknown (see reference). This method give continuous results using:\n\n * alpha = 1/3\n* beta = 1/3\n\n normal_unbiased:\n\nmethod 9 of H&F [[1]](#r08bde0ebf37b-1). This method is probably the best method if the sample distribution function is known to be normal. This method give continuous results using:\n\n * alpha = 3/8\n* beta = 3/8\n\n lower:\n\nNumPy method kept for backwards compatibility. Takes `i` as the interpolation point.\n\n higher:\n\nNumPy method kept for backwards compatibility. Takes `j` as the interpolation point.\n\n nearest:\n\nNumPy method kept for backwards compatibility. Takes `i` or `j`, whichever is nearest.\n\n midpoint:\n\nNumPy method kept for backwards compatibility. Uses `(i + j) / 2`.\n\n #### References\n\n \n1([1](#id1),[2](#id2),[3](#id3),[4](#id4),[5](#id5),[6](#id6),[7](#id7),[8](#id8),[9](#id9),[10](#id10))\n \n<NAME> and <NAME>, “Sample quantiles in statistical packages,” The American Statistician, 50(4), pp. 361-365, 1996\n\n #### Examples\n\n \n```\n>>> a = np.array([[10, 7, 4], [3, 2, 1]])\n>>> a\narray([[10, 7, 4],\n [ 3, 2, 1]])\n>>> np.percentile(a, 50)\n3.5\n>>> np.percentile(a, 50, axis=0)\narray([6.5, 4.5, 2.5])\n>>> np.percentile(a, 50, axis=1)\narray([7., 2.])\n>>> np.percentile(a, 50, axis=1, keepdims=True)\narray([[7.],\n [2.]])\n\n```\n \n```\n>>> m = np.percentile(a, 50, axis=0)\n>>> out = np.zeros_like(m)\n>>> np.percentile(a, 50, axis=0, out=out)\narray([6.5, 4.5, 2.5])\n>>> m\narray([6.5, 4.5, 2.5])\n\n```\n \n```\n>>> b = a.copy()\n>>> np.percentile(b, 50, axis=1, overwrite_input=True)\narray([7., 2.])\n>>> assert not np.all(a == b)\n\n```\n The different methods can be visualized graphically:\n\n \n```\nimport matplotlib.pyplot as plt\n\na = np.arange(4)\np = np.linspace(0, 100, 6001)\nax = plt.gca()\nlines = [\n ('linear', '-', 'C0'),\n ('inverted_cdf', ':', 'C1'),\n # Almost the same as `inverted_cdf`:\n ('averaged_inverted_cdf', '-.', 'C1'),\n ('closest_observation', ':', 'C2'),\n ('interpolated_inverted_cdf', '--', 'C1'),\n ('hazen', '--', 'C3'),\n ('weibull', '-.', 'C4'),\n ('median_unbiased', '--', 'C5'),\n ('normal_unbiased', '-.', 'C6'),\n ]\nfor method, style, color in lines:\n ax.plot(\n p, np.percentile(a, p, method=method),\n label=method, linestyle=style, color=color)\nax.set(\n title='Percentiles for different methods and data: ' + str(a),\n xlabel='Percentile',\n ylabel='Estimated percentile value',\n yticks=a)\nax.legend()\nplt.show()\n\n```\n ![../../_images/numpy-percentile-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.percentile.htmlnumpy.nanpercentile\n===================\n\n numpy.nanpercentile(*a*, *q*, *axis=None*, *out=None*, *overwrite_input=False*, *method='linear'*, *keepdims=<no value>*, ***, *interpolation=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L1231-L1385)\n \nCompute the qth percentile of the data along the specified axis, while ignoring nan values.\n\n Returns the qth percentile(s) of the array elements.\n\n New in version 1.9.0.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array, containing nan values to be ignored.\n\n \n**q**array_like of float\n\nPercentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined.\n\n \n**method**str, optional\n\nThis parameter specifies the method to use for estimating the percentile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [[1]](#re21b1d0b0470-1) are:\n\n 1. ‘inverted_cdf’\n2. ‘averaged_inverted_cdf’\n3. ‘closest_observation’\n4. ‘interpolated_inverted_cdf’\n5. ‘hazen’\n6. ‘weibull’\n7. ‘linear’ (default)\n8. ‘median_unbiased’\n9. ‘normal_unbiased’\n\n The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default ‘linear’ (7.) option:\n\n * ‘lower’\n* ‘higher’,\n* ‘midpoint’\n* ‘nearest’\n\n Changed in version 1.22.0: This argument was previously called “interpolation” and only offered the “linear” default and last four options.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`.\n\n If this is anything but the default value it will be passed through (in the special case of an empty array) to the [`mean`](numpy.mean#numpy.mean \"numpy.mean\") function of the underlying array. If the array is a sub-class and [`mean`](numpy.mean#numpy.mean \"numpy.mean\") does not have the kwarg `keepdims` this will raise a RuntimeError.\n\n \n**interpolation**str, optional\n\nDeprecated name for the method keyword argument.\n\n Deprecated since version 1.22.0.\n\n Returns \n \n**percentile**scalar or ndarray\n\nIf `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than `float64`, the output data-type is `float64`. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead.\n\n See also\n\n [`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\")\n[`nanmedian`](numpy.nanmedian#numpy.nanmedian \"numpy.nanmedian\")\n\nequivalent to `nanpercentile(..., 50)`\n\n \n[`percentile`](numpy.percentile#numpy.percentile \"numpy.percentile\"), [`median`](numpy.median#numpy.median \"numpy.median\"), [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\n[`nanquantile`](numpy.nanquantile#numpy.nanquantile \"numpy.nanquantile\")\n\nequivalent to nanpercentile, except q in range [0, 1].\n\n #### Notes\n\n For more information please see [`numpy.percentile`](numpy.percentile#numpy.percentile \"numpy.percentile\")\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, “Sample quantiles in statistical packages,” The American Statistician, 50(4), pp. 361-365, 1996\n\n #### Examples\n\n \n```\n>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])\n>>> a[0][1] = np.nan\n>>> a\narray([[10., nan, 4.],\n [ 3., 2., 1.]])\n>>> np.percentile(a, 50)\nnan\n>>> np.nanpercentile(a, 50)\n3.0\n>>> np.nanpercentile(a, 50, axis=0)\narray([6.5, 2. , 2.5])\n>>> np.nanpercentile(a, 50, axis=1, keepdims=True)\narray([[7.],\n [2.]])\n>>> m = np.nanpercentile(a, 50, axis=0)\n>>> out = np.zeros_like(m)\n>>> np.nanpercentile(a, 50, axis=0, out=out)\narray([6.5, 2. , 2.5])\n>>> m\narray([6.5, 2. , 2.5])\n\n```\n \n```\n>>> b = a.copy()\n>>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)\narray([7., 2.])\n>>> assert not np.all(a==b)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanpercentile.htmlnumpy.quantile\n==============\n\n numpy.quantile(*a*, *q*, *axis=None*, *out=None*, *overwrite_input=False*, *method='linear'*, *keepdims=False*, ***, *interpolation=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L4175-L4413)\n \nCompute the q-th quantile of the data along the specified axis.\n\n New in version 1.15.0.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array.\n\n \n**q**array_like of float\n\nQuantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the array.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined.\n\n \n**method**str, optional\n\nThis parameter specifies the method to use for estimating the quantile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [[1]](#re01cd3f3acfe-1) are:\n\n 1. ‘inverted_cdf’\n2. ‘averaged_inverted_cdf’\n3. ‘closest_observation’\n4. ‘interpolated_inverted_cdf’\n5. ‘hazen’\n6. ‘weibull’\n7. ‘linear’ (default)\n8. ‘median_unbiased’\n9. ‘normal_unbiased’\n\n The first three methods are discontinuous. NumPy further defines the following discontinuous variations of the default ‘linear’ (7.) option:\n\n * ‘lower’\n* ‘higher’,\n* ‘midpoint’\n* ‘nearest’\n\n Changed in version 1.22.0: This argument was previously called “interpolation” and only offered the “linear” default and last four options.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`.\n\n \n**interpolation**str, optional\n\nDeprecated name for the method keyword argument.\n\n Deprecated since version 1.22.0.\n\n Returns \n \n**quantile**scalar or ndarray\n\nIf `q` is a single quantile and `axis=None`, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than `float64`, the output data-type is `float64`. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead.\n\n See also\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n[`percentile`](numpy.percentile#numpy.percentile \"numpy.percentile\")\n\nequivalent to quantile, but with q in the range [0, 100].\n\n [`median`](numpy.median#numpy.median \"numpy.median\")\n\nequivalent to `quantile(..., 0.5)`\n\n [`nanquantile`](numpy.nanquantile#numpy.nanquantile \"numpy.nanquantile\")\n #### Notes\n\n Given a vector `V` of length `N`, the q-th quantile of `V` is the value `q` of the way from the minimum to the maximum in a sorted copy of `V`. The values and distances of the two nearest neighbors as well as the `method` parameter will determine the quantile if the normalized ranking does not match the location of `q` exactly. This function is the same as the median if `q=0.5`, the same as the minimum if `q=0.0` and the same as the maximum if `q=1.0`.\n\n The optional `method` parameter specifies the method to use when the desired quantile lies between two data points `i < j`. If `g` is the fractional part of the index surrounded by `i` and `j`, and alpha and beta are correction constants modifying i and j:\n\n \\[i + g = (q - alpha) / ( n - alpha - beta + 1 )\\] The different methods then work as follows\n\n inverted_cdf:\n\nmethod 1 of H&F [[1]](#re01cd3f3acfe-1). This method gives discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 ; then take i\n\n averaged_inverted_cdf:\n\nmethod 2 of H&F [[1]](#re01cd3f3acfe-1). This method gives discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 ; then average between bounds\n\n closest_observation:\n\nmethod 3 of H&F [[1]](#re01cd3f3acfe-1). This method gives discontinuous results:\n\n * if g > 0 ; then take j\n* if g = 0 and index is odd ; then take j\n* if g = 0 and index is even ; then take i\n\n interpolated_inverted_cdf:\n\nmethod 4 of H&F [[1]](#re01cd3f3acfe-1). This method gives continuous results using:\n\n * alpha = 0\n* beta = 1\n\n hazen:\n\nmethod 5 of H&F [[1]](#re01cd3f3acfe-1). This method gives continuous results using:\n\n * alpha = 1/2\n* beta = 1/2\n\n weibull:\n\nmethod 6 of H&F [[1]](#re01cd3f3acfe-1). This method gives continuous results using:\n\n * alpha = 0\n* beta = 0\n\n linear:\n\nmethod 7 of H&F [[1]](#re01cd3f3acfe-1). This method gives continuous results using:\n\n * alpha = 1\n* beta = 1\n\n median_unbiased:\n\nmethod 8 of H&F [[1]](#re01cd3f3acfe-1). This method is probably the best method if the sample distribution function is unknown (see reference). This method gives continuous results using:\n\n * alpha = 1/3\n* beta = 1/3\n\n normal_unbiased:\n\nmethod 9 of H&F [[1]](#re01cd3f3acfe-1). This method is probably the best method if the sample distribution function is known to be normal. This method gives continuous results using:\n\n * alpha = 3/8\n* beta = 3/8\n\n lower:\n\nNumPy method kept for backwards compatibility. Takes `i` as the interpolation point.\n\n higher:\n\nNumPy method kept for backwards compatibility. Takes `j` as the interpolation point.\n\n nearest:\n\nNumPy method kept for backwards compatibility. Takes `i` or `j`, whichever is nearest.\n\n midpoint:\n\nNumPy method kept for backwards compatibility. Uses `(i + j) / 2`.\n\n #### References\n\n \n1([1](#id1),[2](#id2),[3](#id3),[4](#id4),[5](#id5),[6](#id6),[7](#id7),[8](#id8),[9](#id9),[10](#id10))\n \n<NAME> and <NAME>, “Sample quantiles in statistical packages,” The American Statistician, 50(4), pp. 361-365, 1996\n\n #### Examples\n\n \n```\n>>> a = np.array([[10, 7, 4], [3, 2, 1]])\n>>> a\narray([[10, 7, 4],\n [ 3, 2, 1]])\n>>> np.quantile(a, 0.5)\n3.5\n>>> np.quantile(a, 0.5, axis=0)\narray([6.5, 4.5, 2.5])\n>>> np.quantile(a, 0.5, axis=1)\narray([7., 2.])\n>>> np.quantile(a, 0.5, axis=1, keepdims=True)\narray([[7.],\n [2.]])\n>>> m = np.quantile(a, 0.5, axis=0)\n>>> out = np.zeros_like(m)\n>>> np.quantile(a, 0.5, axis=0, out=out)\narray([6.5, 4.5, 2.5])\n>>> m\narray([6.5, 4.5, 2.5])\n>>> b = a.copy()\n>>> np.quantile(b, 0.5, axis=1, overwrite_input=True)\narray([7., 2.])\n>>> assert not np.all(a == b)\n\n```\n See also [`numpy.percentile`](numpy.percentile#numpy.percentile \"numpy.percentile\") for a visualization of most methods.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.quantile.htmlnumpy.nanquantile\n=================\n\n numpy.nanquantile(*a*, *q*, *axis=None*, *out=None*, *overwrite_input=False*, *method='linear'*, *keepdims=<no value>*, ***, *interpolation=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L1393-L1542)\n \nCompute the qth quantile of the data along the specified axis, while ignoring nan values. Returns the qth quantile(s) of the array elements.\n\n New in version 1.15.0.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array, containing nan values to be ignored\n\n \n**q**array_like of float\n\nQuantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the array.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined.\n\n \n**method**str, optional\n\nThis parameter specifies the method to use for estimating the quantile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [[1]](#r02de30f409d2-1) are:\n\n 1. ‘inverted_cdf’\n2. ‘averaged_inverted_cdf’\n3. ‘closest_observation’\n4. ‘interpolated_inverted_cdf’\n5. ‘hazen’\n6. ‘weibull’\n7. ‘linear’ (default)\n8. ‘median_unbiased’\n9. ‘normal_unbiased’\n\n The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default ‘linear’ (7.) option:\n\n * ‘lower’\n* ‘higher’,\n* ‘midpoint’\n* ‘nearest’\n\n Changed in version 1.22.0: This argument was previously called “interpolation” and only offered the “linear” default and last four options.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`.\n\n If this is anything but the default value it will be passed through (in the special case of an empty array) to the [`mean`](numpy.mean#numpy.mean \"numpy.mean\") function of the underlying array. If the array is a sub-class and [`mean`](numpy.mean#numpy.mean \"numpy.mean\") does not have the kwarg `keepdims` this will raise a RuntimeError.\n\n \n**interpolation**str, optional\n\nDeprecated name for the method keyword argument.\n\n Deprecated since version 1.22.0.\n\n Returns \n \n**quantile**scalar or ndarray\n\nIf `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than `float64`, the output data-type is `float64`. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead.\n\n See also\n\n [`quantile`](numpy.quantile#numpy.quantile \"numpy.quantile\")\n\n[`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\"), [`nanmedian`](numpy.nanmedian#numpy.nanmedian \"numpy.nanmedian\")\n\n[`nanmedian`](numpy.nanmedian#numpy.nanmedian \"numpy.nanmedian\")\n\nequivalent to `nanquantile(..., 0.5)`\n\n [`nanpercentile`](numpy.nanpercentile#numpy.nanpercentile \"numpy.nanpercentile\")\n\nsame as nanquantile, but with q in the range [0, 100].\n\n #### Notes\n\n For more information please see [`numpy.quantile`](numpy.quantile#numpy.quantile \"numpy.quantile\")\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, “Sample quantiles in statistical packages,” The American Statistician, 50(4), pp. 361-365, 1996\n\n #### Examples\n\n \n```\n>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])\n>>> a[0][1] = np.nan\n>>> a\narray([[10., nan, 4.],\n [ 3., 2., 1.]])\n>>> np.quantile(a, 0.5)\nnan\n>>> np.nanquantile(a, 0.5)\n3.0\n>>> np.nanquantile(a, 0.5, axis=0)\narray([6.5, 2. , 2.5])\n>>> np.nanquantile(a, 0.5, axis=1, keepdims=True)\narray([[7.],\n [2.]])\n>>> m = np.nanquantile(a, 0.5, axis=0)\n>>> out = np.zeros_like(m)\n>>> np.nanquantile(a, 0.5, axis=0, out=out)\narray([6.5, 2. , 2.5])\n>>> m\narray([6.5, 2. , 2.5])\n>>> b = a.copy()\n>>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)\narray([7., 2.])\n>>> assert not np.all(a==b)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanquantile.htmlnumpy.nanmedian\n===============\n\n numpy.nanmedian(*a*, *axis=None*, *out=None*, *overwrite_input=False*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L1126-L1222)\n \nCompute the median along the specified axis, while ignoring NaNs.\n\n Returns the median of the array elements.\n\n New in version 1.9.0.\n\n Parameters \n \n**a**array_like\n\nInput array or object that can be converted to an array.\n\n \n**axis**{int, sequence of int, None}, optional\n\nAxis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array. A sequence of axes is supported since version 1.9.0.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.\n\n \n**overwrite_input**bool, optional\n\nIf True, then allow use of memory of input array `a` for calculations. The input array will be modified by the call to [`median`](numpy.median#numpy.median \"numpy.median\"). This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. If `overwrite_input` is `True` and `a` is not already an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), an error will be raised.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If this is anything but the default value it will be passed through (in the special case of an empty array) to the [`mean`](numpy.mean#numpy.mean \"numpy.mean\") function of the underlying array. If the array is a sub-class and [`mean`](numpy.mean#numpy.mean \"numpy.mean\") does not have the kwarg `keepdims` this will raise a RuntimeError.\n\n Returns \n \n**median**ndarray\n\nA new array holding the result. If the input contains integers or floats smaller than `float64`, then the output data-type is `np.float64`. Otherwise, the data-type of the output is the same as that of the input. If `out` is specified, that array is returned instead.\n\n See also\n\n \n[`mean`](numpy.mean#numpy.mean \"numpy.mean\"), [`median`](numpy.median#numpy.median \"numpy.median\"), [`percentile`](numpy.percentile#numpy.percentile \"numpy.percentile\")\n\n #### Notes\n\n Given a vector `V` of length `N`, the median of `V` is the middle value of a sorted copy of `V`, `V_sorted` - i.e., `V_sorted[(N-1)/2]`, when `N` is odd and the average of the two middle values of `V_sorted` when `N` is even.\n\n #### Examples\n\n \n```\n>>> a = np.array([[10.0, 7, 4], [3, 2, 1]])\n>>> a[0, 1] = np.nan\n>>> a\narray([[10., nan, 4.],\n [ 3., 2., 1.]])\n>>> np.median(a)\nnan\n>>> np.nanmedian(a)\n3.0\n>>> np.nanmedian(a, axis=0)\narray([6.5, 2. , 2.5])\n>>> np.median(a, axis=1)\narray([nan, 2.])\n>>> b = a.copy()\n>>> np.nanmedian(b, axis=1, overwrite_input=True)\narray([7., 2.])\n>>> assert not np.all(a==b)\n>>> b = a.copy()\n>>> np.nanmedian(b, axis=None, overwrite_input=True)\n3.0\n>>> assert not np.all(a==b)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanmedian.htmlnumpy.nanmean\n=============\n\n numpy.nanmean(*a*, *axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*, ***, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L952-L1055)\n \nCompute the arithmetic mean along the specified axis, ignoring NaNs.\n\n Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\") intermediate and return values are used for integer inputs.\n\n For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.\n\n New in version 1.8.0.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the means are computed. The default is to compute the mean of the flattened array.\n\n \n**dtype**data-type, optional\n\nType to use in computing the mean. For integer inputs, the default is [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"); for inexact inputs, it is the same as the input dtype.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. The default is `None`; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See [Output type determination](../../user/basics.ufuncs#ufuncs-output-type) for more details.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If the value is anything but the default, then `keepdims` will be passed through to the [`mean`](numpy.mean#numpy.mean \"numpy.mean\") or [`sum`](numpy.sum#numpy.sum \"numpy.sum\") methods of sub-classes of [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"). If the sub-classes methods does not implement `keepdims` any exceptions will be raised.\n\n \n**where**array_like of bool, optional\n\nElements to include in the mean. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**m**ndarray, see dtype parameter above\n\nIf `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. Nan is returned for slices that contain only NaNs.\n\n See also\n\n [`average`](numpy.average#numpy.average \"numpy.average\")\n\nWeighted average\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nArithmetic mean taken while not ignoring NaNs\n\n \n[`var`](numpy.var#numpy.var \"numpy.var\"), [`nanvar`](numpy.nanvar#numpy.nanvar \"numpy.nanvar\")\n\n #### Notes\n\n The arithmetic mean is the sum of the non-NaN elements along the axis divided by the number of non-NaN elements.\n\n Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for [`float32`](../arrays.scalars#numpy.float32 \"numpy.float32\"). Specifying a higher-precision accumulator using the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") keyword can alleviate this issue.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, np.nan], [3, 4]])\n>>> np.nanmean(a)\n2.6666666666666665\n>>> np.nanmean(a, axis=0)\narray([2., 4.])\n>>> np.nanmean(a, axis=1)\narray([1., 3.5]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanmean.htmlnumpy.nanstd\n============\n\n numpy.nanstd(*a*, *axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*, ***, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L1777-L1886)\n \nCompute the standard deviation along the specified axis, while ignoring NaNs.\n\n Returns the standard deviation, a measure of the spread of a distribution, of the non-NaN array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis.\n\n For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised.\n\n New in version 1.8.0.\n\n Parameters \n \n**a**array_like\n\nCalculate the standard deviation of the non-NaN values.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array.\n\n \n**dtype**dtype, optional\n\nType to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary.\n\n \n**ddof**int, optional\n\nMeans Delta Degrees of Freedom. The divisor used in calculations is `N - ddof`, where `N` represents the number of non-NaN elements. By default `ddof` is zero.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n If this value is anything but the default it is passed through as-is to the relevant functions of the sub-classes. If these functions do not have a `keepdims` kwarg, a RuntimeError will be raised.\n\n \n**where**array_like of bool, optional\n\nElements to include in the standard deviation. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**standard_deviation**ndarray, see dtype parameter above.\n\nIf `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.\n\n See also\n\n \n[`var`](numpy.var#numpy.var \"numpy.var\"), [`mean`](numpy.mean#numpy.mean \"numpy.mean\"), [`std`](numpy.std#numpy.std \"numpy.std\")\n\n[`nanvar`](numpy.nanvar#numpy.nanvar \"numpy.nanvar\"), [`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\")\n\n[Output type determination](../../user/basics.ufuncs#ufuncs-output-type)\n #### Notes\n\n The standard deviation is the square root of the average of the squared deviations from the mean: `std = sqrt(mean(abs(x - x.mean())**2))`.\n\n The average squared deviation is normally calculated as `x.sum() / N`, where `N = len(x)`. If, however, `ddof` is specified, the divisor `N - ddof` is used instead. In standard statistical practice, `ddof=1` provides an unbiased estimator of the variance of the infinite population. `ddof=0` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with `ddof=1`, it will not be an unbiased estimate of the standard deviation per se.\n\n Note that, for complex numbers, [`std`](numpy.std#numpy.std \"numpy.std\") takes the absolute value before squaring, so that the result is always real and nonnegative.\n\n For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") keyword can alleviate this issue.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, np.nan], [3, 4]])\n>>> np.nanstd(a)\n1.247219128924647\n>>> np.nanstd(a, axis=0)\narray([1., 0.])\n>>> np.nanstd(a, axis=1)\narray([0., 0.5]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanstd.htmlnumpy.nanvar\n============\n\n numpy.nanvar(*a*, *axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=<no value>*, ***, *where=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/nanfunctions.py#L1616-L1769)\n \nCompute the variance along the specified axis, while ignoring NaNs.\n\n Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.\n\n For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised.\n\n New in version 1.8.0.\n\n Parameters \n \n**a**array_like\n\nArray containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted.\n\n \n**axis**{int, tuple of int, None}, optional\n\nAxis or axes along which the variance is computed. The default is to compute the variance of the flattened array.\n\n \n**dtype**data-type, optional\n\nType to use in computing the variance. For arrays of integer type the default is [`float64`](../arrays.scalars#numpy.float64 \"numpy.float64\"); for arrays of float types it is the same as the array type.\n\n \n**out**ndarray, optional\n\nAlternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.\n\n \n**ddof**int, optional\n\n“Delta Degrees of Freedom”: the divisor used in the calculation is `N - ddof`, where `N` represents the number of non-NaN elements. By default `ddof` is zero.\n\n \n**keepdims**bool, optional\n\nIf this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`.\n\n \n**where**array_like of bool, optional\n\nElements to include in the variance. See [`reduce`](numpy.ufunc.reduce#numpy.ufunc.reduce \"numpy.ufunc.reduce\") for details.\n\n New in version 1.22.0.\n\n Returns \n \n**variance**ndarray, see dtype parameter above\n\nIf `out` is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.\n\n See also\n\n [`std`](numpy.std#numpy.std \"numpy.std\")\n\nStandard deviation\n\n [`mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nAverage\n\n [`var`](numpy.var#numpy.var \"numpy.var\")\n\nVariance while not ignoring NaNs\n\n \n[`nanstd`](numpy.nanstd#numpy.nanstd \"numpy.nanstd\"), [`nanmean`](numpy.nanmean#numpy.nanmean \"numpy.nanmean\")\n\n[Output type determination](../../user/basics.ufuncs#ufuncs-output-type)\n #### Notes\n\n The variance is the average of the squared deviations from the mean, i.e., `var = mean(abs(x - x.mean())**2)`.\n\n The mean is normally calculated as `x.sum() / N`, where `N = len(x)`. If, however, `ddof` is specified, the divisor `N - ddof` is used instead. In standard statistical practice, `ddof=1` provides an unbiased estimator of the variance of a hypothetical infinite population. `ddof=0` provides a maximum likelihood estimate of the variance for normally distributed variables.\n\n Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.\n\n For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for [`float32`](../arrays.scalars#numpy.float32 \"numpy.float32\") (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue.\n\n For this function to work on sub-classes of ndarray, they must define [`sum`](numpy.sum#numpy.sum \"numpy.sum\") with the kwarg `keepdims`\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, np.nan], [3, 4]])\n>>> np.nanvar(a)\n1.5555555555555554\n>>> np.nanvar(a, axis=0)\narray([1., 0.])\n>>> np.nanvar(a, axis=1)\narray([0., 0.25]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nanvar.htmlnumpy.correlate\n===============\n\n numpy.correlate(*a*, *v*, *mode='valid'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/numeric.py#L676-L747)\n \nCross-correlation of two 1-dimensional sequences.\n\n This function computes the correlation as generally defined in signal processing texts:\n\n \\[c_k = \\sum_n a_{n+k} \\cdot \\overline{v_n}\\] with a and v sequences being zero-padded where necessary and \\(\\overline x\\) denoting complex conjugation.\n\n Parameters \n \n**a, v**array_like\n\nInput sequences.\n\n \n**mode**{‘valid’, ‘same’, ‘full’}, optional\n\nRefer to the [`convolve`](numpy.convolve#numpy.convolve \"numpy.convolve\") docstring. Note that the default is ‘valid’, unlike [`convolve`](numpy.convolve#numpy.convolve \"numpy.convolve\"), which uses ‘full’.\n\n \n**old_behavior**bool\n\n`old_behavior` was removed in NumPy 1.10. If you need the old behavior, use `multiarray.correlate`.\n\n Returns \n \n**out**ndarray\n\nDiscrete cross-correlation of `a` and `v`.\n\n See also\n\n [`convolve`](numpy.convolve#numpy.convolve \"numpy.convolve\")\n\nDiscrete, linear convolution of two one-dimensional sequences.\n\n `multiarray.correlate`\n\nOld, no conjugate, version of correlate.\n\n [`scipy.signal.correlate`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.correlate.html#scipy.signal.correlate \"(in SciPy v1.8.1)\")\n\nuses FFT which has superior performance on large arrays.\n\n #### Notes\n\n The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is:\n\n \\[c'_k = \\sum_n a_{n} \\cdot \\overline{v_{n+k}}\\] which is related to \\(c_k\\) by \\(c'_k = c_{-k}\\).\n\n [`numpy.correlate`](#numpy.correlate \"numpy.correlate\") may perform slowly in large arrays (i.e. n = 1e5) because it does not use the FFT to compute the convolution; in that case, [`scipy.signal.correlate`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.correlate.html#scipy.signal.correlate \"(in SciPy v1.8.1)\") might be preferable.\n\n #### Examples\n\n \n```\n>>> np.correlate([1, 2, 3], [0, 1, 0.5])\narray([3.5])\n>>> np.correlate([1, 2, 3], [0, 1, 0.5], \"same\")\narray([2. , 3.5, 3. ])\n>>> np.correlate([1, 2, 3], [0, 1, 0.5], \"full\")\narray([0.5, 2. , 3.5, 3. , 0. ])\n\n```\n Using complex sequences:\n\n \n```\n>>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')\narray([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])\n\n```\n Note that you get the time reversed, complex conjugated result (\\(\\overline{c_{-k}}\\)) when the two input sequences a and v change places:\n\n \n```\n>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')\narray([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.correlate.htmlnumpy.histogram\n===============\n\n numpy.histogram(*a*, *bins=10*, *range=None*, *normed=None*, *weights=None*, *density=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/histograms.py#L678-L929)\n \nCompute the histogram of a dataset.\n\n Parameters \n \n**a**array_like\n\nInput data. The histogram is computed over the flattened array.\n\n \n**bins**int or sequence of scalars or str, optional\n\nIf `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin widths.\n\n New in version 1.11.0.\n\n If `bins` is a string, it defines the method used to calculate the optimal bin width, as defined by [`histogram_bin_edges`](numpy.histogram_bin_edges#numpy.histogram_bin_edges \"numpy.histogram_bin_edges\").\n\n \n**range**(float, float), optional\n\nThe lower and upper range of the bins. If not provided, range is simply `(a.min(), a.max())`. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data.\n\n \n**normed**bool, optional\n\n Deprecated since version 1.6.0.\n\n This is equivalent to the `density` argument, but produces incorrect results for unequal bin widths. It should not be used.\n\n Changed in version 1.15.0: DeprecationWarnings are actually emitted.\n\n \n**weights**array_like, optional\n\nAn array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). If `density` is True, the weights are normalized, so that the integral of the density over the range remains 1.\n\n \n**density**bool, optional\n\nIf `False`, the result will contain the number of samples in each bin. If `True`, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability *mass* function.\n\n Overrides the `normed` keyword if given.\n\n Returns \n \n**hist**array\n\nThe values of the histogram. See `density` and `weights` for a description of the possible semantics.\n\n \n**bin_edges**array of dtype float\n\nReturn the bin edges `(length(hist)+1)`.\n\n See also\n\n \n[`histogramdd`](numpy.histogramdd#numpy.histogramdd \"numpy.histogramdd\"), [`bincount`](numpy.bincount#numpy.bincount \"numpy.bincount\"), [`searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\"), [`digitize`](numpy.digitize#numpy.digitize \"numpy.digitize\"), [`histogram_bin_edges`](numpy.histogram_bin_edges#numpy.histogram_bin_edges \"numpy.histogram_bin_edges\")\n\n #### Notes\n\n All but the last (righthand-most) bin is half-open. In other words, if `bins` is:\n\n \n```\n[1, 2, 3, 4]\n\n```\n then the first bin is `[1, 2)` (including 1, but excluding 2) and the second `[2, 3)`. The last bin, however, is `[3, 4]`, which *includes* 4.\n\n #### Examples\n\n \n```\n>>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3])\n(array([0, 2, 1]), array([0, 1, 2, 3]))\n>>> np.histogram(np.arange(4), bins=np.arange(5), density=True)\n(array([0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))\n>>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])\n(array([1, 4, 1]), array([0, 1, 2, 3]))\n\n```\n \n```\n>>> a = np.arange(5)\n>>> hist, bin_edges = np.histogram(a, density=True)\n>>> hist\narray([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])\n>>> hist.sum()\n2.4999999999999996\n>>> np.sum(hist * np.diff(bin_edges))\n1.0\n\n```\n New in version 1.11.0.\n\n Automated Bin Selection Methods example, using 2 peak random data with 2000 points:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> rng = np.random.RandomState(10) # deterministic random data\n>>> a = np.hstack((rng.normal(size=1000),\n... rng.normal(loc=5, scale=2, size=1000)))\n>>> _ = plt.hist(a, bins='auto') # arguments are passed to np.histogram\n>>> plt.title(\"Histogram with 'auto' bins\")\nText(0.5, 1.0, \"Histogram with 'auto' bins\")\n>>> plt.show()\n\n```\n ![../../_images/numpy-histogram-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.histogram.htmlnumpy.histogram2d\n=================\n\n numpy.histogram2d(*x*, *y*, *bins=10*, *range=None*, *normed=None*, *weights=None*, *density=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/twodim_base.py#L655-L826)\n \nCompute the bi-dimensional histogram of two data samples.\n\n Parameters \n \n**x**array_like, shape (N,)\n\nAn array containing the x coordinates of the points to be histogrammed.\n\n \n**y**array_like, shape (N,)\n\nAn array containing the y coordinates of the points to be histogrammed.\n\n \n**bins**int or array_like or [int, int] or [array, array], optional\n\nThe bin specification:\n\n * If int, the number of bins for the two dimensions (nx=ny=bins).\n* If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).\n* If [int, int], the number of bins in each dimension (nx, ny = bins).\n* If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).\n* A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges.\n\n \n**range**array_like, shape(2,2), optional\n\nThe leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): `[[xmin, xmax], [ymin, ymax]]`. All values outside of this range will be considered outliers and not tallied in the histogram.\n\n \n**density**bool, optional\n\nIf False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, `bin_count / sample_count / bin_area`.\n\n \n**normed**bool, optional\n\nAn alias for the density argument that behaves identically. To avoid confusion with the broken normed argument to [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\"), `density` should be preferred.\n\n \n**weights**array_like, shape(N,), optional\n\nAn array of values `w_i` weighing each sample `(x_i, y_i)`. Weights are normalized to 1 if `normed` is True. If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin.\n\n Returns \n \n**H**ndarray, shape(nx, ny)\n\nThe bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension.\n\n \n**xedges**ndarray, shape(nx+1,)\n\nThe bin edges along the first dimension.\n\n \n**yedges**ndarray, shape(ny+1,)\n\nThe bin edges along the second dimension.\n\n See also\n\n [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\")\n\n1D histogram\n\n [`histogramdd`](numpy.histogramdd#numpy.histogramdd \"numpy.histogramdd\")\n\nMultidimensional histogram\n\n #### Notes\n\n When `normed` is True, then the returned histogram is the sample density, defined such that the sum over bins of the product `bin_value * bin_area` is 1.\n\n Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with [`histogramdd`](numpy.histogramdd#numpy.histogramdd \"numpy.histogramdd\").\n\n #### Examples\n\n \n```\n>>> from matplotlib.image import NonUniformImage\n>>> import matplotlib.pyplot as plt\n\n```\n Construct a 2-D histogram with variable bin width. First define the bin edges:\n\n \n```\n>>> xedges = [0, 1, 3, 5]\n>>> yedges = [0, 2, 3, 4, 6]\n\n```\n Next we create a histogram H with random bin content:\n\n \n```\n>>> x = np.random.normal(2, 1, 100)\n>>> y = np.random.normal(1, 1, 100)\n>>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges))\n>>> # Histogram does not follow Cartesian convention (see Notes),\n>>> # therefore transpose H for visualization purposes.\n>>> H = H.T\n\n```\n [`imshow`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow \"(in Matplotlib v3.5.2)\") can only display square bins:\n\n \n```\n>>> fig = plt.figure(figsize=(7, 3))\n>>> ax = fig.add_subplot(131, title='imshow: square bins')\n>>> plt.imshow(H, interpolation='nearest', origin='lower',\n... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])\n<matplotlib.image.AxesImage object at 0x...```\n [`pcolormesh`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh \"(in Matplotlib v3.5.2)\") can display actual edges:\n\n \n```\n>>> ax = fig.add_subplot(132, title='pcolormesh: actual edges',\n... aspect='equal')\n>>> X, Y = np.meshgrid(xedges, yedges)\n>>> ax.pcolormesh(X, Y, H)\n<matplotlib.collections.QuadMesh object at 0x...```\n [`NonUniformImage`](https://matplotlib.org/stable/api/image_api.html#matplotlib.image.NonUniformImage \"(in Matplotlib v3.5.2)\") can be used to display actual bin edges with interpolation:\n\n \n```\n>>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated',\n... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]])\n>>> im = NonUniformImage(ax, interpolation='bilinear')\n>>> xcenters = (xedges[:-1] + xedges[1:]) / 2\n>>> ycenters = (yedges[:-1] + yedges[1:]) / 2\n>>> im.set_data(xcenters, ycenters, H)\n>>> ax.images.append(im)\n>>> plt.show()\n\n```\n ![../../_images/numpy-histogram2d-1_00_00.png] It is also possible to construct a 2-D histogram without specifying bin edges:\n\n \n```\n>>> # Generate non-symmetric test data\n>>> n = 10000\n>>> x = np.linspace(1, 100, n)\n>>> y = 2*np.log(x) + np.random.rand(n) - 0.5\n>>> # Compute 2d histogram. Note the order of x/y and xedges/yedges\n>>> H, yedges, xedges = np.histogram2d(y, x, bins=20)\n\n```\n Now we can plot the histogram using [`pcolormesh`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh \"(in Matplotlib v3.5.2)\"), and a [`hexbin`](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.hexbin.html#matplotlib.pyplot.hexbin \"(in Matplotlib v3.5.2)\") for comparison.\n\n \n```\n>>> # Plot histogram using pcolormesh\n>>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)\n>>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow')\n>>> ax1.plot(x, 2*np.log(x), 'k-')\n>>> ax1.set_xlim(x.min(), x.max())\n>>> ax1.set_ylim(y.min(), y.max())\n>>> ax1.set_xlabel('x')\n>>> ax1.set_ylabel('y')\n>>> ax1.set_title('histogram2d')\n>>> ax1.grid()\n\n```\n \n```\n>>> # Create hexbin plot for comparison\n>>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow')\n>>> ax2.plot(x, 2*np.log(x), 'k-')\n>>> ax2.set_title('hexbin')\n>>> ax2.set_xlim(x.min(), x.max())\n>>> ax2.set_xlabel('x')\n>>> ax2.grid()\n\n```\n \n```\n>>> plt.show()\n\n```\n ![../../_images/numpy-histogram2d-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.histogram2d.htmlnumpy.histogramdd\n=================\n\n numpy.histogramdd(*sample*, *bins=10*, *range=None*, *normed=None*, *weights=None*, *density=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/histograms.py#L943-L1129)\n \nCompute the multidimensional histogram of some data.\n\n Parameters \n \n**sample**(N, D) array, or (D, N) array_like\n\nThe data to be histogrammed.\n\n Note the unusual interpretation of sample when an array_like:\n\n * When an array, each row is a coordinate in a D-dimensional space - such as `histogramdd(np.array([p1, p2, p3]))`.\n* When an array_like, each element is the list of values for single coordinate - such as `histogramdd((X, Y, Z))`.\n\n The first form should be preferred.\n\n \n**bins**sequence or int, optional\n\nThe bin specification:\n\n * A sequence of arrays describing the monotonically increasing bin edges along each dimension.\n* The number of bins for each dimension (nx, ny, … =bins)\n* The number of bins for all dimensions (nx=ny=…=bins).\n\n \n**range**sequence, optional\n\nA sequence of length D, each an optional (lower, upper) tuple giving the outer bin edges to be used if the edges are not given explicitly in `bins`. An entry of None in the sequence results in the minimum and maximum values being used for the corresponding dimension. The default, None, is equivalent to passing a tuple of D None values.\n\n \n**density**bool, optional\n\nIf False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, `bin_count / sample_count / bin_volume`.\n\n \n**normed**bool, optional\n\nAn alias for the density argument that behaves identically. To avoid confusion with the broken normed argument to [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\"), `density` should be preferred.\n\n \n**weights**(N,) array_like, optional\n\nAn array of values `w_i` weighing each sample `(x_i, y_i, z_i, …)`. Weights are normalized to 1 if normed is True. If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin.\n\n Returns \n \n**H**ndarray\n\nThe multidimensional histogram of sample x. See normed and weights for the different possible semantics.\n\n \n**edges**list\n\nA list of D arrays describing the bin edges for each dimension.\n\n See also\n\n [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\")\n\n1-D histogram\n\n [`histogram2d`](numpy.histogram2d#numpy.histogram2d \"numpy.histogram2d\")\n\n2-D histogram\n\n #### Examples\n\n \n```\n>>> r = np.random.randn(100,3)\n>>> H, edges = np.histogramdd(r, bins = (5, 8, 4))\n>>> H.shape, edges[0].size, edges[1].size, edges[2].size\n((5, 8, 4), 6, 9, 5)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.histogramdd.htmlnumpy.histogram_bin_edges\n===========================\n\n numpy.histogram_bin_edges(*a*, *bins=10*, *range=None*, *weights=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/histograms.py#L470-L670)\n \nFunction to calculate only the edges of the bins used by the [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\") function.\n\n Parameters \n \n**a**array_like\n\nInput data. The histogram is computed over the flattened array.\n\n \n**bins**int or sequence of scalars or str, optional\n\nIf `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths.\n\n If `bins` is a string from the list below, [`histogram_bin_edges`](#numpy.histogram_bin_edges \"numpy.histogram_bin_edges\") will use the method chosen to calculate the optimal bin width and consequently the number of bins (see `Notes` for more detail on the estimators) from the data that falls within the requested range. While the bin width will be optimal for the actual data in the range, the number of bins will be computed to fill the entire range, including the empty portions. For visualisation, using the ‘auto’ option is suggested. Weighted data is not supported for automated bin size selection.\n\n ‘auto’\n\nMaximum of the ‘sturges’ and ‘fd’ estimators. Provides good all around performance.\n\n ‘fd’ (Freedman Diaconis Estimator)\n\nRobust (resilient to outliers) estimator that takes into account data variability and data size.\n\n ‘doane’\n\nAn improved version of Sturges’ estimator that works better with non-normal datasets.\n\n ‘scott’\n\nLess robust estimator that takes into account data variability and data size.\n\n ‘stone’\n\nEstimator based on leave-one-out cross-validation estimate of the integrated squared error. Can be regarded as a generalization of Scott’s rule.\n\n ‘rice’\n\nEstimator does not take variability into account, only data size. Commonly overestimates number of bins required.\n\n ‘sturges’\n\nR’s default method, only accounts for data size. Only optimal for gaussian data and underestimates number of bins for large non-gaussian datasets.\n\n ‘sqrt’\n\nSquare root (of data size) estimator, used by Excel and other programs for its speed and simplicity.\n\n \n**range**(float, float), optional\n\nThe lower and upper range of the bins. If not provided, range is simply `(a.min(), a.max())`. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data.\n\n \n**weights**array_like, optional\n\nAn array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). This is currently not used by any of the bin estimators, but may be in the future.\n\n Returns \n \n**bin_edges**array of dtype float\n\nThe edges to pass into [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\")\n\n See also\n\n [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\")\n #### Notes\n\n The methods to estimate the optimal number of bins are well founded in literature, and are inspired by the choices R provides for histogram visualisation. Note that having the number of bins proportional to \\(n^{1/3}\\) is asymptotically optimal, which is why it appears in most estimators. These are simply plug-in methods that give good starting points for number of bins. In the equations below, \\(h\\) is the binwidth and \\(n_h\\) is the number of bins. All estimators that compute bin counts are recast to bin width using the [`ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\") of the data. The final bin count is obtained from `np.round(np.ceil(range / h))`. The final bin width is often less than what is returned by the estimators below.\n\n ‘auto’ (maximum of the ‘sturges’ and ‘fd’ estimators)\n\nA compromise to get a good value. For small datasets the Sturges value will usually be chosen, while larger datasets will usually default to FD. Avoids the overly conservative behaviour of FD and Sturges for small and large datasets respectively. Switchover point is usually \\(a.size \\approx 1000\\).\n\n ‘fd’ (Freedman Diaconis Estimator)\n\n \\[h = 2 \\frac{IQR}{n^{1/3}}\\] The binwidth is proportional to the interquartile range (IQR) and inversely proportional to cube root of a.size. Can be too conservative for small datasets, but is quite good for large datasets. The IQR is very robust to outliers.\n\n ‘scott’\n\n \\[h = \\sigma \\sqrt[3]{\\frac{24 \\sqrt{\\pi}}{n}}\\] The binwidth is proportional to the standard deviation of the data and inversely proportional to cube root of `x.size`. Can be too conservative for small datasets, but is quite good for large datasets. The standard deviation is not very robust to outliers. Values are very similar to the Freedman-Diaconis estimator in the absence of outliers.\n\n ‘rice’\n\n \\[n_h = 2n^{1/3}\\] The number of bins is only proportional to cube root of `a.size`. It tends to overestimate the number of bins and it does not take into account data variability.\n\n ‘sturges’\n\n \\[n_h = \\log _{2}(n) + 1\\] The number of bins is the base 2 log of `a.size`. This estimator assumes normality of data and is too conservative for larger, non-normal datasets. This is the default method in R’s `hist` method.\n\n ‘doane’\n\n \\[ \\begin{align}\\begin{aligned}n_h = 1 + \\log_{2}(n) + \\log_{2}\\left(1 + \\frac{|g_1|}{\\sigma_{g_1}}\\right)\\\\g_1 = mean\\left[\\left(\\frac{x - \\mu}{\\sigma}\\right)^3\\right]\\\\\\sigma_{g_1} = \\sqrt{\\frac{6(n - 2)}{(n + 1)(n + 3)}}\\end{aligned}\\end{align} \\] An improved version of Sturges’ formula that produces better estimates for non-normal datasets. This estimator attempts to account for the skew of the data.\n\n ‘sqrt’\n\n \\[n_h = \\sqrt n\\] The simplest and fastest estimator. Only takes into account the data size.\n\n #### Examples\n\n \n```\n>>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5])\n>>> np.histogram_bin_edges(arr, bins='auto', range=(0, 1))\narray([0. , 0.25, 0.5 , 0.75, 1. ])\n>>> np.histogram_bin_edges(arr, bins=2)\narray([0. , 2.5, 5. ])\n\n```\n For consistency with histogram, an array of pre-computed bins is passed through unmodified:\n\n \n```\n>>> np.histogram_bin_edges(arr, [1, 2])\narray([1, 2])\n\n```\n This function allows one set of bins to be computed, and reused across multiple histograms:\n\n \n```\n>>> shared_bins = np.histogram_bin_edges(arr, bins='auto')\n>>> shared_bins\narray([0., 1., 2., 3., 4., 5.])\n\n```\n \n```\n>>> group_id = np.array([0, 1, 1, 0, 1, 1, 0, 1, 1])\n>>> hist_0, _ = np.histogram(arr[group_id == 0], bins=shared_bins)\n>>> hist_1, _ = np.histogram(arr[group_id == 1], bins=shared_bins)\n\n```\n \n```\n>>> hist_0; hist_1\narray([1, 1, 0, 1, 0])\narray([2, 0, 1, 1, 2])\n\n```\n Which gives more easily comparable results than using separate bins for each histogram:\n\n \n```\n>>> hist_0, bins_0 = np.histogram(arr[group_id == 0], bins='auto')\n>>> hist_1, bins_1 = np.histogram(arr[group_id == 1], bins='auto')\n>>> hist_0; hist_1\narray([1, 1, 1])\narray([2, 1, 1, 2])\n>>> bins_0; bins_1\narray([0., 1., 2., 3.])\narray([0. , 1.25, 2.5 , 3.75, 5. ])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.histogram_bin_edges.htmlnumpy.digitize\n==============\n\n numpy.digitize(*x*, *bins*, *right=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L5447-L5555)\n \nReturn the indices of the bins to which each value in input array belongs.\n\n \n\n| `right` | order of bins | returned index `i` satisfies |\n| --- | --- | --- |\n| `False` | increasing | `bins[i-1] <= x < bins[i]` |\n| `True` | increasing | `bins[i-1] < x <= bins[i]` |\n| `False` | decreasing | `bins[i-1] > x >= bins[i]` |\n| `True` | decreasing | `bins[i-1] >= x > bins[i]` |\n\n If values in `x` are beyond the bounds of `bins`, 0 or `len(bins)` is returned as appropriate.\n\n Parameters \n \n**x**array_like\n\nInput array to be binned. Prior to NumPy 1.10.0, this array had to be 1-dimensional, but can now have any shape.\n\n \n**bins**array_like\n\nArray of bins. It has to be 1-dimensional and monotonic.\n\n \n**right**bool, optional\n\nIndicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins.\n\n Returns \n \n**indices**ndarray of ints\n\nOutput array of indices, of same shape as `x`.\n\n Raises \n ValueError\n\nIf `bins` is not monotonic.\n\n TypeError\n\nIf the type of the input is complex.\n\n See also\n\n \n[`bincount`](numpy.bincount#numpy.bincount \"numpy.bincount\"), [`histogram`](numpy.histogram#numpy.histogram \"numpy.histogram\"), [`unique`](numpy.unique#numpy.unique \"numpy.unique\"), [`searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n #### Notes\n\n If values in `x` are such that they fall outside the bin range, attempting to index `bins` with the indices that [`digitize`](#numpy.digitize \"numpy.digitize\") returns will result in an IndexError.\n\n New in version 1.10.0.\n\n `np.digitize` is implemented in terms of `np.searchsorted`. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1-dimensional.\n\n For monotonically _increasing_ `bins`, the following are equivalent:\n\n \n```\nnp.digitize(x, bins, right=True)\nnp.searchsorted(bins, x, side='left')\n\n```\n Note that as the order of the arguments are reversed, the side must be too. The [`searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\") call is marginally faster, as it does not do any monotonicity checks. Perhaps more importantly, it supports all dtypes.\n\n #### Examples\n\n \n```\n>>> x = np.array([0.2, 6.4, 3.0, 1.6])\n>>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])\n>>> inds = np.digitize(x, bins)\n>>> inds\narray([1, 4, 3, 2])\n>>> for n in range(x.size):\n... print(bins[inds[n]-1], \"<=\", x[n], \"<\", bins[inds[n]])\n...\n0.0 <= 0.2 < 1.0\n4.0 <= 6.4 < 10.0\n2.5 <= 3.0 < 4.0\n1.0 <= 1.6 < 2.5\n\n```\n \n```\n>>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])\n>>> bins = np.array([0, 5, 10, 15, 20])\n>>> np.digitize(x,bins,right=True)\narray([1, 2, 3, 4, 4])\n>>> np.digitize(x,bins,right=False)\narray([1, 3, 3, 4, 5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.digitize.htmlnumpy.testing.assert_allclose\n==============================\n\n testing.assert_allclose(*actual*, *desired*, *rtol=1e-07*, *atol=0*, *equal_nan=True*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1473-L1528)\n \nRaises an AssertionError if two objects are not equal up to desired tolerance.\n\n The test is equivalent to `allclose(actual, desired, rtol, atol)` (note that `allclose` has different default values). It compares the difference between `actual` and `desired` to `atol + rtol * abs(desired)`.\n\n New in version 1.5.0.\n\n Parameters \n \n**actual**array_like\n\nArray obtained.\n\n \n**desired**array_like\n\nArray desired.\n\n \n**rtol**float, optional\n\nRelative tolerance.\n\n \n**atol**float, optional\n\nAbsolute tolerance.\n\n \n**equal_nan**bool, optional.\n\nIf True, NaNs will compare equal.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired are not equal up to specified precision.\n\n See also\n\n \n[`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\"), [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\")\n\n #### Examples\n\n \n```\n>>> x = [1e-5, 1e-3, 1e-1]\n>>> y = np.arccos(np.cos(x))\n>>> np.testing.assert_allclose(x, y, rtol=1e-5, atol=0)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_allclose.htmlnumpy.testing.assert_array_almost_equal_nulp\n================================================\n\n testing.assert_array_almost_equal_nulp(*x*, *y*, *nulp=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1531-L1591)\n \nCompare two arrays relatively to their spacing.\n\n This is a relatively robust method to compare two arrays whose amplitude is variable.\n\n Parameters \n \n**x, y**array_like\n\nInput arrays.\n\n \n**nulp**int, optional\n\nThe maximum number of unit in the last place for tolerance (see Notes). Default is 1.\n\n Returns \n None\n Raises \n AssertionError\n\nIf the spacing between `x` and `y` for one or more elements is larger than `nulp`.\n\n See also\n\n [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\")\n\nCheck that all items of arrays differ in at most N Units in the Last Place.\n\n [`spacing`](numpy.spacing#numpy.spacing \"numpy.spacing\")\n\nReturn the distance between x and the nearest adjacent number.\n\n #### Notes\n\n An assertion is raised if the following condition is not met:\n\n \n```\nabs(x - y) <= nulps * spacing(maximum(abs(x), abs(y)))\n\n```\n #### Examples\n\n \n```\n>>> x = np.array([1., 1e-10, 1e-20])\n>>> eps = np.finfo(x.dtype).eps\n>>> np.testing.assert_array_almost_equal_nulp(x, x*eps/2 + x)\n\n```\n \n```\n>>> np.testing.assert_array_almost_equal_nulp(x, x*eps + x)\nTraceback (most recent call last):\n ...\nAssertionError: X and Y are not equal to 1 ULP (max is 2)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_array_almost_equal_nulp.htmlnumpy.testing.assert_array_max_ulp\n=====================================\n\n testing.assert_array_max_ulp(*a*, *b*, *maxulp=1*, *dtype=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1594-L1643)\n \nCheck that all items of arrays differ in at most N Units in the Last Place.\n\n Parameters \n \n**a, b**array_like\n\nInput arrays to be compared.\n\n \n**maxulp**int, optional\n\nThe maximum number of units in the last place that elements of `a` and `b` can differ. Default is 1.\n\n \n**dtype**dtype, optional\n\nData-type to convert `a` and `b` to if given. Default is None.\n\n Returns \n \n**ret**ndarray\n\nArray containing number of representable floating point numbers between items in `a` and `b`.\n\n Raises \n AssertionError\n\nIf one or more elements differ by more than `maxulp`.\n\n See also\n\n [`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\")\n\nCompare two arrays relatively to their spacing.\n\n #### Notes\n\n For computing the ULP difference, this API does not differentiate between various representations of NAN (ULP difference between 0x7fc00000 and 0xffc00000 is zero).\n\n #### Examples\n\n \n```\n>>> a = np.linspace(0., 1., 100)\n>>> res = np.testing.assert_array_max_ulp(a, np.arcsin(np.sin(a)))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_array_max_ulp.htmlnumpy.testing.assert_array_equal\n==================================\n\n testing.assert_array_equal(*x*, *y*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L855-L935)\n \nRaises an AssertionError if two array_like objects are not equal.\n\n Given two array_like objects, check that the shape is equal and all elements of these objects are equal (but see the Notes for the special handling of a scalar). An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.\n\n The usual caution for verifying equality with floating point numbers is advised.\n\n Parameters \n \n**x**array_like\n\nThe actual object to check.\n\n \n**y**array_like\n\nThe desired, expected object.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired objects are not equal.\n\n See also\n\n [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\")\n\nCompare two array_like objects for equality with desired relative and/or absolute precision.\n\n \n[`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\"), [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\"), [`assert_equal`](numpy.testing.assert_equal#numpy.testing.assert_equal \"numpy.testing.assert_equal\")\n\n #### Notes\n\n When one of `x` and `y` is a scalar and the other is array_like, the function checks that each element of the array_like object is equal to the scalar.\n\n #### Examples\n\n The first assert does not raise an exception:\n\n \n```\n>>> np.testing.assert_array_equal([1.0,2.33333,np.nan],\n... [np.exp(0),2.33333, np.nan])\n\n```\n Assert fails with numerical imprecision with floats:\n\n \n```\n>>> np.testing.assert_array_equal([1.0,np.pi,np.nan],\n... [1, np.sqrt(np.pi)**2, np.nan])\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not equal\n\nMismatched elements: 1 / 3 (33.3%)\nMax absolute difference: 4.4408921e-16\nMax relative difference: 1.41357986e-16\n x: array([1. , 3.141593, nan])\n y: array([1. , 3.141593, nan])\n\n```\n Use [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\") or one of the nulp (number of floating point values) functions for these cases instead:\n\n \n```\n>>> np.testing.assert_allclose([1.0,np.pi,np.nan],\n... [1, np.sqrt(np.pi)**2, np.nan],\n... rtol=1e-10, atol=0)\n\n```\n As mentioned in the Notes section, [`assert_array_equal`](#numpy.testing.assert_array_equal \"numpy.testing.assert_array_equal\") has special handling for scalars. Here the test checks that each value in `x` is 3:\n\n \n```\n>>> x = np.full((2, 5), fill_value=3)\n>>> np.testing.assert_array_equal(x, 3)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_array_equal.htmlnumpy.testing.assert_array_less\n=================================\n\n testing.assert_array_less(*x*, *y*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1051-L1131)\n \nRaises an AssertionError if two array_like objects are not ordered by less than.\n\n Given two array_like objects, check that the shape is equal and all elements of the first object are strictly smaller than those of the second object. An exception is raised at shape mismatch or incorrectly ordered values. Shape mismatch does not raise if an object has zero dimension. In contrast to the standard usage in numpy, NaNs are compared, no assertion is raised if both objects have NaNs in the same positions.\n\n Parameters \n \n**x**array_like\n\nThe smaller object to check.\n\n \n**y**array_like\n\nThe larger object to compare.\n\n \n**err_msg**string\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired objects are not equal.\n\n See also\n\n [`assert_array_equal`](numpy.testing.assert_array_equal#numpy.testing.assert_array_equal \"numpy.testing.assert_array_equal\")\n\ntests objects for equality\n\n [`assert_array_almost_equal`](numpy.testing.assert_array_almost_equal#numpy.testing.assert_array_almost_equal \"numpy.testing.assert_array_almost_equal\")\n\ntest objects for equality up to precision\n\n #### Examples\n\n \n```\n>>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1.1, 2.0, np.nan])\n>>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1, 2.0, np.nan])\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not less-ordered\n\nMismatched elements: 1 / 3 (33.3%)\nMax absolute difference: 1.\nMax relative difference: 0.5\n x: array([ 1., 1., nan])\n y: array([ 1., 2., nan])\n\n```\n \n```\n>>> np.testing.assert_array_less([1.0, 4.0], 3)\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not less-ordered\n\nMismatched elements: 1 / 2 (50%)\nMax absolute difference: 2.\nMax relative difference: 0.66666667\n x: array([1., 4.])\n y: array(3)\n\n```\n \n```\n>>> np.testing.assert_array_less([1.0, 2.0, 3.0], [4])\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not less-ordered\n\n(shapes (3,), (1,) mismatch)\n x: array([1., 2., 3.])\n y: array([4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_array_less.htmlnumpy.testing.assert_equal\n===========================\n\n testing.assert_equal(*actual*, *desired*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L275-L432)\n \nRaises an AssertionError if two objects are not equal.\n\n Given two objects (scalars, lists, tuples, dictionaries or numpy arrays), check that all elements of these objects are equal. An exception is raised at the first conflicting values.\n\n When one of `actual` and `desired` is a scalar and the other is array_like, the function checks that each element of the array_like object is equal to the scalar.\n\n This function handles NaN comparisons as if NaN was a “normal” number. That is, AssertionError is not raised if both objects have NaNs in the same positions. This is in contrast to the IEEE standard on NaNs, which says that NaN compared to anything must return False.\n\n Parameters \n \n**actual**array_like\n\nThe object to check.\n\n \n**desired**array_like\n\nThe expected object.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired are not equal.\n\n #### Examples\n\n \n```\n>>> np.testing.assert_equal([4,5], [4,6])\nTraceback (most recent call last):\n ...\nAssertionError:\nItems are not equal:\nitem=1\n ACTUAL: 5\n DESIRED: 6\n\n```\n The following comparison does not raise an exception. There are NaNs in the inputs, but they are in the same positions.\n\n \n```\n>>> np.testing.assert_equal(np.array([1.0, 2.0, np.nan]), [1, 2, np.nan])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_equal.htmlnumpy.testing.assert_raises\n============================\n\n testing.assert_raises(*exception_class*, *callable*, **args*, ***kwargs) assert_raises(exception_class*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1304-L1330)\n testing.assert_raises(*exception_class*) → [None](https://docs.python.org/3/library/constants.html#None \"(in Python v3.10)\")\n \nFail unless an exception of class exception_class is thrown by callable when invoked with arguments args and keyword arguments kwargs. If a different type of exception is thrown, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception.\n\n Alternatively, [`assert_raises`](#numpy.testing.assert_raises \"numpy.testing.assert_raises\") can be used as a context manager:\n\n \n```\n>>> from numpy.testing import assert_raises\n>>> with assert_raises(ZeroDivisionError):\n... 1 / 0\n\n```\n is equivalent to\n\n \n```\n>>> def div(x, y):\n... return x / y\n>>> assert_raises(ZeroDivisionError, div, 1, 0)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_raises.htmlnumpy.testing.assert_raises_regex\n===================================\n\n testing.assert_raises_regex(*exception_class*, *expected_regexp*, *callable*, **args*, ***kwargs) assert_raises_regex(exception_class*, *expected_regexp*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1333-L1351)\n \nFail unless an exception of class exception_class and with message that matches expected_regexp is thrown by callable when invoked with arguments args and keyword arguments kwargs.\n\n Alternatively, can be used as a context manager like [`assert_raises`](numpy.testing.assert_raises#numpy.testing.assert_raises \"numpy.testing.assert_raises\").\n\n #### Notes\n\n New in version 1.9.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_raises_regex.htmlnumpy.testing.assert_warns\n===========================\n\n testing.assert_warns(*warning_class*, **args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1749-L1800)\n \nFail unless the given callable throws the specified warning.\n\n A warning of class warning_class should be thrown by the callable when invoked with arguments args and keyword arguments kwargs. If a different type of warning is thrown, it will not be caught.\n\n If called with all arguments other than the warning class omitted, may be used as a context manager:\n\n with assert_warns(SomeWarning):\n\ndo_something()\n\n The ability to be used as a context manager is new in NumPy v1.11.0.\n\n New in version 1.4.0.\n\n Parameters \n \n**warning_class**class\n\nThe class defining the warning that `func` is expected to throw.\n\n \n**func**callable, optional\n\nCallable to test\n\n \n***args**Arguments\n\nArguments for `func`.\n\n \n****kwargs**Kwargs\n\nKeyword arguments for `func`.\n\n Returns \n The value returned by `func`.\n #### Examples\n\n \n```\n>>> import warnings\n>>> def deprecated_func(num):\n... warnings.warn(\"Please upgrade\", DeprecationWarning)\n... return num*num\n>>> with np.testing.assert_warns(DeprecationWarning):\n... assert deprecated_func(4) == 16\n>>> # or passing a func\n>>> ret = np.testing.assert_warns(DeprecationWarning, deprecated_func, 4)\n>>> assert ret == 16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_warns.htmlnumpy.testing.assert_no_warnings\n==================================\n\n testing.assert_no_warnings(**args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1814-L1847)\n \nFail if the given callable produces any warnings.\n\n If called with all arguments omitted, may be used as a context manager:\n\n with assert_no_warnings():\n\ndo_something()\n\n The ability to be used as a context manager is new in NumPy v1.11.0.\n\n New in version 1.7.0.\n\n Parameters \n \n**func**callable\n\nThe callable to test.\n\n \n***args**Arguments\n\nArguments passed to `func`.\n\n \n****kwargs**Kwargs\n\nKeyword arguments passed to `func`.\n\n Returns \n The value returned by `func`.\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_no_warnings.htmlnumpy.testing.assert_no_gc_cycles\n====================================\n\n testing.assert_no_gc_cycles(**args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L2357-L2389)\n \nFail if the given callable produces any reference cycles.\n\n If called with all arguments omitted, may be used as a context manager:\n\n with assert_no_gc_cycles():\n\ndo_something()\n\n New in version 1.15.0.\n\n Parameters \n \n**func**callable\n\nThe callable to test.\n\n \n***args**Arguments\n\nArguments passed to `func`.\n\n \n****kwargs**Kwargs\n\nKeyword arguments passed to `func`.\n\n Returns \n Nothing. The result is deliberately discarded to ensure that all cycles\nare found.\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_no_gc_cycles.htmlnumpy.testing.assert_string_equal\n===================================\n\n testing.assert_string_equal(*actual*, *desired*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1138-L1206)\n \nTest if two strings are equal.\n\n If the given strings are equal, [`assert_string_equal`](#numpy.testing.assert_string_equal \"numpy.testing.assert_string_equal\") does nothing. If they are not equal, an AssertionError is raised, and the diff between the strings is shown.\n\n Parameters \n \n**actual**str\n\nThe string to test for equality against the expected string.\n\n \n**desired**str\n\nThe expected string.\n\n #### Examples\n\n \n```\n>>> np.testing.assert_string_equal('abc', 'abc')\n>>> np.testing.assert_string_equal('abc', 'abcd')\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\n...\nAssertionError: Differences in strings:\n- abc+ abcd? +\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_string_equal.htmlnumpy.testing.assert_\n======================\n\n testing.assert_(*val*, *msg=''*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L78-L95)\n \nAssert that works in release mode. Accepts callable msg to allow deferring evaluation until failure.\n\n The Python built-in `assert` does not work when executing code in optimized mode (the `-O` flag) - no byte-code is generated for it.\n\n For documentation on usage, refer to the Python documentation.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_.htmlnumpy.testing.assert_almost_equal\n===================================\n\n testing.assert_almost_equal(*actual*, *desired*, *decimal=7*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L476-L599)\n \nRaises an AssertionError if two items are not equal up to desired precision.\n\n Note\n\n It is recommended to use one of [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\"), [`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\") or [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\") instead of this function for more consistent floating point comparisons.\n\n The test verifies that the elements of `actual` and `desired` satisfy.\n\n `abs(desired-actual) < 1.5 * 10**(-decimal)`\n\n That is a looser test than originally documented, but agrees with what the actual implementation in [`assert_array_almost_equal`](numpy.testing.assert_array_almost_equal#numpy.testing.assert_array_almost_equal \"numpy.testing.assert_array_almost_equal\") did up to rounding vagaries. An exception is raised at conflicting values. For ndarrays this delegates to assert_array_almost_equal\n\n Parameters \n \n**actual**array_like\n\nThe object to check.\n\n \n**desired**array_like\n\nThe expected object.\n\n \n**decimal**int, optional\n\nDesired precision, default is 7.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired are not equal up to specified precision.\n\n See also\n\n [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\")\n\nCompare two array_like objects for equality with desired relative and/or absolute precision.\n\n \n[`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\"), [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\"), [`assert_equal`](numpy.testing.assert_equal#numpy.testing.assert_equal \"numpy.testing.assert_equal\")\n\n #### Examples\n\n \n```\n>>> from numpy.testing import assert_almost_equal\n>>> assert_almost_equal(2.3333333333333, 2.33333334)\n>>> assert_almost_equal(2.3333333333333, 2.33333334, decimal=10)\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not almost equal to 10 decimals\n ACTUAL: 2.3333333333333\n DESIRED: 2.33333334\n\n```\n \n```\n>>> assert_almost_equal(np.array([1.0,2.3333333333333]),\n... np.array([1.0,2.33333334]), decimal=9)\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not almost equal to 9 decimals\n\nMismatched elements: 1 / 2 (50%)\nMax absolute difference: 6.66669964e-09\nMax relative difference: 2.85715698e-09\n x: array([1. , 2.333333333])\n y: array([1. , 2.33333334])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_almost_equal.htmlnumpy.testing.assert_approx_equal\n===================================\n\n testing.assert_approx_equal(*actual*, *desired*, *significant=7*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L602-L698)\n \nRaises an AssertionError if two items are not equal up to significant digits.\n\n Note\n\n It is recommended to use one of [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\"), [`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\") or [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\") instead of this function for more consistent floating point comparisons.\n\n Given two numbers, check that they are approximately equal. Approximately equal is defined as the number of significant digits that agree.\n\n Parameters \n \n**actual**scalar\n\nThe object to check.\n\n \n**desired**scalar\n\nThe expected object.\n\n \n**significant**int, optional\n\nDesired precision, default is 7.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired are not equal up to specified precision.\n\n See also\n\n [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\")\n\nCompare two array_like objects for equality with desired relative and/or absolute precision.\n\n \n[`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\"), [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\"), [`assert_equal`](numpy.testing.assert_equal#numpy.testing.assert_equal \"numpy.testing.assert_equal\")\n\n #### Examples\n\n \n```\n>>> np.testing.assert_approx_equal(0.12345677777777e-20, 0.1234567e-20)\n>>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345671e-20,\n... significant=8)\n>>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345672e-20,\n... significant=8)\nTraceback (most recent call last):\n ...\nAssertionError:\nItems are not equal to 8 significant digits:\n ACTUAL: 1.234567e-21\n DESIRED: 1.2345672e-21\n\n```\n the evaluated condition that raises the exception is\n\n \n```\n>>> abs(0.12345670e-20/1e-21 - 0.12345672e-20/1e-21) >= 10**-(8-1)\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_approx_equal.htmlnumpy.testing.assert_array_almost_equal\n==========================================\n\n testing.assert_array_almost_equal(*x*, *y*, *decimal=6*, *err_msg=''*, *verbose=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L938-L1048)\n \nRaises an AssertionError if two objects are not equal up to desired precision.\n\n Note\n\n It is recommended to use one of [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\"), [`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\") or [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\") instead of this function for more consistent floating point comparisons.\n\n The test verifies identical shapes and that the elements of `actual` and `desired` satisfy.\n\n `abs(desired-actual) < 1.5 * 10**(-decimal)`\n\n That is a looser test than originally documented, but agrees with what the actual implementation did up to rounding vagaries. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.\n\n Parameters \n \n**x**array_like\n\nThe actual object to check.\n\n \n**y**array_like\n\nThe desired, expected object.\n\n \n**decimal**int, optional\n\nDesired precision, default is 6.\n\n \n**err_msg**str, optional\n\nThe error message to be printed in case of failure.\n\n \n**verbose**bool, optional\n\nIf True, the conflicting values are appended to the error message.\n\n Raises \n AssertionError\n\nIf actual and desired are not equal up to specified precision.\n\n See also\n\n [`assert_allclose`](numpy.testing.assert_allclose#numpy.testing.assert_allclose \"numpy.testing.assert_allclose\")\n\nCompare two array_like objects for equality with desired relative and/or absolute precision.\n\n \n[`assert_array_almost_equal_nulp`](numpy.testing.assert_array_almost_equal_nulp#numpy.testing.assert_array_almost_equal_nulp \"numpy.testing.assert_array_almost_equal_nulp\"), [`assert_array_max_ulp`](numpy.testing.assert_array_max_ulp#numpy.testing.assert_array_max_ulp \"numpy.testing.assert_array_max_ulp\"), [`assert_equal`](numpy.testing.assert_equal#numpy.testing.assert_equal \"numpy.testing.assert_equal\")\n\n #### Examples\n\n the first assert does not raise an exception\n\n \n```\n>>> np.testing.assert_array_almost_equal([1.0,2.333,np.nan],\n... [1.0,2.333,np.nan])\n\n```\n \n```\n>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],\n... [1.0,2.33339,np.nan], decimal=5)\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not almost equal to 5 decimals\n\nMismatched elements: 1 / 3 (33.3%)\nMax absolute difference: 6.e-05\nMax relative difference: 2.57136612e-05\n x: array([1. , 2.33333, nan])\n y: array([1. , 2.33339, nan])\n\n```\n \n```\n>>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],\n... [1.0,2.33333, 5], decimal=5)\nTraceback (most recent call last):\n ...\nAssertionError:\nArrays are not almost equal to 5 decimals\n\nx and y nan location mismatch:\n x: array([1. , 2.33333, nan])\n y: array([1. , 2.33333, 5. ])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.assert_array_almost_equal.htmlnumpy.testing.print_assert_equal\n==================================\n\n testing.print_assert_equal(*test_string*, *actual*, *desired*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L435-L473)\n \nTest if two objects are equal, and print an error message if test fails.\n\n The test is performed with `actual == desired`.\n\n Parameters \n \n**test_string**str\n\nThe message supplied to AssertionError.\n\n \n**actual**object\n\nThe object to test for equality against `desired`.\n\n \n**desired**object\n\nThe expected result.\n\n #### Examples\n\n \n```\n>>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 1])\n>>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 2])\nTraceback (most recent call last):\n...\nAssertionError: Test XYZ of func xyz failed\nACTUAL:\n[0, 1]\nDESIRED:\n[0, 2]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.print_assert_equal.htmlnumpy.testing.dec.deprecated\n============================\n\n testing.dec.deprecated(*conditional=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/decorators.py#L253-L304)\n \n Deprecated since version 1.21: This decorator is retained for compatibility with the nose testing framework, which is being phased out. Please use the nose2 or pytest frameworks instead.\n\n Filter deprecation warnings while running the test suite.\n\n This decorator can be used to filter DeprecationWarning’s, to avoid printing them during the test suite run, while checking that the test actually raises a DeprecationWarning.\n\n Parameters \n \n**conditional**bool or callable, optional\n\nFlag to determine whether to mark test as deprecated or not. If the condition is a callable, it is used at runtime to dynamically make the decision. Default is True.\n\n Returns \n \n**decorator**function\n\nThe [`deprecated`](#numpy.testing.dec.deprecated \"numpy.testing.dec.deprecated\") decorator itself.\n\n #### Notes\n\n New in version 1.4.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.dec.deprecated.htmlnumpy.testing.dec.knownfailureif\n================================\n\n testing.dec.knownfailureif(*fail_condition*, *msg=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/decorators.py#L191-L251)\n \n Deprecated since version 1.21: This decorator is retained for compatibility with the nose testing framework, which is being phased out. Please use the nose2 or pytest frameworks instead.\n\n Make function raise KnownFailureException exception if given condition is true.\n\n If the condition is a callable, it is used at runtime to dynamically make the decision. This is useful for tests that may require costly imports, to delay the cost until the test suite is actually executed.\n\n Parameters \n \n**fail_condition**bool or callable\n\nFlag to determine whether to mark the decorated test as a known failure (if True) or not (if False).\n\n \n**msg**str, optional\n\nMessage to give on raising a KnownFailureException exception. Default is None.\n\n Returns \n \n**decorator**function\n\nDecorator, which, when applied to a function, causes KnownFailureException to be raised when `fail_condition` is True, and the function to be called normally otherwise.\n\n #### Notes\n\n The decorator itself is decorated with the `nose.tools.make_decorator` function in order to transmit function name, and various other metadata.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.dec.knownfailureif.htmlnumpy.testing.dec.setastest\n===========================\n\n testing.dec.setastest(*tf=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/decorators.py#L67-L105)\n \n Deprecated since version 1.21: This decorator is retained for compatibility with the nose testing framework, which is being phased out. Please use the nose2 or pytest frameworks instead.\n\n Signals to nose that this function is or is not a test.\n\n Parameters \n \n**tf**bool\n\nIf True, specifies that the decorated callable is a test. If False, specifies that the decorated callable is not a test. Default is True.\n\n #### Notes\n\n This decorator can’t use the nose namespace, because it can be called from a non-test module. See also `istest` and `nottest` in `nose.tools`.\n\n #### Examples\n\n [`setastest`](#numpy.testing.dec.setastest \"numpy.testing.dec.setastest\") can be used in the following way:\n\n \n```\nfrom numpy.testing import dec\n\n@dec.setastest(False)\ndef func_with_test_in_name(arg1, arg2):\n pass\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.dec.setastest.htmlnumpy.testing.dec.skipif\n========================\n\n testing.dec.skipif(*skip_condition*, *msg=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/decorators.py#L107-L188)\n \n Deprecated since version 1.21: This decorator is retained for compatibility with the nose testing framework, which is being phased out. Please use the nose2 or pytest frameworks instead.\n\n Make function raise SkipTest exception if a given condition is true.\n\n If the condition is a callable, it is used at runtime to dynamically make the decision. This is useful for tests that may require costly imports, to delay the cost until the test suite is actually executed.\n\n Parameters \n \n**skip_condition**bool or callable\n\nFlag to determine whether to skip the decorated test.\n\n \n**msg**str, optional\n\nMessage to give on raising a SkipTest exception. Default is None.\n\n Returns \n \n**decorator**function\n\nDecorator which, when applied to a function, causes SkipTest to be raised when `skip_condition` is True, and the function to be called normally otherwise.\n\n #### Notes\n\n The decorator itself is decorated with the `nose.tools.make_decorator` function in order to transmit function name, and various other metadata.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.dec.skipif.htmlnumpy.testing.dec.slow\n======================\n\n testing.dec.slow(*t*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/decorators.py#L25-L65)\n \n Deprecated since version 1.21: This decorator is retained for compatibility with the nose testing framework, which is being phased out. Please use the nose2 or pytest frameworks instead.\n\n Label a test as ‘slow’.\n\n The exact definition of a slow test is obviously both subjective and hardware-dependent, but in general any individual test that requires more than a second or two should be labeled as slow (the whole suite consists of thousands of tests, so even a second is significant).\n\n Parameters \n \n**t**callable\n\nThe test to label as slow.\n\n Returns \n \n**t**callable\n\nThe decorated test `t`.\n\n #### Examples\n\n The [`numpy.testing`](../routines.testing#module-numpy.testing \"numpy.testing\") module includes `import decorators as dec`. A test can be decorated as slow like this:\n\n \n```\nfrom numpy.testing import *\n\n@dec.slow\ndef test_big(self):\n print('Big, slow test')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.dec.slow.htmlnumpy.testing.decorate_methods\n===============================\n\n testing.decorate_methods(*cls*, *decorator*, *testmatch=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1354-L1398)\n \nApply a decorator to all methods in a class matching a regular expression.\n\n The given decorator is applied to all public methods of `cls` that are matched by the regular expression `testmatch` (`testmatch.search(methodname)`). Methods that are private, i.e. start with an underscore, are ignored.\n\n Parameters \n \n**cls**class\n\nClass whose methods to decorate.\n\n \n**decorator**function\n\nDecorator to apply to methods\n\n \n**testmatch**compiled regexp or str, optional\n\nThe regular expression. Default value is None, in which case the nose default (`re.compile(r'(?:^|[\\b_\\.%s-])[Tt]est' % os.sep)`) is used. If `testmatch` is a string, it is compiled to a regular expression first.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.decorate_methods.htmlnumpy.testing.Tester\n====================\n\n numpy.testing.Tester[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/nosetester.py#L112-L536)\n \nalias of `numpy.testing._private.nosetester.NoseTester`\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.Tester.htmlnumpy.testing.clear_and_catch_warnings\n=========================================\n\n *class*numpy.testing.clear_and_catch_warnings(*record=False*, *modules=()*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1961-L2024)\n \nContext manager that resets warning registry for catching warnings\n\n Warnings can be slippery, because, whenever a warning is triggered, Python adds a `__warningregistry__` member to the *calling* module. This makes it impossible to retrigger the warning in this module, whatever you put in the warnings filters. This context manager accepts a sequence of `modules` as a keyword argument to its constructor and:\n\n * stores and removes any `__warningregistry__` entries in given `modules` on entry;\n* resets `__warningregistry__` to its previous state on exit.\n\n This makes it possible to trigger any warning afresh inside the context manager without disturbing the state of warnings outside.\n\n For compatibility with Python 3.0, please consider all arguments to be keyword-only.\n\n Parameters \n \n**record**bool, optional\n\nSpecifies whether warnings should be captured by a custom implementation of `warnings.showwarning()` and be appended to a list returned by the context manager. Otherwise None is returned by the context manager. The objects appended to the list are arguments whose attributes mirror the arguments to `showwarning()`.\n\n \n**modules**sequence, optional\n\nSequence of modules for which to reset warnings registry on entry and restore on exit. To work correctly, all ‘ignore’ filters should filter by one of these modules.\n\n #### Examples\n\n \n```\n>>> import warnings\n>>> with np.testing.clear_and_catch_warnings(\n... modules=[np.core.fromnumeric]):\n... warnings.simplefilter('always')\n... warnings.filterwarnings('ignore', module='np.core.fromnumeric')\n... # do something that raises a warning but ignore those in\n... # np.core.fromnumeric\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.clear_and_catch_warnings.htmlnumpy.testing.measure\n=====================\n\n testing.measure(*code_str*, *times=1*, *label=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1401-L1444)\n \nReturn elapsed time for executing code in the namespace of the caller.\n\n The supplied code string is compiled with the Python builtin `compile`. The precision of the timing is 10 milli-seconds. If the code will execute fast on this timescale, it can be executed many times to get reasonable timing accuracy.\n\n Parameters \n \n**code_str**str\n\nThe code to be timed.\n\n \n**times**int, optional\n\nThe number of times the code is executed. Default is 1. The code is only compiled once.\n\n \n**label**str, optional\n\nA label to identify `code_str` with. This is passed into `compile` as the second argument (for run-time error messages).\n\n Returns \n \n**elapsed**float\n\nTotal elapsed time in seconds for executing `code_str` `times` times.\n\n #### Examples\n\n \n```\n>>> times = 10\n>>> etime = np.testing.measure('for i in range(1000): np.sqrt(i**2)', times=times)\n>>> print(\"Time for a single execution : \", etime / times, \"s\") \nTime for a single execution : 0.005 s\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.measure.htmlnumpy.testing.run_module_suite\n================================\n\n testing.run_module_suite(*file_to_run=None*, *argv=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/nosetester.py#L61-L109)\n \nRun a test module.\n\n Equivalent to calling `$ nosetests <argv> <file_to_run>` from the command line\n\n Parameters \n \n**file_to_run**str, optional\n\nPath to test module, or None. By default, run the module from which this function is called.\n\n \n**argv**list of strings\n\nArguments to be passed to the nose test runner. `argv[0]` is ignored. All command line arguments accepted by `nosetests` will work. If it is the default value None, sys.argv is used.\n\n New in version 1.9.0.\n\n #### Examples\n\n Adding the following:\n\n \n```\nif __name__ == \"__main__\" :\n run_module_suite(argv=sys.argv)\n\n```\n at the end of a test module will run the tests when that module is called in the python interpreter.\n\n Alternatively, calling:\n\n \n```\n>>> run_module_suite(file_to_run=\"numpy/tests/test_matlib.py\") \n\n```\n from an interpreter will run all the test routine in ‘test_matlib.py’.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.run_module_suite.htmlnumpy.testing.rundocs\n=====================\n\n testing.rundocs(*filename=None*, *raise_on_error=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L1209-L1252)\n \nRun doctests found in the given file.\n\n By default [`rundocs`](#numpy.testing.rundocs \"numpy.testing.rundocs\") raises an AssertionError on failure.\n\n Parameters \n \n**filename**str\n\nThe path to the file for which the doctests are run.\n\n \n**raise_on_error**bool\n\nWhether to raise an AssertionError when a doctest fails. Default is True.\n\n #### Notes\n\n The doctests can be run by the user/developer by adding the `doctests` argument to the `test()` call. For example, to run all tests (including doctests) for `numpy.lib`:\n\n \n```\n>>> np.lib.test(doctests=True) \n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.rundocs.htmlnumpy.testing.suppress_warnings\n================================\n\n *class*numpy.testing.suppress_warnings(*forwarding_rule='always'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L2027-L2302)\n \nContext manager and decorator doing much the same as `warnings.catch_warnings`.\n\n However, it also provides a filter mechanism to work around <https://bugs.python.org/issue4180>.\n\n This bug causes Python before 3.4 to not reliably show warnings again after they have been ignored once (even within catch_warnings). It means that no “ignore” filter can be used easily, since following tests might need to see the warning. Additionally it allows easier specificity for testing warnings and can be nested.\n\n Parameters \n \n**forwarding_rule**str, optional\n\nOne of “always”, “once”, “module”, or “location”. Analogous to the usual warnings module filter mode, it is useful to reduce noise mostly on the outmost level. Unsuppressed and unrecorded warnings will be forwarded based on this rule. Defaults to “always”. “location” is equivalent to the warnings “default”, match by exact location the warning warning originated from.\n\n #### Notes\n\n Filters added inside the context manager will be discarded again when leaving it. Upon entering all filters defined outside a context will be applied automatically.\n\n When a recording filter is added, matching warnings are stored in the `log` attribute as well as in the list returned by `record`.\n\n If filters are added and the `module` keyword is given, the warning registry of this module will additionally be cleared when applying it, entering the context, or exiting it. This could cause warnings to appear a second time after leaving the context if they were configured to be printed once (default) and were already printed before the context was entered.\n\n Nesting this context manager will work as expected when the forwarding rule is “always” (default). Unfiltered and unrecorded warnings will be passed out and be matched by the outer level. On the outmost level they will be printed (or caught by another warnings context). The forwarding rule argument can modify this behaviour.\n\n Like `catch_warnings` this context manager is not threadsafe.\n\n #### Examples\n\n With a context manager:\n\n \n```\nwith np.testing.suppress_warnings() as sup:\n sup.filter(DeprecationWarning, \"Some text\")\n sup.filter(module=np.ma.core)\n log = sup.record(FutureWarning, \"Does this occur?\")\n command_giving_warnings()\n # The FutureWarning was given once, the filtered warnings were\n # ignored. All other warnings abide outside settings (may be\n # printed/error)\n assert_(len(log) == 1)\n assert_(len(sup.log) == 1) # also stored in log attribute\n\n```\n Or as a decorator:\n\n \n```\nsup = np.testing.suppress_warnings()\nsup.filter(module=np.ma.core) # module must match exactly\n@sup\ndef some_function():\n # do something which causes a warning in np.ma.core\n pass\n\n```\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.testing.suppress_warnings.__call__#numpy.testing.suppress_warnings.__call__ \"numpy.testing.suppress_warnings.__call__\")(func) | Function decorator to apply certain suppressions to a whole function. |\n| [`filter`](numpy.testing.suppress_warnings.filter#numpy.testing.suppress_warnings.filter \"numpy.testing.suppress_warnings.filter\")([category, message, module]) | Add a new suppressing filter or apply it if the state is entered. |\n| [`record`](numpy.testing.suppress_warnings.record#numpy.testing.suppress_warnings.record \"numpy.testing.suppress_warnings.record\")([category, message, module]) | Append a new recording filter or apply it if the state is entered. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.suppress_warnings.htmlTesting Guidelines\n==================\n\n Introduction\n------------\n\n Until the 1.15 release, NumPy used the [nose](https://nose.readthedocs.io/en/latest/) testing framework, it now uses the [pytest](https://pytest.readthedocs.io) framework. The older framework is still maintained in order to support downstream projects that use the old numpy framework, but all tests for NumPy should use pytest.\n\n Our goal is that every module and package in NumPy should have a thorough set of unit tests. These tests should exercise the full functionality of a given routine as well as its robustness to erroneous or unexpected input arguments. Well-designed tests with good coverage make an enormous difference to the ease of refactoring. Whenever a new bug is found in a routine, you should write a new test for that specific case and add it to the test suite to prevent that bug from creeping back in unnoticed.\n\n Note\n\n SciPy uses the testing framework from [`numpy.testing`](routines.testing#module-numpy.testing \"numpy.testing\"), so all of the NumPy examples shown below are also applicable to SciPy\n\n Testing NumPy\n-------------\n\n NumPy can be tested in a number of ways, choose any way you feel comfortable.\n\n ### Running tests from inside Python\n\n You can test an installed NumPy by [`numpy.test`](#numpy.test \"numpy.test\"), for example, To run NumPy’s full test suite, use the following:\n\n \n```\n>>> import numpy\n>>> numpy.test(label='slow')\n\n```\n The test method may take two or more arguments; the first `label` is a string specifying what should be tested and the second `verbose` is an integer giving the level of output verbosity. See the docstring [`numpy.test`](#numpy.test \"numpy.test\") for details. The default value for `label` is ‘fast’ - which will run the standard tests. The string ‘full’ will run the full battery of tests, including those identified as being slow to run. If `verbose` is 1 or less, the tests will just show information messages about the tests that are run; but if it is greater than 1, then the tests will also provide warnings on missing tests. So if you want to run every test and get messages about which modules don’t have tests:\n\n \n```\n>>> numpy.test(label='full', verbose=2) # or numpy.test('full', 2)\n\n```\n Finally, if you are only interested in testing a subset of NumPy, for example, the `core` module, use the following:\n\n \n```\n>>> numpy.core.test()\n\n```\n ### Running tests from the command line\n\n If you want to build NumPy in order to work on NumPy itself, use `runtests.py`.To run NumPy’s full test suite:\n\n \n```\n$ python runtests.py\n\n```\n Testing a subset of NumPy:\n\n \n```\n$python runtests.py -t numpy/core/tests\n\n```\n For detailed info on testing, see [Testing builds](../dev/development_environment#testing-builds)\n\n ### Other methods of running tests\n\n Run tests using your favourite IDE such as [vscode](https://code.visualstudio.com/docs/python/testing#_enable-a-test-framework) or [pycharm](https://www.jetbrains.com/help/pycharm/testing-your-first-python-application.html)\n\n Writing your own tests\n----------------------\n\n If you are writing a package that you’d like to become part of NumPy, please write the tests as you develop the package. Every Python module, extension module, or subpackage in the NumPy package directory should have a corresponding `test_<name>.py` file. Pytest examines these files for test methods (named `test*`) and test classes (named `Test*`).\n\n Suppose you have a NumPy module `numpy/xxx/yyy.py` containing a function `zzz()`. To test this function you would create a test module called `test_yyy.py`. If you only need to test one aspect of `zzz`, you can simply add a test function:\n\n \n```\ndef test_zzz():\n assert zzz() == 'Hello from zzz'\n\n```\n More often, we need to group a number of tests together, so we create a test class:\n\n \n```\nimport pytest\n\n# import xxx symbols\nfrom numpy.xxx.yyy import zzz\nimport pytest\n\nclass TestZzz:\n def test_simple(self):\n assert zzz() == 'Hello from zzz'\n\n def test_invalid_parameter(self):\n with pytest.raises(ValueError, match='.*some matching regex.*'):\n ...\n\n```\n Within these test methods, `assert` and related functions are used to test whether a certain assumption is valid. If the assertion fails, the test fails. `pytest` internally rewrites the `assert` statement to give informative output when it fails, so should be preferred over the legacy variant `numpy.testing.assert_`. Whereas plain `assert` statements are ignored when running Python in optimized mode with `-O`, this is not an issue when running tests with pytest.\n\n Similarly, the pytest functions [`pytest.raises`](https://docs.pytest.org/en/stable/reference/reference.html#pytest.raises \"(in pytest v7.1.2)\") and [`pytest.warns`](https://docs.pytest.org/en/stable/reference/reference.html#pytest.warns \"(in pytest v7.1.2)\") should be preferred over their legacy counterparts [`numpy.testing.assert_raises`](generated/numpy.testing.assert_raises#numpy.testing.assert_raises \"numpy.testing.assert_raises\") and [`numpy.testing.assert_warns`](generated/numpy.testing.assert_warns#numpy.testing.assert_warns \"numpy.testing.assert_warns\"), since the pytest variants are more broadly used and allow more explicit targeting of warnings and errors when used with the `match` regex.\n\n Note that `test_` functions or methods should not have a docstring, because that makes it hard to identify the test from the output of running the test suite with `verbose=2` (or similar verbosity setting). Use plain comments (`#`) if necessary.\n\n Also since much of NumPy is legacy code that was originally written without unit tests, there are still several modules that don’t have tests yet. Please feel free to choose one of these modules and develop tests for it.\n\n ### Using C code in tests\n\n NumPy exposes a rich [C-API](c-api/index#c-api) . These are tested using c-extension modules written “as-if” they know nothing about the internals of NumPy, rather using the official C-API interfaces only. Examples of such modules are tests for a user-defined `rational` dtype in `_rational_tests` or the ufunc machinery tests in `_umath_tests` which are part of the binary distribution. Starting from version 1.21, you can also write snippets of C code in tests that will be compiled locally into c-extension modules and loaded into python.\n\n numpy.testing.extbuild.build_and_import_extension(*modname*, *functions*, ***, *prologue=''*, *build_dir=None*, *include_dirs=[]*, *more_init=''*)\n \nBuild and imports a c-extension module `modname` from a list of function fragments `functions`.\n\n Parameters \n \n**functions**list of fragments\n\nEach fragment is a sequence of func_name, calling convention, snippet.\n\n \n**prologue**string\n\nCode to precede the rest, usually extra `#include` or `#define` macros.\n\n \n**build_dir**pathlib.Path\n\nWhere to build the module, usually a temporary directory\n\n \n**include_dirs**list\n\nExtra directories to find include files when compiling\n\n \n**more_init**string\n\nCode to appear in the module PyMODINIT_FUNC\n\n Returns \n out: module\n\nThe module will have been loaded and is ready for use\n\n #### Examples\n\n \n```\n>>> functions = [(\"test_bytes\", \"METH_O\", \"\"\"\n if ( !PyBytesCheck(args)) {\n Py_RETURN_FALSE;\n }\n Py_RETURN_TRUE;\n\"\"\")]\n>>> mod = build_and_import_extension(\"testme\", functions)\n>>> assert not mod.test_bytes(u'abc')\n>>> assert mod.test_bytes(b'abc')\n\n```\n \n ### Labeling tests\n\n Unlabeled tests like the ones above are run in the default `numpy.test()` run. If you want to label your test as slow - and therefore reserved for a full `numpy.test(label='full')` run, you can label it with `pytest.mark.slow`:\n\n \n```\nimport pytest\n\n@pytest.mark.slow\ndef test_big(self):\n print('Big, slow test')\n\n```\n Similarly for methods:\n\n \n```\nclass test_zzz:\n @pytest.mark.slow\n def test_simple(self):\n assert_(zzz() == 'Hello from zzz')\n\n```\n ### Easier setup and teardown functions / methods\n\n Testing looks for module-level or class-level setup and teardown functions by name; thus:\n\n \n```\ndef setup():\n \"\"\"Module-level setup\"\"\"\n print('doing setup')\n\ndef teardown():\n \"\"\"Module-level teardown\"\"\"\n print('doing teardown')\n\nclass TestMe:\n def setup():\n \"\"\"Class-level setup\"\"\"\n print('doing setup')\n\n def teardown():\n \"\"\"Class-level teardown\"\"\"\n print('doing teardown')\n\n```\n Setup and teardown functions to functions and methods are known as “fixtures”, and their use is not encouraged.\n\n ### Parametric tests\n\n One very nice feature of testing is allowing easy testing across a range of parameters - a nasty problem for standard unit tests. Use the `pytest.mark.parametrize` decorator.\n\n ### Doctests\n\n Doctests are a convenient way of documenting the behavior of a function and allowing that behavior to be tested at the same time. The output of an interactive Python session can be included in the docstring of a function, and the test framework can run the example and compare the actual output to the expected output.\n\n The doctests can be run by adding the `doctests` argument to the `test()` call; for example, to run all tests (including doctests) for numpy.lib:\n\n \n```\n>>> import numpy as np\n>>> np.lib.test(doctests=True)\n\n```\n The doctests are run as if they are in a fresh Python instance which has executed `import numpy as np`. Tests that are part of a NumPy subpackage will have that subpackage already imported. E.g. for a test in `numpy/linalg/tests/`, the namespace will be created such that `from numpy import linalg` has already executed.\n\n ### `tests/`\n\n Rather than keeping the code and the tests in the same directory, we put all the tests for a given subpackage in a `tests/` subdirectory. For our example, if it doesn’t already exist you will need to create a `tests/` directory in `numpy/xxx/`. So the path for `test_yyy.py` is `numpy/xxx/tests/test_yyy.py`.\n\n Once the `numpy/xxx/tests/test_yyy.py` is written, its possible to run the tests by going to the `tests/` directory and typing:\n\n \n```\npython test_yyy.py\n\n```\n Or if you add `numpy/xxx/tests/` to the Python path, you could run the tests interactively in the interpreter like this:\n\n \n```\n>>> import test_yyy\n>>> test_yyy.test()\n\n```\n ### \n`__init__.py` and `setup.py`\n\n Usually, however, adding the `tests/` directory to the python path isn’t desirable. Instead it would better to invoke the test straight from the module `xxx`. To this end, simply place the following lines at the end of your package’s `__init__.py` file:\n\n \n```\n...\ndef test(level=1, verbosity=1):\n from numpy.testing import Tester\n return Tester().test(level, verbosity)\n\n```\n You will also need to add the tests directory in the configuration section of your setup.py:\n\n \n```\n...\ndef configuration(parent_package='', top_path=None):\n ...\n config.add_subpackage('tests')\n return config\n...\n\n```\n Now you can do the following to test your module:\n\n \n```\n>>> import numpy\n>>> numpy.xxx.test()\n\n```\n Also, when invoking the entire NumPy test suite, your tests will be found and run:\n\n \n```\n>>> import numpy\n>>> numpy.test()\n# your tests are included and run automatically!\n\n```\n Tips & Tricks\n-------------\n\n ### Creating many similar tests\n\n If you have a collection of tests that must be run multiple times with minor variations, it can be helpful to create a base class containing all the common tests, and then create a subclass for each variation. Several examples of this technique exist in NumPy; below are excerpts from one in [numpy/linalg/tests/test_linalg.py](https://github.com/numpy/numpy/blob/main/numpy/linalg/tests/test_linalg.py):\n\n \n```\nclass LinalgTestCase:\n def test_single(self):\n a = array([[1., 2.], [3., 4.]], dtype=single)\n b = array([2., 1.], dtype=single)\n self.do(a, b)\n\n def test_double(self):\n a = array([[1., 2.], [3., 4.]], dtype=double)\n b = array([2., 1.], dtype=double)\n self.do(a, b)\n\n ...\n\nclass TestSolve(LinalgTestCase):\n def do(self, a, b):\n x = linalg.solve(a, b)\n assert_allclose(b, dot(a, x))\n assert imply(isinstance(b, matrix), isinstance(x, matrix))\n\nclass TestInv(LinalgTestCase):\n def do(self, a, b):\n a_inv = linalg.inv(a)\n assert_allclose(dot(a, a_inv), identity(asarray(a).shape[0]))\n assert imply(isinstance(a, matrix), isinstance(a_inv, matrix))\n\n```\n In this case, we wanted to test solving a linear algebra problem using matrices of several data types, using `linalg.solve` and `linalg.inv`. The common test cases (for single-precision, double-precision, etc. matrices) are collected in `LinalgTestCase`.\n\n ### Known failures & skipping tests\n\n Sometimes you might want to skip a test or mark it as a known failure, such as when the test suite is being written before the code it’s meant to test, or if a test only fails on a particular architecture.\n\n To skip a test, simply use `skipif`:\n\n \n```\nimport pytest\n\n@pytest.mark.skipif(SkipMyTest, reason=\"Skipping this test because...\")\ndef test_something(foo):\n ...\n\n```\n The test is marked as skipped if `SkipMyTest` evaluates to nonzero, and the message in verbose test output is the second argument given to `skipif`. Similarly, a test can be marked as a known failure by using `xfail`:\n\n \n```\nimport pytest\n\n@pytest.mark.xfail(MyTestFails, reason=\"This test is known to fail because...\")\ndef test_something_else(foo):\n ...\n\n```\n Of course, a test can be unconditionally skipped or marked as a known failure by using `skip` or `xfail` without argument, respectively.\n\n A total of the number of skipped and known failing tests is displayed at the end of the test run. Skipped tests are marked as `'S'` in the test results (or `'SKIPPED'` for `verbose > 1`), and known failing tests are marked as `'x'` (or `'XFAIL'` if `verbose >\n1`).\n\n ### Tests on random data\n\n Tests on random data are good, but since test failures are meant to expose new bugs or regressions, a test that passes most of the time but fails occasionally with no code changes is not helpful. Make the random data deterministic by setting the random number seed before generating it. Use either Python’s `random.seed(some_number)` or NumPy’s `numpy.random.seed(some_number)`, depending on the source of random numbers.\n\n Alternatively, you can use [Hypothesis](https://hypothesis.readthedocs.io/en/latest/) to generate arbitrary data. Hypothesis manages both Python’s and Numpy’s random seeds for you, and provides a very concise and powerful way to describe data (including `hypothesis.extra.numpy`, e.g. for a set of mutually-broadcastable shapes).\n\n The advantages over random generation include tools to replay and share failures without requiring a fixed seed, reporting *minimal* examples for each failure, and better-than-naive-random techniques for triggering bugs.\n\n ### Documentation for `numpy.test`\n\n numpy.test(*label='fast'*, *verbose=1*, *extra_argv=None*, *doctests=False*, *coverage=False*, *durations=- 1*, *tests=None*)\n \nPytest test runner.\n\n A test function is typically added to a package’s __init__.py like so:\n\n \n```\nfrom numpy._pytesttester import PytestTester\ntest = PytestTester(__name__).test\ndel PytestTester\n\n```\n Calling this test function finds and runs all tests associated with the module and all its sub-modules.\n\n Parameters \n \n**module_name**module name\n\nThe name of the module to test.\n\n #### Notes\n\n Unlike the previous `nose`-based implementation, this class is not publicly exposed as it performs some `numpy`-specific warning suppression.\n\n Attributes \n \n**module_name**str\n\nFull path to the package to test.\n\n \n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/testing.htmlnumpy.bartlett\n==============\n\n numpy.bartlett(*M*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L2966-L3071)\n \nReturn the Bartlett window.\n\n The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain.\n\n Parameters \n \n**M**int\n\nNumber of points in the output window. If zero or less, an empty array is returned.\n\n Returns \n \n**out**array\n\nThe triangular window, with the maximum value normalized to one (the value one appears only if the number of samples is odd), with the first and last samples equal to zero.\n\n See also\n\n \n[`blackman`](numpy.blackman#numpy.blackman \"numpy.blackman\"), [`hamming`](numpy.hamming#numpy.hamming \"numpy.hamming\"), [`hanning`](numpy.hanning#numpy.hanning \"numpy.hanning\"), [`kaiser`](numpy.kaiser#numpy.kaiser \"numpy.kaiser\")\n\n #### Notes\n\n The Bartlett window is defined as\n\n \\[w(n) = \\frac{2}{M-1} \\left( \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right| \\right)\\] Most references to the Bartlett window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. Note that convolution with this window produces linear interpolation. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. The Fourier transform of the Bartlett window is the product of two sinc functions. Note the excellent discussion in Kanasewich [[2]](#r3a7a5a2c0d2a-2).\n\n #### References\n\n 1 \n<NAME>, “Periodogram Analysis and Continuous Spectra”, Biometrika 37, 1-16, 1950.\n\n [2](#id1) \n<NAME>, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 109-110.\n\n 3 \n<NAME> and <NAME>, “Discrete-Time Signal Processing”, Prentice-Hall, 1999, pp. 468-471.\n\n 4 \nWikipedia, “Window function”, <https://en.wikipedia.org/wiki/Window_function 5 \n<NAME>, <NAME>, <NAME>, and <NAME>, “Numerical Recipes”, Cambridge University Press, 1986, page 429.\n\n #### Examples\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> np.bartlett(12)\narray([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, # may vary\n 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636,\n 0.18181818, 0. ])\n\n```\n Plot the window and its frequency response (requires SciPy and matplotlib):\n\n \n```\n>>> from numpy.fft import fft, fftshift\n>>> window = np.bartlett(51)\n>>> plt.plot(window)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Bartlett window\")\nText(0.5, 1.0, 'Bartlett window')\n>>> plt.ylabel(\"Amplitude\")\nText(0, 0.5, 'Amplitude')\n>>> plt.xlabel(\"Sample\")\nText(0.5, 0, 'Sample')\n>>> plt.show()\n\n```\n ![../../_images/numpy-bartlett-1_00_00.png] \n```\n>>> plt.figure()\n<Figure size 640x480 with 0 Axes>\n>>> A = fft(window, 2048) / 25.5\n>>> mag = np.abs(fftshift(A))\n>>> freq = np.linspace(-0.5, 0.5, len(A))\n>>> with np.errstate(divide='ignore', invalid='ignore'):\n... response = 20 * np.log10(mag)\n...\n>>> response = np.clip(response, -100, 100)\n>>> plt.plot(freq, response)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Frequency response of Bartlett window\")\nText(0.5, 1.0, 'Frequency response of Bartlett window')\n>>> plt.ylabel(\"Magnitude [dB]\")\nText(0, 0.5, 'Magnitude [dB]')\n>>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\nText(0.5, 0, 'Normalized frequency [cycles per sample]')\n>>> _ = plt.axis('tight')\n>>> plt.show()\n\n```\n ![../../_images/numpy-bartlett-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.bartlett.htmlnumpy.blackman\n==============\n\n numpy.blackman(*M*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L2866-L2963)\n \nReturn the Blackman window.\n\n The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window.\n\n Parameters \n \n**M**int\n\nNumber of points in the output window. If zero or less, an empty array is returned.\n\n Returns \n \n**out**ndarray\n\nThe window, with the maximum value normalized to one (the value one appears only if the number of samples is odd).\n\n See also\n\n \n[`bartlett`](numpy.bartlett#numpy.bartlett \"numpy.bartlett\"), [`hamming`](numpy.hamming#numpy.hamming \"numpy.hamming\"), [`hanning`](numpy.hanning#numpy.hanning \"numpy.hanning\"), [`kaiser`](numpy.kaiser#numpy.kaiser \"numpy.kaiser\")\n\n #### Notes\n\n The Blackman window is defined as\n\n \\[w(n) = 0.42 - 0.5 \\cos(2\\pi n/M) + 0.08 \\cos(4\\pi n/M)\\] Most references to the Blackman window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. It is known as a “near optimal” tapering function, almost as good (by some measures) as the kaiser window.\n\n #### References\n\n <NAME>. and <NAME>., (1958) The measurement of power spectra, Dover Publications, New York.\n\n <NAME>., and <NAME>. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.\n\n #### Examples\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> np.blackman(12)\narray([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary\n 4.14397981e-01, 7.36045180e-01, 9.67046769e-01,\n 9.67046769e-01, 7.36045180e-01, 4.14397981e-01,\n 1.59903635e-01, 3.26064346e-02, -1.38777878e-17])\n\n```\n Plot the window and the frequency response:\n\n \n```\n>>> from numpy.fft import fft, fftshift\n>>> window = np.blackman(51)\n>>> plt.plot(window)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Blackman window\")\nText(0.5, 1.0, 'Blackman window')\n>>> plt.ylabel(\"Amplitude\")\nText(0, 0.5, 'Amplitude')\n>>> plt.xlabel(\"Sample\")\nText(0.5, 0, 'Sample')\n>>> plt.show()\n\n```\n ![../../_images/numpy-blackman-1_00_00.png] \n```\n>>> plt.figure()\n<Figure size 640x480 with 0 Axes>\n>>> A = fft(window, 2048) / 25.5\n>>> mag = np.abs(fftshift(A))\n>>> freq = np.linspace(-0.5, 0.5, len(A))\n>>> with np.errstate(divide='ignore', invalid='ignore'):\n... response = 20 * np.log10(mag)\n...\n>>> response = np.clip(response, -100, 100)\n>>> plt.plot(freq, response)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Frequency response of Blackman window\")\nText(0.5, 1.0, 'Frequency response of Blackman window')\n>>> plt.ylabel(\"Magnitude [dB]\")\nText(0, 0.5, 'Magnitude [dB]')\n>>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\nText(0.5, 0, 'Normalized frequency [cycles per sample]')\n>>> _ = plt.axis('tight')\n>>> plt.show()\n\n```\n ![../../_images/numpy-blackman-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.blackman.htmlnumpy.hamming\n=============\n\n numpy.hamming(*M*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L3178-L3275)\n \nReturn the Hamming window.\n\n The Hamming window is a taper formed by using a weighted cosine.\n\n Parameters \n \n**M**int\n\nNumber of points in the output window. If zero or less, an empty array is returned.\n\n Returns \n \n**out**ndarray\n\nThe window, with the maximum value normalized to one (the value one appears only if the number of samples is odd).\n\n See also\n\n \n[`bartlett`](numpy.bartlett#numpy.bartlett \"numpy.bartlett\"), [`blackman`](numpy.blackman#numpy.blackman \"numpy.blackman\"), [`hanning`](numpy.hanning#numpy.hanning \"numpy.hanning\"), [`kaiser`](numpy.kaiser#numpy.kaiser \"numpy.kaiser\")\n\n #### Notes\n\n The Hamming window is defined as\n\n \\[w(n) = 0.54 - 0.46\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) \\qquad 0 \\leq n \\leq M-1\\] The Hamming was named for <NAME>, an associate of <NAME> and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.\n\n #### References\n\n 1 \n<NAME>. and <NAME>., (1958) The measurement of power spectra, Dover Publications, New York.\n\n 2 \n<NAME>, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 109-110.\n\n 3 \nWikipedia, “Window function”, <https://en.wikipedia.org/wiki/Window_function 4 \n<NAME>, <NAME>, <NAME>, and <NAME>, “Numerical Recipes”, Cambridge University Press, 1986, page 425.\n\n #### Examples\n\n \n```\n>>> np.hamming(12)\narray([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary\n 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909,\n 0.15302337, 0.08 ])\n\n```\n Plot the window and the frequency response:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from numpy.fft import fft, fftshift\n>>> window = np.hamming(51)\n>>> plt.plot(window)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Hamming window\")\nText(0.5, 1.0, 'Hamming window')\n>>> plt.ylabel(\"Amplitude\")\nText(0, 0.5, 'Amplitude')\n>>> plt.xlabel(\"Sample\")\nText(0.5, 0, 'Sample')\n>>> plt.show()\n\n```\n ![../../_images/numpy-hamming-1_00_00.png] \n```\n>>> plt.figure()\n<Figure size 640x480 with 0 Axes>\n>>> A = fft(window, 2048) / 25.5\n>>> mag = np.abs(fftshift(A))\n>>> freq = np.linspace(-0.5, 0.5, len(A))\n>>> response = 20 * np.log10(mag)\n>>> response = np.clip(response, -100, 100)\n>>> plt.plot(freq, response)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Frequency response of Hamming window\")\nText(0.5, 1.0, 'Frequency response of Hamming window')\n>>> plt.ylabel(\"Magnitude [dB]\")\nText(0, 0.5, 'Magnitude [dB]')\n>>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\nText(0.5, 0, 'Normalized frequency [cycles per sample]')\n>>> plt.axis('tight')\n...\n>>> plt.show()\n\n```\n ![../../_images/numpy-hamming-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.hamming.htmlnumpy.hanning\n=============\n\n numpy.hanning(*M*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L3074-L3175)\n \nReturn the Hanning window.\n\n The Hanning window is a taper formed by using a weighted cosine.\n\n Parameters \n \n**M**int\n\nNumber of points in the output window. If zero or less, an empty array is returned.\n\n Returns \n \n**out**ndarray, shape(M,)\n\nThe window, with the maximum value normalized to one (the value one appears only if `M` is odd).\n\n See also\n\n \n[`bartlett`](numpy.bartlett#numpy.bartlett \"numpy.bartlett\"), [`blackman`](numpy.blackman#numpy.blackman \"numpy.blackman\"), [`hamming`](numpy.hamming#numpy.hamming \"numpy.hamming\"), [`kaiser`](numpy.kaiser#numpy.kaiser \"numpy.kaiser\")\n\n #### Notes\n\n The Hanning window is defined as\n\n \\[w(n) = 0.5 - 0.5\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) \\qquad 0 \\leq n \\leq M-1\\] The Hanning was named for <NAME>, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window.\n\n Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.\n\n #### References\n\n 1 \n<NAME>. and <NAME>., (1958) The measurement of power spectra, Dover Publications, New York.\n\n 2 \n<NAME>, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 106-108.\n\n 3 \nWikipedia, “Window function”, <https://en.wikipedia.org/wiki/Window_function 4 \n<NAME>, <NAME>, <NAME>, and <NAME>, “Numerical Recipes”, Cambridge University Press, 1986, page 425.\n\n #### Examples\n\n \n```\n>>> np.hanning(12)\narray([0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037,\n 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,\n 0.07937323, 0. ])\n\n```\n Plot the window and its frequency response:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from numpy.fft import fft, fftshift\n>>> window = np.hanning(51)\n>>> plt.plot(window)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Hann window\")\nText(0.5, 1.0, 'Hann window')\n>>> plt.ylabel(\"Amplitude\")\nText(0, 0.5, 'Amplitude')\n>>> plt.xlabel(\"Sample\")\nText(0.5, 0, 'Sample')\n>>> plt.show()\n\n```\n ![../../_images/numpy-hanning-1_00_00.png] \n```\n>>> plt.figure()\n<Figure size 640x480 with 0 Axes>\n>>> A = fft(window, 2048) / 25.5\n>>> mag = np.abs(fftshift(A))\n>>> freq = np.linspace(-0.5, 0.5, len(A))\n>>> with np.errstate(divide='ignore', invalid='ignore'):\n... response = 20 * np.log10(mag)\n...\n>>> response = np.clip(response, -100, 100)\n>>> plt.plot(freq, response)\n[<matplotlib.lines.Line2D object at 0x...>]\n>>> plt.title(\"Frequency response of the Hann window\")\nText(0.5, 1.0, 'Frequency response of the Hann window')\n>>> plt.ylabel(\"Magnitude [dB]\")\nText(0, 0.5, 'Magnitude [dB]')\n>>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\nText(0.5, 0, 'Normalized frequency [cycles per sample]')\n>>> plt.axis('tight')\n...\n>>> plt.show()\n\n```\n ![../../_images/numpy-hanning-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.hanning.htmlnumpy.ndarray.setfield\n======================\n\n method\n\n ndarray.setfield(*val*, *dtype*, *offset=0*)\n \nPut a value into a specified place in a field defined by a data-type.\n\n Place `val` into `a`’s field defined by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") and beginning `offset` bytes into the field.\n\n Parameters \n \n**val**object\n\nValue to be placed in field.\n\n \n**dtype**dtype object\n\nData-type of the field in which to place `val`.\n\n \n**offset**int, optional\n\nThe number of bytes into the field at which to place `val`.\n\n Returns \n None\n See also\n\n [`getfield`](numpy.ndarray.getfield#numpy.ndarray.getfield \"numpy.ndarray.getfield\")\n #### Examples\n\n \n```\n>>> x = np.eye(3)\n>>> x.getfield(np.float64)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n>>> x.setfield(3, np.int32)\n>>> x.getfield(np.int32)\narray([[3, 3, 3],\n [3, 3, 3],\n [3, 3, 3]], dtype=int32)\n>>> x\narray([[1.0e+000, 1.5e-323, 1.5e-323],\n [1.5e-323, 1.0e+000, 1.5e-323],\n [1.5e-323, 1.5e-323, 1.0e+000]])\n>>> x.setfield(np.eye(3), np.int32)\n>>> x\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ndarray.setfield.htmlnumpy.ndarray.conjugate\n=======================\n\n method\n\n ndarray.conjugate()\n \nReturn the complex conjugate, element-wise.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ndarray.conjugate.htmlnumpy.vectorize.__call__\n============================\n\n method\n\n vectorize.__call__(**args*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/function_base.py#L2300-L2328)\n \nReturn arrays with the results of `pyfunc` broadcast (vectorized) over `args` and `kwargs` not in `excluded`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.vectorize.__call__.htmlnumpy.nditer.reset\n==================\n\n method\n\n nditer.reset()\n \nReset the iterator to its initial state.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.reset.htmlnumpy.ndarray.newbyteorder\n==========================\n\n method\n\n ndarray.newbyteorder(*new_order='S'*, */*)\n \nReturn the array with the same data viewed with a different byte order.\n\n Equivalent to:\n\n \n```\narr.view(arr.dtype.newbytorder(new_order))\n\n```\n Changes are also made in all fields and sub-arrays of the array data type.\n\n Parameters \n \n**new_order**string, optional\n\nByte order to force; a value from the byte order specifications below. `new_order` codes can be any of:\n\n * ‘S’ - swap dtype from current to opposite endian\n* {‘<’, ‘little’} - little endian\n* {‘>’, ‘big’} - big endian\n* {‘=’, ‘native’} - native order, equivalent to [`sys.byteorder`](https://docs.python.org/3/library/sys.html#sys.byteorder \"(in Python v3.10)\")\n* {‘|’, ‘I’} - ignore (no change to byte order)\n\n The default value (‘S’) results in swapping the current byte order.\n\n Returns \n \n**new_arr**array\n\nNew array object with the dtype reflecting given change to the byte order.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ndarray.newbyteorder.htmlImporting data with genfromtxt\n==============================\n\n NumPy provides several functions to create arrays from tabular data. We focus here on the [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") function.\n\n In a nutshell, [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") runs two main loops. The first loop converts each line of the file in a sequence of strings. The second loop converts each string to the appropriate data type. This mechanism is slower than a single loop, but gives more flexibility. In particular, [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") is able to take missing data into account, when other faster and simpler functions like [`loadtxt`](../reference/generated/numpy.loadtxt#numpy.loadtxt \"numpy.loadtxt\") cannot.\n\n Note\n\n When giving examples, we will use the following conventions:\n\n \n```\n>>> import numpy as np\n>>> from io import StringIO\n\n```\n Defining the input\n------------------\n\n The only mandatory argument of [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") is the source of the data. It can be a string, a list of strings, a generator or an open file-like object with a `read` method, for example, a file or [`io.StringIO`](https://docs.python.org/3/library/io.html#io.StringIO \"(in Python v3.10)\") object. If a single string is provided, it is assumed to be the name of a local or remote file. If a list of strings or a generator returning strings is provided, each string is treated as one line in a file. When the URL of a remote file is passed, the file is automatically downloaded to the current directory and opened.\n\n Recognized file types are text files and archives. Currently, the function recognizes `gzip` and `bz2` (`bzip2`) archives. The type of the archive is determined from the extension of the file: if the filename ends with `'.gz'`, a `gzip` archive is expected; if it ends with `'bz2'`, a `bzip2` archive is assumed.\n\n Splitting the lines into columns\n--------------------------------\n\n ### The `delimiter` argument\n\n Once the file is defined and open for reading, [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") splits each non-empty line into a sequence of strings. Empty or commented lines are just skipped. The `delimiter` keyword is used to define how the splitting should take place.\n\n Quite often, a single character marks the separation between columns. For example, comma-separated files (CSV) use a comma (`,`) or a semicolon (`;`) as delimiter:\n\n \n```\n>>> data = u\"1, 2, 3\\n4, 5, 6\"\n>>> np.genfromtxt(StringIO(data), delimiter=\",\")\narray([[1., 2., 3.],\n [4., 5., 6.]])\n\n```\n Another common separator is `\"\\t\"`, the tabulation character. However, we are not limited to a single character, any string will do. By default, [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") assumes `delimiter=None`, meaning that the line is split along white spaces (including tabs) and that consecutive white spaces are considered as a single white space.\n\n Alternatively, we may be dealing with a fixed-width file, where columns are defined as a given number of characters. In that case, we need to set `delimiter` to a single integer (if all the columns have the same size) or to a sequence of integers (if columns can have different sizes):\n\n \n```\n>>> data = u\" 1 2 3\\n 4 5 67\\n890123 4\"\n>>> np.genfromtxt(StringIO(data), delimiter=3)\narray([[ 1., 2., 3.],\n [ 4., 5., 67.],\n [890., 123., 4.]])\n>>> data = u\"123456789\\n 4 7 9\\n 4567 9\"\n>>> np.genfromtxt(StringIO(data), delimiter=(4, 3, 2))\narray([[1234., 567., 89.],\n [ 4., 7., 9.],\n [ 4., 567., 9.]])\n\n```\n ### The `autostrip` argument\n\n By default, when a line is decomposed into a series of strings, the individual entries are not stripped of leading nor trailing white spaces. This behavior can be overwritten by setting the optional argument `autostrip` to a value of `True`:\n\n \n```\n>>> data = u\"1, abc , 2\\n 3, xxx, 4\"\n>>> # Without autostrip\n>>> np.genfromtxt(StringIO(data), delimiter=\",\", dtype=\"|U5\")\narray([['1', ' abc ', ' 2'],\n ['3', ' xxx', ' 4']], dtype='<U5')\n>>> # With autostrip\n>>> np.genfromtxt(StringIO(data), delimiter=\",\", dtype=\"|U5\", autostrip=True)\narray([['1', 'abc', '2'],\n ['3', 'xxx', '4']], dtype='<U5')\n\n```\n ### The `comments` argument\n\n The optional argument `comments` is used to define a character string that marks the beginning of a comment. By default, [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") assumes `comments='#'`. The comment marker may occur anywhere on the line. Any character present after the comment marker(s) is simply ignored:\n\n \n```\n>>> data = u\"\"\"#\n... # Skip me !\n... # Skip me too !\n... 1, 2\n... 3, 4\n... 5, 6 #This is the third line of the data\n... 7, 8\n... # And here comes the last line\n... 9, 0\n... \"\"\"\n>>> np.genfromtxt(StringIO(data), comments=\"#\", delimiter=\",\")\narray([[1., 2.],\n [3., 4.],\n [5., 6.],\n [7., 8.],\n [9., 0.]])\n\n```\n New in version 1.7.0: When `comments` is set to `None`, no lines are treated as comments.\n\n Note\n\n There is one notable exception to this behavior: if the optional argument `names=True`, the first commented line will be examined for names.\n\n Skipping lines and choosing columns\n-----------------------------------\n\n ### The `skip_header` and `skip_footer` arguments\n\n The presence of a header in the file can hinder data processing. In that case, we need to use the `skip_header` optional argument. The values of this argument must be an integer which corresponds to the number of lines to skip at the beginning of the file, before any other action is performed. Similarly, we can skip the last `n` lines of the file by using the `skip_footer` attribute and giving it a value of `n`:\n\n \n```\n>>> data = u\"\\n\".join(str(i) for i in range(10))\n>>> np.genfromtxt(StringIO(data),)\narray([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])\n>>> np.genfromtxt(StringIO(data),\n... skip_header=3, skip_footer=5)\narray([3., 4.])\n\n```\n By default, `skip_header=0` and `skip_footer=0`, meaning that no lines are skipped.\n\n ### The `usecols` argument\n\n In some cases, we are not interested in all the columns of the data but only a few of them. We can select which columns to import with the `usecols` argument. This argument accepts a single integer or a sequence of integers corresponding to the indices of the columns to import. Remember that by convention, the first column has an index of 0. Negative integers behave the same as regular Python negative indexes.\n\n For example, if we want to import only the first and the last columns, we can use `usecols=(0, -1)`:\n\n \n```\n>>> data = u\"1 2 3\\n4 5 6\"\n>>> np.genfromtxt(StringIO(data), usecols=(0, -1))\narray([[1., 3.],\n [4., 6.]])\n\n```\n If the columns have names, we can also select which columns to import by giving their name to the `usecols` argument, either as a sequence of strings or a comma-separated string:\n\n \n```\n>>> data = u\"1 2 3\\n4 5 6\"\n>>> np.genfromtxt(StringIO(data),\n... names=\"a, b, c\", usecols=(\"a\", \"c\"))\narray([(1., 3.), (4., 6.)], dtype=[('a', '<f8'), ('c', '<f8')])\n>>> np.genfromtxt(StringIO(data),\n... names=\"a, b, c\", usecols=(\"a, c\"))\n array([(1., 3.), (4., 6.)], dtype=[('a', '<f8'), ('c', '<f8')])\n\n```\n Choosing the data type\n----------------------\n\n The main way to control how the sequences of strings we have read from the file are converted to other types is to set the `dtype` argument. Acceptable values for this argument are:\n\n * a single type, such as `dtype=float`. The output will be 2D with the given dtype, unless a name has been associated with each column with the use of the `names` argument (see below). Note that `dtype=float` is the default for [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\").\n* a sequence of types, such as `dtype=(int, float, float)`.\n* a comma-separated string, such as `dtype=\"i4,f8,|U3\"`.\n* a dictionary with two keys `'names'` and `'formats'`.\n* a sequence of tuples `(name, type)`, such as `dtype=[('A', int), ('B', float)]`.\n* an existing [`numpy.dtype`](../reference/generated/numpy.dtype#numpy.dtype \"numpy.dtype\") object.\n* the special value `None`. In that case, the type of the columns will be determined from the data itself (see below).\n\n In all the cases but the first one, the output will be a 1D array with a structured dtype. This dtype has as many fields as items in the sequence. The field names are defined with the `names` keyword.\n\n When `dtype=None`, the type of each column is determined iteratively from its data. We start by checking whether a string can be converted to a boolean (that is, if the string matches `true` or `false` in lower cases); then whether it can be converted to an integer, then to a float, then to a complex and eventually to a string.\n\n The option `dtype=None` is provided for convenience. However, it is significantly slower than setting the dtype explicitly.\n\n Setting the names\n-----------------\n\n ### The `names` argument\n\n A natural approach when dealing with tabular data is to allocate a name to each column. A first possibility is to use an explicit structured dtype, as mentioned previously:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, dtype=[(_, int) for _ in \"abc\"])\narray([(1, 2, 3), (4, 5, 6)],\n dtype=[('a', '<i8'), ('b', '<i8'), ('c', '<i8')])\n\n```\n Another simpler possibility is to use the `names` keyword with a sequence of strings or a comma-separated string:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, names=\"A, B, C\")\narray([(1., 2., 3.), (4., 5., 6.)],\n dtype=[('A', '<f8'), ('B', '<f8'), ('C', '<f8')])\n\n```\n In the example above, we used the fact that by default, `dtype=float`. By giving a sequence of names, we are forcing the output to a structured dtype.\n\n We may sometimes need to define the column names from the data itself. In that case, we must use the `names` keyword with a value of `True`. The names will then be read from the first line (after the `skip_header` ones), even if the line is commented out:\n\n \n```\n>>> data = StringIO(\"So it goes\\n#a b c\\n1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, skip_header=1, names=True)\narray([(1., 2., 3.), (4., 5., 6.)],\n dtype=[('a', '<f8'), ('b', '<f8'), ('c', '<f8')])\n\n```\n The default value of `names` is `None`. If we give any other value to the keyword, the new names will overwrite the field names we may have defined with the dtype:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> ndtype=[('a',int), ('b', float), ('c', int)]\n>>> names = [\"A\", \"B\", \"C\"]\n>>> np.genfromtxt(data, names=names, dtype=ndtype)\narray([(1, 2., 3), (4, 5., 6)],\n dtype=[('A', '<i8'), ('B', '<f8'), ('C', '<i8')])\n\n```\n ### The `defaultfmt` argument\n\n If `names=None` but a structured dtype is expected, names are defined with the standard NumPy default of `\"f%i\"`, yielding names like `f0`, `f1` and so forth:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, dtype=(int, float, int))\narray([(1, 2., 3), (4, 5., 6)],\n dtype=[('f0', '<i8'), ('f1', '<f8'), ('f2', '<i8')])\n\n```\n In the same way, if we don’t give enough names to match the length of the dtype, the missing names will be defined with this default template:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, dtype=(int, float, int), names=\"a\")\narray([(1, 2., 3), (4, 5., 6)],\n dtype=[('a', '<i8'), ('f0', '<f8'), ('f1', '<i8')])\n\n```\n We can overwrite this default with the `defaultfmt` argument, that takes any format string:\n\n \n```\n>>> data = StringIO(\"1 2 3\\n 4 5 6\")\n>>> np.genfromtxt(data, dtype=(int, float, int), defaultfmt=\"var_%02i\")\narray([(1, 2., 3), (4, 5., 6)],\n dtype=[('var_00', '<i8'), ('var_01', '<f8'), ('var_02', '<i8')])\n\n```\n Note\n\n We need to keep in mind that `defaultfmt` is used only if some names are expected but not defined.\n\n ### Validating names\n\n NumPy arrays with a structured dtype can also be viewed as [`recarray`](../reference/generated/numpy.recarray#numpy.recarray \"numpy.recarray\"), where a field can be accessed as if it were an attribute. For that reason, we may need to make sure that the field name doesn’t contain any space or invalid character, or that it does not correspond to the name of a standard attribute (like `size` or `shape`), which would confuse the interpreter. [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") accepts three optional arguments that provide a finer control on the names:\n\n `deletechars`\n\nGives a string combining all the characters that must be deleted from the name. By default, invalid characters are `~!@#$%^&*()-=+~\\|]}[{';:\n/?.>,<`.\n\n `excludelist`\n\nGives a list of the names to exclude, such as `return`, `file`, `print`… If one of the input name is part of this list, an underscore character (`'_'`) will be appended to it.\n\n `case_sensitive`\n\nWhether the names should be case-sensitive (`case_sensitive=True`), converted to upper case (`case_sensitive=False` or `case_sensitive='upper'`) or to lower case (`case_sensitive='lower'`).\n\n Tweaking the conversion\n-----------------------\n\n ### The `converters` argument\n\n Usually, defining a dtype is sufficient to define how the sequence of strings must be converted. However, some additional control may sometimes be required. For example, we may want to make sure that a date in a format `YYYY/MM/DD` is converted to a [`datetime`](https://docs.python.org/3/library/datetime.html#datetime.datetime \"(in Python v3.10)\") object, or that a string like `xx%` is properly converted to a float between 0 and 1. In such cases, we should define conversion functions with the `converters` arguments.\n\n The value of this argument is typically a dictionary with column indices or column names as keys and a conversion functions as values. These conversion functions can either be actual functions or lambda functions. In any case, they should accept only a string as input and output only a single element of the wanted type.\n\n In the following example, the second column is converted from as string representing a percentage to a float between 0 and 1:\n\n \n```\n>>> convertfunc = lambda x: float(x.strip(b\"%\"))/100.\n>>> data = u\"1, 2.3%, 45.\\n6, 78.9%, 0\"\n>>> names = (\"i\", \"p\", \"n\")\n>>> # General case .....\n>>> np.genfromtxt(StringIO(data), delimiter=\",\", names=names)\narray([(1., nan, 45.), (6., nan, 0.)],\n dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])\n\n```\n We need to keep in mind that by default, `dtype=float`. A float is therefore expected for the second column. However, the strings `' 2.3%'` and `' 78.9%'` cannot be converted to float and we end up having `np.nan` instead. Let’s now use a converter:\n\n \n```\n>>> # Converted case ...\n>>> np.genfromtxt(StringIO(data), delimiter=\",\", names=names,\n... converters={1: convertfunc})\narray([(1., 0.023, 45.), (6., 0.789, 0.)],\n dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])\n\n```\n The same results can be obtained by using the name of the second column (`\"p\"`) as key instead of its index (1):\n\n \n```\n>>> # Using a name for the converter ...\n>>> np.genfromtxt(StringIO(data), delimiter=\",\", names=names,\n... converters={\"p\": convertfunc})\narray([(1., 0.023, 45.), (6., 0.789, 0.)],\n dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])\n\n```\n Converters can also be used to provide a default for missing entries. In the following example, the converter `convert` transforms a stripped string into the corresponding float or into -999 if the string is empty. We need to explicitly strip the string from white spaces as it is not done by default:\n\n \n```\n>>> data = u\"1, , 3\\n 4, 5, 6\"\n>>> convert = lambda x: float(x.strip() or -999)\n>>> np.genfromtxt(StringIO(data), delimiter=\",\",\n... converters={1: convert})\narray([[ 1., -999., 3.],\n [ 4., 5., 6.]])\n\n```\n ### Using missing and filling values\n\n Some entries may be missing in the dataset we are trying to import. In a previous example, we used a converter to transform an empty string into a float. However, user-defined converters may rapidly become cumbersome to manage.\n\n The [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\") function provides two other complementary mechanisms: the `missing_values` argument is used to recognize missing data and a second argument, `filling_values`, is used to process these missing data.\n\n ### `missing_values`\n\n By default, any empty string is marked as missing. We can also consider more complex strings, such as `\"N/A\"` or `\"???\"` to represent missing or invalid data. The `missing_values` argument accepts three kinds of values:\n\n a string or a comma-separated string\n\nThis string will be used as the marker for missing data for all the columns\n\n a sequence of strings\n\nIn that case, each item is associated to a column, in order.\n\n a dictionary\n\nValues of the dictionary are strings or sequence of strings. The corresponding keys can be column indices (integers) or column names (strings). In addition, the special key `None` can be used to define a default applicable to all columns.\n\n ### `filling_values`\n\n We know how to recognize missing data, but we still need to provide a value for these missing entries. By default, this value is determined from the expected dtype according to this table:\n\n \n\n| Expected type | Default |\n| --- | --- |\n| `bool` | `False` |\n| `int` | `-1` |\n| `float` | `np.nan` |\n| `complex` | `np.nan+0j` |\n| `string` | `'???'` |\n\n We can get a finer control on the conversion of missing values with the `filling_values` optional argument. Like `missing_values`, this argument accepts different kind of values:\n\n a single value\n\nThis will be the default for all columns\n\n a sequence of values\n\nEach entry will be the default for the corresponding column\n\n a dictionary\n\nEach key can be a column index or a column name, and the corresponding value should be a single object. We can use the special key `None` to define a default for all columns.\n\n In the following example, we suppose that the missing values are flagged with `\"N/A\"` in the first column and by `\"???\"` in the third column. We wish to transform these missing values to 0 if they occur in the first and second column, and to -999 if they occur in the last column:\n\n \n```\n>>> data = u\"N/A, 2, 3\\n4, ,???\"\n>>> kwargs = dict(delimiter=\",\",\n... dtype=int,\n... names=\"a,b,c\",\n... missing_values={0:\"N/A\", 'b':\" \", 2:\"???\"},\n... filling_values={0:0, 'b':0, 2:-999})\n>>> np.genfromtxt(StringIO(data), **kwargs)\narray([(0, 2, 3), (4, 0, -999)],\n dtype=[('a', '<i8'), ('b', '<i8'), ('c', '<i8')])\n\n```\n ### `usemask`\n\n We may also want to keep track of the occurrence of missing data by constructing a boolean mask, with `True` entries where data was missing and `False` otherwise. To do that, we just have to set the optional argument `usemask` to `True` (the default is `False`). The output array will then be a [`MaskedArray`](../reference/maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\").\n\n Shortcut functions\n------------------\n\n In addition to [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\"), the `numpy.lib.npyio` module provides several convenience functions derived from [`genfromtxt`](../reference/generated/numpy.genfromtxt#numpy.genfromtxt \"numpy.genfromtxt\"). These functions work the same way as the original, but they have different default values.\n\n `numpy.lib.npyio.recfromtxt`\n\nReturns a standard [`numpy.recarray`](../reference/generated/numpy.recarray#numpy.recarray \"numpy.recarray\") (if `usemask=False`) or a `numpy.ma.mrecords.MaskedRecords` array (if `usemaske=True`). The default dtype is `dtype=None`, meaning that the types of each column will be automatically determined.\n\n `numpy.lib.npyio.recfromcsv`\n\nLike `numpy.lib.npyio.recfromtxt`, but with a default `delimiter=\",\"`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/user/basics.io.genfromtxt.htmlnumpy.matrix.all\n================\n\n method\n\n matrix.all(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L571-L609)\n \nTest whether all matrix elements along a given axis evaluate to True.\n\n Parameters \n **See `numpy.all` for complete descriptions**\n See also\n\n [`numpy.all`](numpy.all#numpy.all \"numpy.all\")\n #### Notes\n\n This is the same as [`ndarray.all`](numpy.ndarray.all#numpy.ndarray.all \"numpy.ndarray.all\"), but it returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> y = x[0]; y\nmatrix([[0, 1, 2, 3]])\n>>> (x == y)\nmatrix([[ True, True, True, True],\n [False, False, False, False],\n [False, False, False, False]])\n>>> (x == y).all()\nFalse\n>>> (x == y).all(0)\nmatrix([[False, False, False, False]])\n>>> (x == y).all(1)\nmatrix([[ True],\n [False],\n [False]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.all.htmlnumpy.matrix.any\n================\n\n method\n\n matrix.any(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L548-L569)\n \nTest whether any array element along a given axis evaluates to True.\n\n Refer to [`numpy.any`](numpy.any#numpy.any \"numpy.any\") for full documentation.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which logical OR is performed\n\n \n**out**ndarray, optional\n\nOutput to existing array instead of creating new one, must have same shape as expected output\n\n Returns \n \n**any**bool, ndarray\n\nReturns a single bool if `axis` is `None`; otherwise, returns [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.any.htmlnumpy.matrix.argmax\n===================\n\n method\n\n matrix.argmax(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L646-L683)\n \nIndexes of the maximum values along an axis.\n\n Return the indexes of the first occurrences of the maximum values along the specified axis. If axis is None, the index is for the flattened matrix.\n\n Parameters \n **See `numpy.argmax` for complete descriptions**\n See also\n\n [`numpy.argmax`](numpy.argmax#numpy.argmax \"numpy.argmax\")\n #### Notes\n\n This is the same as [`ndarray.argmax`](numpy.ndarray.argmax#numpy.ndarray.argmax \"numpy.ndarray.argmax\"), but returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object where [`ndarray.argmax`](numpy.ndarray.argmax#numpy.ndarray.argmax \"numpy.ndarray.argmax\") would return an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\").\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.argmax()\n11\n>>> x.argmax(0)\nmatrix([[2, 2, 2, 2]])\n>>> x.argmax(1)\nmatrix([[3],\n [3],\n [3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.argmax.htmlnumpy.matrix.argmin\n===================\n\n method\n\n matrix.argmin(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L720-L757)\n \nIndexes of the minimum values along an axis.\n\n Return the indexes of the first occurrences of the minimum values along the specified axis. If axis is None, the index is for the flattened matrix.\n\n Parameters \n **See `numpy.argmin` for complete descriptions.**\n See also\n\n [`numpy.argmin`](numpy.argmin#numpy.argmin \"numpy.argmin\")\n #### Notes\n\n This is the same as [`ndarray.argmin`](numpy.ndarray.argmin#numpy.ndarray.argmin \"numpy.ndarray.argmin\"), but returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object where [`ndarray.argmin`](numpy.ndarray.argmin#numpy.ndarray.argmin \"numpy.ndarray.argmin\") would return an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\").\n\n #### Examples\n\n \n```\n>>> x = -np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, -1, -2, -3],\n [ -4, -5, -6, -7],\n [ -8, -9, -10, -11]])\n>>> x.argmin()\n11\n>>> x.argmin(0)\nmatrix([[2, 2, 2, 2]])\n>>> x.argmin(1)\nmatrix([[3],\n [3],\n [3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.argmin.htmlnumpy.matrix.argpartition\n=========================\n\n method\n\n matrix.argpartition(*kth*, *axis=- 1*, *kind='introselect'*, *order=None*)\n \nReturns the indices that would partition this array.\n\n Refer to [`numpy.argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\") for full documentation.\n\n New in version 1.8.0.\n\n See also\n\n [`numpy.argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.argpartition.htmlnumpy.matrix.argsort\n====================\n\n method\n\n matrix.argsort(*axis=- 1*, *kind=None*, *order=None*)\n \nReturns the indices that would sort this array.\n\n Refer to [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\") for full documentation.\n\n See also\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.argsort.htmlnumpy.matrix.astype\n===================\n\n method\n\n matrix.astype(*dtype*, *order='K'*, *casting='unsafe'*, *subok=True*, *copy=True*)\n \nCopy of the array, cast to a specified type.\n\n Parameters \n \n**dtype**str or dtype\n\nTypecode or data-type to which the array is cast.\n\n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.\n\n \n**casting**{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional\n\nControls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.\n\n * ‘no’ means the data types should not be cast at all.\n* ‘equiv’ means only byte-order changes are allowed.\n* ‘safe’ means only casts which can preserve values are allowed.\n* ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.\n* ‘unsafe’ means any data conversions may be done.\n\n \n**subok**bool, optional\n\nIf True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.\n\n \n**copy**bool, optional\n\nBy default, astype always returns a newly allocated array. If this is set to false, and the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy.\n\n Returns \n \n**arr_t**ndarray\n\nUnless [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False and the other conditions for returning the input array are satisfied (see description for [`copy`](numpy.copy#numpy.copy \"numpy.copy\") input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`.\n\n Raises \n ComplexWarning\n\nWhen casting from complex to float or int. To avoid this, one should use `a.real.astype(t)`.\n\n #### Notes\n\n Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.\n\n Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 2.5])\n>>> x\narray([1. , 2. , 2.5])\n\n```\n \n```\n>>> x.astype(int)\narray([1, 2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.astype.htmlnumpy.matrix.byteswap\n=====================\n\n method\n\n matrix.byteswap(*inplace=False*)\n \nSwap the bytes of the array elements\n\n Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.\n\n Parameters \n \n**inplace**bool, optional\n\nIf `True`, swap bytes in-place, default is `False`.\n\n Returns \n \n**out**ndarray\n\nThe byteswapped array. If `inplace` is `True`, this is a view to self.\n\n #### Examples\n\n \n```\n>>> A = np.array([1, 256, 8755], dtype=np.int16)\n>>> list(map(hex, A))\n['0x1', '0x100', '0x2233']\n>>> A.byteswap(inplace=True)\narray([ 256, 1, 13090], dtype=int16)\n>>> list(map(hex, A))\n['0x100', '0x1', '0x3322']\n\n```\n Arrays of byte-strings are not swapped\n\n \n```\n>>> A = np.array([b'ceg', b'fac'])\n>>> A.byteswap()\narray([b'ceg', b'fac'], dtype='|S3')\n\n```\n \n`A.newbyteorder().byteswap()` produces an array with the same values\n\nbut different representation in memory\n\n \n```\n>>> A = np.array([1, 2, 3])\n>>> A.view(np.uint8)\narray([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n 0, 0], dtype=uint8)\n>>> A.newbyteorder().byteswap(inplace=True)\narray([1, 2, 3])\n>>> A.view(np.uint8)\narray([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n 0, 3], dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.byteswap.htmlnumpy.matrix.choose\n===================\n\n method\n\n matrix.choose(*choices*, *out=None*, *mode='raise'*)\n \nUse an index array to construct a new array from a set of choices.\n\n Refer to [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\") for full documentation.\n\n See also\n\n [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.choose.htmlnumpy.matrix.clip\n=================\n\n method\n\n matrix.clip(*min=None*, *max=None*, *out=None*, ***kwargs*)\n \nReturn an array whose values are limited to `[min, max]`. One of max or min must be given.\n\n Refer to [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\") for full documentation.\n\n See also\n\n [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.clip.htmlnumpy.matrix.compress\n=====================\n\n method\n\n matrix.compress(*condition*, *axis=None*, *out=None*)\n \nReturn selected slices of this array along given axis.\n\n Refer to [`numpy.compress`](numpy.compress#numpy.compress \"numpy.compress\") for full documentation.\n\n See also\n\n [`numpy.compress`](numpy.compress#numpy.compress \"numpy.compress\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.compress.htmlnumpy.matrix.conj\n=================\n\n method\n\n matrix.conj()\n \nComplex-conjugate all elements.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.conj.htmlnumpy.matrix.conjugate\n======================\n\n method\n\n matrix.conjugate()\n \nReturn the complex conjugate, element-wise.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.conjugate.htmlnumpy.matrix.copy\n=================\n\n method\n\n matrix.copy(*order='C'*)\n \nReturn a copy of the array.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of `a` as closely as possible. (Note that this function and [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)\n\n See also\n\n [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\")\n\nSimilar function with different default behavior\n\n [`numpy.copyto`](numpy.copyto#numpy.copyto \"numpy.copyto\")\n #### Notes\n\n This function is the preferred method for creating an array copy. The function [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.\n\n #### Examples\n\n \n```\n>>> x = np.array([[1,2,3],[4,5,6]], order='F')\n\n```\n \n```\n>>> y = x.copy()\n\n```\n \n```\n>>> x.fill(0)\n\n```\n \n```\n>>> x\narray([[0, 0, 0],\n [0, 0, 0]])\n\n```\n \n```\n>>> y\narray([[1, 2, 3],\n [4, 5, 6]])\n\n```\n \n```\n>>> y.flags['C_CONTIGUOUS']\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.copy.htmlnumpy.matrix.cumprod\n====================\n\n method\n\n matrix.cumprod(*axis=None*, *dtype=None*, *out=None*)\n \nReturn the cumulative product of the elements along the given axis.\n\n Refer to [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\") for full documentation.\n\n See also\n\n [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.cumprod.htmlnumpy.matrix.cumsum\n===================\n\n method\n\n matrix.cumsum(*axis=None*, *dtype=None*, *out=None*)\n \nReturn the cumulative sum of the elements along the given axis.\n\n Refer to [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\") for full documentation.\n\n See also\n\n [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.cumsum.htmlnumpy.matrix.diagonal\n=====================\n\n method\n\n matrix.diagonal(*offset=0*, *axis1=0*, *axis2=1*)\n \nReturn specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.\n\n Refer to [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\") for full documentation.\n\n See also\n\n [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.diagonal.htmlnumpy.matrix.dump\n=================\n\n method\n\n matrix.dump(*file*)\n \nDump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.\n\n Parameters \n \n**file**str or Path\n\nA string naming the dump file.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.dump.htmlnumpy.matrix.dumps\n==================\n\n method\n\n matrix.dumps()\n \nReturns the pickle of the array as a string. pickle.loads will convert the string back to an array.\n\n Parameters \n **None**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.dumps.htmlnumpy.matrix.fill\n=================\n\n method\n\n matrix.fill(*value*)\n \nFill the array with a scalar value.\n\n Parameters \n \n**value**scalar\n\nAll elements of `a` will be assigned this value.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2])\n>>> a.fill(0)\n>>> a\narray([0, 0])\n>>> a = np.empty(2)\n>>> a.fill(1)\n>>> a\narray([1., 1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.fill.htmlnumpy.matrix.flatten\n====================\n\n method\n\n matrix.flatten(*order='C'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L376-L411)\n \nReturn a flattened copy of the matrix.\n\n All `N` elements of the matrix are placed into a single row.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\n‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran-style) order. ‘A’ means to flatten in column-major order if `m` is Fortran *contiguous* in memory, row-major order otherwise. ‘K’ means to flatten `m` in the order the elements occur in memory. The default is ‘C’.\n\n Returns \n \n**y**matrix\n\nA copy of the matrix, flattened to a `(1, N)` matrix where `N` is the number of elements in the original matrix.\n\n See also\n\n [`ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nReturn a flattened array.\n\n [`flat`](numpy.matrix.flat#numpy.matrix.flat \"numpy.matrix.flat\")\n\nA 1-D flat iterator over the matrix.\n\n #### Examples\n\n \n```\n>>> m = np.matrix([[1,2], [3,4]])\n>>> m.flatten()\nmatrix([[1, 2, 3, 4]])\n>>> m.flatten('F')\nmatrix([[1, 3, 2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.flatten.htmlnumpy.matrix.getA\n=================\n\n method\n\n matrix.getA()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L837-L865)\n \nReturn `self` as an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") object.\n\n Equivalent to `np.asarray(self)`.\n\n Parameters \n **None**\n Returns \n \n**ret**ndarray\n\n`self` as an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\")\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.getA()\narray([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getA.htmlnumpy.matrix.getA1\n==================\n\n method\n\n matrix.getA1()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L867-L894)\n \nReturn `self` as a flattened [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\").\n\n Equivalent to `np.asarray(x).ravel()`\n\n Parameters \n **None**\n Returns \n \n**ret**ndarray\n\n`self`, 1-D, as an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\")\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.getA1()\narray([ 0, 1, 2, ..., 9, 10, 11])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getA1.htmlnumpy.matrix.getH\n=================\n\n method\n\n matrix.getH()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L968-L1001)\n \nReturns the (complex) conjugate transpose of `self`.\n\n Equivalent to `np.transpose(self)` if `self` is real-valued.\n\n Parameters \n **None**\n Returns \n \n**ret**matrix object\n\ncomplex conjugate transpose of `self`\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4)))\n>>> z = x - 1j*x; z\nmatrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],\n [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],\n [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])\n>>> z.getH()\nmatrix([[ 0. -0.j, 4. +4.j, 8. +8.j],\n [ 1. +1.j, 5. +5.j, 9. +9.j],\n [ 2. +2.j, 6. +6.j, 10.+10.j],\n [ 3. +3.j, 7. +7.j, 11.+11.j]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getH.htmlnumpy.matrix.getI\n=================\n\n method\n\n matrix.getI()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L792-L835)\n \nReturns the (multiplicative) inverse of invertible `self`.\n\n Parameters \n **None**\n Returns \n \n**ret**matrix object\n\nIf `self` is non-singular, `ret` is such that `ret * self` == `self * ret` == `np.matrix(np.eye(self[0,:].size))` all return `True`.\n\n Raises \n numpy.linalg.LinAlgError: Singular matrix\n\nIf `self` is singular.\n\n See also\n\n [`linalg.inv`](numpy.linalg.inv#numpy.linalg.inv \"numpy.linalg.inv\")\n #### Examples\n\n \n```\n>>> m = np.matrix('[1, 2; 3, 4]'); m\nmatrix([[1, 2],\n [3, 4]])\n>>> m.getI()\nmatrix([[-2. , 1. ],\n [ 1.5, -0.5]])\n>>> m.getI() * m\nmatrix([[ 1., 0.], # may vary\n [ 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getI.htmlnumpy.matrix.getT\n=================\n\n method\n\n matrix.getT()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L935-L966)\n \nReturns the transpose of the matrix.\n\n Does *not* conjugate! For the complex conjugate transpose, use `.H`.\n\n Parameters \n **None**\n Returns \n \n**ret**matrix object\n\nThe (non-conjugated) transpose of the matrix.\n\n See also\n\n \n[`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\"), [`getH`](numpy.matrix.geth#numpy.matrix.getH \"numpy.matrix.getH\")\n\n #### Examples\n\n \n```\n>>> m = np.matrix('[1, 2; 3, 4]')\n>>> m\nmatrix([[1, 2],\n [3, 4]])\n>>> m.getT()\nmatrix([[1, 3],\n [2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getT.htmlnumpy.matrix.getfield\n=====================\n\n method\n\n matrix.getfield(*dtype*, *offset=0*)\n \nReturns a field of the given array as a certain type.\n\n A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.\n\n Parameters \n \n**dtype**str or dtype\n\nThe data type of the view. The dtype size of the view can not be larger than that of the array itself.\n\n \n**offset**int\n\nNumber of bytes to skip before beginning the element view.\n\n #### Examples\n\n \n```\n>>> x = np.diag([1.+1.j]*2)\n>>> x[1, 1] = 2 + 4.j\n>>> x\narray([[1.+1.j, 0.+0.j],\n [0.+0.j, 2.+4.j]])\n>>> x.getfield(np.float64)\narray([[1., 0.],\n [0., 2.]])\n\n```\n By choosing an offset of 8 bytes we can select the complex part of the array for our view:\n\n \n```\n>>> x.getfield(np.float64, offset=8)\narray([[1., 0.],\n [0., 4.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.getfield.htmlnumpy.matrix.item\n=================\n\n method\n\n matrix.item(**args*)\n \nCopy an element of an array to a standard Python scalar and return it.\n\n Parameters \n \n***args**Arguments (variable number and type)\n\n* none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned.\n* int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.\n* tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.\n\n Returns \n \n**z**Standard Python scalar object\n\nA copy of the specified element of the array as a suitable Python scalar\n\n #### Notes\n\n When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.\n\n [`item`](#numpy.matrix.item \"numpy.matrix.item\") is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.item(3)\n1\n>>> x.item(7)\n0\n>>> x.item((0, 1))\n2\n>>> x.item((2, 2))\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.item.htmlnumpy.matrix.itemset\n====================\n\n method\n\n matrix.itemset(**args*)\n \nInsert scalar into an array (scalar is cast to array’s dtype, if possible)\n\n There must be at least 1 argument, and define the last argument as *item*. Then, `a.itemset(*args)` is equivalent to but faster than `a[args] = item`. The item should be a scalar value and `args` must select a single item in the array `a`.\n\n Parameters \n \n***args**Arguments\n\nIf one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.\n\n #### Notes\n\n Compared to indexing syntax, [`itemset`](#numpy.matrix.itemset \"numpy.matrix.itemset\") provides some speed increase for placing a scalar into a particular location in an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using [`itemset`](#numpy.matrix.itemset \"numpy.matrix.itemset\") (and [`item`](numpy.matrix.item#numpy.matrix.item \"numpy.matrix.item\")) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.itemset(4, 0)\n>>> x.itemset((2, 2), 9)\n>>> x\narray([[2, 2, 6],\n [1, 0, 6],\n [1, 0, 9]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.itemset.htmlnumpy.matrix.max\n================\n\n method\n\n matrix.max(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L611-L644)\n \nReturn the maximum value along an axis.\n\n Parameters \n **See `amax` for complete descriptions**\n See also\n\n \n[`amax`](numpy.amax#numpy.amax \"numpy.amax\"), [`ndarray.max`](numpy.ndarray.max#numpy.ndarray.max \"numpy.ndarray.max\")\n\n #### Notes\n\n This is the same as [`ndarray.max`](numpy.ndarray.max#numpy.ndarray.max \"numpy.ndarray.max\"), but returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object where [`ndarray.max`](numpy.ndarray.max#numpy.ndarray.max \"numpy.ndarray.max\") would return an ndarray.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.max()\n11\n>>> x.max(0)\nmatrix([[ 8, 9, 10, 11]])\n>>> x.max(1)\nmatrix([[ 3],\n [ 7],\n [11]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.max.htmlnumpy.matrix.mean\n=================\n\n method\n\n matrix.mean(*axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L413-L445)\n \nReturns the average of the matrix elements along the given axis.\n\n Refer to [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\") for full documentation.\n\n See also\n\n [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\")\n #### Notes\n\n Same as [`ndarray.mean`](numpy.ndarray.mean#numpy.ndarray.mean \"numpy.ndarray.mean\") except that, where that returns an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), this returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3, 4)))\n>>> x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.mean()\n5.5\n>>> x.mean(0)\nmatrix([[4., 5., 6., 7.]])\n>>> x.mean(1)\nmatrix([[ 1.5],\n [ 5.5],\n [ 9.5]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.mean.htmlnumpy.matrix.min\n================\n\n method\n\n matrix.min(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L685-L718)\n \nReturn the minimum value along an axis.\n\n Parameters \n **See `amin` for complete descriptions.**\n See also\n\n \n[`amin`](numpy.amin#numpy.amin \"numpy.amin\"), [`ndarray.min`](numpy.ndarray.min#numpy.ndarray.min \"numpy.ndarray.min\")\n\n #### Notes\n\n This is the same as [`ndarray.min`](numpy.ndarray.min#numpy.ndarray.min \"numpy.ndarray.min\"), but returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object where [`ndarray.min`](numpy.ndarray.min#numpy.ndarray.min \"numpy.ndarray.min\") would return an ndarray.\n\n #### Examples\n\n \n```\n>>> x = -np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, -1, -2, -3],\n [ -4, -5, -6, -7],\n [ -8, -9, -10, -11]])\n>>> x.min()\n-11\n>>> x.min(0)\nmatrix([[ -8, -9, -10, -11]])\n>>> x.min(1)\nmatrix([[ -3],\n [ -7],\n [-11]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.min.htmlnumpy.matrix.newbyteorder\n=========================\n\n method\n\n matrix.newbyteorder(*new_order='S'*, */*)\n \nReturn the array with the same data viewed with a different byte order.\n\n Equivalent to:\n\n \n```\narr.view(arr.dtype.newbytorder(new_order))\n\n```\n Changes are also made in all fields and sub-arrays of the array data type.\n\n Parameters \n \n**new_order**string, optional\n\nByte order to force; a value from the byte order specifications below. `new_order` codes can be any of:\n\n * ‘S’ - swap dtype from current to opposite endian\n* {‘<’, ‘little’} - little endian\n* {‘>’, ‘big’} - big endian\n* {‘=’, ‘native’} - native order, equivalent to [`sys.byteorder`](https://docs.python.org/3/library/sys.html#sys.byteorder \"(in Python v3.10)\")\n* {‘|’, ‘I’} - ignore (no change to byte order)\n\n The default value (‘S’) results in swapping the current byte order.\n\n Returns \n \n**new_arr**array\n\nNew array object with the dtype reflecting given change to the byte order.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.newbyteorder.htmlnumpy.matrix.nonzero\n====================\n\n method\n\n matrix.nonzero()\n \nReturn the indices of the elements that are non-zero.\n\n Refer to [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\") for full documentation.\n\n See also\n\n [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.nonzero.htmlnumpy.matrix.partition\n======================\n\n method\n\n matrix.partition(*kth*, *axis=- 1*, *kind='introselect'*, *order=None*)\n \nRearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.\n\n New in version 1.8.0.\n\n Parameters \n \n**kth**int or sequence of ints\n\nElement index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.\n\n Deprecated since version 1.22.0: Passing booleans as index is deprecated.\n\n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘introselect’}, optional\n\nSelection algorithm. Default is ‘introselect’.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nReturn a partitioned copy of an array.\n\n [`argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\")\n\nIndirect partition.\n\n [`sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nFull sort.\n\n #### Notes\n\n See `np.partition` for notes on the different algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([3, 4, 2, 1])\n>>> a.partition(3)\n>>> a\narray([2, 1, 3, 4])\n\n```\n \n```\n>>> a.partition((1, 3))\n>>> a\narray([1, 2, 3, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.partition.htmlnumpy.matrix.prod\n=================\n\n method\n\n matrix.prod(*axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L515-L546)\n \nReturn the product of the array elements over the given axis.\n\n Refer to [`prod`](numpy.prod#numpy.prod \"numpy.prod\") for full documentation.\n\n See also\n\n \n[`prod`](numpy.prod#numpy.prod \"numpy.prod\"), [`ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\")\n\n #### Notes\n\n Same as [`ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\"), except, where that returns an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), this returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object instead.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.prod()\n0\n>>> x.prod(0)\nmatrix([[ 0, 45, 120, 231]])\n>>> x.prod(1)\nmatrix([[ 0],\n [ 840],\n [7920]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.prod.htmlnumpy.matrix.ptp\n================\n\n method\n\n matrix.ptp(*axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L759-L790)\n \nPeak-to-peak (maximum - minimum) value along the given axis.\n\n Refer to [`numpy.ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\") for full documentation.\n\n See also\n\n [`numpy.ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\")\n #### Notes\n\n Same as [`ndarray.ptp`](numpy.ndarray.ptp#numpy.ndarray.ptp \"numpy.ndarray.ptp\"), except, where that would return an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") object, this returns a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.ptp()\n11\n>>> x.ptp(0)\nmatrix([[8, 8, 8, 8]])\n>>> x.ptp(1)\nmatrix([[3],\n [3],\n [3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.ptp.htmlnumpy.matrix.put\n================\n\n method\n\n matrix.put(*indices*, *values*, *mode='raise'*)\n \nSet `a.flat[n] = values[n]` for all `n` in indices.\n\n Refer to [`numpy.put`](numpy.put#numpy.put \"numpy.put\") for full documentation.\n\n See also\n\n [`numpy.put`](numpy.put#numpy.put \"numpy.put\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.put.htmlnumpy.matrix.ravel\n==================\n\n method\n\n matrix.ravel(*order='C'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L897-L933)\n \nReturn a flattened matrix.\n\n Refer to [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\") for more documentation.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nThe elements of `m` are read using this index order. ‘C’ means to index the elements in C-like order, with the last axis index changing fastest, back to the first axis index changing slowest. ‘F’ means to index the elements in Fortran-like index order, with the first index changing fastest, and the last index changing slowest. Note that the ‘C’ and ‘F’ options take no account of the memory layout of the underlying array, and only refer to the order of axis indexing. ‘A’ means to read the elements in Fortran-like index order if `m` is Fortran *contiguous* in memory, C-like order otherwise. ‘K’ means to read the elements in the order they occur in memory, except for reversing the data when strides are negative. By default, ‘C’ index order is used.\n\n Returns \n \n**ret**matrix\n\nReturn the matrix flattened to shape `(1, N)` where `N` is the number of elements in the original matrix. A copy is made only if necessary.\n\n See also\n\n [`matrix.flatten`](numpy.matrix.flatten#numpy.matrix.flatten \"numpy.matrix.flatten\")\n\nreturns a similar output matrix but always a copy\n\n [`matrix.flat`](numpy.matrix.flat#numpy.matrix.flat \"numpy.matrix.flat\")\n\na flat iterator on the array.\n\n [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nrelated function which returns an ndarray\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.ravel.htmlnumpy.matrix.repeat\n===================\n\n method\n\n matrix.repeat(*repeats*, *axis=None*)\n \nRepeat elements of an array.\n\n Refer to [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\") for full documentation.\n\n See also\n\n [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.repeat.htmlnumpy.matrix.reshape\n====================\n\n method\n\n matrix.reshape(*shape*, *order='C'*)\n \nReturns an array containing the same data with a new shape.\n\n Refer to [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\") for full documentation.\n\n See also\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nequivalent function\n\n #### Notes\n\n Unlike the free function [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), this method on [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") allows the elements of the shape parameter to be passed in as separate arguments. For example, `a.reshape(10, 11)` is equivalent to `a.reshape((10, 11))`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.reshape.htmlnumpy.matrix.resize\n===================\n\n method\n\n matrix.resize(*new_shape*, *refcheck=True*)\n \nChange shape and size of array in-place.\n\n Parameters \n \n**new_shape**tuple of ints, or `n` ints\n\nShape of resized array.\n\n \n**refcheck**bool, optional\n\nIf False, reference count will not be checked. Default is True.\n\n Returns \n None\n Raises \n ValueError\n\nIf `a` does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.\n\n SystemError\n\nIf the `order` keyword argument is specified. This behaviour is a bug in NumPy.\n\n See also\n\n [`resize`](numpy.resize#numpy.resize \"numpy.resize\")\n\nReturn a new array with the specified shape.\n\n #### Notes\n\n This reallocates space for the data area if necessary.\n\n Only contiguous arrays (data elements consecutive in memory) can be resized.\n\n The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False.\n\n #### Examples\n\n Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:\n\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='C')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [1]])\n\n```\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='F')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [2]])\n\n```\n Enlarging an array: as above, but missing entries are filled with zeros:\n\n \n```\n>>> b = np.array([[0, 1], [2, 3]])\n>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n>>> b\narray([[0, 1, 2],\n [3, 0, 0]])\n\n```\n Referencing an array prevents resizing…\n\n \n```\n>>> c = a\n>>> a.resize((1, 1))\nTraceback (most recent call last):\n...\nValueError: cannot resize an array that references or is referenced ...\n\n```\n Unless `refcheck` is False:\n\n \n```\n>>> a.resize((1, 1), refcheck=False)\n>>> a\narray([[0]])\n>>> c\narray([[0]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.resize.htmlnumpy.matrix.round\n==================\n\n method\n\n matrix.round(*decimals=0*, *out=None*)\n \nReturn `a` with each element rounded to the given number of decimals.\n\n Refer to [`numpy.around`](numpy.around#numpy.around \"numpy.around\") for full documentation.\n\n See also\n\n [`numpy.around`](numpy.around#numpy.around \"numpy.around\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.round.htmlnumpy.matrix.searchsorted\n=========================\n\n method\n\n matrix.searchsorted(*v*, *side='left'*, *sorter=None*)\n \nFind indices where elements of v should be inserted in a to maintain order.\n\n For full documentation, see [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n See also\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.searchsorted.htmlnumpy.matrix.setfield\n=====================\n\n method\n\n matrix.setfield(*val*, *dtype*, *offset=0*)\n \nPut a value into a specified place in a field defined by a data-type.\n\n Place `val` into `a`’s field defined by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") and beginning `offset` bytes into the field.\n\n Parameters \n \n**val**object\n\nValue to be placed in field.\n\n \n**dtype**dtype object\n\nData-type of the field in which to place `val`.\n\n \n**offset**int, optional\n\nThe number of bytes into the field at which to place `val`.\n\n Returns \n None\n See also\n\n [`getfield`](numpy.matrix.getfield#numpy.matrix.getfield \"numpy.matrix.getfield\")\n #### Examples\n\n \n```\n>>> x = np.eye(3)\n>>> x.getfield(np.float64)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n>>> x.setfield(3, np.int32)\n>>> x.getfield(np.int32)\narray([[3, 3, 3],\n [3, 3, 3],\n [3, 3, 3]], dtype=int32)\n>>> x\narray([[1.0e+000, 1.5e-323, 1.5e-323],\n [1.5e-323, 1.0e+000, 1.5e-323],\n [1.5e-323, 1.5e-323, 1.0e+000]])\n>>> x.setfield(np.eye(3), np.int32)\n>>> x\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.setfield.htmlnumpy.matrix.setflags\n=====================\n\n method\n\n matrix.setflags(*write=None*, *align=None*, *uic=None*)\n \nSet array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.\n\n These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)\n\n Parameters \n \n**write**bool, optional\n\nDescribes whether or not `a` can be written to.\n\n \n**align**bool, optional\n\nDescribes whether or not `a` is aligned properly for its type.\n\n \n**uic**bool, optional\n\nDescribes whether or not `a` is a copy of another “base” array.\n\n #### Notes\n\n Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n\n WRITEABLE (W) the data area can be written to;\n\n ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);\n\n WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.\n\n All flags can be accessed using the single (upper case) letter as well as the full name.\n\n #### Examples\n\n \n```\n>>> y = np.array([[3, 1, 7],\n... [2, 0, 0],\n... [8, 5, 9]])\n>>> y\narray([[3, 1, 7],\n [2, 0, 0],\n [8, 5, 9]])\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : True\n ALIGNED : True\n WRITEBACKIFCOPY : False\n>>> y.setflags(write=0, align=0)\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : False\n ALIGNED : False\n WRITEBACKIFCOPY : False\n>>> y.setflags(uic=1)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: cannot set WRITEBACKIFCOPY flag to True\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.setflags.htmlnumpy.matrix.sort\n=================\n\n method\n\n matrix.sort(*axis=- 1*, *kind=None*, *order=None*)\n \nSort an array in-place. Refer to [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for full documentation.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nSorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.\n\n Changed in version 1.15.0: The ‘stable’ option was added.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nReturn a sorted copy of an array.\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nIndirect sort.\n\n [`numpy.lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort on multiple keys.\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nFind elements in sorted array.\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nPartial sort.\n\n #### Notes\n\n See [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,4], [3,1]])\n>>> a.sort(axis=1)\n>>> a\narray([[1, 4],\n [1, 3]])\n>>> a.sort(axis=0)\n>>> a\narray([[1, 3],\n [1, 4]])\n\n```\n Use the `order` keyword to specify a field to use when sorting a structured array:\n\n \n```\n>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n>>> a.sort(order='y')\n>>> a\narray([(b'c', 1), (b'a', 2)],\n dtype=[('x', 'S1'), ('y', '<i8')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.sort.htmlnumpy.matrix.squeeze\n====================\n\n method\n\n matrix.squeeze(*axis=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L323-L372)\n \nReturn a possibly reshaped matrix.\n\n Refer to [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\") for more documentation.\n\n Parameters \n \n**axis**None or int or tuple of ints, optional\n\nSelects a subset of the axes of length one in the shape. If an axis is selected with shape entry greater than one, an error is raised.\n\n Returns \n \n**squeezed**matrix\n\nThe matrix, but as a (1, N) matrix if it had shape (N, 1).\n\n See also\n\n [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\")\n\nrelated function\n\n #### Notes\n\n If `m` has a single column then that column is returned as the single row of a matrix. Otherwise `m` is returned. The returned matrix is always either `m` itself or a view into `m`. Supplying an axis keyword argument will not affect the returned matrix but it may cause an error to be raised.\n\n #### Examples\n\n \n```\n>>> c = np.matrix([[1], [2]])\n>>> c\nmatrix([[1],\n [2]])\n>>> c.squeeze()\nmatrix([[1, 2]])\n>>> r = c.T\n>>> r\nmatrix([[1, 2]])\n>>> r.squeeze()\nmatrix([[1, 2]])\n>>> m = np.matrix([[1, 2], [3, 4]])\n>>> m.squeeze()\nmatrix([[1, 2],\n [3, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.squeeze.htmlnumpy.matrix.std\n================\n\n method\n\n matrix.std(*axis=None*, *dtype=None*, *out=None*, *ddof=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L447-L479)\n \nReturn the standard deviation of the array elements along the given axis.\n\n Refer to [`numpy.std`](numpy.std#numpy.std \"numpy.std\") for full documentation.\n\n See also\n\n [`numpy.std`](numpy.std#numpy.std \"numpy.std\")\n #### Notes\n\n This is the same as [`ndarray.std`](numpy.ndarray.std#numpy.ndarray.std \"numpy.ndarray.std\"), except that where an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") would be returned, a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object is returned instead.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3, 4)))\n>>> x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.std()\n3.4520525295346629 # may vary\n>>> x.std(0)\nmatrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary\n>>> x.std(1)\nmatrix([[ 1.11803399],\n [ 1.11803399],\n [ 1.11803399]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.std.htmlnumpy.matrix.sum\n================\n\n method\n\n matrix.sum(*axis=None*, *dtype=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L287-L319)\n \nReturns the sum of the matrix elements, along the given axis.\n\n Refer to [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\") for full documentation.\n\n See also\n\n [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\")\n #### Notes\n\n This is the same as [`ndarray.sum`](numpy.ndarray.sum#numpy.ndarray.sum \"numpy.ndarray.sum\"), except that where an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") would be returned, a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object is returned instead.\n\n #### Examples\n\n \n```\n>>> x = np.matrix([[1, 2], [4, 3]])\n>>> x.sum()\n10\n>>> x.sum(axis=1)\nmatrix([[3],\n [7]])\n>>> x.sum(axis=1, dtype='float')\nmatrix([[3.],\n [7.]])\n>>> out = np.zeros((2, 1), dtype='float')\n>>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))\nmatrix([[3.],\n [7.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.sum.htmlnumpy.matrix.swapaxes\n=====================\n\n method\n\n matrix.swapaxes(*axis1*, *axis2*)\n \nReturn a view of the array with `axis1` and `axis2` interchanged.\n\n Refer to [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\") for full documentation.\n\n See also\n\n [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.swapaxes.htmlnumpy.matrix.take\n=================\n\n method\n\n matrix.take(*indices*, *axis=None*, *out=None*, *mode='raise'*)\n \nReturn an array formed from the elements of `a` at the given indices.\n\n Refer to [`numpy.take`](numpy.take#numpy.take \"numpy.take\") for full documentation.\n\n See also\n\n [`numpy.take`](numpy.take#numpy.take \"numpy.take\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.take.htmlnumpy.matrix.tobytes\n====================\n\n method\n\n matrix.tobytes(*order='C'*)\n \nConstruct Python bytes containing the raw data bytes in the array.\n\n Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the `order` parameter.\n\n New in version 1.9.0.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’}, optional\n\nControls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for *Any*) means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.\n\n Returns \n \n**s**bytes\n\nPython bytes exhibiting a copy of `a`’s raw data.\n\n #### Examples\n\n \n```\n>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n>>> x.tobytes()\nb'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n>>> x.tobytes('C') == x.tobytes()\nTrue\n>>> x.tobytes('F')\nb'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.tobytes.htmlnumpy.matrix.tofile\n===================\n\n method\n\n matrix.tofile(*fid*, *sep=''*, *format='%s'*)\n \nWrite array to a file as text or binary (default).\n\n Data is always written in ‘C’ order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile().\n\n Parameters \n \n**fid**file or str or Path\n\nAn open file object, or a string containing a filename.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n**sep**str\n\nSeparator between array items for text output. If “” (empty), a binary file is written, equivalent to `file.write(a.tobytes())`.\n\n \n**format**str\n\nFormat string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.\n\n #### Notes\n\n This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.\n\n When fid is a file object, array contents are directly written to the file, bypassing the file object’s `write` method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support `fileno()` (e.g., BytesIO).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.tofile.htmlnumpy.matrix.tolist\n===================\n\n method\n\n matrix.tolist()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L264-L284)\n \nReturn the matrix as a (possibly nested) list.\n\n See [`ndarray.tolist`](numpy.ndarray.tolist#numpy.ndarray.tolist \"numpy.ndarray.tolist\") for full documentation.\n\n See also\n\n [`ndarray.tolist`](numpy.ndarray.tolist#numpy.ndarray.tolist \"numpy.ndarray.tolist\")\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.tolist()\n[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.tolist.htmlnumpy.matrix.tostring\n=====================\n\n method\n\n matrix.tostring(*order='C'*)\n \nA compatibility alias for [`tobytes`](numpy.matrix.tobytes#numpy.matrix.tobytes \"numpy.matrix.tobytes\"), with exactly the same behavior.\n\n Despite its name, it returns `bytes` not [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\")s.\n\n Deprecated since version 1.19.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.tostring.htmlnumpy.matrix.trace\n==================\n\n method\n\n matrix.trace(*offset=0*, *axis1=0*, *axis2=1*, *dtype=None*, *out=None*)\n \nReturn the sum along diagonals of the array.\n\n Refer to [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\") for full documentation.\n\n See also\n\n [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.trace.htmlnumpy.matrix.transpose\n======================\n\n method\n\n matrix.transpose(**axes*)\n \nReturns a view of the array with axes transposed.\n\n For a 1-D array this has no effect, as a transposed vector is simply the same vector. To convert a 1-D array into a 2D column vector, an additional dimension must be added. `np.atleast2d(a).T` achieves this, as does `a[:, np.newaxis]`. For a 2-D array, this is a standard matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and `a.shape = (i[0], i[1], ... i[n-2], i[n-1])`, then `a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])`.\n\n Parameters \n \n**axes**None, tuple of ints, or `n` ints\n\n* None or no argument: reverses the order of the axes.\n* tuple of ints: `i` in the `j`-th place in the tuple means `a`’s `i`-th axis becomes `a.transpose()`’s `j`-th axis.\n* `n` ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)\n\n Returns \n \n**out**ndarray\n\nView of `a`, with axes suitably permuted.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n\nEquivalent function\n\n [`ndarray.T`](numpy.ndarray.t#numpy.ndarray.T \"numpy.ndarray.T\")\n\nArray property returning the array transposed.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nGive a new shape to an array without changing its data.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> a\narray([[1, 2],\n [3, 4]])\n>>> a.transpose()\narray([[1, 3],\n [2, 4]])\n>>> a.transpose((1, 0))\narray([[1, 3],\n [2, 4]])\n>>> a.transpose(1, 0)\narray([[1, 3],\n [2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.transpose.htmlnumpy.matrix.var\n================\n\n method\n\n matrix.var(*axis=None*, *dtype=None*, *out=None*, *ddof=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/matrixlib/defmatrix.py#L481-L513)\n \nReturns the variance of the matrix elements, along the given axis.\n\n Refer to [`numpy.var`](numpy.var#numpy.var \"numpy.var\") for full documentation.\n\n See also\n\n [`numpy.var`](numpy.var#numpy.var \"numpy.var\")\n #### Notes\n\n This is the same as [`ndarray.var`](numpy.ndarray.var#numpy.ndarray.var \"numpy.ndarray.var\"), except that where an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") would be returned, a [`matrix`](numpy.matrix#numpy.matrix \"numpy.matrix\") object is returned instead.\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3, 4)))\n>>> x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.var()\n11.916666666666666\n>>> x.var(0)\nmatrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary\n>>> x.var(1)\nmatrix([[1.25],\n [1.25],\n [1.25]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.var.htmlnumpy.matrix.view\n=================\n\n method\n\n matrix.view(*[dtype][, type]*)\n \nNew view of array with the same data.\n\n Note\n\n Passing None for `dtype` is different from omitting the parameter, since the former invokes `dtype(None)` which is an alias for `dtype('float_')`.\n\n Parameters \n \n**dtype**data-type or ndarray sub-class, optional\n\nData-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the `type` parameter).\n\n \n**type**Python type, optional\n\nType of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.\n\n #### Notes\n\n `a.view()` is used two different ways:\n\n `a.view(some_dtype)` or `a.view(dtype=some_dtype)` constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.\n\n `a.view(ndarray_subclass)` or `a.view(type=ndarray_subclass)` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.\n\n For `a.view(some_dtype)`, if `some_dtype` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of `a` must be contiguous. This axis will be resized in the result.\n\n Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.\n\n #### Examples\n\n \n```\n>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n\n```\n Viewing array data using a different type and dtype:\n\n \n```\n>>> y = x.view(dtype=np.int16, type=np.matrix)\n>>> y\nmatrix([[513]], dtype=int16)\n>>> print(type(y))\n<class 'numpy.matrix'```\n Creating a view on a structured array so it can be used in calculations\n\n \n```\n>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n>>> xv = x.view(dtype=np.int8).reshape(-1,2)\n>>> xv\narray([[1, 2],\n [3, 4]], dtype=int8)\n>>> xv.mean(0)\narray([2., 3.])\n\n```\n Making changes to the view changes the underlying array\n\n \n```\n>>> xv[0,1] = 20\n>>> x\narray([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n\n```\n Using a view to convert an array to a recarray:\n\n \n```\n>>> z = x.view(np.recarray)\n>>> z.a\narray([1, 3], dtype=int8)\n\n```\n Views share data:\n\n \n```\n>>> x[0] = (9, 10)\n>>> z[0]\n(9, 10)\n\n```\n Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n\n \n```\n>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n>>> y = x[:, ::2]\n>>> y\narray([[1, 3],\n [4, 6]], dtype=int16)\n>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\nTraceback (most recent call last):\n ...\nValueError: To change to a dtype of a different size, the last axis must be contiguous\n>>> z = y.copy()\n>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\narray([[(1, 3)],\n [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n\n```\n However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:\n\n \n```\n>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n>>> x.transpose(1, 0, 2).view(np.int16)\narray([[[ 256, 770],\n [3340, 3854]],\n\n [[1284, 1798],\n [4368, 4882]],\n\n [[2312, 2826],\n [5396, 5910]]], dtype=int16)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.view.htmlnumpy.matrix.data\n=================\n\n attribute\n\n matrix.data\n \nPython buffer object pointing to the start of the array’s data.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.data.htmlnumpy.matrix.A1\n===============\n\n property\n\n *property*matrix.A1\n \nReturn `self` as a flattened [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\").\n\n Equivalent to `np.asarray(x).ravel()`\n\n Parameters \n **None**\n Returns \n \n**ret**ndarray\n\n`self`, 1-D, as an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\")\n\n #### Examples\n\n \n```\n>>> x = np.matrix(np.arange(12).reshape((3,4))); x\nmatrix([[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]])\n>>> x.getA1()\narray([ 0, 1, 2, ..., 9, 10, 11])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.A1.htmlnumpy.matrix.base\n=================\n\n attribute\n\n matrix.base\n \nBase object if memory is from some other object.\n\n #### Examples\n\n The base of an array that owns its memory is None:\n\n \n```\n>>> x = np.array([1,2,3,4])\n>>> x.base is None\nTrue\n\n```\n Slicing creates a view, whose memory is shared with x:\n\n \n```\n>>> y = x[2:]\n>>> y.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.base.htmlnumpy.matrix.ctypes\n===================\n\n attribute\n\n matrix.ctypes\n \nAn object to simplify the interaction of the array with the ctypes module.\n\n This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.\n\n Parameters \n **None**\n Returns \n \n**c**Python object\n\nPossessing attributes data, shape, strides, etc.\n\n See also\n\n [`numpy.ctypeslib`](../routines.ctypeslib#module-numpy.ctypeslib \"numpy.ctypeslib\")\n #### Notes\n\n Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):\n\n _ctypes.data\n \nA pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as `self._array_interface_['data'][0]`.\n\n Note that unlike `data_as`, a reference will not be kept to the array: code like `ctypes.c_void_p((a + b).ctypes.data)` will result in a pointer to a deallocated array, and should be spelt `(a + b).ctypes.data_as(ctypes.c_void_p)`\n\n \n _ctypes.shape\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to `dtype('p')` on this platform (see [`c_intp`](../routines.ctypeslib#numpy.ctypeslib.c_intp \"numpy.ctypeslib.c_intp\")). This base-type could be [`ctypes.c_int`](https://docs.python.org/3/library/ctypes.html#ctypes.c_int \"(in Python v3.10)\"), [`ctypes.c_long`](https://docs.python.org/3/library/ctypes.html#ctypes.c_long \"(in Python v3.10)\"), or [`ctypes.c_longlong`](https://docs.python.org/3/library/ctypes.html#ctypes.c_longlong \"(in Python v3.10)\") depending on the platform. The ctypes array contains the shape of the underlying array.\n\n \n _ctypes.strides\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.\n\n \n _ctypes.data_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L267-L284)\n \nReturn the data pointer cast to a particular c-types object. For example, calling `self._as_parameter_` is equivalent to `self.data_as(ctypes.c_void_p)`. Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: `self.data_as(ctypes.POINTER(ctypes.c_double))`.\n\n The returned pointer will keep a reference to the array.\n\n \n _ctypes.shape_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L286-L293)\n \nReturn the shape tuple as an array of some other c-types type. For example: `self.shape_as(ctypes.c_short)`.\n\n \n _ctypes.strides_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L295-L302)\n \nReturn the strides tuple as an array of some other c-types type. For example: `self.strides_as(ctypes.c_longlong)`.\n\n \n If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the `as_parameter` attribute which will return an integer equal to the data attribute.\n\n #### Examples\n\n \n```\n>>> import ctypes\n>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n>>> x\narray([[0, 1],\n [2, 3]], dtype=int32)\n>>> x.ctypes.data\n31962608 # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\nc_uint(0)\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\nc_ulong(4294967296)\n>>> x.ctypes.shape\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n>>> x.ctypes.strides\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.ctypes.htmlnumpy.matrix.flags\n==================\n\n attribute\n\n matrix.flags\n \nInformation about the memory layout of the array.\n\n #### Notes\n\n The [`flags`](#numpy.matrix.flags \"numpy.matrix.flags\") object can be accessed dictionary-like (as in `a.flags['WRITEABLE']`), or by using lowercased attribute names (as in `a.flags.writeable`). Short flag names are only supported in dictionary access.\n\n Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n The array flags cannot be set arbitrarily:\n\n * WRITEBACKIFCOPY can only be set `False`.\n* ALIGNED can only be set `True` if the data is truly aligned.\n* WRITEABLE can only be set `True` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.\n\n Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.\n\n Even for contiguous arrays a stride for a given dimension `arr.strides[dim]` may be *arbitrary* if `arr.shape[dim] == 1` or the array has no elements. It does *not* generally hold that `self.strides[-1] == self.itemsize` for C-style contiguous arrays or `self.strides[0] == self.itemsize` for Fortran-style contiguous arrays is true.\n\n Attributes \n **C_CONTIGUOUS (C)**\n\nThe data is in a single, C-style contiguous segment.\n\n **F_CONTIGUOUS (F)**\n\nThe data is in a single, Fortran-style contiguous segment.\n\n **OWNDATA (O)**\n\nThe array owns the memory it uses or borrows it from another object.\n\n **WRITEABLE (W)**\n\nThe data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.\n\n **ALIGNED (A)**\n\nThe data and all elements are aligned appropriately for the hardware.\n\n **WRITEBACKIFCOPY (X)**\n\nThis array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.\n\n **FNC**\n\nF_CONTIGUOUS and not C_CONTIGUOUS.\n\n **FORC**\n\nF_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n\n **BEHAVED (B)**\n\nALIGNED and WRITEABLE.\n\n **CARRAY (CA)**\n\nBEHAVED and C_CONTIGUOUS.\n\n **FARRAY (FA)**\n\nBEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.flags.htmlnumpy.matrix.flat\n=================\n\n attribute\n\n matrix.flat\n \nA 1-D iterator over the array.\n\n This is a [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\") instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.\n\n See also\n\n [`flatten`](numpy.matrix.flatten#numpy.matrix.flatten \"numpy.matrix.flatten\")\n\nReturn a copy of the array collapsed into one dimension.\n\n [`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> x = np.arange(1, 7).reshape(2, 3)\n>>> x\narray([[1, 2, 3],\n [4, 5, 6]])\n>>> x.flat[3]\n4\n>>> x.T\narray([[1, 4],\n [2, 5],\n [3, 6]])\n>>> x.T.flat[3]\n5\n>>> type(x.flat)\n<class 'numpy.flatiter'```\n An assignment example:\n\n \n```\n>>> x.flat = 3; x\narray([[3, 3, 3],\n [3, 3, 3]])\n>>> x.flat[[1,4]] = 1; x\narray([[3, 1, 3],\n [3, 1, 3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.flat.htmlnumpy.matrix.itemsize\n=====================\n\n attribute\n\n matrix.itemsize\n \nLength of one array element in bytes.\n\n #### Examples\n\n \n```\n>>> x = np.array([1,2,3], dtype=np.float64)\n>>> x.itemsize\n8\n>>> x = np.array([1,2,3], dtype=np.complex128)\n>>> x.itemsize\n16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.itemsize.htmlnumpy.matrix.nbytes\n===================\n\n attribute\n\n matrix.nbytes\n \nTotal bytes consumed by the elements of the array.\n\n #### Notes\n\n Does not include memory consumed by non-element attributes of the array object.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3,5,2), dtype=np.complex128)\n>>> x.nbytes\n480\n>>> np.prod(x.shape) * x.itemsize\n480\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.nbytes.htmlnumpy.matrix.ndim\n=================\n\n attribute\n\n matrix.ndim\n \nNumber of array dimensions.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> x.ndim\n1\n>>> y = np.zeros((2, 3, 4))\n>>> y.ndim\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.ndim.htmlnumpy.matrix.size\n=================\n\n attribute\n\n matrix.size\n \nNumber of elements in the array.\n\n Equal to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.\n\n #### Notes\n\n `a.size` returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested `np.prod(a.shape)`, which returns an instance of `np.int_`), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n>>> x.size\n30\n>>> np.prod(x.shape)\n30\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.size.htmlnumpy.matrix.strides\n====================\n\n attribute\n\n matrix.strides\n \nTuple of bytes to step in each dimension when traversing an array.\n\n The byte offset of element `(i[0], i[1], ..., i[n])` in an array `a` is:\n\n \n```\noffset = sum(np.array(i) * a.strides)\n\n```\n A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.\n\n Warning\n\n Setting `arr.strides` is discouraged and may be deprecated in the future. [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\") should be preferred to create a new view of the same data in a safer way.\n\n See also\n\n [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\")\n #### Notes\n\n Imagine an array of 32-bit integers (each 4 bytes):\n\n \n```\nx = np.array([[0, 1, 2, 3, 4],\n [5, 6, 7, 8, 9]], dtype=np.int32)\n\n```\n This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be `(20, 4)`.\n\n #### Examples\n\n \n```\n>>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n>>> y\narray([[[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]],\n [[12, 13, 14, 15],\n [16, 17, 18, 19],\n [20, 21, 22, 23]]])\n>>> y.strides\n(48, 16, 4)\n>>> y[1,1,1]\n17\n>>> offset=sum(y.strides * np.array((1,1,1)))\n>>> offset/y.itemsize\n17\n\n```\n \n```\n>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n>>> x.strides\n(32, 4, 224, 1344)\n>>> i = np.array([3,5,2,2])\n>>> offset = sum(i * x.strides)\n>>> x[3,5,2,2]\n813\n>>> offset / x.itemsize\n813\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.matrix.strides.htmlnumpy.recarray.all\n==================\n\n method\n\n recarray.all(*axis=None*, *out=None*, *keepdims=False*, ***, *where=True*)\n \nReturns True if all elements evaluate to True.\n\n Refer to [`numpy.all`](numpy.all#numpy.all \"numpy.all\") for full documentation.\n\n See also\n\n [`numpy.all`](numpy.all#numpy.all \"numpy.all\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.all.htmlnumpy.recarray.any\n==================\n\n method\n\n recarray.any(*axis=None*, *out=None*, *keepdims=False*, ***, *where=True*)\n \nReturns True if any of the elements of `a` evaluate to True.\n\n Refer to [`numpy.any`](numpy.any#numpy.any \"numpy.any\") for full documentation.\n\n See also\n\n [`numpy.any`](numpy.any#numpy.any \"numpy.any\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.any.htmlnumpy.recarray.argmax\n=====================\n\n method\n\n recarray.argmax(*axis=None*, *out=None*, ***, *keepdims=False*)\n \nReturn indices of the maximum values along the given axis.\n\n Refer to [`numpy.argmax`](numpy.argmax#numpy.argmax \"numpy.argmax\") for full documentation.\n\n See also\n\n [`numpy.argmax`](numpy.argmax#numpy.argmax \"numpy.argmax\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.argmax.htmlnumpy.recarray.argmin\n=====================\n\n method\n\n recarray.argmin(*axis=None*, *out=None*, ***, *keepdims=False*)\n \nReturn indices of the minimum values along the given axis.\n\n Refer to [`numpy.argmin`](numpy.argmin#numpy.argmin \"numpy.argmin\") for detailed documentation.\n\n See also\n\n [`numpy.argmin`](numpy.argmin#numpy.argmin \"numpy.argmin\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.argmin.htmlnumpy.recarray.argpartition\n===========================\n\n method\n\n recarray.argpartition(*kth*, *axis=- 1*, *kind='introselect'*, *order=None*)\n \nReturns the indices that would partition this array.\n\n Refer to [`numpy.argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\") for full documentation.\n\n New in version 1.8.0.\n\n See also\n\n [`numpy.argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.argpartition.htmlnumpy.recarray.argsort\n======================\n\n method\n\n recarray.argsort(*axis=- 1*, *kind=None*, *order=None*)\n \nReturns the indices that would sort this array.\n\n Refer to [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\") for full documentation.\n\n See also\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.argsort.htmlnumpy.recarray.astype\n=====================\n\n method\n\n recarray.astype(*dtype*, *order='K'*, *casting='unsafe'*, *subok=True*, *copy=True*)\n \nCopy of the array, cast to a specified type.\n\n Parameters \n \n**dtype**str or dtype\n\nTypecode or data-type to which the array is cast.\n\n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.\n\n \n**casting**{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional\n\nControls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.\n\n * ‘no’ means the data types should not be cast at all.\n* ‘equiv’ means only byte-order changes are allowed.\n* ‘safe’ means only casts which can preserve values are allowed.\n* ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.\n* ‘unsafe’ means any data conversions may be done.\n\n \n**subok**bool, optional\n\nIf True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.\n\n \n**copy**bool, optional\n\nBy default, astype always returns a newly allocated array. If this is set to false, and the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy.\n\n Returns \n \n**arr_t**ndarray\n\nUnless [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False and the other conditions for returning the input array are satisfied (see description for [`copy`](numpy.copy#numpy.copy \"numpy.copy\") input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`.\n\n Raises \n ComplexWarning\n\nWhen casting from complex to float or int. To avoid this, one should use `a.real.astype(t)`.\n\n #### Notes\n\n Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.\n\n Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 2.5])\n>>> x\narray([1. , 2. , 2.5])\n\n```\n \n```\n>>> x.astype(int)\narray([1, 2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.astype.htmlnumpy.recarray.byteswap\n=======================\n\n method\n\n recarray.byteswap(*inplace=False*)\n \nSwap the bytes of the array elements\n\n Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.\n\n Parameters \n \n**inplace**bool, optional\n\nIf `True`, swap bytes in-place, default is `False`.\n\n Returns \n \n**out**ndarray\n\nThe byteswapped array. If `inplace` is `True`, this is a view to self.\n\n #### Examples\n\n \n```\n>>> A = np.array([1, 256, 8755], dtype=np.int16)\n>>> list(map(hex, A))\n['0x1', '0x100', '0x2233']\n>>> A.byteswap(inplace=True)\narray([ 256, 1, 13090], dtype=int16)\n>>> list(map(hex, A))\n['0x100', '0x1', '0x3322']\n\n```\n Arrays of byte-strings are not swapped\n\n \n```\n>>> A = np.array([b'ceg', b'fac'])\n>>> A.byteswap()\narray([b'ceg', b'fac'], dtype='|S3')\n\n```\n \n`A.newbyteorder().byteswap()` produces an array with the same values\n\nbut different representation in memory\n\n \n```\n>>> A = np.array([1, 2, 3])\n>>> A.view(np.uint8)\narray([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n 0, 0], dtype=uint8)\n>>> A.newbyteorder().byteswap(inplace=True)\narray([1, 2, 3])\n>>> A.view(np.uint8)\narray([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n 0, 3], dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.byteswap.htmlnumpy.recarray.choose\n=====================\n\n method\n\n recarray.choose(*choices*, *out=None*, *mode='raise'*)\n \nUse an index array to construct a new array from a set of choices.\n\n Refer to [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\") for full documentation.\n\n See also\n\n [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.choose.htmlnumpy.recarray.clip\n===================\n\n method\n\n recarray.clip(*min=None*, *max=None*, *out=None*, ***kwargs*)\n \nReturn an array whose values are limited to `[min, max]`. One of max or min must be given.\n\n Refer to [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\") for full documentation.\n\n See also\n\n [`numpy.clip`](numpy.clip#numpy.clip \"numpy.clip\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.clip.htmlnumpy.recarray.compress\n=======================\n\n method\n\n recarray.compress(*condition*, *axis=None*, *out=None*)\n \nReturn selected slices of this array along given axis.\n\n Refer to [`numpy.compress`](numpy.compress#numpy.compress \"numpy.compress\") for full documentation.\n\n See also\n\n [`numpy.compress`](numpy.compress#numpy.compress \"numpy.compress\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.compress.htmlnumpy.recarray.conj\n===================\n\n method\n\n recarray.conj()\n \nComplex-conjugate all elements.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.conj.htmlnumpy.recarray.conjugate\n========================\n\n method\n\n recarray.conjugate()\n \nReturn the complex conjugate, element-wise.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.conjugate.htmlnumpy.recarray.copy\n===================\n\n method\n\n recarray.copy(*order='C'*)\n \nReturn a copy of the array.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of `a` as closely as possible. (Note that this function and [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)\n\n See also\n\n [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\")\n\nSimilar function with different default behavior\n\n [`numpy.copyto`](numpy.copyto#numpy.copyto \"numpy.copyto\")\n #### Notes\n\n This function is the preferred method for creating an array copy. The function [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.\n\n #### Examples\n\n \n```\n>>> x = np.array([[1,2,3],[4,5,6]], order='F')\n\n```\n \n```\n>>> y = x.copy()\n\n```\n \n```\n>>> x.fill(0)\n\n```\n \n```\n>>> x\narray([[0, 0, 0],\n [0, 0, 0]])\n\n```\n \n```\n>>> y\narray([[1, 2, 3],\n [4, 5, 6]])\n\n```\n \n```\n>>> y.flags['C_CONTIGUOUS']\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.copy.htmlnumpy.recarray.cumprod\n======================\n\n method\n\n recarray.cumprod(*axis=None*, *dtype=None*, *out=None*)\n \nReturn the cumulative product of the elements along the given axis.\n\n Refer to [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\") for full documentation.\n\n See also\n\n [`numpy.cumprod`](numpy.cumprod#numpy.cumprod \"numpy.cumprod\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.cumprod.htmlnumpy.recarray.cumsum\n=====================\n\n method\n\n recarray.cumsum(*axis=None*, *dtype=None*, *out=None*)\n \nReturn the cumulative sum of the elements along the given axis.\n\n Refer to [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\") for full documentation.\n\n See also\n\n [`numpy.cumsum`](numpy.cumsum#numpy.cumsum \"numpy.cumsum\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.cumsum.htmlnumpy.recarray.diagonal\n=======================\n\n method\n\n recarray.diagonal(*offset=0*, *axis1=0*, *axis2=1*)\n \nReturn specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.\n\n Refer to [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\") for full documentation.\n\n See also\n\n [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.diagonal.htmlnumpy.recarray.dump\n===================\n\n method\n\n recarray.dump(*file*)\n \nDump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.\n\n Parameters \n \n**file**str or Path\n\nA string naming the dump file.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.dump.htmlnumpy.recarray.dumps\n====================\n\n method\n\n recarray.dumps()\n \nReturns the pickle of the array as a string. pickle.loads will convert the string back to an array.\n\n Parameters \n **None**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.dumps.htmlnumpy.recarray.fill\n===================\n\n method\n\n recarray.fill(*value*)\n \nFill the array with a scalar value.\n\n Parameters \n \n**value**scalar\n\nAll elements of `a` will be assigned this value.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2])\n>>> a.fill(0)\n>>> a\narray([0, 0])\n>>> a = np.empty(2)\n>>> a.fill(1)\n>>> a\narray([1., 1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.fill.htmlnumpy.recarray.flatten\n======================\n\n method\n\n recarray.flatten(*order='C'*)\n \nReturn a copy of the array collapsed into one dimension.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\n‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran- style) order. ‘A’ means to flatten in column-major order if `a` is Fortran *contiguous* in memory, row-major order otherwise. ‘K’ means to flatten `a` in the order the elements occur in memory. The default is ‘C’.\n\n Returns \n \n**y**ndarray\n\nA copy of the input array, flattened to one dimension.\n\n See also\n\n [`ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nReturn a flattened array.\n\n [`flat`](numpy.recarray.flat#numpy.recarray.flat \"numpy.recarray.flat\")\n\nA 1-D flat iterator over the array.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,2], [3,4]])\n>>> a.flatten()\narray([1, 2, 3, 4])\n>>> a.flatten('F')\narray([1, 3, 2, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.flatten.htmlnumpy.recarray.getfield\n=======================\n\n method\n\n recarray.getfield(*dtype*, *offset=0*)\n \nReturns a field of the given array as a certain type.\n\n A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.\n\n Parameters \n \n**dtype**str or dtype\n\nThe data type of the view. The dtype size of the view can not be larger than that of the array itself.\n\n \n**offset**int\n\nNumber of bytes to skip before beginning the element view.\n\n #### Examples\n\n \n```\n>>> x = np.diag([1.+1.j]*2)\n>>> x[1, 1] = 2 + 4.j\n>>> x\narray([[1.+1.j, 0.+0.j],\n [0.+0.j, 2.+4.j]])\n>>> x.getfield(np.float64)\narray([[1., 0.],\n [0., 2.]])\n\n```\n By choosing an offset of 8 bytes we can select the complex part of the array for our view:\n\n \n```\n>>> x.getfield(np.float64, offset=8)\narray([[1., 0.],\n [0., 4.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.getfield.htmlnumpy.recarray.item\n===================\n\n method\n\n recarray.item(**args*)\n \nCopy an element of an array to a standard Python scalar and return it.\n\n Parameters \n \n***args**Arguments (variable number and type)\n\n* none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned.\n* int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.\n* tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.\n\n Returns \n \n**z**Standard Python scalar object\n\nA copy of the specified element of the array as a suitable Python scalar\n\n #### Notes\n\n When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.\n\n [`item`](#numpy.recarray.item \"numpy.recarray.item\") is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.item(3)\n1\n>>> x.item(7)\n0\n>>> x.item((0, 1))\n2\n>>> x.item((2, 2))\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.item.htmlnumpy.recarray.itemset\n======================\n\n method\n\n recarray.itemset(**args*)\n \nInsert scalar into an array (scalar is cast to array’s dtype, if possible)\n\n There must be at least 1 argument, and define the last argument as *item*. Then, `a.itemset(*args)` is equivalent to but faster than `a[args] = item`. The item should be a scalar value and `args` must select a single item in the array `a`.\n\n Parameters \n \n***args**Arguments\n\nIf one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.\n\n #### Notes\n\n Compared to indexing syntax, [`itemset`](#numpy.recarray.itemset \"numpy.recarray.itemset\") provides some speed increase for placing a scalar into a particular location in an [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\"), if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using [`itemset`](#numpy.recarray.itemset \"numpy.recarray.itemset\") (and [`item`](numpy.recarray.item#numpy.recarray.item \"numpy.recarray.item\")) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.itemset(4, 0)\n>>> x.itemset((2, 2), 9)\n>>> x\narray([[2, 2, 6],\n [1, 0, 6],\n [1, 0, 9]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.itemset.htmlnumpy.recarray.max\n==================\n\n method\n\n recarray.max(*axis=None*, *out=None*, *keepdims=False*, *initial=<no value>*, *where=True*)\n \nReturn the maximum along a given axis.\n\n Refer to [`numpy.amax`](numpy.amax#numpy.amax \"numpy.amax\") for full documentation.\n\n See also\n\n [`numpy.amax`](numpy.amax#numpy.amax \"numpy.amax\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.max.htmlnumpy.recarray.mean\n===================\n\n method\n\n recarray.mean(*axis=None*, *dtype=None*, *out=None*, *keepdims=False*, ***, *where=True*)\n \nReturns the average of the array elements along given axis.\n\n Refer to [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\") for full documentation.\n\n See also\n\n [`numpy.mean`](numpy.mean#numpy.mean \"numpy.mean\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.mean.htmlnumpy.recarray.min\n==================\n\n method\n\n recarray.min(*axis=None*, *out=None*, *keepdims=False*, *initial=<no value>*, *where=True*)\n \nReturn the minimum along a given axis.\n\n Refer to [`numpy.amin`](numpy.amin#numpy.amin \"numpy.amin\") for full documentation.\n\n See also\n\n [`numpy.amin`](numpy.amin#numpy.amin \"numpy.amin\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.min.htmlnumpy.recarray.newbyteorder\n===========================\n\n method\n\n recarray.newbyteorder(*new_order='S'*, */*)\n \nReturn the array with the same data viewed with a different byte order.\n\n Equivalent to:\n\n \n```\narr.view(arr.dtype.newbytorder(new_order))\n\n```\n Changes are also made in all fields and sub-arrays of the array data type.\n\n Parameters \n \n**new_order**string, optional\n\nByte order to force; a value from the byte order specifications below. `new_order` codes can be any of:\n\n * ‘S’ - swap dtype from current to opposite endian\n* {‘<’, ‘little’} - little endian\n* {‘>’, ‘big’} - big endian\n* {‘=’, ‘native’} - native order, equivalent to [`sys.byteorder`](https://docs.python.org/3/library/sys.html#sys.byteorder \"(in Python v3.10)\")\n* {‘|’, ‘I’} - ignore (no change to byte order)\n\n The default value (‘S’) results in swapping the current byte order.\n\n Returns \n \n**new_arr**array\n\nNew array object with the dtype reflecting given change to the byte order.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.newbyteorder.htmlnumpy.recarray.nonzero\n======================\n\n method\n\n recarray.nonzero()\n \nReturn the indices of the elements that are non-zero.\n\n Refer to [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\") for full documentation.\n\n See also\n\n [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.nonzero.htmlnumpy.recarray.partition\n========================\n\n method\n\n recarray.partition(*kth*, *axis=- 1*, *kind='introselect'*, *order=None*)\n \nRearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.\n\n New in version 1.8.0.\n\n Parameters \n \n**kth**int or sequence of ints\n\nElement index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.\n\n Deprecated since version 1.22.0: Passing booleans as index is deprecated.\n\n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘introselect’}, optional\n\nSelection algorithm. Default is ‘introselect’.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nReturn a partitioned copy of an array.\n\n [`argpartition`](numpy.argpartition#numpy.argpartition \"numpy.argpartition\")\n\nIndirect partition.\n\n [`sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nFull sort.\n\n #### Notes\n\n See `np.partition` for notes on the different algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([3, 4, 2, 1])\n>>> a.partition(3)\n>>> a\narray([2, 1, 3, 4])\n\n```\n \n```\n>>> a.partition((1, 3))\n>>> a\narray([1, 2, 3, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.partition.htmlnumpy.recarray.prod\n===================\n\n method\n\n recarray.prod(*axis=None*, *dtype=None*, *out=None*, *keepdims=False*, *initial=1*, *where=True*)\n \nReturn the product of the array elements over the given axis\n\n Refer to [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\") for full documentation.\n\n See also\n\n [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.prod.htmlnumpy.recarray.ptp\n==================\n\n method\n\n recarray.ptp(*axis=None*, *out=None*, *keepdims=False*)\n \nPeak to peak (maximum - minimum) value along a given axis.\n\n Refer to [`numpy.ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\") for full documentation.\n\n See also\n\n [`numpy.ptp`](numpy.ptp#numpy.ptp \"numpy.ptp\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.ptp.htmlnumpy.recarray.put\n==================\n\n method\n\n recarray.put(*indices*, *values*, *mode='raise'*)\n \nSet `a.flat[n] = values[n]` for all `n` in indices.\n\n Refer to [`numpy.put`](numpy.put#numpy.put \"numpy.put\") for full documentation.\n\n See also\n\n [`numpy.put`](numpy.put#numpy.put \"numpy.put\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.put.htmlnumpy.recarray.ravel\n====================\n\n method\n\n recarray.ravel([*order*])\n \nReturn a flattened array.\n\n Refer to [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\") for full documentation.\n\n See also\n\n [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nequivalent function\n\n [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\")\n\na flat iterator on the array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.ravel.htmlnumpy.recarray.repeat\n=====================\n\n method\n\n recarray.repeat(*repeats*, *axis=None*)\n \nRepeat elements of an array.\n\n Refer to [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\") for full documentation.\n\n See also\n\n [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.repeat.htmlnumpy.recarray.reshape\n======================\n\n method\n\n recarray.reshape(*shape*, *order='C'*)\n \nReturns an array containing the same data with a new shape.\n\n Refer to [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\") for full documentation.\n\n See also\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nequivalent function\n\n #### Notes\n\n Unlike the free function [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), this method on [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") allows the elements of the shape parameter to be passed in as separate arguments. For example, `a.reshape(10, 11)` is equivalent to `a.reshape((10, 11))`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.reshape.htmlnumpy.recarray.resize\n=====================\n\n method\n\n recarray.resize(*new_shape*, *refcheck=True*)\n \nChange shape and size of array in-place.\n\n Parameters \n \n**new_shape**tuple of ints, or `n` ints\n\nShape of resized array.\n\n \n**refcheck**bool, optional\n\nIf False, reference count will not be checked. Default is True.\n\n Returns \n None\n Raises \n ValueError\n\nIf `a` does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.\n\n SystemError\n\nIf the `order` keyword argument is specified. This behaviour is a bug in NumPy.\n\n See also\n\n [`resize`](numpy.resize#numpy.resize \"numpy.resize\")\n\nReturn a new array with the specified shape.\n\n #### Notes\n\n This reallocates space for the data area if necessary.\n\n Only contiguous arrays (data elements consecutive in memory) can be resized.\n\n The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False.\n\n #### Examples\n\n Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:\n\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='C')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [1]])\n\n```\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='F')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [2]])\n\n```\n Enlarging an array: as above, but missing entries are filled with zeros:\n\n \n```\n>>> b = np.array([[0, 1], [2, 3]])\n>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n>>> b\narray([[0, 1, 2],\n [3, 0, 0]])\n\n```\n Referencing an array prevents resizing…\n\n \n```\n>>> c = a\n>>> a.resize((1, 1))\nTraceback (most recent call last):\n...\nValueError: cannot resize an array that references or is referenced ...\n\n```\n Unless `refcheck` is False:\n\n \n```\n>>> a.resize((1, 1), refcheck=False)\n>>> a\narray([[0]])\n>>> c\narray([[0]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.resize.htmlnumpy.recarray.round\n====================\n\n method\n\n recarray.round(*decimals=0*, *out=None*)\n \nReturn `a` with each element rounded to the given number of decimals.\n\n Refer to [`numpy.around`](numpy.around#numpy.around \"numpy.around\") for full documentation.\n\n See also\n\n [`numpy.around`](numpy.around#numpy.around \"numpy.around\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.round.htmlnumpy.recarray.searchsorted\n===========================\n\n method\n\n recarray.searchsorted(*v*, *side='left'*, *sorter=None*)\n \nFind indices where elements of v should be inserted in a to maintain order.\n\n For full documentation, see [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n See also\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.searchsorted.htmlnumpy.recarray.setfield\n=======================\n\n method\n\n recarray.setfield(*val*, *dtype*, *offset=0*)\n \nPut a value into a specified place in a field defined by a data-type.\n\n Place `val` into `a`’s field defined by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") and beginning `offset` bytes into the field.\n\n Parameters \n \n**val**object\n\nValue to be placed in field.\n\n \n**dtype**dtype object\n\nData-type of the field in which to place `val`.\n\n \n**offset**int, optional\n\nThe number of bytes into the field at which to place `val`.\n\n Returns \n None\n See also\n\n [`getfield`](numpy.recarray.getfield#numpy.recarray.getfield \"numpy.recarray.getfield\")\n #### Examples\n\n \n```\n>>> x = np.eye(3)\n>>> x.getfield(np.float64)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n>>> x.setfield(3, np.int32)\n>>> x.getfield(np.int32)\narray([[3, 3, 3],\n [3, 3, 3],\n [3, 3, 3]], dtype=int32)\n>>> x\narray([[1.0e+000, 1.5e-323, 1.5e-323],\n [1.5e-323, 1.0e+000, 1.5e-323],\n [1.5e-323, 1.5e-323, 1.0e+000]])\n>>> x.setfield(np.eye(3), np.int32)\n>>> x\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.setfield.htmlnumpy.recarray.setflags\n=======================\n\n method\n\n recarray.setflags(*write=None*, *align=None*, *uic=None*)\n \nSet array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.\n\n These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)\n\n Parameters \n \n**write**bool, optional\n\nDescribes whether or not `a` can be written to.\n\n \n**align**bool, optional\n\nDescribes whether or not `a` is aligned properly for its type.\n\n \n**uic**bool, optional\n\nDescribes whether or not `a` is a copy of another “base” array.\n\n #### Notes\n\n Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n\n WRITEABLE (W) the data area can be written to;\n\n ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);\n\n WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.\n\n All flags can be accessed using the single (upper case) letter as well as the full name.\n\n #### Examples\n\n \n```\n>>> y = np.array([[3, 1, 7],\n... [2, 0, 0],\n... [8, 5, 9]])\n>>> y\narray([[3, 1, 7],\n [2, 0, 0],\n [8, 5, 9]])\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : True\n ALIGNED : True\n WRITEBACKIFCOPY : False\n>>> y.setflags(write=0, align=0)\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : False\n ALIGNED : False\n WRITEBACKIFCOPY : False\n>>> y.setflags(uic=1)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: cannot set WRITEBACKIFCOPY flag to True\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.setflags.htmlnumpy.recarray.sort\n===================\n\n method\n\n recarray.sort(*axis=- 1*, *kind=None*, *order=None*)\n \nSort an array in-place. Refer to [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for full documentation.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nSorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.\n\n Changed in version 1.15.0: The ‘stable’ option was added.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nReturn a sorted copy of an array.\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nIndirect sort.\n\n [`numpy.lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort on multiple keys.\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nFind elements in sorted array.\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nPartial sort.\n\n #### Notes\n\n See [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,4], [3,1]])\n>>> a.sort(axis=1)\n>>> a\narray([[1, 4],\n [1, 3]])\n>>> a.sort(axis=0)\n>>> a\narray([[1, 3],\n [1, 4]])\n\n```\n Use the `order` keyword to specify a field to use when sorting a structured array:\n\n \n```\n>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n>>> a.sort(order='y')\n>>> a\narray([(b'c', 1), (b'a', 2)],\n dtype=[('x', 'S1'), ('y', '<i8')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.sort.htmlnumpy.recarray.squeeze\n======================\n\n method\n\n recarray.squeeze(*axis=None*)\n \nRemove axes of length one from `a`.\n\n Refer to [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\") for full documentation.\n\n See also\n\n [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.squeeze.htmlnumpy.recarray.std\n==================\n\n method\n\n recarray.std(*axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=False*, ***, *where=True*)\n \nReturns the standard deviation of the array elements along given axis.\n\n Refer to [`numpy.std`](numpy.std#numpy.std \"numpy.std\") for full documentation.\n\n See also\n\n [`numpy.std`](numpy.std#numpy.std \"numpy.std\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.std.htmlnumpy.recarray.sum\n==================\n\n method\n\n recarray.sum(*axis=None*, *dtype=None*, *out=None*, *keepdims=False*, *initial=0*, *where=True*)\n \nReturn the sum of the array elements over the given axis.\n\n Refer to [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\") for full documentation.\n\n See also\n\n [`numpy.sum`](numpy.sum#numpy.sum \"numpy.sum\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.sum.htmlnumpy.recarray.swapaxes\n=======================\n\n method\n\n recarray.swapaxes(*axis1*, *axis2*)\n \nReturn a view of the array with `axis1` and `axis2` interchanged.\n\n Refer to [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\") for full documentation.\n\n See also\n\n [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.swapaxes.htmlnumpy.recarray.take\n===================\n\n method\n\n recarray.take(*indices*, *axis=None*, *out=None*, *mode='raise'*)\n \nReturn an array formed from the elements of `a` at the given indices.\n\n Refer to [`numpy.take`](numpy.take#numpy.take \"numpy.take\") for full documentation.\n\n See also\n\n [`numpy.take`](numpy.take#numpy.take \"numpy.take\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.take.htmlnumpy.recarray.tobytes\n======================\n\n method\n\n recarray.tobytes(*order='C'*)\n \nConstruct Python bytes containing the raw data bytes in the array.\n\n Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the `order` parameter.\n\n New in version 1.9.0.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’}, optional\n\nControls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for *Any*) means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.\n\n Returns \n \n**s**bytes\n\nPython bytes exhibiting a copy of `a`’s raw data.\n\n #### Examples\n\n \n```\n>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n>>> x.tobytes()\nb'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n>>> x.tobytes('C') == x.tobytes()\nTrue\n>>> x.tobytes('F')\nb'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.tobytes.htmlnumpy.recarray.tofile\n=====================\n\n method\n\n recarray.tofile(*fid*, *sep=''*, *format='%s'*)\n \nWrite array to a file as text or binary (default).\n\n Data is always written in ‘C’ order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile().\n\n Parameters \n \n**fid**file or str or Path\n\nAn open file object, or a string containing a filename.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n**sep**str\n\nSeparator between array items for text output. If “” (empty), a binary file is written, equivalent to `file.write(a.tobytes())`.\n\n \n**format**str\n\nFormat string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.\n\n #### Notes\n\n This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.\n\n When fid is a file object, array contents are directly written to the file, bypassing the file object’s `write` method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support `fileno()` (e.g., BytesIO).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.tofile.htmlnumpy.recarray.tolist\n=====================\n\n method\n\n recarray.tolist()\n \nReturn the array as an `a.ndim`-levels deep nested list of Python scalars.\n\n Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the [`item`](numpy.ndarray.item#numpy.ndarray.item \"numpy.ndarray.item\") function.\n\n If `a.ndim` is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.\n\n Parameters \n **none**\n Returns \n \n**y**object, or list of object, or list of list of object, or …\n\nThe possibly nested list of array elements.\n\n #### Notes\n\n The array may be recreated via `a = np.array(a.tolist())`, although this may sometimes lose precision.\n\n #### Examples\n\n For a 1D array, `a.tolist()` is almost the same as `list(a)`, except that `tolist` changes numpy scalars to Python scalars:\n\n \n```\n>>> a = np.uint32([1, 2])\n>>> a_list = list(a)\n>>> a_list\n[1, 2]\n>>> type(a_list[0])\n<class 'numpy.uint32'>\n>>> a_tolist = a.tolist()\n>>> a_tolist\n[1, 2]\n>>> type(a_tolist[0])\n<class 'int'```\n Additionally, for a 2D array, `tolist` applies recursively:\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> list(a)\n[array([1, 2]), array([3, 4])]\n>>> a.tolist()\n[[1, 2], [3, 4]]\n\n```\n The base case for this recursion is a 0D array:\n\n \n```\n>>> a = np.array(1)\n>>> list(a)\nTraceback (most recent call last):\n ...\nTypeError: iteration over a 0-d array\n>>> a.tolist()\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.tolist.htmlnumpy.recarray.tostring\n=======================\n\n method\n\n recarray.tostring(*order='C'*)\n \nA compatibility alias for [`tobytes`](numpy.recarray.tobytes#numpy.recarray.tobytes \"numpy.recarray.tobytes\"), with exactly the same behavior.\n\n Despite its name, it returns `bytes` not [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\")s.\n\n Deprecated since version 1.19.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.tostring.htmlnumpy.recarray.trace\n====================\n\n method\n\n recarray.trace(*offset=0*, *axis1=0*, *axis2=1*, *dtype=None*, *out=None*)\n \nReturn the sum along diagonals of the array.\n\n Refer to [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\") for full documentation.\n\n See also\n\n [`numpy.trace`](numpy.trace#numpy.trace \"numpy.trace\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.trace.htmlnumpy.recarray.transpose\n========================\n\n method\n\n recarray.transpose(**axes*)\n \nReturns a view of the array with axes transposed.\n\n For a 1-D array this has no effect, as a transposed vector is simply the same vector. To convert a 1-D array into a 2D column vector, an additional dimension must be added. `np.atleast2d(a).T` achieves this, as does `a[:, np.newaxis]`. For a 2-D array, this is a standard matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and `a.shape = (i[0], i[1], ... i[n-2], i[n-1])`, then `a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])`.\n\n Parameters \n \n**axes**None, tuple of ints, or `n` ints\n\n* None or no argument: reverses the order of the axes.\n* tuple of ints: `i` in the `j`-th place in the tuple means `a`’s `i`-th axis becomes `a.transpose()`’s `j`-th axis.\n* `n` ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)\n\n Returns \n \n**out**ndarray\n\nView of `a`, with axes suitably permuted.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n\nEquivalent function\n\n [`ndarray.T`](numpy.ndarray.t#numpy.ndarray.T \"numpy.ndarray.T\")\n\nArray property returning the array transposed.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nGive a new shape to an array without changing its data.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> a\narray([[1, 2],\n [3, 4]])\n>>> a.transpose()\narray([[1, 3],\n [2, 4]])\n>>> a.transpose((1, 0))\narray([[1, 3],\n [2, 4]])\n>>> a.transpose(1, 0)\narray([[1, 3],\n [2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.transpose.htmlnumpy.recarray.var\n==================\n\n method\n\n recarray.var(*axis=None*, *dtype=None*, *out=None*, *ddof=0*, *keepdims=False*, ***, *where=True*)\n \nReturns the variance of the array elements, along given axis.\n\n Refer to [`numpy.var`](numpy.var#numpy.var \"numpy.var\") for full documentation.\n\n See also\n\n [`numpy.var`](numpy.var#numpy.var \"numpy.var\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.var.htmlnumpy.recarray.view\n===================\n\n method\n\n recarray.view(*[dtype][, type]*)\n \nNew view of array with the same data.\n\n Note\n\n Passing None for `dtype` is different from omitting the parameter, since the former invokes `dtype(None)` which is an alias for `dtype('float_')`.\n\n Parameters \n \n**dtype**data-type or ndarray sub-class, optional\n\nData-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the `type` parameter).\n\n \n**type**Python type, optional\n\nType of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.\n\n #### Notes\n\n `a.view()` is used two different ways:\n\n `a.view(some_dtype)` or `a.view(dtype=some_dtype)` constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.\n\n `a.view(ndarray_subclass)` or `a.view(type=ndarray_subclass)` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.\n\n For `a.view(some_dtype)`, if `some_dtype` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of `a` must be contiguous. This axis will be resized in the result.\n\n Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.\n\n #### Examples\n\n \n```\n>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n\n```\n Viewing array data using a different type and dtype:\n\n \n```\n>>> y = x.view(dtype=np.int16, type=np.matrix)\n>>> y\nmatrix([[513]], dtype=int16)\n>>> print(type(y))\n<class 'numpy.matrix'```\n Creating a view on a structured array so it can be used in calculations\n\n \n```\n>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n>>> xv = x.view(dtype=np.int8).reshape(-1,2)\n>>> xv\narray([[1, 2],\n [3, 4]], dtype=int8)\n>>> xv.mean(0)\narray([2., 3.])\n\n```\n Making changes to the view changes the underlying array\n\n \n```\n>>> xv[0,1] = 20\n>>> x\narray([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n\n```\n Using a view to convert an array to a recarray:\n\n \n```\n>>> z = x.view(np.recarray)\n>>> z.a\narray([1, 3], dtype=int8)\n\n```\n Views share data:\n\n \n```\n>>> x[0] = (9, 10)\n>>> z[0]\n(9, 10)\n\n```\n Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n\n \n```\n>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n>>> y = x[:, ::2]\n>>> y\narray([[1, 3],\n [4, 6]], dtype=int16)\n>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\nTraceback (most recent call last):\n ...\nValueError: To change to a dtype of a different size, the last axis must be contiguous\n>>> z = y.copy()\n>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\narray([[(1, 3)],\n [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n\n```\n However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:\n\n \n```\n>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n>>> x.transpose(1, 0, 2).view(np.int16)\narray([[[ 256, 770],\n [3340, 3854]],\n\n [[1284, 1798],\n [4368, 4882]],\n\n [[2312, 2826],\n [5396, 5910]]], dtype=int16)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.view.htmlnumpy.recarray.strides\n======================\n\n attribute\n\n recarray.strides\n \nTuple of bytes to step in each dimension when traversing an array.\n\n The byte offset of element `(i[0], i[1], ..., i[n])` in an array `a` is:\n\n \n```\noffset = sum(np.array(i) * a.strides)\n\n```\n A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.\n\n Warning\n\n Setting `arr.strides` is discouraged and may be deprecated in the future. [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\") should be preferred to create a new view of the same data in a safer way.\n\n See also\n\n [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\")\n #### Notes\n\n Imagine an array of 32-bit integers (each 4 bytes):\n\n \n```\nx = np.array([[0, 1, 2, 3, 4],\n [5, 6, 7, 8, 9]], dtype=np.int32)\n\n```\n This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be `(20, 4)`.\n\n #### Examples\n\n \n```\n>>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n>>> y\narray([[[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]],\n [[12, 13, 14, 15],\n [16, 17, 18, 19],\n [20, 21, 22, 23]]])\n>>> y.strides\n(48, 16, 4)\n>>> y[1,1,1]\n17\n>>> offset=sum(y.strides * np.array((1,1,1)))\n>>> offset/y.itemsize\n17\n\n```\n \n```\n>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n>>> x.strides\n(32, 4, 224, 1344)\n>>> i = np.array([3,5,2,2])\n>>> offset = sum(i * x.strides)\n>>> x[3,5,2,2]\n813\n>>> offset / x.itemsize\n813\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.strides.htmlnumpy.recarray.T\n================\n\n attribute\n\n recarray.T\n \nThe transposed array.\n\n Same as `self.transpose()`.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n #### Examples\n\n \n```\n>>> x = np.array([[1.,2.],[3.,4.]])\n>>> x\narray([[ 1., 2.],\n [ 3., 4.]])\n>>> x.T\narray([[ 1., 3.],\n [ 2., 4.]])\n>>> x = np.array([1.,2.,3.,4.])\n>>> x\narray([ 1., 2., 3., 4.])\n>>> x.T\narray([ 1., 2., 3., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.T.htmlnumpy.recarray.base\n===================\n\n attribute\n\n recarray.base\n \nBase object if memory is from some other object.\n\n #### Examples\n\n The base of an array that owns its memory is None:\n\n \n```\n>>> x = np.array([1,2,3,4])\n>>> x.base is None\nTrue\n\n```\n Slicing creates a view, whose memory is shared with x:\n\n \n```\n>>> y = x[2:]\n>>> y.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.base.htmlnumpy.recarray.ctypes\n=====================\n\n attribute\n\n recarray.ctypes\n \nAn object to simplify the interaction of the array with the ctypes module.\n\n This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.\n\n Parameters \n **None**\n Returns \n \n**c**Python object\n\nPossessing attributes data, shape, strides, etc.\n\n See also\n\n [`numpy.ctypeslib`](../routines.ctypeslib#module-numpy.ctypeslib \"numpy.ctypeslib\")\n #### Notes\n\n Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):\n\n _ctypes.data\n \nA pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as `self._array_interface_['data'][0]`.\n\n Note that unlike `data_as`, a reference will not be kept to the array: code like `ctypes.c_void_p((a + b).ctypes.data)` will result in a pointer to a deallocated array, and should be spelt `(a + b).ctypes.data_as(ctypes.c_void_p)`\n\n \n _ctypes.shape\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to `dtype('p')` on this platform (see [`c_intp`](../routines.ctypeslib#numpy.ctypeslib.c_intp \"numpy.ctypeslib.c_intp\")). This base-type could be [`ctypes.c_int`](https://docs.python.org/3/library/ctypes.html#ctypes.c_int \"(in Python v3.10)\"), [`ctypes.c_long`](https://docs.python.org/3/library/ctypes.html#ctypes.c_long \"(in Python v3.10)\"), or [`ctypes.c_longlong`](https://docs.python.org/3/library/ctypes.html#ctypes.c_longlong \"(in Python v3.10)\") depending on the platform. The ctypes array contains the shape of the underlying array.\n\n \n _ctypes.strides\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.\n\n \n _ctypes.data_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L267-L284)\n \nReturn the data pointer cast to a particular c-types object. For example, calling `self._as_parameter_` is equivalent to `self.data_as(ctypes.c_void_p)`. Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: `self.data_as(ctypes.POINTER(ctypes.c_double))`.\n\n The returned pointer will keep a reference to the array.\n\n \n _ctypes.shape_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L286-L293)\n \nReturn the shape tuple as an array of some other c-types type. For example: `self.shape_as(ctypes.c_short)`.\n\n \n _ctypes.strides_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L295-L302)\n \nReturn the strides tuple as an array of some other c-types type. For example: `self.strides_as(ctypes.c_longlong)`.\n\n \n If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the `as_parameter` attribute which will return an integer equal to the data attribute.\n\n #### Examples\n\n \n```\n>>> import ctypes\n>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n>>> x\narray([[0, 1],\n [2, 3]], dtype=int32)\n>>> x.ctypes.data\n31962608 # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\nc_uint(0)\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\nc_ulong(4294967296)\n>>> x.ctypes.shape\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n>>> x.ctypes.strides\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.ctypes.htmlnumpy.recarray.data\n===================\n\n attribute\n\n recarray.data\n \nPython buffer object pointing to the start of the array’s data.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.data.htmlnumpy.recarray.flags\n====================\n\n attribute\n\n recarray.flags\n \nInformation about the memory layout of the array.\n\n #### Notes\n\n The [`flags`](#numpy.recarray.flags \"numpy.recarray.flags\") object can be accessed dictionary-like (as in `a.flags['WRITEABLE']`), or by using lowercased attribute names (as in `a.flags.writeable`). Short flag names are only supported in dictionary access.\n\n Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n The array flags cannot be set arbitrarily:\n\n * WRITEBACKIFCOPY can only be set `False`.\n* ALIGNED can only be set `True` if the data is truly aligned.\n* WRITEABLE can only be set `True` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.\n\n Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.\n\n Even for contiguous arrays a stride for a given dimension `arr.strides[dim]` may be *arbitrary* if `arr.shape[dim] == 1` or the array has no elements. It does *not* generally hold that `self.strides[-1] == self.itemsize` for C-style contiguous arrays or `self.strides[0] == self.itemsize` for Fortran-style contiguous arrays is true.\n\n Attributes \n **C_CONTIGUOUS (C)**\n\nThe data is in a single, C-style contiguous segment.\n\n **F_CONTIGUOUS (F)**\n\nThe data is in a single, Fortran-style contiguous segment.\n\n **OWNDATA (O)**\n\nThe array owns the memory it uses or borrows it from another object.\n\n **WRITEABLE (W)**\n\nThe data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.\n\n **ALIGNED (A)**\n\nThe data and all elements are aligned appropriately for the hardware.\n\n **WRITEBACKIFCOPY (X)**\n\nThis array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.\n\n **FNC**\n\nF_CONTIGUOUS and not C_CONTIGUOUS.\n\n **FORC**\n\nF_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n\n **BEHAVED (B)**\n\nALIGNED and WRITEABLE.\n\n **CARRAY (CA)**\n\nBEHAVED and C_CONTIGUOUS.\n\n **FARRAY (FA)**\n\nBEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.flags.htmlnumpy.recarray.flat\n===================\n\n attribute\n\n recarray.flat\n \nA 1-D iterator over the array.\n\n This is a [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\") instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.\n\n See also\n\n [`flatten`](numpy.recarray.flatten#numpy.recarray.flatten \"numpy.recarray.flatten\")\n\nReturn a copy of the array collapsed into one dimension.\n\n [`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> x = np.arange(1, 7).reshape(2, 3)\n>>> x\narray([[1, 2, 3],\n [4, 5, 6]])\n>>> x.flat[3]\n4\n>>> x.T\narray([[1, 4],\n [2, 5],\n [3, 6]])\n>>> x.T.flat[3]\n5\n>>> type(x.flat)\n<class 'numpy.flatiter'```\n An assignment example:\n\n \n```\n>>> x.flat = 3; x\narray([[3, 3, 3],\n [3, 3, 3]])\n>>> x.flat[[1,4]] = 1; x\narray([[3, 1, 3],\n [3, 1, 3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.flat.htmlnumpy.recarray.itemsize\n=======================\n\n attribute\n\n recarray.itemsize\n \nLength of one array element in bytes.\n\n #### Examples\n\n \n```\n>>> x = np.array([1,2,3], dtype=np.float64)\n>>> x.itemsize\n8\n>>> x = np.array([1,2,3], dtype=np.complex128)\n>>> x.itemsize\n16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.itemsize.htmlnumpy.recarray.nbytes\n=====================\n\n attribute\n\n recarray.nbytes\n \nTotal bytes consumed by the elements of the array.\n\n #### Notes\n\n Does not include memory consumed by non-element attributes of the array object.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3,5,2), dtype=np.complex128)\n>>> x.nbytes\n480\n>>> np.prod(x.shape) * x.itemsize\n480\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.nbytes.htmlnumpy.recarray.ndim\n===================\n\n attribute\n\n recarray.ndim\n \nNumber of array dimensions.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> x.ndim\n1\n>>> y = np.zeros((2, 3, 4))\n>>> y.ndim\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.ndim.htmlnumpy.recarray.size\n===================\n\n attribute\n\n recarray.size\n \nNumber of elements in the array.\n\n Equal to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.\n\n #### Notes\n\n `a.size` returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested `np.prod(a.shape)`, which returns an instance of `np.int_`), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n>>> x.size\n30\n>>> np.prod(x.shape)\n30\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.recarray.size.htmlnumpy.dtype.isalignedstruct\n===========================\n\n attribute\n\n dtype.isalignedstruct\n \nBoolean indicating whether the dtype is a struct which maintains field alignment. This flag is sticky, so when combining multiple structs together, it is preserved and produces new dtypes which are also aligned.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.dtype.isalignedstruct.htmlnumpy.ma.MaskedArray.__array__\n==================================\n\n method\n\n ma.MaskedArray.__array__([*dtype*, ]*/*) → reference if type unchanged, copy otherwise.\n \nReturns either a new reference to self if dtype is not given or a new array of provided data type if dtype is different from the current dtype of the array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__array__.htmlnumpy.ma.MaskedArray.base\n=========================\n\n attribute\n\n ma.MaskedArray.base\n \nBase object if memory is from some other object.\n\n #### Examples\n\n The base of an array that owns its memory is None:\n\n \n```\n>>> x = np.array([1,2,3,4])\n>>> x.base is None\nTrue\n\n```\n Slicing creates a view, whose memory is shared with x:\n\n \n```\n>>> y = x[2:]\n>>> y.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.base.htmlnumpy.ma.MaskedArray.ctypes\n===========================\n\n attribute\n\n ma.MaskedArray.ctypes\n \nAn object to simplify the interaction of the array with the ctypes module.\n\n This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.\n\n Parameters \n **None**\n Returns \n \n**c**Python object\n\nPossessing attributes data, shape, strides, etc.\n\n See also\n\n [`numpy.ctypeslib`](../routines.ctypeslib#module-numpy.ctypeslib \"numpy.ctypeslib\")\n #### Notes\n\n Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):\n\n _ctypes.data\n \nA pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as `self._array_interface_['data'][0]`.\n\n Note that unlike `data_as`, a reference will not be kept to the array: code like `ctypes.c_void_p((a + b).ctypes.data)` will result in a pointer to a deallocated array, and should be spelt `(a + b).ctypes.data_as(ctypes.c_void_p)`\n\n \n _ctypes.shape\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to `dtype('p')` on this platform (see [`c_intp`](../routines.ctypeslib#numpy.ctypeslib.c_intp \"numpy.ctypeslib.c_intp\")). This base-type could be [`ctypes.c_int`](https://docs.python.org/3/library/ctypes.html#ctypes.c_int \"(in Python v3.10)\"), [`ctypes.c_long`](https://docs.python.org/3/library/ctypes.html#ctypes.c_long \"(in Python v3.10)\"), or [`ctypes.c_longlong`](https://docs.python.org/3/library/ctypes.html#ctypes.c_longlong \"(in Python v3.10)\") depending on the platform. The ctypes array contains the shape of the underlying array.\n\n \n _ctypes.strides\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.\n\n \n _ctypes.data_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L267-L284)\n \nReturn the data pointer cast to a particular c-types object. For example, calling `self._as_parameter_` is equivalent to `self.data_as(ctypes.c_void_p)`. Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: `self.data_as(ctypes.POINTER(ctypes.c_double))`.\n\n The returned pointer will keep a reference to the array.\n\n \n _ctypes.shape_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L286-L293)\n \nReturn the shape tuple as an array of some other c-types type. For example: `self.shape_as(ctypes.c_short)`.\n\n \n _ctypes.strides_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L295-L302)\n \nReturn the strides tuple as an array of some other c-types type. For example: `self.strides_as(ctypes.c_longlong)`.\n\n \n If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the `as_parameter` attribute which will return an integer equal to the data attribute.\n\n #### Examples\n\n \n```\n>>> import ctypes\n>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n>>> x\narray([[0, 1],\n [2, 3]], dtype=int32)\n>>> x.ctypes.data\n31962608 # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\nc_uint(0)\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\nc_ulong(4294967296)\n>>> x.ctypes.shape\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n>>> x.ctypes.strides\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.ctypes.htmlnumpy.ma.MaskedArray.dtype\n==========================\n\n property\n\n *property*ma.MaskedArray.dtype\n \nData-type of the array’s elements.\n\n Warning\n\n Setting `arr.dtype` is discouraged and may be deprecated in the future. Setting will replace the `dtype` without modifying the memory (see also [`ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\") and [`ndarray.astype`](numpy.ndarray.astype#numpy.ndarray.astype \"numpy.ndarray.astype\")).\n\n Parameters \n **None**\n Returns \n \n**d**numpy dtype object\n\n See also\n\n [`ndarray.astype`](numpy.ndarray.astype#numpy.ndarray.astype \"numpy.ndarray.astype\")\n\nCast the values contained in the array to a new data-type.\n\n [`ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\")\n\nCreate a view of the same data but a different data-type.\n\n [`numpy.dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n #### Examples\n\n \n```\n>>> x\narray([[0, 1],\n [2, 3]])\n>>> x.dtype\ndtype('int32')\n>>> type(x.dtype)\n<type 'numpy.dtype'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.dtype.htmlnumpy.ma.MaskedArray.flags\n==========================\n\n attribute\n\n ma.MaskedArray.flags\n \nInformation about the memory layout of the array.\n\n #### Notes\n\n The [`flags`](#numpy.ma.MaskedArray.flags \"numpy.ma.MaskedArray.flags\") object can be accessed dictionary-like (as in `a.flags['WRITEABLE']`), or by using lowercased attribute names (as in `a.flags.writeable`). Short flag names are only supported in dictionary access.\n\n Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n The array flags cannot be set arbitrarily:\n\n * WRITEBACKIFCOPY can only be set `False`.\n* ALIGNED can only be set `True` if the data is truly aligned.\n* WRITEABLE can only be set `True` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.\n\n Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.\n\n Even for contiguous arrays a stride for a given dimension `arr.strides[dim]` may be *arbitrary* if `arr.shape[dim] == 1` or the array has no elements. It does *not* generally hold that `self.strides[-1] == self.itemsize` for C-style contiguous arrays or `self.strides[0] == self.itemsize` for Fortran-style contiguous arrays is true.\n\n Attributes \n **C_CONTIGUOUS (C)**\n\nThe data is in a single, C-style contiguous segment.\n\n **F_CONTIGUOUS (F)**\n\nThe data is in a single, Fortran-style contiguous segment.\n\n **OWNDATA (O)**\n\nThe array owns the memory it uses or borrows it from another object.\n\n **WRITEABLE (W)**\n\nThe data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.\n\n **ALIGNED (A)**\n\nThe data and all elements are aligned appropriately for the hardware.\n\n **WRITEBACKIFCOPY (X)**\n\nThis array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.\n\n **FNC**\n\nF_CONTIGUOUS and not C_CONTIGUOUS.\n\n **FORC**\n\nF_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n\n **BEHAVED (B)**\n\nALIGNED and WRITEABLE.\n\n **CARRAY (CA)**\n\nBEHAVED and C_CONTIGUOUS.\n\n **FARRAY (FA)**\n\nBEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.flags.htmlnumpy.ma.MaskedArray.itemsize\n=============================\n\n attribute\n\n ma.MaskedArray.itemsize\n \nLength of one array element in bytes.\n\n #### Examples\n\n \n```\n>>> x = np.array([1,2,3], dtype=np.float64)\n>>> x.itemsize\n8\n>>> x = np.array([1,2,3], dtype=np.complex128)\n>>> x.itemsize\n16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.itemsize.htmlnumpy.ma.MaskedArray.nbytes\n===========================\n\n attribute\n\n ma.MaskedArray.nbytes\n \nTotal bytes consumed by the elements of the array.\n\n #### Notes\n\n Does not include memory consumed by non-element attributes of the array object.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3,5,2), dtype=np.complex128)\n>>> x.nbytes\n480\n>>> np.prod(x.shape) * x.itemsize\n480\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.nbytes.htmlnumpy.ma.MaskedArray.ndim\n=========================\n\n attribute\n\n ma.MaskedArray.ndim\n \nNumber of array dimensions.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> x.ndim\n1\n>>> y = np.zeros((2, 3, 4))\n>>> y.ndim\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.ndim.htmlnumpy.ma.MaskedArray.shape\n==========================\n\n property\n\n *property*ma.MaskedArray.shape\n \nTuple of array dimensions.\n\n The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.\n\n Warning\n\n Setting `arr.shape` is discouraged and may be deprecated in the future. Using [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\") is the preferred approach.\n\n See also\n\n [`numpy.shape`](numpy.shape#numpy.shape \"numpy.shape\")\n\nEquivalent getter function.\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nFunction similar to setting `shape`.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nMethod similar to setting `shape`.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3, 4])\n>>> x.shape\n(4,)\n>>> y = np.zeros((2, 3, 4))\n>>> y.shape\n(2, 3, 4)\n>>> y.shape = (3, 8)\n>>> y\narray([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n [ 0., 0., 0., 0., 0., 0., 0., 0.],\n [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n>>> y.shape = (3, 6)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: total size of new array must be unchanged\n>>> np.zeros((4,2))[::2].shape = (-1,)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nAttributeError: Incompatible shape for in-place modification. Use\n`.reshape()` to make a copy with the desired shape.\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.shape.htmlnumpy.ma.MaskedArray.size\n=========================\n\n attribute\n\n ma.MaskedArray.size\n \nNumber of elements in the array.\n\n Equal to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.\n\n #### Notes\n\n `a.size` returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested `np.prod(a.shape)`, which returns an instance of `np.int_`), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n>>> x.size\n30\n>>> np.prod(x.shape)\n30\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.size.htmlnumpy.ma.MaskedArray.strides\n============================\n\n attribute\n\n ma.MaskedArray.strides\n \nTuple of bytes to step in each dimension when traversing an array.\n\n The byte offset of element `(i[0], i[1], ..., i[n])` in an array `a` is:\n\n \n```\noffset = sum(np.array(i) * a.strides)\n\n```\n A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.\n\n Warning\n\n Setting `arr.strides` is discouraged and may be deprecated in the future. [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\") should be preferred to create a new view of the same data in a safer way.\n\n See also\n\n [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\")\n #### Notes\n\n Imagine an array of 32-bit integers (each 4 bytes):\n\n \n```\nx = np.array([[0, 1, 2, 3, 4],\n [5, 6, 7, 8, 9]], dtype=np.int32)\n\n```\n This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be `(20, 4)`.\n\n #### Examples\n\n \n```\n>>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n>>> y\narray([[[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]],\n [[12, 13, 14, 15],\n [16, 17, 18, 19],\n [20, 21, 22, 23]]])\n>>> y.strides\n(48, 16, 4)\n>>> y[1,1,1]\n17\n>>> offset=sum(y.strides * np.array((1,1,1)))\n>>> offset/y.itemsize\n17\n\n```\n \n```\n>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n>>> x.strides\n(32, 4, 224, 1344)\n>>> i = np.array([3,5,2,2])\n>>> offset = sum(i * x.strides)\n>>> x[3,5,2,2]\n813\n>>> offset / x.itemsize\n813\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.strides.htmlnumpy.ma.MaskedArray.imag\n=========================\n\n property\n\n *property*ma.MaskedArray.imag\n \nThe imaginary part of the masked array.\n\n This property is a view on the imaginary part of this `MaskedArray`.\n\n See also\n\n [`real`](numpy.real#numpy.real \"numpy.real\")\n #### Examples\n\n \n```\n>>> x = np.ma.array([1+1.j, -2j, 3.45+1.6j], mask=[False, True, False])\n>>> x.imag\nmasked_array(data=[1.0, --, 1.6],\n mask=[False, True, False],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.imag.htmlnumpy.ma.MaskedArray.real\n=========================\n\n property\n\n *property*ma.MaskedArray.real\n \nThe real part of the masked array.\n\n This property is a view on the real part of this `MaskedArray`.\n\n See also\n\n [`imag`](numpy.imag#numpy.imag \"numpy.imag\")\n #### Examples\n\n \n```\n>>> x = np.ma.array([1+1.j, -2j, 3.45+1.6j], mask=[False, True, False])\n>>> x.real\nmasked_array(data=[1.0, --, 3.45],\n mask=[False, True, False],\n fill_value=1e+20)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.real.htmlnumpy.ma.MaskedArray.flat\n=========================\n\n property\n\n *property*ma.MaskedArray.flat\n \nReturn a flat iterator, or set a flattened version of self to value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.flat.htmlnumpy.ma.MaskedArray.__array_priority__\n============================================\n\n attribute\n\n ma.MaskedArray.__array_priority__*=15*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__array_priority__.htmlnumpy.ma.MaskedArray.__float__\n==================================\n\n method\n\n ma.MaskedArray.__float__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4407-L4418)\n \nConvert to float.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__float__.htmlnumpy.ma.MaskedArray.__int__\n================================\n\n method\n\n ma.MaskedArray.__int__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4420-L4430)\n \nConvert to int.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__int__.htmlnumpy.ma.MaskedArray.view\n=========================\n\n method\n\n ma.MaskedArray.view(*dtype=None*, *type=None*, *fill_value=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3121-L3209)\n \nReturn a view of the MaskedArray data.\n\n Parameters \n \n**dtype**data-type or ndarray sub-class, optional\n\nData-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. As with `ndarray.view`, dtype can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the `type` parameter).\n\n \n**type**Python type, optional\n\nType of the returned view, either ndarray or a subclass. The default None results in type preservation.\n\n \n**fill_value**scalar, optional\n\nThe value to use for invalid entries (None by default). If None, then this argument is inferred from the passed [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), or in its absence the original array, as discussed in the notes below.\n\n See also\n\n [`numpy.ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\")\n\nEquivalent method on ndarray object.\n\n #### Notes\n\n `a.view()` is used two different ways:\n\n `a.view(some_dtype)` or `a.view(dtype=some_dtype)` constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.\n\n `a.view(ndarray_subclass)` or `a.view(type=ndarray_subclass)` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.\n\n If [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") is not specified, but [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") is specified (and is not an ndarray sub-class), the [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") of the MaskedArray will be reset. If neither [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") nor [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") are specified (or if [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") is an ndarray sub-class), then the fill value is preserved. Finally, if [`fill_value`](../maskedarray.baseclass#numpy.ma.MaskedArray.fill_value \"numpy.ma.MaskedArray.fill_value\") is specified, but [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") is not, the fill value is set to the specified value.\n\n For `a.view(some_dtype)`, if `some_dtype` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of `a` (shown by `print(a)`). It also depends on exactly how `a` is stored in memory. Therefore if `a` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.view.htmlnumpy.ma.MaskedArray.astype\n===========================\n\n method\n\n ma.MaskedArray.astype(*dtype*, *order='K'*, *casting='unsafe'*, *subok=True*, *copy=True*)\n \nCopy of the array, cast to a specified type.\n\n Parameters \n \n**dtype**str or dtype\n\nTypecode or data-type to which the array is cast.\n\n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.\n\n \n**casting**{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional\n\nControls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.\n\n * ‘no’ means the data types should not be cast at all.\n* ‘equiv’ means only byte-order changes are allowed.\n* ‘safe’ means only casts which can preserve values are allowed.\n* ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.\n* ‘unsafe’ means any data conversions may be done.\n\n \n**subok**bool, optional\n\nIf True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.\n\n \n**copy**bool, optional\n\nBy default, astype always returns a newly allocated array. If this is set to false, and the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy.\n\n Returns \n \n**arr_t**ndarray\n\nUnless [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False and the other conditions for returning the input array are satisfied (see description for [`copy`](numpy.copy#numpy.copy \"numpy.copy\") input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`.\n\n Raises \n ComplexWarning\n\nWhen casting from complex to float or int. To avoid this, one should use `a.real.astype(t)`.\n\n #### Notes\n\n Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.\n\n Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 2.5])\n>>> x\narray([1. , 2. , 2.5])\n\n```\n \n```\n>>> x.astype(int)\narray([1, 2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.astype.htmlnumpy.ma.MaskedArray.byteswap\n=============================\n\n method\n\n ma.MaskedArray.byteswap(*inplace=False*)\n \nSwap the bytes of the array elements\n\n Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.\n\n Parameters \n \n**inplace**bool, optional\n\nIf `True`, swap bytes in-place, default is `False`.\n\n Returns \n \n**out**ndarray\n\nThe byteswapped array. If `inplace` is `True`, this is a view to self.\n\n #### Examples\n\n \n```\n>>> A = np.array([1, 256, 8755], dtype=np.int16)\n>>> list(map(hex, A))\n['0x1', '0x100', '0x2233']\n>>> A.byteswap(inplace=True)\narray([ 256, 1, 13090], dtype=int16)\n>>> list(map(hex, A))\n['0x100', '0x1', '0x3322']\n\n```\n Arrays of byte-strings are not swapped\n\n \n```\n>>> A = np.array([b'ceg', b'fac'])\n>>> A.byteswap()\narray([b'ceg', b'fac'], dtype='|S3')\n\n```\n \n`A.newbyteorder().byteswap()` produces an array with the same values\n\nbut different representation in memory\n\n \n```\n>>> A = np.array([1, 2, 3])\n>>> A.view(np.uint8)\narray([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n 0, 0], dtype=uint8)\n>>> A.newbyteorder().byteswap(inplace=True)\narray([1, 2, 3])\n>>> A.view(np.uint8)\narray([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n 0, 3], dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.byteswap.htmlnumpy.ma.MaskedArray.toflex\n===========================\n\n method\n\n ma.MaskedArray.toflex()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6169-L6226)\n \nTransforms a masked array into a flexible-type array.\n\n The flexible type array that is returned will have two fields:\n\n * the `_data` field stores the `_data` part of the array.\n* the `_mask` field stores the `_mask` part of the array.\n\n Parameters \n **None**\n Returns \n \n**record**ndarray\n\nA new flexible-type [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") with two fields: the first element containing a value, the second element containing the corresponding mask boolean. The returned record shape matches self.shape.\n\n #### Notes\n\n A side-effect of transforming a masked array into a flexible [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") is that meta information (`fill_value`, …) will be lost.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.toflex()\narray([[(1, False), (2, True), (3, False)],\n [(4, True), (5, False), (6, True)],\n [(7, False), (8, True), (9, False)]],\n dtype=[('_data', '<i8'), ('_mask', '?')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.toflex.htmlnumpy.ma.MaskedArray.tostring\n=============================\n\n method\n\n ma.MaskedArray.tostring(*fill_value=None*, *order='C'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6099-L6112)\n \nA compatibility alias for [`tobytes`](numpy.ma.maskedarray.tobytes#numpy.ma.MaskedArray.tobytes \"numpy.ma.MaskedArray.tobytes\"), with exactly the same behavior.\n\n Despite its name, it returns `bytes` not [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\")s.\n\n Deprecated since version 1.19.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.tostring.htmlnumpy.ma.MaskedArray.T\n======================\n\n property\n\n *property*ma.MaskedArray.T\n \nThe transposed array.\n\n Same as `self.transpose()`.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n #### Examples\n\n \n```\n>>> x = np.array([[1.,2.],[3.,4.]])\n>>> x\narray([[ 1., 2.],\n [ 3., 4.]])\n>>> x.T\narray([[ 1., 3.],\n [ 2., 4.]])\n>>> x = np.array([1.,2.,3.,4.])\n>>> x\narray([ 1., 2., 3., 4.])\n>>> x.T\narray([ 1., 2., 3., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.T.htmlnumpy.ma.MaskedArray.choose\n===========================\n\n method\n\n ma.MaskedArray.choose(*choices*, *out=None*, *mode='raise'*)\n \nUse an index array to construct a new array from a set of choices.\n\n Refer to [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\") for full documentation.\n\n See also\n\n [`numpy.choose`](numpy.choose#numpy.choose \"numpy.choose\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.choose.htmlnumpy.ma.MaskedArray.compress\n=============================\n\n method\n\n ma.MaskedArray.compress(*condition*, *axis=None*, *out=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3883-L3953)\n \nReturn `a` where condition is `True`.\n\n If condition is a [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\"), missing values are considered as `False`.\n\n Parameters \n \n**condition**var\n\nBoolean 1-d array selecting which entries to return. If len(condition) is less than the size of a along the axis, then output is truncated to length of condition array.\n\n \n**axis**{None, int}, optional\n\nAxis along which the operation must be performed.\n\n \n**out**{None, ndarray}, optional\n\nAlternative output array in which to place the result. It must have the same shape as the expected output but the type will be cast if necessary.\n\n Returns \n \n**result**MaskedArray\n\nA [`MaskedArray`](../maskedarray.baseclass#numpy.ma.MaskedArray \"numpy.ma.MaskedArray\") object.\n\n #### Notes\n\n Please note the difference with [`compressed`](numpy.ma.maskedarray.compressed#numpy.ma.MaskedArray.compressed \"numpy.ma.MaskedArray.compressed\") ! The output of [`compress`](numpy.compress#numpy.compress \"numpy.compress\") has a mask, the output of [`compressed`](numpy.ma.maskedarray.compressed#numpy.ma.MaskedArray.compressed \"numpy.ma.MaskedArray.compressed\") does not.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.compress([1, 0, 1])\nmasked_array(data=[1, 3],\n mask=[False, False],\n fill_value=999999)\n\n```\n \n```\n>>> x.compress([1, 0, 1], axis=1)\nmasked_array(\n data=[[1, 3],\n [--, --],\n [7, 9]],\n mask=[[False, False],\n [ True, True],\n [False, False]],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.compress.htmlnumpy.ma.MaskedArray.diagonal\n=============================\n\n method\n\n ma.MaskedArray.diagonal(*offset=0*, *axis1=0*, *axis2=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2577-L2587)\n \nReturn specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.\n\n Refer to [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\") for full documentation.\n\n See also\n\n [`numpy.diagonal`](numpy.diagonal#numpy.diagonal \"numpy.diagonal\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.diagonal.htmlnumpy.ma.MaskedArray.fill\n=========================\n\n method\n\n ma.MaskedArray.fill(*value*)\n \nFill the array with a scalar value.\n\n Parameters \n \n**value**scalar\n\nAll elements of `a` will be assigned this value.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2])\n>>> a.fill(0)\n>>> a\narray([0, 0])\n>>> a = np.empty(2)\n>>> a.fill(1)\n>>> a\narray([1., 1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.fill.htmlnumpy.ma.MaskedArray.item\n=========================\n\n method\n\n ma.MaskedArray.item(**args*)\n \nCopy an element of an array to a standard Python scalar and return it.\n\n Parameters \n \n***args**Arguments (variable number and type)\n\n* none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned.\n* int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.\n* tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.\n\n Returns \n \n**z**Standard Python scalar object\n\nA copy of the specified element of the array as a suitable Python scalar\n\n #### Notes\n\n When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.\n\n [`item`](#numpy.ma.MaskedArray.item \"numpy.ma.MaskedArray.item\") is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.item(3)\n1\n>>> x.item(7)\n0\n>>> x.item((0, 1))\n2\n>>> x.item((2, 2))\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.item.htmlnumpy.ma.MaskedArray.put\n========================\n\n method\n\n ma.MaskedArray.put(*indices*, *values*, *mode='raise'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4723-L4806)\n \nSet storage-indexed locations to corresponding values.\n\n Sets self._data.flat[n] = values[n] for each n in indices. If `values` is shorter than [`indices`](numpy.indices#numpy.indices \"numpy.indices\") then it will repeat. If `values` has some masked values, the initial mask is updated in consequence, else the corresponding values are unmasked.\n\n Parameters \n \n**indices**1-D array_like\n\nTarget indices, interpreted as integers.\n\n \n**values**array_like\n\nValues to place in self._data copy at target indices.\n\n \n**mode**{‘raise’, ‘wrap’, ‘clip’}, optional\n\nSpecifies how out-of-bounds indices will behave. ‘raise’ : raise an error. ‘wrap’ : wrap around. ‘clip’ : clip to the range.\n\n #### Notes\n\n `values` can be a scalar or length 1 array.\n\n #### Examples\n\n \n```\n>>> x = np.ma.array([[1,2,3],[4,5,6],[7,8,9]], mask=[0] + [1,0]*4)\n>>> x\nmasked_array(\n data=[[1, --, 3],\n [--, 5, --],\n [7, --, 9]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n>>> x.put([0,4,8],[10,20,30])\n>>> x\nmasked_array(\n data=[[10, --, 3],\n [--, 20, --],\n [7, --, 30]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n\n```\n \n```\n>>> x.put(4,999)\n>>> x\nmasked_array(\n data=[[10, --, 3],\n [--, 999, --],\n [7, --, 30]],\n mask=[[False, True, False],\n [ True, False, True],\n [False, True, False]],\n fill_value=999999)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.put.htmlnumpy.ma.MaskedArray.repeat\n===========================\n\n method\n\n ma.MaskedArray.repeat(*repeats*, *axis=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2577-L2587)\n \nRepeat elements of an array.\n\n Refer to [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\") for full documentation.\n\n See also\n\n [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.repeat.htmlnumpy.ma.MaskedArray.searchsorted\n=================================\n\n method\n\n ma.MaskedArray.searchsorted(*v*, *side='left'*, *sorter=None*)\n \nFind indices where elements of v should be inserted in a to maintain order.\n\n For full documentation, see [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n See also\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.searchsorted.htmlnumpy.ma.MaskedArray.take\n=========================\n\n method\n\n ma.MaskedArray.take(*indices*, *axis=None*, *out=None*, *mode='raise'*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6012-L6036)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.take.htmlnumpy.ma.MaskedArray.dump\n=========================\n\n method\n\n ma.MaskedArray.dump(*file*)\n \nDump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.\n\n Parameters \n \n**file**str or Path\n\nA string naming the dump file.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.dump.htmlnumpy.ma.MaskedArray.dumps\n==========================\n\n method\n\n ma.MaskedArray.dumps()\n \nReturns the pickle of the array as a string. pickle.loads will convert the string back to an array.\n\n Parameters \n **None**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.dumps.htmlnumpy.ma.MaskedArray.conj\n=========================\n\n method\n\n ma.MaskedArray.conj()\n \nComplex-conjugate all elements.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.conj.htmlnumpy.ma.MaskedArray.conjugate\n==============================\n\n method\n\n ma.MaskedArray.conjugate()\n \nReturn the complex conjugate, element-wise.\n\n Refer to [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\") for full documentation.\n\n See also\n\n [`numpy.conjugate`](numpy.conjugate#numpy.conjugate \"numpy.conjugate\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.conjugate.htmlnumpy.ma.MaskedArray.product\n============================\n\n method\n\n ma.MaskedArray.product(*axis=None*, *dtype=None*, *out=None*, *keepdims=<no value>*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L5186-L5225)\n \nReturn the product of the array elements over the given axis.\n\n Masked elements are set to 1 internally for computation.\n\n Refer to [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\") for full documentation.\n\n See also\n\n [`numpy.ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\")\n\ncorresponding function for ndarrays\n\n [`numpy.prod`](numpy.prod#numpy.prod \"numpy.prod\")\n\nequivalent function\n\n #### Notes\n\n Arithmetic is modular when using integer types, and no error is raised on overflow.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.product.htmlnumpy.ma.MaskedArray.__lt__\n===============================\n\n method\n\n ma.MaskedArray.__lt__(*value*, */*)\n \nReturn self<value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__lt__.htmlnumpy.ma.MaskedArray.__le__\n===============================\n\n method\n\n ma.MaskedArray.__le__(*value*, */*)\n \nReturn self<=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__le__.htmlnumpy.ma.MaskedArray.__gt__\n===============================\n\n method\n\n ma.MaskedArray.__gt__(*value*, */*)\n \nReturn self>value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__gt__.htmlnumpy.ma.MaskedArray.__ge__\n===============================\n\n method\n\n ma.MaskedArray.__ge__(*value*, */*)\n \nReturn self>=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ge__.htmlnumpy.ma.MaskedArray.__eq__\n===============================\n\n method\n\n ma.MaskedArray.__eq__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4151-L4162)\n \nCheck whether other equals self elementwise.\n\n When either of the elements is masked, the result is masked as well, but the underlying boolean data are still set, with self and other considered equal if both are masked, and unequal otherwise.\n\n For structured arrays, all fields are combined, with masked values ignored. The result is masked if all fields were masked, with self and other considered equal only if both were fully masked.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__eq__.htmlnumpy.ma.MaskedArray.__ne__\n===============================\n\n method\n\n ma.MaskedArray.__ne__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4164-L4175)\n \nCheck whether other does not equal self elementwise.\n\n When either of the elements is masked, the result is masked as well, but the underlying boolean data are still set, with self and other considered equal if both are masked, and unequal otherwise.\n\n For structured arrays, all fields are combined, with masked values ignored. The result is masked if all fields were masked, with self and other considered equal only if both were fully masked.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ne__.htmlnumpy.ma.MaskedArray.__bool__\n=================================\n\n method\n\n ma.MaskedArray.__bool__(*/*)\n \nTrue if self else False\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__bool__.htmlnumpy.ma.MaskedArray.__abs__\n================================\n\n method\n\n ma.MaskedArray.__abs__(*self*)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__abs__.htmlnumpy.ma.MaskedArray.__add__\n================================\n\n method\n\n ma.MaskedArray.__add__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4177-L4184)\n \nAdd self to other, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__add__.htmlnumpy.ma.MaskedArray.__radd__\n=================================\n\n method\n\n ma.MaskedArray.__radd__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4186-L4193)\n \nAdd other to self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__radd__.htmlnumpy.ma.MaskedArray.__sub__\n================================\n\n method\n\n ma.MaskedArray.__sub__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4195-L4202)\n \nSubtract other from self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__sub__.htmlnumpy.ma.MaskedArray.__rsub__\n=================================\n\n method\n\n ma.MaskedArray.__rsub__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4204-L4209)\n \nSubtract self from other, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rsub__.htmlnumpy.ma.MaskedArray.__mul__\n================================\n\n method\n\n ma.MaskedArray.__mul__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4211-L4215)\n \nMultiply self by other, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__mul__.htmlnumpy.ma.MaskedArray.__rmul__\n=================================\n\n method\n\n ma.MaskedArray.__rmul__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4217-L4224)\n \nMultiply other by self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rmul__.htmlnumpy.ma.MaskedArray.__div__\n================================\n\n method\n\n ma.MaskedArray.__div__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4226-L4233)\n \nDivide other into self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__div__.htmlnumpy.ma.MaskedArray.__truediv__\n====================================\n\n method\n\n ma.MaskedArray.__truediv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4235-L4242)\n \nDivide other into self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__truediv__.htmlnumpy.ma.MaskedArray.__rtruediv__\n=====================================\n\n method\n\n ma.MaskedArray.__rtruediv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4244-L4249)\n \nDivide self into other, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rtruediv__.htmlnumpy.ma.MaskedArray.__floordiv__\n=====================================\n\n method\n\n ma.MaskedArray.__floordiv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4251-L4258)\n \nDivide other into self, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__floordiv__.htmlnumpy.ma.MaskedArray.__rfloordiv__\n======================================\n\n method\n\n ma.MaskedArray.__rfloordiv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4260-L4265)\n \nDivide self into other, and return a new masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rfloordiv__.htmlnumpy.ma.MaskedArray.__mod__\n================================\n\n method\n\n ma.MaskedArray.__mod__(*value*, */*)\n \nReturn self%value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__mod__.htmlnumpy.ma.MaskedArray.__rmod__\n=================================\n\n method\n\n ma.MaskedArray.__rmod__(*value*, */*)\n \nReturn value%self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rmod__.htmlnumpy.ma.MaskedArray.__divmod__\n===================================\n\n method\n\n ma.MaskedArray.__divmod__(*value*, */*)\n \nReturn divmod(self, value).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__divmod__.htmlnumpy.ma.MaskedArray.__rdivmod__\n====================================\n\n method\n\n ma.MaskedArray.__rdivmod__(*value*, */*)\n \nReturn divmod(value, self).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rdivmod__.htmlnumpy.ma.MaskedArray.__pow__\n================================\n\n method\n\n ma.MaskedArray.__pow__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4267-L4274)\n \nRaise self to the power other, masking the potential NaNs/Infs\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__pow__.htmlnumpy.ma.MaskedArray.__rpow__\n=================================\n\n method\n\n ma.MaskedArray.__rpow__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4276-L4281)\n \nRaise other to the power self, masking the potential NaNs/Infs\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rpow__.htmlnumpy.ma.MaskedArray.__lshift__\n===================================\n\n method\n\n ma.MaskedArray.__lshift__(*value*, */*)\n \nReturn self<<value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__lshift__.htmlnumpy.ma.MaskedArray.__rlshift__\n====================================\n\n method\n\n ma.MaskedArray.__rlshift__(*value*, */*)\n \nReturn value<<self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rlshift__.htmlnumpy.ma.MaskedArray.__rshift__\n===================================\n\n method\n\n ma.MaskedArray.__rshift__(*value*, */*)\n \nReturn self>>value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rshift__.htmlnumpy.ma.MaskedArray.__rrshift__\n====================================\n\n method\n\n ma.MaskedArray.__rrshift__(*value*, */*)\n \nReturn value>>self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rrshift__.htmlnumpy.ma.MaskedArray.__and__\n================================\n\n method\n\n ma.MaskedArray.__and__(*value*, */*)\n \nReturn self&value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__and__.htmlnumpy.ma.MaskedArray.__rand__\n=================================\n\n method\n\n ma.MaskedArray.__rand__(*value*, */*)\n \nReturn value&self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rand__.htmlnumpy.ma.MaskedArray.__or__\n===============================\n\n method\n\n ma.MaskedArray.__or__(*value*, */*)\n \nReturn self|value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__or__.htmlnumpy.ma.MaskedArray.__ror__\n================================\n\n method\n\n ma.MaskedArray.__ror__(*value*, */*)\n \nReturn value|self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ror__.htmlnumpy.ma.MaskedArray.__xor__\n================================\n\n method\n\n ma.MaskedArray.__xor__(*value*, */*)\n \nReturn self^value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__xor__.htmlnumpy.ma.MaskedArray.__rxor__\n=================================\n\n method\n\n ma.MaskedArray.__rxor__(*value*, */*)\n \nReturn value^self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__rxor__.htmlnumpy.ma.MaskedArray.__iadd__\n=================================\n\n method\n\n ma.MaskedArray.__iadd__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4283-L4298)\n \nAdd other to self in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__iadd__.htmlnumpy.ma.MaskedArray.__isub__\n=================================\n\n method\n\n ma.MaskedArray.__isub__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4300-L4314)\n \nSubtract other from self in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__isub__.htmlnumpy.ma.MaskedArray.__imul__\n=================================\n\n method\n\n ma.MaskedArray.__imul__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4316-L4330)\n \nMultiply self by other in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__imul__.htmlnumpy.ma.MaskedArray.__idiv__\n=================================\n\n method\n\n ma.MaskedArray.__idiv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4332-L4348)\n \nDivide self by other in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__idiv__.htmlnumpy.ma.MaskedArray.__itruediv__\n=====================================\n\n method\n\n ma.MaskedArray.__itruediv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4368-L4384)\n \nTrue divide self by other in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__itruediv__.htmlnumpy.ma.MaskedArray.__ifloordiv__\n======================================\n\n method\n\n ma.MaskedArray.__ifloordiv__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4350-L4366)\n \nFloor divide self by other in-place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ifloordiv__.htmlnumpy.ma.MaskedArray.__imod__\n=================================\n\n method\n\n ma.MaskedArray.__imod__(*value*, */*)\n \nReturn self%=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__imod__.htmlnumpy.ma.MaskedArray.__ipow__\n=================================\n\n method\n\n ma.MaskedArray.__ipow__(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4386-L4405)\n \nRaise self to the power other, in place.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ipow__.htmlnumpy.ma.MaskedArray.__ilshift__\n====================================\n\n method\n\n ma.MaskedArray.__ilshift__(*value*, */*)\n \nReturn self<<=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ilshift__.htmlnumpy.ma.MaskedArray.__irshift__\n====================================\n\n method\n\n ma.MaskedArray.__irshift__(*value*, */*)\n \nReturn self>>=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__irshift__.htmlnumpy.ma.MaskedArray.__iand__\n=================================\n\n method\n\n ma.MaskedArray.__iand__(*value*, */*)\n \nReturn self&=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__iand__.htmlnumpy.ma.MaskedArray.__ior__\n================================\n\n method\n\n ma.MaskedArray.__ior__(*value*, */*)\n \nReturn self|=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ior__.htmlnumpy.ma.MaskedArray.__ixor__\n=================================\n\n method\n\n ma.MaskedArray.__ixor__(*value*, */*)\n \nReturn self^=value.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__ixor__.htmlnumpy.ma.MaskedArray.__repr__\n=================================\n\n method\n\n ma.MaskedArray.__repr__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3989-L4071)\n \nLiteral string representation.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__repr__.htmlnumpy.ma.MaskedArray.__str__\n================================\n\n method\n\n ma.MaskedArray.__str__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3986-L3987)\n \nReturn str(self).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__str__.htmlnumpy.ma.MaskedArray.ids\n========================\n\n method\n\n ma.MaskedArray.ids()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4808-L4832)\n \nReturn the addresses of the data and mask areas.\n\n Parameters \n **None**\n #### Examples\n\n \n```\n>>> x = np.ma.array([1, 2, 3], mask=[0, 1, 1])\n>>> x.ids()\n(166670640, 166659832) # may vary\n\n```\n If the array has no mask, the address of `nomask` is returned. This address is typically not close to the data in memory:\n\n \n```\n>>> x = np.ma.array([1, 2, 3])\n>>> x.ids()\n(166691080, 3083169284) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.ids.htmlnumpy.ma.MaskedArray.iscontiguous\n=================================\n\n method\n\n ma.MaskedArray.iscontiguous()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L4834-L4859)\n \nReturn a boolean indicating whether the data is contiguous.\n\n Parameters \n **None**\n #### Examples\n\n \n```\n>>> x = np.ma.array([1, 2, 3])\n>>> x.iscontiguous()\nTrue\n\n```\n [`iscontiguous`](#numpy.ma.MaskedArray.iscontiguous \"numpy.ma.MaskedArray.iscontiguous\") returns one of the flags of the masked array:\n\n \n```\n>>> x.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : True\n OWNDATA : False\n WRITEABLE : True\n ALIGNED : True\n WRITEBACKIFCOPY : False\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.iscontiguous.htmlnumpy.ma.MaskedArray.__copy__\n=================================\n\n method\n\n ma.MaskedArray.__copy__()\n \nUsed if [`copy.copy`](https://docs.python.org/3/library/copy.html#copy.copy \"(in Python v3.10)\") is called on an array. Returns a copy of the array.\n\n Equivalent to `a.copy(order='K')`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__copy__.htmlnumpy.ma.MaskedArray.__deepcopy__\n=====================================\n\n method\n\n ma.MaskedArray.__deepcopy__(*memo*, */*) → Deep copy of array.[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6264-L6272)\n \nUsed if [`copy.deepcopy`](https://docs.python.org/3/library/copy.html#copy.deepcopy \"(in Python v3.10)\") is called on an array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__deepcopy__.htmlnumpy.ma.MaskedArray.__getstate__\n=====================================\n\n method\n\n ma.MaskedArray.__getstate__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6230-L6237)\n \nReturn the internal state of the masked array, for pickling purposes.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__getstate__.htmlnumpy.ma.MaskedArray.__reduce__\n===================================\n\n method\n\n ma.MaskedArray.__reduce__()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6256-L6262)\n \nReturn a 3-tuple for pickling a MaskedArray.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__reduce__.htmlnumpy.ma.MaskedArray.__setstate__\n=====================================\n\n method\n\n ma.MaskedArray.__setstate__(*state*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L6239-L6254)\n \nRestore the internal state of the masked array, for pickling purposes. `state` is typically the output of the `__getstate__` output, and is a 5-tuple:\n\n * class name\n* a tuple giving the shape of the data\n* a typecode for the data\n* a binary string for the data\n* a binary string for the mask.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__setstate__.htmlnumpy.ma.MaskedArray.__new__\n================================\n\n method\n\n *static*ma.MaskedArray.__new__(*cls*, *data=None*, *mask=False*, *dtype=None*, *copy=False*, *subok=True*, *ndmin=0*, *fill_value=None*, *keep_mask=True*, *hard_mask=None*, *shrink=True*, *order=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L2814-L2943)\n \nCreate a new masked array from scratch.\n\n #### Notes\n\n A masked array can also be created by taking a .view(MaskedArray).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__new__.htmlnumpy.ma.MaskedArray.__array_wrap__\n========================================\n\n method\n\n ma.MaskedArray.__array_wrap__(*obj*, *context=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3065-L3119)\n \nSpecial hook for ufuncs.\n\n Wraps the numpy array and sets the mask according to context.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__array_wrap__.htmlnumpy.ma.MaskedArray.__len__\n================================\n\n method\n\n ma.MaskedArray.__len__(*/*)\n \nReturn len(self).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__len__.htmlnumpy.ma.MaskedArray.__getitem__\n====================================\n\n method\n\n ma.MaskedArray.__getitem__(*indx*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3211-L3335)\n \nx.__getitem__(y) <==> x[y]\n\n Return the item described by i, as a masked array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__getitem__.htmlnumpy.ma.MaskedArray.__setitem__\n====================================\n\n method\n\n ma.MaskedArray.__setitem__(*indx*, *value*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3337-L3404)\n \nx.__setitem__(i, y) <==> x[i]=y\n\n Set item described by index. If value is masked, masks those locations.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__setitem__.htmlnumpy.ma.MaskedArray.__delitem__\n====================================\n\n method\n\n ma.MaskedArray.__delitem__(*key*, */*)\n \nDelete self[key].\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__delitem__.htmlnumpy.ma.MaskedArray.__contains__\n=====================================\n\n method\n\n ma.MaskedArray.__contains__(*key*, */*)\n \nReturn key in self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__contains__.htmlnumpy.ma.MaskedArray.__setmask__\n====================================\n\n method\n\n ma.MaskedArray.__setmask__(*mask*, *copy=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/ma/core.py#L3435-L3502)\n \nSet the mask.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ma.MaskedArray.__setmask__.htmlnumpy.ufunc.__call__\n========================\n\n method\n\n ufunc.__call__(**args*, ***kwargs*)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ufunc.__call__.htmlnumpy.dtype.ndim\n================\n\n attribute\n\n dtype.ndim\n \nNumber of dimensions of the sub-array if this data type describes a sub-array, and `0` otherwise.\n\n New in version 1.13.0.\n\n #### Examples\n\n \n```\n>>> x = np.dtype(float)\n>>> x.ndim\n0\n\n```\n \n```\n>>> x = np.dtype((float, 8))\n>>> x.ndim\n1\n\n```\n \n```\n>>> x = np.dtype(('i4', (3, 4)))\n>>> x.ndim\n2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.dtype.ndim.htmlnumpy.random.RandomState.rand\n=============================\n\n method\n\n random.RandomState.rand(*d0*, *d1*, *...*, *dn*)\n \nRandom values in a given shape.\n\n Note\n\n This is a convenience function for users porting code from Matlab, and wraps [`random_sample`](numpy.random.randomstate.random_sample#numpy.random.RandomState.random_sample \"numpy.random.RandomState.random_sample\"). That function takes a tuple to specify the size of the output, which is consistent with other NumPy functions like [`numpy.zeros`](../../generated/numpy.zeros#numpy.zeros \"numpy.zeros\") and [`numpy.ones`](../../generated/numpy.ones#numpy.ones \"numpy.ones\").\n\n Create an array of the given shape and populate it with random samples from a uniform distribution over `[0, 1)`.\n\n Parameters \n \n**d0, d1, …, dn**int, optional\n\nThe dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.\n\n Returns \n \n**out**ndarray, shape `(d0, d1, ..., dn)`\n\nRandom values.\n\n See also\n\n [`random`](../index#module-numpy.random \"numpy.random\")\n #### Examples\n\n \n```\n>>> np.random.rand(3,2)\narray([[ 0.14022471, 0.96360618], #random\n [ 0.37601032, 0.25528411], #random\n [ 0.49313049, 0.94909878]]) #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.rand.htmlnumpy.random.RandomState.randn\n==============================\n\n method\n\n random.RandomState.randn(*d0*, *d1*, *...*, *dn*)\n \nReturn a sample (or samples) from the “standard normal” distribution.\n\n Note\n\n This is a convenience function for users porting code from Matlab, and wraps [`standard_normal`](numpy.random.randomstate.standard_normal#numpy.random.RandomState.standard_normal \"numpy.random.RandomState.standard_normal\"). That function takes a tuple to specify the size of the output, which is consistent with other NumPy functions like [`numpy.zeros`](../../generated/numpy.zeros#numpy.zeros \"numpy.zeros\") and [`numpy.ones`](../../generated/numpy.ones#numpy.ones \"numpy.ones\").\n\n Note\n\n New code should use the `standard_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n If positive int_like arguments are provided, [`randn`](#numpy.random.RandomState.randn \"numpy.random.RandomState.randn\") generates an array of shape `(d0, d1, ..., dn)`, filled with random floats sampled from a univariate “normal” (Gaussian) distribution of mean 0 and variance 1. A single float randomly sampled from the distribution is returned if no argument is provided.\n\n Parameters \n \n**d0, d1, …, dn**int, optional\n\nThe dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.\n\n Returns \n \n**Z**ndarray or float\n\nA `(d0, d1, ..., dn)`-shaped array of floating-point samples from the standard normal distribution, or a single such float if no parameters were supplied.\n\n See also\n\n [`standard_normal`](numpy.random.randomstate.standard_normal#numpy.random.RandomState.standard_normal \"numpy.random.RandomState.standard_normal\")\n\nSimilar, but takes a tuple as its argument.\n\n [`normal`](numpy.random.randomstate.normal#numpy.random.RandomState.normal \"numpy.random.RandomState.normal\")\n\nAlso accepts mu and sigma arguments.\n\n [`random.Generator.standard_normal`](numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n For random samples from \\(N(\\mu, \\sigma^2)\\), use:\n\n `sigma * np.random.randn(...) + mu`\n\n #### Examples\n\n \n```\n>>> np.random.randn()\n2.1923875335537315 # random\n\n```\n Two-by-four array of samples from N(3, 6.25):\n\n \n```\n>>> 3 + 2.5 * np.random.randn(2, 4)\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.randn.htmlnumpy.distutils.ccompiler.CCompiler_compile\n============================================\n\n distutils.ccompiler.CCompiler_compile(*self*, *sources*, *output_dir=None*, *macros=None*, *include_dirs=None*, *debug=0*, *extra_preargs=None*, *extra_postargs=None*, *depends=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L232-L368)\n \nCompile one or more source files.\n\n Please refer to the Python distutils API reference for more details.\n\n Parameters \n \n**sources**list of str\n\nA list of filenames\n\n \n**output_dir**str, optional\n\nPath to the output directory.\n\n \n**macros**list of tuples\n\nA list of macro definitions.\n\n \n**include_dirs**list of str, optional\n\nThe directories to add to the default include file search path for this compilation only.\n\n \n**debug**bool, optional\n\nWhether or not to output debug symbols in or alongside the object file(s).\n\n \n**extra_preargs, extra_postargs**?\n\nExtra pre- and post-arguments.\n\n \n**depends**list of str, optional\n\nA list of file names that all targets depend on.\n\n Returns \n \n**objects**list of str\n\nA list of object file names, one per source file `sources`.\n\n Raises \n CompileError\n\nIf compilation fails.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_compile.htmlnumpy.distutils.ccompiler.CCompiler_customize\n==============================================\n\n distutils.ccompiler.CCompiler_customize(*self*, *dist*, *need_cxx=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L469-L548)\n \nDo any platform-specific customization of a compiler instance.\n\n This method calls [`distutils.sysconfig.customize_compiler`](https://docs.python.org/3/distutils/apiref.html#distutils.sysconfig.customize_compiler \"(in Python v3.10)\") for platform-specific customization, as well as optionally remove a flag to suppress spurious warnings in case C++ code is being compiled.\n\n Parameters \n \n**dist**object\n\nThis parameter is not used for anything.\n\n \n**need_cxx**bool, optional\n\nWhether or not C++ has to be compiled. If so (True), the `\"-Wstrict-prototypes\"` option is removed to prevent spurious warnings. Default is False.\n\n Returns \n None\n #### Notes\n\n All the default options used by distutils can be extracted with:\n\n \n```\nfrom distutils import sysconfig\nsysconfig.get_config_vars('CC', 'CXX', 'OPT', 'BASECFLAGS',\n 'CCSHARED', 'LDSHARED', 'SO')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_customize.htmlnumpy.distutils.ccompiler.CCompiler_customize_cmd\n===================================================\n\n distutils.ccompiler.CCompiler_customize_cmd(*self*, *cmd*, *ignore=()*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L372-L418)\n \nCustomize compiler using distutils command.\n\n Parameters \n \n**cmd**class instance\n\nAn instance inheriting from [`distutils.cmd.Command`](https://docs.python.org/3/distutils/apiref.html#distutils.cmd.Command \"(in Python v3.10)\").\n\n \n**ignore**sequence of str, optional\n\nList of `CCompiler` commands (without `'set_'`) that should not be altered. Strings that are checked for are: `('include_dirs', 'define', 'undef', 'libraries', 'library_dirs',\n'rpath', 'link_objects')`.\n\n Returns \n None\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_customize_cmd.htmlnumpy.distutils.ccompiler.CCompiler_cxx_compiler\n==================================================\n\n distutils.ccompiler.CCompiler_cxx_compiler(*self*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L668-L695)\n \nReturn the C++ compiler.\n\n Parameters \n **None**\n Returns \n \n**cxx**class instance\n\nThe C++ compiler, as a `CCompiler` instance.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_cxx_compiler.htmlnumpy.distutils.ccompiler.CCompiler_find_executables\n======================================================\n\n distutils.ccompiler.CCompiler_find_executables(*self*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L98-L105)\n \nDoes nothing here, but is called by the get_version method and can be overridden by subclasses. In particular it is redefined in the `FCompiler` class where more documentation can be found.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_find_executables.htmlnumpy.distutils.ccompiler.CCompiler_get_version\n=================================================\n\n distutils.ccompiler.CCompiler_get_version(*self*, *force=False*, *ok_status=[0]*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L599-L664)\n \nReturn compiler version, or None if compiler is not available.\n\n Parameters \n \n**force**bool, optional\n\nIf True, force a new determination of the version, even if the compiler already has a version attribute. Default is False.\n\n \n**ok_status**list of int, optional\n\nThe list of status values returned by the version look-up process for which a version string is returned. If the status value is not in `ok_status`, None is returned. Default is `[0]`.\n\n Returns \n \n**version**str or None\n\nVersion string, in the format of `distutils.version.LooseVersion`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_get_version.htmlnumpy.distutils.ccompiler.CCompiler_object_filenames\n======================================================\n\n distutils.ccompiler.CCompiler_object_filenames(*self*, *source_filenames*, *strip_dir=0*, *output_dir=''*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L185-L228)\n \nReturn the name of the object files for the given source files.\n\n Parameters \n \n**source_filenames**list of str\n\nThe list of paths to source files. Paths can be either relative or absolute, this is handled transparently.\n\n \n**strip_dir**bool, optional\n\nWhether to strip the directory from the returned paths. If True, the file name prepended by `output_dir` is returned. Default is False.\n\n \n**output_dir**str, optional\n\nIf given, this path is prepended to the returned paths to the object files.\n\n Returns \n \n**obj_names**list of str\n\nThe list of paths to the object files corresponding to the source files in `source_filenames`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_object_filenames.htmlnumpy.distutils.ccompiler.CCompiler_show_customization\n========================================================\n\n distutils.ccompiler.CCompiler_show_customization(*self*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L440-L465)\n \nPrint the compiler customizations to stdout.\n\n Parameters \n **None**\n Returns \n None\n #### Notes\n\n Printing is only done if the distutils log threshold is < 2.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_show_customization.htmlnumpy.distutils.ccompiler.CCompiler_spawn\n==========================================\n\n distutils.ccompiler.CCompiler_spawn(*self*, *cmd*, *display=None*, *env=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L112-L181)\n \nExecute a command in a sub-process.\n\n Parameters \n \n**cmd**str\n\nThe command to execute.\n\n \n**display**str or sequence of str, optional\n\nThe text to add to the log file kept by [`numpy.distutils`](../distutils#module-numpy.distutils \"numpy.distutils\"). If not given, `display` is equal to [`cmd`](https://docs.python.org/3/library/cmd.html#module-cmd \"(in Python v3.10)\").\n\n \n**env**a dictionary for environment variables, optional\n\n Returns \n None\n Raises \n DistutilsExecError\n\nIf the command failed, i.e. the exit status was not 0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.CCompiler_spawn.htmlnumpy.distutils.ccompiler.gen_lib_options\n===========================================\n\n distutils.ccompiler.gen_lib_options(*compiler*, *library_dirs*, *runtime_library_dirs*, *libraries*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L781-L797)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.gen_lib_options.htmlnumpy.distutils.ccompiler.new_compiler\n=======================================\n\n distutils.ccompiler.new_compiler(*plat=None*, *compiler=None*, *verbose=None*, *dry_run=0*, *force=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L734-L776)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.new_compiler.htmlnumpy.distutils.ccompiler.replace_method\n=========================================\n\n distutils.ccompiler.replace_method(*klass*, *method_name*, *func*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L87-L90)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.replace_method.htmlnumpy.distutils.ccompiler.simple_version_match\n================================================\n\n distutils.ccompiler.simple_version_match(*pat='[-.\\\\d]+'*, *ignore=''*, *start=''*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler.py#L552-L597)\n \nSimple matching of version numbers, for use in CCompiler and FCompiler.\n\n Parameters \n \n**pat**str, optional\n\nA regular expression matching version numbers. Default is `r'[-.\\d]+'`.\n\n \n**ignore**str, optional\n\nA regular expression matching patterns to skip. Default is `''`, in which case nothing is skipped.\n\n \n**start**str, optional\n\nA regular expression matching the start of where to start looking for version numbers. Default is `''`, in which case searching is started at the beginning of the version string given to `matcher`.\n\n Returns \n \n**matcher**callable\n\nA function that is appropriate to use as the `.version_match` attribute of a `CCompiler` class. `matcher` takes a single parameter, a version string.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler.simple_version_match.htmlnumpy.distutils.ccompiler_opt.new_ccompiler_opt\n==================================================\n\n distutils.ccompiler_opt.new_ccompiler_opt(*compiler*, *dispatch_hpath*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2635-L2655)\n \nCreate a new instance of ‘CCompilerOpt’ and generate the dispatch header which contains the #definitions and headers of platform-specific instruction-sets for the enabled CPU baseline and dispatch-able features.\n\n Parameters \n \n**compiler**CCompiler instance\n\n**dispatch_hpath**str\n\npath of the dispatch header\n\n ****kwargs: passed as-is to `CCompilerOpt(…)`**\n**Returns**\n**——-**\n**new instance of CCompilerOpt**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.new_ccompiler_opt.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt\n===========================================\n\n *class*numpy.distutils.ccompiler_opt.CCompilerOpt(*ccompiler*, *cpu_baseline='min'*, *cpu_dispatch='max'*, *cache_path=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2200-L2633)\n \nA helper class for `CCompiler` aims to provide extra build options to effectively control of compiler optimizations that are directly related to CPU features.\n\n Attributes \n **conf_cache_factors**\n**conf_tmp_path**\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`cache_flush`](numpy.distutils.ccompiler_opt.ccompileropt.cache_flush#numpy.distutils.ccompiler_opt.CCompilerOpt.cache_flush \"numpy.distutils.ccompiler_opt.CCompilerOpt.cache_flush\")() | Force update the cache. |\n| [`cc_normalize_flags`](numpy.distutils.ccompiler_opt.ccompileropt.cc_normalize_flags#numpy.distutils.ccompiler_opt.CCompilerOpt.cc_normalize_flags \"numpy.distutils.ccompiler_opt.CCompilerOpt.cc_normalize_flags\")(flags) | Remove the conflicts that caused due gathering implied features flags. |\n| [`conf_features_partial`](numpy.distutils.ccompiler_opt.ccompileropt.conf_features_partial#numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features_partial \"numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features_partial\")() | Return a dictionary of supported CPU features by the platform, and accumulate the rest of undefined options in [`conf_features`](numpy.distutils.ccompiler_opt.ccompileropt.conf_features#numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features \"numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features\"), the returned dict has same rules and notes in class attribute [`conf_features`](numpy.distutils.ccompiler_opt.ccompileropt.conf_features#numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features \"numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features\"), also its override any options that been set in 'conf_features'. |\n| [`cpu_baseline_flags`](numpy.distutils.ccompiler_opt.ccompileropt.cpu_baseline_flags#numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_flags \"numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_flags\")() | Returns a list of final CPU baseline compiler flags |\n| [`cpu_baseline_names`](numpy.distutils.ccompiler_opt.ccompileropt.cpu_baseline_names#numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_names \"numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_names\")() | return a list of final CPU baseline feature names |\n| [`cpu_dispatch_names`](numpy.distutils.ccompiler_opt.ccompileropt.cpu_dispatch_names#numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_dispatch_names \"numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_dispatch_names\")() | return a list of final CPU dispatch feature names |\n| [`dist_compile`](numpy.distutils.ccompiler_opt.ccompileropt.dist_compile#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_compile \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_compile\")(sources, flags[, ccompiler]) | Wrap CCompiler.compile() |\n| [`dist_error`](numpy.distutils.ccompiler_opt.ccompileropt.dist_error#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_error \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_error\")(*args) | Raise a compiler error |\n| [`dist_fatal`](numpy.distutils.ccompiler_opt.ccompileropt.dist_fatal#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_fatal \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_fatal\")(*args) | Raise a distutils error |\n| [`dist_info`](numpy.distutils.ccompiler_opt.ccompileropt.dist_info#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_info \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_info\")() | Return a tuple containing info about (platform, compiler, extra_args), required by the abstract class '_CCompiler' for discovering the platform environment. |\n| [`dist_load_module`](numpy.distutils.ccompiler_opt.ccompileropt.dist_load_module#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_load_module \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_load_module\")(name, path) | Load a module from file, required by the abstract class '_Cache'. |\n| [`dist_log`](numpy.distutils.ccompiler_opt.ccompileropt.dist_log#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_log \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_log\")(*args[, stderr]) | Print a console message |\n| [`dist_test`](numpy.distutils.ccompiler_opt.ccompileropt.dist_test#numpy.distutils.ccompiler_opt.CCompilerOpt.dist_test \"numpy.distutils.ccompiler_opt.CCompilerOpt.dist_test\")(source, flags[, macros]) | Return True if 'CCompiler.compile()' able to compile a source file with certain flags. |\n| [`feature_ahead`](numpy.distutils.ccompiler_opt.ccompileropt.feature_ahead#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_ahead \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_ahead\")(names) | Return list of features in 'names' after remove any implied features and keep the origins. |\n| [`feature_c_preprocessor`](numpy.distutils.ccompiler_opt.ccompileropt.feature_c_preprocessor#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_c_preprocessor \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_c_preprocessor\")(feature_name[, tabs]) | Generate C preprocessor definitions and include headers of a CPU feature. |\n| [`feature_detect`](numpy.distutils.ccompiler_opt.ccompileropt.feature_detect#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_detect \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_detect\")(names) | Return a list of CPU features that required to be detected sorted from the lowest to highest interest. |\n| [`feature_get_til`](numpy.distutils.ccompiler_opt.ccompileropt.feature_get_til#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_get_til \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_get_til\")(names, keyisfalse) | same as `feature_implies_c()` but stop collecting implied features when feature's option that provided through parameter 'keyisfalse' is False, also sorting the returned features. |\n| [`feature_implies`](numpy.distutils.ccompiler_opt.ccompileropt.feature_implies#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies\")(names[, keep_origins]) | Return a set of CPU features that implied by 'names' |\n| [`feature_implies_c`](numpy.distutils.ccompiler_opt.ccompileropt.feature_implies_c#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies_c \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies_c\")(names) | same as feature_implies() but combining 'names' |\n| [`feature_is_exist`](numpy.distutils.ccompiler_opt.ccompileropt.feature_is_exist#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_is_exist \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_is_exist\")(name) | Returns True if a certain feature is exist and covered within `_Config.conf_features`. |\n| [`feature_names`](numpy.distutils.ccompiler_opt.ccompileropt.feature_names#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_names \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_names\")([names, force_flags, macros]) | Returns a set of CPU feature names that supported by platform and the **C** compiler. |\n| [`feature_sorted`](numpy.distutils.ccompiler_opt.ccompileropt.feature_sorted#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_sorted \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_sorted\")(names[, reverse]) | Sort a list of CPU features ordered by the lowest interest. |\n| [`feature_untied`](numpy.distutils.ccompiler_opt.ccompileropt.feature_untied#numpy.distutils.ccompiler_opt.CCompilerOpt.feature_untied \"numpy.distutils.ccompiler_opt.CCompilerOpt.feature_untied\")(names) | same as 'feature_ahead()' but if both features implied each other and keep the highest interest. |\n| [`generate_dispatch_header`](numpy.distutils.ccompiler_opt.ccompileropt.generate_dispatch_header#numpy.distutils.ccompiler_opt.CCompilerOpt.generate_dispatch_header \"numpy.distutils.ccompiler_opt.CCompilerOpt.generate_dispatch_header\")(header_path) | Generate the dispatch header which contains the #definitions and headers for platform-specific instruction-sets for the enabled CPU baseline and dispatch-able features. |\n| [`is_cached`](numpy.distutils.ccompiler_opt.ccompileropt.is_cached#numpy.distutils.ccompiler_opt.CCompilerOpt.is_cached \"numpy.distutils.ccompiler_opt.CCompilerOpt.is_cached\")() | Returns True if the class loaded from the cache file |\n| [`me`](numpy.distutils.ccompiler_opt.ccompileropt.me#numpy.distutils.ccompiler_opt.CCompilerOpt.me \"numpy.distutils.ccompiler_opt.CCompilerOpt.me\")(cb) | A static method that can be treated as a decorator to dynamically cache certain methods. |\n| [`parse_targets`](numpy.distutils.ccompiler_opt.ccompileropt.parse_targets#numpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets \"numpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets\")(source) | Fetch and parse configuration statements that required for defining the targeted CPU features, statements should be declared in the top of source in between **C** comment and start with a special mark **@targets**. |\n| [`try_dispatch`](numpy.distutils.ccompiler_opt.ccompileropt.try_dispatch#numpy.distutils.ccompiler_opt.CCompilerOpt.try_dispatch \"numpy.distutils.ccompiler_opt.CCompilerOpt.try_dispatch\")(sources[, src_dir, ccompiler]) | Compile one or more dispatch-able sources and generates object files, also generates abstract C config headers and macros that used later for the final runtime dispatching process. |\n\n \n\n| | |\n| --- | --- |\n| **cache_hash** | |\n| **cc_test_cexpr** | |\n| **cc_test_flags** | |\n| **feature_can_autovec** | |\n| **feature_extra_checks** | |\n| **feature_flags** | |\n| **feature_is_supported** | |\n| **feature_test** | |\n| **report** | |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.try_dispatch\n=========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.try_dispatch(*sources*, *src_dir=None*, *ccompiler=None*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2256-L2341)\n \nCompile one or more dispatch-able sources and generates object files, also generates abstract C config headers and macros that used later for the final runtime dispatching process.\n\n The mechanism behind it is to takes each source file that specified in ‘sources’ and branching it into several files depend on special configuration statements that must be declared in the top of each source which contains targeted CPU features, then it compiles every branched source with the proper compiler flags.\n\n Parameters \n \n**sources**list\n\nMust be a list of dispatch-able sources file paths, and configuration statements must be declared inside each file.\n\n \n**src_dir**str\n\nPath of parent directory for the generated headers and wrapped sources. If None(default) the files will generated in-place.\n\n \n**ccompiler**CCompiler\n\nDistutils `CCompiler` instance to be used for compilation. If None (default), the provided instance during the initialization will be used instead.\n\n \n****kwargs**any\n\nArguments to pass on to the `CCompiler.compile()`\n\n Returns \n \n**list**generated object files\n\n Raises \n CompileError\n\nRaises by `CCompiler.compile()` on compiling failure.\n\n DistutilsError\n\nSome errors during checking the sanity of configuration statements.\n\n See also\n\n [`parse_targets`](numpy.distutils.ccompiler_opt.ccompileropt.parse_targets#numpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets \"numpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets\")\n\nParsing the configuration statements of dispatch-able sources.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.try_dispatch.htmlnumpy.distutils.exec_command.exec_command\n===========================================\n\n distutils.exec_command.exec_command(*command*, *execute_in=''*, *use_shell=None*, *use_tee=None*, *_with_python=1*, ***env*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L177-L250)\n \nReturn (status,output) of executed command.\n\n Deprecated since version 1.17: Use subprocess.Popen instead\n\n Parameters \n \n**command**str\n\nA concatenated string of executable and arguments.\n\n \n**execute_in**str\n\nBefore running command `cd execute_in` and after `cd -`.\n\n \n**use_shell**{bool, None}, optional\n\nIf True, execute `sh -c command`. Default None (True)\n\n \n**use_tee**{bool, None}, optional\n\nIf True use tee. Default None (True)\n\n Returns \n \n**res**str\n\nBoth stdout and stderr messages.\n\n #### Notes\n\n On NT, DOS systems the returned status is correct for external commands. Wild cards will not work for non-posix systems or when use_shell=0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.exec_command.htmlnumpy.distutils.exec_command.filepath_from_subprocess_output\n================================================================\n\n distutils.exec_command.filepath_from_subprocess_output(*output*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L63-L77)\n \nConvert `bytes` in the encoding used by a subprocess into a filesystem-appropriate [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\").\n\n Inherited from [`exec_command`](numpy.distutils.exec_command.exec_command#numpy.distutils.exec_command.exec_command \"numpy.distutils.exec_command.exec_command\"), and possibly incorrect.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.filepath_from_subprocess_output.htmlnumpy.distutils.exec_command.find_executable\n==============================================\n\n distutils.exec_command.find_executable(*exe*, *path=None*, *_cache={}*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L116-L163)\n \nReturn full path of a executable or None.\n\n Symbolic links are not followed.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.find_executable.htmlnumpy.distutils.exec_command.forward_bytes_to_stdout\n========================================================\n\n distutils.exec_command.forward_bytes_to_stdout(*val*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L80-L96)\n \nForward bytes from a subprocess call to the console, without attempting to decode them.\n\n The assumption is that the subprocess call already returned bytes in a suitable encoding.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.forward_bytes_to_stdout.htmlnumpy.distutils.exec_command.get_pythonexe\n============================================\n\n distutils.exec_command.get_pythonexe()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L107-L114)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.get_pythonexe.htmlnumpy.distutils.exec_command.temp_file_name\n==============================================\n\n distutils.exec_command.temp_file_name()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/exec_command.py#L99-L105)\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.exec_command.temp_file_name.htmlnumpy.nditer.close\n==================\n\n method\n\n nditer.close()\n \nResolve all writeback semantics in writeable operands.\n\n New in version 1.15.0.\n\n See also\n\n [Modifying Array Values](../arrays.nditer#nditer-context-manager)\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.close.htmlnumpy.nditer.copy\n=================\n\n method\n\n nditer.copy()\n \nGet a copy of the iterator in its current state.\n\n #### Examples\n\n \n```\n>>> x = np.arange(10)\n>>> y = x + 1\n>>> it = np.nditer([x, y])\n>>> next(it)\n(array(0), array(1))\n>>> it2 = it.copy()\n>>> next(it2)\n(array(1), array(2))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.copy.htmlnumpy.nditer.debug_print\n=========================\n\n method\n\n nditer.debug_print()\n \nPrint the current state of the [`nditer`](numpy.nditer#numpy.nditer \"numpy.nditer\") instance and debug info to stdout.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.debug_print.htmlnumpy.nditer.enable_external_loop\n===================================\n\n method\n\n nditer.enable_external_loop()\n \nWhen the “external_loop” was not used during construction, but is desired, this modifies the iterator to behave as if the flag was specified.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.enable_external_loop.htmlnumpy.nditer.iternext\n=====================\n\n method\n\n nditer.iternext()\n \nCheck whether iterations are left, and perform a single internal iteration without returning the result. Used in the C-style pattern do-while pattern. For an example, see [`nditer`](numpy.nditer#numpy.nditer \"numpy.nditer\").\n\n Returns \n \n**iternext**bool\n\nWhether or not there are iterations left.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.iternext.htmlnumpy.nditer.remove_axis\n=========================\n\n method\n\n nditer.remove_axis(*i*, */*)\n \nRemoves axis `i` from the iterator. Requires that the flag “multi_index” be enabled.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.remove_axis.htmlnumpy.nditer.remove_multi_index\n=================================\n\n method\n\n nditer.remove_multi_index()\n \nWhen the “multi_index” flag was specified, this removes it, allowing the internal iteration structure to be optimized further.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.remove_multi_index.htmlnumpy.nditer.itersize\n=====================\n\n attribute\n\n nditer.itersize\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.itersize.htmlnumpy.nditer.value\n==================\n\n attribute\n\n nditer.value\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.value.htmlnumpy.nditer.index\n==================\n\n attribute\n\n nditer.index\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.index.htmlnumpy.nditer.multi_index\n=========================\n\n attribute\n\n nditer.multi_index\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.nditer.multi_index.htmlnumpy.ndindex.ndincr\n====================\n\n method\n\n ndindex.ndincr()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/index_tricks.py#L668-L682)\n \nIncrement the multi-dimensional index by one.\n\n This method is for backward compatibility only: do not use.\n\n Deprecated since version 1.20.0: This method has been advised against since numpy 1.8.0, but only started emitting DeprecationWarning as of this version.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.ndindex.ndincr.htmlnumpy.flatiter.copy\n===================\n\n method\n\n flatiter.copy()\n \nGet a copy of the iterator as a 1-D array.\n\n #### Examples\n\n \n```\n>>> x = np.arange(6).reshape(2, 3)\n>>> x\narray([[0, 1, 2],\n [3, 4, 5]])\n>>> fl = x.flat\n>>> fl.copy()\narray([0, 1, 2, 3, 4, 5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.flatiter.copy.htmlnumpy.flatiter.base\n===================\n\n attribute\n\n flatiter.base\n \nA reference to the array that is iterated over.\n\n #### Examples\n\n \n```\n>>> x = np.arange(5)\n>>> fl = x.flat\n>>> fl.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.flatiter.base.htmlnumpy.flatiter.coords\n=====================\n\n attribute\n\n flatiter.coords\n \nAn N-dimensional tuple of current coordinates.\n\n #### Examples\n\n \n```\n>>> x = np.arange(6).reshape(2, 3)\n>>> fl = x.flat\n>>> fl.coords\n(0, 0)\n>>> next(fl)\n0\n>>> fl.coords\n(0, 1)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.flatiter.coords.htmlnumpy.flatiter.index\n====================\n\n attribute\n\n flatiter.index\n \nCurrent flat index into the array.\n\n #### Examples\n\n \n```\n>>> x = np.arange(6).reshape(2, 3)\n>>> fl = x.flat\n>>> fl.index\n0\n>>> next(fl)\n0\n>>> fl.index\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.flatiter.index.htmlnumpy.lib.Arrayterator.shape\n============================\n\n property\n\n *property*lib.Arrayterator.shape\n \nThe shape of the array to be iterated over.\n\n For an example, see `Arrayterator`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.Arrayterator.shape.htmlnumpy.lib.Arrayterator.flat\n===========================\n\n property\n\n *property*lib.Arrayterator.flat\n \nA 1-D flat iterator for Arrayterator objects.\n\n This iterator returns elements of the array to be iterated over in `Arrayterator` one by one. It is similar to [`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\").\n\n See also\n\n `Arrayterator`\n[`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> a = np.arange(3 * 4 * 5 * 6).reshape(3, 4, 5, 6)\n>>> a_itor = np.lib.Arrayterator(a, 2)\n\n```\n \n```\n>>> for subarr in a_itor.flat:\n... if not subarr:\n... print(subarr, type(subarr))\n...\n0 <class 'numpy.int64'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.Arrayterator.flat.htmlnumpy.chararray.astype\n======================\n\n method\n\n chararray.astype(*dtype*, *order='K'*, *casting='unsafe'*, *subok=True*, *copy=True*)\n \nCopy of the array, cast to a specified type.\n\n Parameters \n \n**dtype**str or dtype\n\nTypecode or data-type to which the array is cast.\n\n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.\n\n \n**casting**{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional\n\nControls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.\n\n * ‘no’ means the data types should not be cast at all.\n* ‘equiv’ means only byte-order changes are allowed.\n* ‘safe’ means only casts which can preserve values are allowed.\n* ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.\n* ‘unsafe’ means any data conversions may be done.\n\n \n**subok**bool, optional\n\nIf True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.\n\n \n**copy**bool, optional\n\nBy default, astype always returns a newly allocated array. If this is set to false, and the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy.\n\n Returns \n \n**arr_t**ndarray\n\nUnless [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False and the other conditions for returning the input array are satisfied (see description for [`copy`](numpy.copy#numpy.copy \"numpy.copy\") input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`.\n\n Raises \n ComplexWarning\n\nWhen casting from complex to float or int. To avoid this, one should use `a.real.astype(t)`.\n\n #### Notes\n\n Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.\n\n Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 2.5])\n>>> x\narray([1. , 2. , 2.5])\n\n```\n \n```\n>>> x.astype(int)\narray([1, 2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.astype.htmlnumpy.chararray.argsort\n=======================\n\n method\n\n chararray.argsort(*axis=- 1*, *kind=None*, *order=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2121-L2139)\n \nReturns the indices that would sort this array.\n\n Refer to [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\") for full documentation.\n\n See also\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.argsort.htmlnumpy.chararray.copy\n====================\n\n method\n\n chararray.copy(*order='C'*)\n \nReturn a copy of the array.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of `a` as closely as possible. (Note that this function and [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)\n\n See also\n\n [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\")\n\nSimilar function with different default behavior\n\n [`numpy.copyto`](numpy.copyto#numpy.copyto \"numpy.copyto\")\n #### Notes\n\n This function is the preferred method for creating an array copy. The function [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.\n\n #### Examples\n\n \n```\n>>> x = np.array([[1,2,3],[4,5,6]], order='F')\n\n```\n \n```\n>>> y = x.copy()\n\n```\n \n```\n>>> x.fill(0)\n\n```\n \n```\n>>> x\narray([[0, 0, 0],\n [0, 0, 0]])\n\n```\n \n```\n>>> y\narray([[1, 2, 3],\n [4, 5, 6]])\n\n```\n \n```\n>>> y.flags['C_CONTIGUOUS']\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.copy.htmlnumpy.chararray.count\n=====================\n\n method\n\n chararray.count(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2165-L2175)\n \nReturns an array with the number of non-overlapping occurrences of substring `sub` in the range [`start`, `end`].\n\n See also\n\n [`char.count`](numpy.char.count#numpy.char.count \"numpy.char.count\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.count.htmlnumpy.chararray.decode\n======================\n\n method\n\n chararray.decode(*encoding=None*, *errors=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2177-L2186)\n \nCalls `str.decode` element-wise.\n\n See also\n\n [`char.decode`](numpy.char.decode#numpy.char.decode \"numpy.char.decode\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.decode.htmlnumpy.chararray.dump\n====================\n\n method\n\n chararray.dump(*file*)\n \nDump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.\n\n Parameters \n \n**file**str or Path\n\nA string naming the dump file.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.dump.htmlnumpy.chararray.dumps\n=====================\n\n method\n\n chararray.dumps()\n \nReturns the pickle of the array as a string. pickle.loads will convert the string back to an array.\n\n Parameters \n **None**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.dumps.htmlnumpy.chararray.encode\n======================\n\n method\n\n chararray.encode(*encoding=None*, *errors=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2188-L2197)\n \nCalls [`str.encode`](https://docs.python.org/3/library/stdtypes.html#str.encode \"(in Python v3.10)\") element-wise.\n\n See also\n\n [`char.encode`](numpy.char.encode#numpy.char.encode \"numpy.char.encode\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.encode.htmlnumpy.chararray.endswith\n========================\n\n method\n\n chararray.endswith(*suffix*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2199-L2209)\n \nReturns a boolean array which is `True` where the string element in `self` ends with `suffix`, otherwise `False`.\n\n See also\n\n [`char.endswith`](numpy.char.endswith#numpy.char.endswith \"numpy.char.endswith\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.endswith.htmlnumpy.chararray.expandtabs\n==========================\n\n method\n\n chararray.expandtabs(*tabsize=8*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2211-L2221)\n \nReturn a copy of each string element where all tab characters are replaced by one or more spaces.\n\n See also\n\n [`char.expandtabs`](numpy.char.expandtabs#numpy.char.expandtabs \"numpy.char.expandtabs\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.expandtabs.htmlnumpy.chararray.fill\n====================\n\n method\n\n chararray.fill(*value*)\n \nFill the array with a scalar value.\n\n Parameters \n \n**value**scalar\n\nAll elements of `a` will be assigned this value.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2])\n>>> a.fill(0)\n>>> a\narray([0, 0])\n>>> a = np.empty(2)\n>>> a.fill(1)\n>>> a\narray([1., 1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.fill.htmlnumpy.chararray.find\n====================\n\n method\n\n chararray.find(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2223-L2233)\n \nFor each element, return the lowest index in the string where substring `sub` is found.\n\n See also\n\n [`char.find`](numpy.char.find#numpy.char.find \"numpy.char.find\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.find.htmlnumpy.chararray.flatten\n=======================\n\n method\n\n chararray.flatten(*order='C'*)\n \nReturn a copy of the array collapsed into one dimension.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\n‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran- style) order. ‘A’ means to flatten in column-major order if `a` is Fortran *contiguous* in memory, row-major order otherwise. ‘K’ means to flatten `a` in the order the elements occur in memory. The default is ‘C’.\n\n Returns \n \n**y**ndarray\n\nA copy of the input array, flattened to one dimension.\n\n See also\n\n [`ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nReturn a flattened array.\n\n [`flat`](numpy.chararray.flat#numpy.chararray.flat \"numpy.chararray.flat\")\n\nA 1-D flat iterator over the array.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,2], [3,4]])\n>>> a.flatten()\narray([1, 2, 3, 4])\n>>> a.flatten('F')\narray([1, 3, 2, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.flatten.htmlnumpy.chararray.getfield\n========================\n\n method\n\n chararray.getfield(*dtype*, *offset=0*)\n \nReturns a field of the given array as a certain type.\n\n A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.\n\n Parameters \n \n**dtype**str or dtype\n\nThe data type of the view. The dtype size of the view can not be larger than that of the array itself.\n\n \n**offset**int\n\nNumber of bytes to skip before beginning the element view.\n\n #### Examples\n\n \n```\n>>> x = np.diag([1.+1.j]*2)\n>>> x[1, 1] = 2 + 4.j\n>>> x\narray([[1.+1.j, 0.+0.j],\n [0.+0.j, 2.+4.j]])\n>>> x.getfield(np.float64)\narray([[1., 0.],\n [0., 2.]])\n\n```\n By choosing an offset of 8 bytes we can select the complex part of the array for our view:\n\n \n```\n>>> x.getfield(np.float64, offset=8)\narray([[1., 0.],\n [0., 4.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.getfield.htmlnumpy.chararray.index\n=====================\n\n method\n\n chararray.index(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2235-L2244)\n \nLike [`find`](numpy.chararray.find#numpy.chararray.find \"numpy.chararray.find\"), but raises `ValueError` when the substring is not found.\n\n See also\n\n [`char.index`](numpy.char.index#numpy.char.index \"numpy.char.index\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.index.htmlnumpy.chararray.isalnum\n=======================\n\n method\n\n chararray.isalnum()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2246-L2257)\n \nReturns true for each element if all characters in the string are alphanumeric and there is at least one character, false otherwise.\n\n See also\n\n [`char.isalnum`](numpy.char.isalnum#numpy.char.isalnum \"numpy.char.isalnum\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isalnum.htmlnumpy.chararray.isalpha\n=======================\n\n method\n\n chararray.isalpha()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2259-L2270)\n \nReturns true for each element if all characters in the string are alphabetic and there is at least one character, false otherwise.\n\n See also\n\n [`char.isalpha`](numpy.char.isalpha#numpy.char.isalpha \"numpy.char.isalpha\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isalpha.htmlnumpy.chararray.isdecimal\n=========================\n\n method\n\n chararray.isdecimal()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2599-L2609)\n \nFor each element in `self`, return True if there are only decimal characters in the element.\n\n See also\n\n [`char.isdecimal`](numpy.char.isdecimal#numpy.char.isdecimal \"numpy.char.isdecimal\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isdecimal.htmlnumpy.chararray.isdigit\n=======================\n\n method\n\n chararray.isdigit()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2272-L2282)\n \nReturns true for each element if all characters in the string are digits and there is at least one character, false otherwise.\n\n See also\n\n [`char.isdigit`](numpy.char.isdigit#numpy.char.isdigit \"numpy.char.isdigit\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isdigit.htmlnumpy.chararray.islower\n=======================\n\n method\n\n chararray.islower()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2284-L2295)\n \nReturns true for each element if all cased characters in the string are lowercase and there is at least one cased character, false otherwise.\n\n See also\n\n [`char.islower`](numpy.char.islower#numpy.char.islower \"numpy.char.islower\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.islower.htmlnumpy.chararray.isnumeric\n=========================\n\n method\n\n chararray.isnumeric()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2587-L2597)\n \nFor each element in `self`, return True if there are only numeric characters in the element.\n\n See also\n\n [`char.isnumeric`](numpy.char.isnumeric#numpy.char.isnumeric \"numpy.char.isnumeric\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isnumeric.htmlnumpy.chararray.isspace\n=======================\n\n method\n\n chararray.isspace()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2297-L2308)\n \nReturns true for each element if there are only whitespace characters in the string and there is at least one character, false otherwise.\n\n See also\n\n [`char.isspace`](numpy.char.isspace#numpy.char.isspace \"numpy.char.isspace\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isspace.htmlnumpy.chararray.istitle\n=======================\n\n method\n\n chararray.istitle()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2310-L2320)\n \nReturns true for each element if the element is a titlecased string and there is at least one character, false otherwise.\n\n See also\n\n [`char.istitle`](numpy.char.istitle#numpy.char.istitle \"numpy.char.istitle\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.istitle.htmlnumpy.chararray.isupper\n=======================\n\n method\n\n chararray.isupper()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2322-L2333)\n \nReturns true for each element if all cased characters in the string are uppercase and there is at least one character, false otherwise.\n\n See also\n\n [`char.isupper`](numpy.char.isupper#numpy.char.isupper \"numpy.char.isupper\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.isupper.htmlnumpy.chararray.item\n====================\n\n method\n\n chararray.item(**args*)\n \nCopy an element of an array to a standard Python scalar and return it.\n\n Parameters \n \n***args**Arguments (variable number and type)\n\n* none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned.\n* int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.\n* tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.\n\n Returns \n \n**z**Standard Python scalar object\n\nA copy of the specified element of the array as a suitable Python scalar\n\n #### Notes\n\n When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.\n\n [`item`](#numpy.chararray.item \"numpy.chararray.item\") is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.item(3)\n1\n>>> x.item(7)\n0\n>>> x.item((0, 1))\n2\n>>> x.item((2, 2))\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.item.htmlnumpy.chararray.join\n====================\n\n method\n\n chararray.join(*seq*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2335-L2345)\n \nReturn a string which is the concatenation of the strings in the sequence `seq`.\n\n See also\n\n [`char.join`](numpy.char.join#numpy.char.join \"numpy.char.join\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.join.htmlnumpy.chararray.ljust\n=====================\n\n method\n\n chararray.ljust(*width*, *fillchar=' '*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2347-L2357)\n \nReturn an array with the elements of `self` left-justified in a string of length `width`.\n\n See also\n\n [`char.ljust`](numpy.char.ljust#numpy.char.ljust \"numpy.char.ljust\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.ljust.htmlnumpy.chararray.lower\n=====================\n\n method\n\n chararray.lower()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2359-L2369)\n \nReturn an array with the elements of `self` converted to lowercase.\n\n See also\n\n [`char.lower`](numpy.char.lower#numpy.char.lower \"numpy.char.lower\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.lower.htmlnumpy.chararray.lstrip\n======================\n\n method\n\n chararray.lstrip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2371-L2381)\n \nFor each element in `self`, return a copy with the leading characters removed.\n\n See also\n\n [`char.lstrip`](numpy.char.lstrip#numpy.char.lstrip \"numpy.char.lstrip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.lstrip.htmlnumpy.chararray.nonzero\n=======================\n\n method\n\n chararray.nonzero()\n \nReturn the indices of the elements that are non-zero.\n\n Refer to [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\") for full documentation.\n\n See also\n\n [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.nonzero.htmlnumpy.chararray.put\n===================\n\n method\n\n chararray.put(*indices*, *values*, *mode='raise'*)\n \nSet `a.flat[n] = values[n]` for all `n` in indices.\n\n Refer to [`numpy.put`](numpy.put#numpy.put \"numpy.put\") for full documentation.\n\n See also\n\n [`numpy.put`](numpy.put#numpy.put \"numpy.put\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.put.htmlnumpy.chararray.ravel\n=====================\n\n method\n\n chararray.ravel([*order*])\n \nReturn a flattened array.\n\n Refer to [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\") for full documentation.\n\n See also\n\n [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nequivalent function\n\n [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\")\n\na flat iterator on the array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.ravel.htmlnumpy.chararray.repeat\n======================\n\n method\n\n chararray.repeat(*repeats*, *axis=None*)\n \nRepeat elements of an array.\n\n Refer to [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\") for full documentation.\n\n See also\n\n [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.repeat.htmlnumpy.chararray.replace\n=======================\n\n method\n\n chararray.replace(*old*, *new*, *count=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2393-L2403)\n \nFor each element in `self`, return a copy of the string with all occurrences of substring `old` replaced by `new`.\n\n See also\n\n [`char.replace`](numpy.char.replace#numpy.char.replace \"numpy.char.replace\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.replace.htmlnumpy.chararray.reshape\n=======================\n\n method\n\n chararray.reshape(*shape*, *order='C'*)\n \nReturns an array containing the same data with a new shape.\n\n Refer to [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\") for full documentation.\n\n See also\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nequivalent function\n\n #### Notes\n\n Unlike the free function [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), this method on [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") allows the elements of the shape parameter to be passed in as separate arguments. For example, `a.reshape(10, 11)` is equivalent to `a.reshape((10, 11))`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.reshape.htmlnumpy.chararray.resize\n======================\n\n method\n\n chararray.resize(*new_shape*, *refcheck=True*)\n \nChange shape and size of array in-place.\n\n Parameters \n \n**new_shape**tuple of ints, or `n` ints\n\nShape of resized array.\n\n \n**refcheck**bool, optional\n\nIf False, reference count will not be checked. Default is True.\n\n Returns \n None\n Raises \n ValueError\n\nIf `a` does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.\n\n SystemError\n\nIf the `order` keyword argument is specified. This behaviour is a bug in NumPy.\n\n See also\n\n [`resize`](numpy.resize#numpy.resize \"numpy.resize\")\n\nReturn a new array with the specified shape.\n\n #### Notes\n\n This reallocates space for the data area if necessary.\n\n Only contiguous arrays (data elements consecutive in memory) can be resized.\n\n The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False.\n\n #### Examples\n\n Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:\n\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='C')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [1]])\n\n```\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='F')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [2]])\n\n```\n Enlarging an array: as above, but missing entries are filled with zeros:\n\n \n```\n>>> b = np.array([[0, 1], [2, 3]])\n>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n>>> b\narray([[0, 1, 2],\n [3, 0, 0]])\n\n```\n Referencing an array prevents resizing…\n\n \n```\n>>> c = a\n>>> a.resize((1, 1))\nTraceback (most recent call last):\n...\nValueError: cannot resize an array that references or is referenced ...\n\n```\n Unless `refcheck` is False:\n\n \n```\n>>> a.resize((1, 1), refcheck=False)\n>>> a\narray([[0]])\n>>> c\narray([[0]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.resize.htmlnumpy.chararray.rfind\n=====================\n\n method\n\n chararray.rfind(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2405-L2416)\n \nFor each element in `self`, return the highest index in the string where substring `sub` is found, such that `sub` is contained within [`start`, `end`].\n\n See also\n\n [`char.rfind`](numpy.char.rfind#numpy.char.rfind \"numpy.char.rfind\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.rfind.htmlnumpy.chararray.rindex\n======================\n\n method\n\n chararray.rindex(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2418-L2428)\n \nLike [`rfind`](numpy.chararray.rfind#numpy.chararray.rfind \"numpy.chararray.rfind\"), but raises `ValueError` when the substring `sub` is not found.\n\n See also\n\n [`char.rindex`](numpy.char.rindex#numpy.char.rindex \"numpy.char.rindex\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.rindex.htmlnumpy.chararray.rjust\n=====================\n\n method\n\n chararray.rjust(*width*, *fillchar=' '*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2430-L2440)\n \nReturn an array with the elements of `self` right-justified in a string of length `width`.\n\n See also\n\n [`char.rjust`](numpy.char.rjust#numpy.char.rjust \"numpy.char.rjust\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.rjust.htmlnumpy.chararray.rsplit\n======================\n\n method\n\n chararray.rsplit(*sep=None*, *maxsplit=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2452-L2462)\n \nFor each element in `self`, return a list of the words in the string, using `sep` as the delimiter string.\n\n See also\n\n [`char.rsplit`](numpy.char.rsplit#numpy.char.rsplit \"numpy.char.rsplit\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.rsplit.htmlnumpy.chararray.rstrip\n======================\n\n method\n\n chararray.rstrip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2464-L2474)\n \nFor each element in `self`, return a copy with the trailing characters removed.\n\n See also\n\n [`char.rstrip`](numpy.char.rstrip#numpy.char.rstrip \"numpy.char.rstrip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.rstrip.htmlnumpy.chararray.searchsorted\n============================\n\n method\n\n chararray.searchsorted(*v*, *side='left'*, *sorter=None*)\n \nFind indices where elements of v should be inserted in a to maintain order.\n\n For full documentation, see [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n See also\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.searchsorted.htmlnumpy.chararray.setfield\n========================\n\n method\n\n chararray.setfield(*val*, *dtype*, *offset=0*)\n \nPut a value into a specified place in a field defined by a data-type.\n\n Place `val` into `a`’s field defined by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") and beginning `offset` bytes into the field.\n\n Parameters \n \n**val**object\n\nValue to be placed in field.\n\n \n**dtype**dtype object\n\nData-type of the field in which to place `val`.\n\n \n**offset**int, optional\n\nThe number of bytes into the field at which to place `val`.\n\n Returns \n None\n See also\n\n [`getfield`](numpy.chararray.getfield#numpy.chararray.getfield \"numpy.chararray.getfield\")\n #### Examples\n\n \n```\n>>> x = np.eye(3)\n>>> x.getfield(np.float64)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n>>> x.setfield(3, np.int32)\n>>> x.getfield(np.int32)\narray([[3, 3, 3],\n [3, 3, 3],\n [3, 3, 3]], dtype=int32)\n>>> x\narray([[1.0e+000, 1.5e-323, 1.5e-323],\n [1.5e-323, 1.0e+000, 1.5e-323],\n [1.5e-323, 1.5e-323, 1.0e+000]])\n>>> x.setfield(np.eye(3), np.int32)\n>>> x\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.setfield.htmlnumpy.chararray.setflags\n========================\n\n method\n\n chararray.setflags(*write=None*, *align=None*, *uic=None*)\n \nSet array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.\n\n These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)\n\n Parameters \n \n**write**bool, optional\n\nDescribes whether or not `a` can be written to.\n\n \n**align**bool, optional\n\nDescribes whether or not `a` is aligned properly for its type.\n\n \n**uic**bool, optional\n\nDescribes whether or not `a` is a copy of another “base” array.\n\n #### Notes\n\n Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n\n WRITEABLE (W) the data area can be written to;\n\n ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);\n\n WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.\n\n All flags can be accessed using the single (upper case) letter as well as the full name.\n\n #### Examples\n\n \n```\n>>> y = np.array([[3, 1, 7],\n... [2, 0, 0],\n... [8, 5, 9]])\n>>> y\narray([[3, 1, 7],\n [2, 0, 0],\n [8, 5, 9]])\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : True\n ALIGNED : True\n WRITEBACKIFCOPY : False\n>>> y.setflags(write=0, align=0)\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : False\n ALIGNED : False\n WRITEBACKIFCOPY : False\n>>> y.setflags(uic=1)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: cannot set WRITEBACKIFCOPY flag to True\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.setflags.htmlnumpy.chararray.sort\n====================\n\n method\n\n chararray.sort(*axis=- 1*, *kind=None*, *order=None*)\n \nSort an array in-place. Refer to [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for full documentation.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nSorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.\n\n Changed in version 1.15.0: The ‘stable’ option was added.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nReturn a sorted copy of an array.\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nIndirect sort.\n\n [`numpy.lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort on multiple keys.\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nFind elements in sorted array.\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nPartial sort.\n\n #### Notes\n\n See [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,4], [3,1]])\n>>> a.sort(axis=1)\n>>> a\narray([[1, 4],\n [1, 3]])\n>>> a.sort(axis=0)\n>>> a\narray([[1, 3],\n [1, 4]])\n\n```\n Use the `order` keyword to specify a field to use when sorting a structured array:\n\n \n```\n>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n>>> a.sort(order='y')\n>>> a\narray([(b'c', 1), (b'a', 2)],\n dtype=[('x', 'S1'), ('y', '<i8')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.sort.htmlnumpy.chararray.split\n=====================\n\n method\n\n chararray.split(*sep=None*, *maxsplit=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2476-L2486)\n \nFor each element in `self`, return a list of the words in the string, using `sep` as the delimiter string.\n\n See also\n\n [`char.split`](numpy.char.split#numpy.char.split \"numpy.char.split\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.split.htmlnumpy.chararray.splitlines\n==========================\n\n method\n\n chararray.splitlines(*keepends=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2488-L2498)\n \nFor each element in `self`, return a list of the lines in the element, breaking at line boundaries.\n\n See also\n\n [`char.splitlines`](numpy.char.splitlines#numpy.char.splitlines \"numpy.char.splitlines\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.splitlines.htmlnumpy.chararray.squeeze\n=======================\n\n method\n\n chararray.squeeze(*axis=None*)\n \nRemove axes of length one from `a`.\n\n Refer to [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\") for full documentation.\n\n See also\n\n [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.squeeze.htmlnumpy.chararray.startswith\n==========================\n\n method\n\n chararray.startswith(*prefix*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2500-L2510)\n \nReturns a boolean array which is `True` where the string element in `self` starts with `prefix`, otherwise `False`.\n\n See also\n\n [`char.startswith`](numpy.char.startswith#numpy.char.startswith \"numpy.char.startswith\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.startswith.htmlnumpy.chararray.strip\n=====================\n\n method\n\n chararray.strip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2512-L2522)\n \nFor each element in `self`, return a copy with the leading and trailing characters removed.\n\n See also\n\n [`char.strip`](numpy.char.strip#numpy.char.strip \"numpy.char.strip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.strip.htmlnumpy.chararray.swapaxes\n========================\n\n method\n\n chararray.swapaxes(*axis1*, *axis2*)\n \nReturn a view of the array with `axis1` and `axis2` interchanged.\n\n Refer to [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\") for full documentation.\n\n See also\n\n [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.swapaxes.htmlnumpy.chararray.swapcase\n========================\n\n method\n\n chararray.swapcase()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2524-L2534)\n \nFor each element in `self`, return a copy of the string with uppercase characters converted to lowercase and vice versa.\n\n See also\n\n [`char.swapcase`](numpy.char.swapcase#numpy.char.swapcase \"numpy.char.swapcase\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.swapcase.htmlnumpy.chararray.take\n====================\n\n method\n\n chararray.take(*indices*, *axis=None*, *out=None*, *mode='raise'*)\n \nReturn an array formed from the elements of `a` at the given indices.\n\n Refer to [`numpy.take`](numpy.take#numpy.take \"numpy.take\") for full documentation.\n\n See also\n\n [`numpy.take`](numpy.take#numpy.take \"numpy.take\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.take.htmlnumpy.chararray.title\n=====================\n\n method\n\n chararray.title()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2536-L2547)\n \nFor each element in `self`, return a titlecased version of the string: words start with uppercase characters, all remaining cased characters are lowercase.\n\n See also\n\n [`char.title`](numpy.char.title#numpy.char.title \"numpy.char.title\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.title.htmlnumpy.chararray.tofile\n======================\n\n method\n\n chararray.tofile(*fid*, *sep=''*, *format='%s'*)\n \nWrite array to a file as text or binary (default).\n\n Data is always written in ‘C’ order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile().\n\n Parameters \n \n**fid**file or str or Path\n\nAn open file object, or a string containing a filename.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n**sep**str\n\nSeparator between array items for text output. If “” (empty), a binary file is written, equivalent to `file.write(a.tobytes())`.\n\n \n**format**str\n\nFormat string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.\n\n #### Notes\n\n This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.\n\n When fid is a file object, array contents are directly written to the file, bypassing the file object’s `write` method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support `fileno()` (e.g., BytesIO).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.tofile.htmlnumpy.chararray.tolist\n======================\n\n method\n\n chararray.tolist()\n \nReturn the array as an `a.ndim`-levels deep nested list of Python scalars.\n\n Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the [`item`](numpy.ndarray.item#numpy.ndarray.item \"numpy.ndarray.item\") function.\n\n If `a.ndim` is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.\n\n Parameters \n **none**\n Returns \n \n**y**object, or list of object, or list of list of object, or …\n\nThe possibly nested list of array elements.\n\n #### Notes\n\n The array may be recreated via `a = np.array(a.tolist())`, although this may sometimes lose precision.\n\n #### Examples\n\n For a 1D array, `a.tolist()` is almost the same as `list(a)`, except that `tolist` changes numpy scalars to Python scalars:\n\n \n```\n>>> a = np.uint32([1, 2])\n>>> a_list = list(a)\n>>> a_list\n[1, 2]\n>>> type(a_list[0])\n<class 'numpy.uint32'>\n>>> a_tolist = a.tolist()\n>>> a_tolist\n[1, 2]\n>>> type(a_tolist[0])\n<class 'int'```\n Additionally, for a 2D array, `tolist` applies recursively:\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> list(a)\n[array([1, 2]), array([3, 4])]\n>>> a.tolist()\n[[1, 2], [3, 4]]\n\n```\n The base case for this recursion is a 0D array:\n\n \n```\n>>> a = np.array(1)\n>>> list(a)\nTraceback (most recent call last):\n ...\nTypeError: iteration over a 0-d array\n>>> a.tolist()\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.tolist.htmlnumpy.chararray.tostring\n========================\n\n method\n\n chararray.tostring(*order='C'*)\n \nA compatibility alias for [`tobytes`](numpy.chararray.tobytes#numpy.chararray.tobytes \"numpy.chararray.tobytes\"), with exactly the same behavior.\n\n Despite its name, it returns `bytes` not [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\")s.\n\n Deprecated since version 1.19.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.tostring.htmlnumpy.chararray.translate\n=========================\n\n method\n\n chararray.translate(*table*, *deletechars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2549-L2561)\n \nFor each element in `self`, return a copy of the string where all characters occurring in the optional argument `deletechars` are removed, and the remaining characters have been mapped through the given translation table.\n\n See also\n\n [`char.translate`](numpy.char.translate#numpy.char.translate \"numpy.char.translate\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.translate.htmlnumpy.chararray.transpose\n=========================\n\n method\n\n chararray.transpose(**axes*)\n \nReturns a view of the array with axes transposed.\n\n For a 1-D array this has no effect, as a transposed vector is simply the same vector. To convert a 1-D array into a 2D column vector, an additional dimension must be added. `np.atleast2d(a).T` achieves this, as does `a[:, np.newaxis]`. For a 2-D array, this is a standard matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and `a.shape = (i[0], i[1], ... i[n-2], i[n-1])`, then `a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])`.\n\n Parameters \n \n**axes**None, tuple of ints, or `n` ints\n\n* None or no argument: reverses the order of the axes.\n* tuple of ints: `i` in the `j`-th place in the tuple means `a`’s `i`-th axis becomes `a.transpose()`’s `j`-th axis.\n* `n` ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)\n\n Returns \n \n**out**ndarray\n\nView of `a`, with axes suitably permuted.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n\nEquivalent function\n\n [`ndarray.T`](numpy.ndarray.t#numpy.ndarray.T \"numpy.ndarray.T\")\n\nArray property returning the array transposed.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nGive a new shape to an array without changing its data.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> a\narray([[1, 2],\n [3, 4]])\n>>> a.transpose()\narray([[1, 3],\n [2, 4]])\n>>> a.transpose((1, 0))\narray([[1, 3],\n [2, 4]])\n>>> a.transpose(1, 0)\narray([[1, 3],\n [2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.transpose.htmlnumpy.chararray.upper\n=====================\n\n method\n\n chararray.upper()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2563-L2573)\n \nReturn an array with the elements of `self` converted to uppercase.\n\n See also\n\n [`char.upper`](numpy.char.upper#numpy.char.upper \"numpy.char.upper\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.upper.htmlnumpy.chararray.view\n====================\n\n method\n\n chararray.view(*[dtype][, type]*)\n \nNew view of array with the same data.\n\n Note\n\n Passing None for `dtype` is different from omitting the parameter, since the former invokes `dtype(None)` which is an alias for `dtype('float_')`.\n\n Parameters \n \n**dtype**data-type or ndarray sub-class, optional\n\nData-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the `type` parameter).\n\n \n**type**Python type, optional\n\nType of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.\n\n #### Notes\n\n `a.view()` is used two different ways:\n\n `a.view(some_dtype)` or `a.view(dtype=some_dtype)` constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.\n\n `a.view(ndarray_subclass)` or `a.view(type=ndarray_subclass)` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.\n\n For `a.view(some_dtype)`, if `some_dtype` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of `a` must be contiguous. This axis will be resized in the result.\n\n Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.\n\n #### Examples\n\n \n```\n>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n\n```\n Viewing array data using a different type and dtype:\n\n \n```\n>>> y = x.view(dtype=np.int16, type=np.matrix)\n>>> y\nmatrix([[513]], dtype=int16)\n>>> print(type(y))\n<class 'numpy.matrix'```\n Creating a view on a structured array so it can be used in calculations\n\n \n```\n>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n>>> xv = x.view(dtype=np.int8).reshape(-1,2)\n>>> xv\narray([[1, 2],\n [3, 4]], dtype=int8)\n>>> xv.mean(0)\narray([2., 3.])\n\n```\n Making changes to the view changes the underlying array\n\n \n```\n>>> xv[0,1] = 20\n>>> x\narray([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n\n```\n Using a view to convert an array to a recarray:\n\n \n```\n>>> z = x.view(np.recarray)\n>>> z.a\narray([1, 3], dtype=int8)\n\n```\n Views share data:\n\n \n```\n>>> x[0] = (9, 10)\n>>> z[0]\n(9, 10)\n\n```\n Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n\n \n```\n>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n>>> y = x[:, ::2]\n>>> y\narray([[1, 3],\n [4, 6]], dtype=int16)\n>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\nTraceback (most recent call last):\n ...\nValueError: To change to a dtype of a different size, the last axis must be contiguous\n>>> z = y.copy()\n>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\narray([[(1, 3)],\n [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n\n```\n However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:\n\n \n```\n>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n>>> x.transpose(1, 0, 2).view(np.int16)\narray([[[ 256, 770],\n [3340, 3854]],\n\n [[1284, 1798],\n [4368, 4882]],\n\n [[2312, 2826],\n [5396, 5910]]], dtype=int16)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.view.htmlnumpy.chararray.zfill\n=====================\n\n method\n\n chararray.zfill(*width*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2575-L2585)\n \nReturn the numeric string left-filled with zeros in a string of length `width`.\n\n See also\n\n [`char.zfill`](numpy.char.zfill#numpy.char.zfill \"numpy.char.zfill\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.zfill.htmlnumpy.chararray.strides\n=======================\n\n attribute\n\n chararray.strides\n \nTuple of bytes to step in each dimension when traversing an array.\n\n The byte offset of element `(i[0], i[1], ..., i[n])` in an array `a` is:\n\n \n```\noffset = sum(np.array(i) * a.strides)\n\n```\n A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.\n\n Warning\n\n Setting `arr.strides` is discouraged and may be deprecated in the future. [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\") should be preferred to create a new view of the same data in a safer way.\n\n See also\n\n [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\")\n #### Notes\n\n Imagine an array of 32-bit integers (each 4 bytes):\n\n \n```\nx = np.array([[0, 1, 2, 3, 4],\n [5, 6, 7, 8, 9]], dtype=np.int32)\n\n```\n This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be `(20, 4)`.\n\n #### Examples\n\n \n```\n>>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n>>> y\narray([[[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]],\n [[12, 13, 14, 15],\n [16, 17, 18, 19],\n [20, 21, 22, 23]]])\n>>> y.strides\n(48, 16, 4)\n>>> y[1,1,1]\n17\n>>> offset=sum(y.strides * np.array((1,1,1)))\n>>> offset/y.itemsize\n17\n\n```\n \n```\n>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n>>> x.strides\n(32, 4, 224, 1344)\n>>> i = np.array([3,5,2,2])\n>>> offset = sum(i * x.strides)\n>>> x[3,5,2,2]\n813\n>>> offset / x.itemsize\n813\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.strides.htmlnumpy.chararray.T\n=================\n\n attribute\n\n chararray.T\n \nThe transposed array.\n\n Same as `self.transpose()`.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n #### Examples\n\n \n```\n>>> x = np.array([[1.,2.],[3.,4.]])\n>>> x\narray([[ 1., 2.],\n [ 3., 4.]])\n>>> x.T\narray([[ 1., 3.],\n [ 2., 4.]])\n>>> x = np.array([1.,2.,3.,4.])\n>>> x\narray([ 1., 2., 3., 4.])\n>>> x.T\narray([ 1., 2., 3., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.T.htmlnumpy.chararray.base\n====================\n\n attribute\n\n chararray.base\n \nBase object if memory is from some other object.\n\n #### Examples\n\n The base of an array that owns its memory is None:\n\n \n```\n>>> x = np.array([1,2,3,4])\n>>> x.base is None\nTrue\n\n```\n Slicing creates a view, whose memory is shared with x:\n\n \n```\n>>> y = x[2:]\n>>> y.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.base.htmlnumpy.chararray.ctypes\n======================\n\n attribute\n\n chararray.ctypes\n \nAn object to simplify the interaction of the array with the ctypes module.\n\n This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.\n\n Parameters \n **None**\n Returns \n \n**c**Python object\n\nPossessing attributes data, shape, strides, etc.\n\n See also\n\n [`numpy.ctypeslib`](../routines.ctypeslib#module-numpy.ctypeslib \"numpy.ctypeslib\")\n #### Notes\n\n Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):\n\n _ctypes.data\n \nA pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as `self._array_interface_['data'][0]`.\n\n Note that unlike `data_as`, a reference will not be kept to the array: code like `ctypes.c_void_p((a + b).ctypes.data)` will result in a pointer to a deallocated array, and should be spelt `(a + b).ctypes.data_as(ctypes.c_void_p)`\n\n \n _ctypes.shape\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to `dtype('p')` on this platform (see [`c_intp`](../routines.ctypeslib#numpy.ctypeslib.c_intp \"numpy.ctypeslib.c_intp\")). This base-type could be [`ctypes.c_int`](https://docs.python.org/3/library/ctypes.html#ctypes.c_int \"(in Python v3.10)\"), [`ctypes.c_long`](https://docs.python.org/3/library/ctypes.html#ctypes.c_long \"(in Python v3.10)\"), or [`ctypes.c_longlong`](https://docs.python.org/3/library/ctypes.html#ctypes.c_longlong \"(in Python v3.10)\") depending on the platform. The ctypes array contains the shape of the underlying array.\n\n \n _ctypes.strides\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.\n\n \n _ctypes.data_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L267-L284)\n \nReturn the data pointer cast to a particular c-types object. For example, calling `self._as_parameter_` is equivalent to `self.data_as(ctypes.c_void_p)`. Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: `self.data_as(ctypes.POINTER(ctypes.c_double))`.\n\n The returned pointer will keep a reference to the array.\n\n \n _ctypes.shape_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L286-L293)\n \nReturn the shape tuple as an array of some other c-types type. For example: `self.shape_as(ctypes.c_short)`.\n\n \n _ctypes.strides_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L295-L302)\n \nReturn the strides tuple as an array of some other c-types type. For example: `self.strides_as(ctypes.c_longlong)`.\n\n \n If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the `as_parameter` attribute which will return an integer equal to the data attribute.\n\n #### Examples\n\n \n```\n>>> import ctypes\n>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n>>> x\narray([[0, 1],\n [2, 3]], dtype=int32)\n>>> x.ctypes.data\n31962608 # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\nc_uint(0)\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\nc_ulong(4294967296)\n>>> x.ctypes.shape\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n>>> x.ctypes.strides\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.ctypes.htmlnumpy.chararray.data\n====================\n\n attribute\n\n chararray.data\n \nPython buffer object pointing to the start of the array’s data.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.data.htmlnumpy.chararray.flags\n=====================\n\n attribute\n\n chararray.flags\n \nInformation about the memory layout of the array.\n\n #### Notes\n\n The [`flags`](#numpy.chararray.flags \"numpy.chararray.flags\") object can be accessed dictionary-like (as in `a.flags['WRITEABLE']`), or by using lowercased attribute names (as in `a.flags.writeable`). Short flag names are only supported in dictionary access.\n\n Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n The array flags cannot be set arbitrarily:\n\n * WRITEBACKIFCOPY can only be set `False`.\n* ALIGNED can only be set `True` if the data is truly aligned.\n* WRITEABLE can only be set `True` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.\n\n Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.\n\n Even for contiguous arrays a stride for a given dimension `arr.strides[dim]` may be *arbitrary* if `arr.shape[dim] == 1` or the array has no elements. It does *not* generally hold that `self.strides[-1] == self.itemsize` for C-style contiguous arrays or `self.strides[0] == self.itemsize` for Fortran-style contiguous arrays is true.\n\n Attributes \n **C_CONTIGUOUS (C)**\n\nThe data is in a single, C-style contiguous segment.\n\n **F_CONTIGUOUS (F)**\n\nThe data is in a single, Fortran-style contiguous segment.\n\n **OWNDATA (O)**\n\nThe array owns the memory it uses or borrows it from another object.\n\n **WRITEABLE (W)**\n\nThe data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.\n\n **ALIGNED (A)**\n\nThe data and all elements are aligned appropriately for the hardware.\n\n **WRITEBACKIFCOPY (X)**\n\nThis array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.\n\n **FNC**\n\nF_CONTIGUOUS and not C_CONTIGUOUS.\n\n **FORC**\n\nF_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n\n **BEHAVED (B)**\n\nALIGNED and WRITEABLE.\n\n **CARRAY (CA)**\n\nBEHAVED and C_CONTIGUOUS.\n\n **FARRAY (FA)**\n\nBEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.flags.htmlnumpy.chararray.flat\n====================\n\n attribute\n\n chararray.flat\n \nA 1-D iterator over the array.\n\n This is a [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\") instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.\n\n See also\n\n [`flatten`](numpy.chararray.flatten#numpy.chararray.flatten \"numpy.chararray.flatten\")\n\nReturn a copy of the array collapsed into one dimension.\n\n [`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> x = np.arange(1, 7).reshape(2, 3)\n>>> x\narray([[1, 2, 3],\n [4, 5, 6]])\n>>> x.flat[3]\n4\n>>> x.T\narray([[1, 4],\n [2, 5],\n [3, 6]])\n>>> x.T.flat[3]\n5\n>>> type(x.flat)\n<class 'numpy.flatiter'```\n An assignment example:\n\n \n```\n>>> x.flat = 3; x\narray([[3, 3, 3],\n [3, 3, 3]])\n>>> x.flat[[1,4]] = 1; x\narray([[3, 1, 3],\n [3, 1, 3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.flat.htmlnumpy.chararray.itemsize\n========================\n\n attribute\n\n chararray.itemsize\n \nLength of one array element in bytes.\n\n #### Examples\n\n \n```\n>>> x = np.array([1,2,3], dtype=np.float64)\n>>> x.itemsize\n8\n>>> x = np.array([1,2,3], dtype=np.complex128)\n>>> x.itemsize\n16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.itemsize.htmlnumpy.chararray.nbytes\n======================\n\n attribute\n\n chararray.nbytes\n \nTotal bytes consumed by the elements of the array.\n\n #### Notes\n\n Does not include memory consumed by non-element attributes of the array object.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3,5,2), dtype=np.complex128)\n>>> x.nbytes\n480\n>>> np.prod(x.shape) * x.itemsize\n480\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.nbytes.htmlnumpy.chararray.ndim\n====================\n\n attribute\n\n chararray.ndim\n \nNumber of array dimensions.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> x.ndim\n1\n>>> y = np.zeros((2, 3, 4))\n>>> y.ndim\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.ndim.htmlnumpy.chararray.size\n====================\n\n attribute\n\n chararray.size\n \nNumber of elements in the array.\n\n Equal to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.\n\n #### Notes\n\n `a.size` returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested `np.prod(a.shape)`, which returns an instance of `np.int_`), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n>>> x.size\n30\n>>> np.prod(x.shape)\n30\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.size.htmlnumpy.chararray.tobytes\n=======================\n\n method\n\n chararray.tobytes(*order='C'*)\n \nConstruct Python bytes containing the raw data bytes in the array.\n\n Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the `order` parameter.\n\n New in version 1.9.0.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’}, optional\n\nControls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for *Any*) means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.\n\n Returns \n \n**s**bytes\n\nPython bytes exhibiting a copy of `a`’s raw data.\n\n #### Examples\n\n \n```\n>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n>>> x.tobytes()\nb'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n>>> x.tobytes('C') == x.tobytes()\nTrue\n>>> x.tobytes('F')\nb'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.chararray.tobytes.htmlnumpy.record.all\n================\n\n method\n\n record.all()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.all`](numpy.ndarray.all#numpy.ndarray.all \"numpy.ndarray.all\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.all.htmlnumpy.record.any\n================\n\n method\n\n record.any()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.any`](numpy.ndarray.any#numpy.ndarray.any \"numpy.ndarray.any\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.any.htmlnumpy.record.argmax\n===================\n\n method\n\n record.argmax()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.argmax`](numpy.ndarray.argmax#numpy.ndarray.argmax \"numpy.ndarray.argmax\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.argmax.htmlnumpy.record.argmin\n===================\n\n method\n\n record.argmin()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.argmin`](numpy.ndarray.argmin#numpy.ndarray.argmin \"numpy.ndarray.argmin\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.argmin.htmlnumpy.record.argsort\n====================\n\n method\n\n record.argsort()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.argsort`](numpy.ndarray.argsort#numpy.ndarray.argsort \"numpy.ndarray.argsort\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.argsort.htmlnumpy.record.astype\n===================\n\n method\n\n record.astype()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.astype`](numpy.ndarray.astype#numpy.ndarray.astype \"numpy.ndarray.astype\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.astype.htmlnumpy.record.byteswap\n=====================\n\n method\n\n record.byteswap()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.byteswap`](numpy.ndarray.byteswap#numpy.ndarray.byteswap \"numpy.ndarray.byteswap\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.byteswap.htmlnumpy.record.choose\n===================\n\n method\n\n record.choose()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.choose`](numpy.ndarray.choose#numpy.ndarray.choose \"numpy.ndarray.choose\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.choose.htmlnumpy.record.clip\n=================\n\n method\n\n record.clip()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.clip`](numpy.ndarray.clip#numpy.ndarray.clip \"numpy.ndarray.clip\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.clip.htmlnumpy.record.compress\n=====================\n\n method\n\n record.compress()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.compress`](numpy.ndarray.compress#numpy.ndarray.compress \"numpy.ndarray.compress\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.compress.htmlnumpy.record.conjugate\n======================\n\n method\n\n record.conjugate()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.conjugate`](numpy.ndarray.conjugate#numpy.ndarray.conjugate \"numpy.ndarray.conjugate\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.conjugate.htmlnumpy.record.copy\n=================\n\n method\n\n record.copy()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.copy`](numpy.ndarray.copy#numpy.ndarray.copy \"numpy.ndarray.copy\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.copy.htmlnumpy.record.cumprod\n====================\n\n method\n\n record.cumprod()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.cumprod`](numpy.ndarray.cumprod#numpy.ndarray.cumprod \"numpy.ndarray.cumprod\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.cumprod.htmlnumpy.record.cumsum\n===================\n\n method\n\n record.cumsum()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.cumsum`](numpy.ndarray.cumsum#numpy.ndarray.cumsum \"numpy.ndarray.cumsum\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.cumsum.htmlnumpy.record.diagonal\n=====================\n\n method\n\n record.diagonal()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.diagonal`](numpy.ndarray.diagonal#numpy.ndarray.diagonal \"numpy.ndarray.diagonal\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.diagonal.htmlnumpy.record.dump\n=================\n\n method\n\n record.dump()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.dump`](numpy.ndarray.dump#numpy.ndarray.dump \"numpy.ndarray.dump\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.dump.htmlnumpy.record.dumps\n==================\n\n method\n\n record.dumps()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.dumps`](numpy.ndarray.dumps#numpy.ndarray.dumps \"numpy.ndarray.dumps\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.dumps.htmlnumpy.record.fill\n=================\n\n method\n\n record.fill()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.fill`](numpy.ndarray.fill#numpy.ndarray.fill \"numpy.ndarray.fill\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.fill.htmlnumpy.record.flatten\n====================\n\n method\n\n record.flatten()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.flatten`](numpy.ndarray.flatten#numpy.ndarray.flatten \"numpy.ndarray.flatten\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.flatten.htmlnumpy.record.getfield\n=====================\n\n method\n\n record.getfield()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.getfield`](numpy.ndarray.getfield#numpy.ndarray.getfield \"numpy.ndarray.getfield\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.getfield.htmlnumpy.record.item\n=================\n\n method\n\n record.item()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.item`](numpy.ndarray.item#numpy.ndarray.item \"numpy.ndarray.item\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.item.htmlnumpy.record.itemset\n====================\n\n method\n\n record.itemset()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.itemset`](numpy.ndarray.itemset#numpy.ndarray.itemset \"numpy.ndarray.itemset\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.itemset.htmlnumpy.record.max\n================\n\n method\n\n record.max()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.max`](numpy.ndarray.max#numpy.ndarray.max \"numpy.ndarray.max\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.max.htmlnumpy.record.mean\n=================\n\n method\n\n record.mean()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.mean`](numpy.ndarray.mean#numpy.ndarray.mean \"numpy.ndarray.mean\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.mean.htmlnumpy.record.min\n================\n\n method\n\n record.min()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.min`](numpy.ndarray.min#numpy.ndarray.min \"numpy.ndarray.min\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.min.htmlnumpy.record.newbyteorder\n=========================\n\n method\n\n record.newbyteorder(*new_order='S'*, */*)\n \nReturn a new [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") with a different byte order.\n\n Changes are also made in all fields and sub-arrays of the data type.\n\n The `new_order` code can be any from the following:\n\n * ‘S’ - swap dtype from current to opposite endian\n* {‘<’, ‘little’} - little endian\n* {‘>’, ‘big’} - big endian\n* {‘=’, ‘native’} - native order\n* {‘|’, ‘I’} - ignore (no change to byte order)\n\n Parameters \n \n**new_order**str, optional\n\nByte order to force; a value from the byte order specifications above. The default value (‘S’) results in swapping the current byte order.\n\n Returns \n \n**new_dtype**dtype\n\nNew [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") object with the given change to the byte order.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.newbyteorder.htmlnumpy.record.nonzero\n====================\n\n method\n\n record.nonzero()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.nonzero`](numpy.ndarray.nonzero#numpy.ndarray.nonzero \"numpy.ndarray.nonzero\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.nonzero.htmlnumpy.record.pprint\n===================\n\n method\n\n record.pprint()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/records.py#L291-L298)\n \nPretty-print all fields.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.pprint.htmlnumpy.record.prod\n=================\n\n method\n\n record.prod()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.prod`](numpy.ndarray.prod#numpy.ndarray.prod \"numpy.ndarray.prod\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.prod.htmlnumpy.record.ptp\n================\n\n method\n\n record.ptp()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.ptp`](numpy.ndarray.ptp#numpy.ndarray.ptp \"numpy.ndarray.ptp\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.ptp.htmlnumpy.record.put\n================\n\n method\n\n record.put()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.put`](numpy.ndarray.put#numpy.ndarray.put \"numpy.ndarray.put\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.put.htmlnumpy.record.ravel\n==================\n\n method\n\n record.ravel()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.ravel`](numpy.ndarray.ravel#numpy.ndarray.ravel \"numpy.ndarray.ravel\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.ravel.htmlnumpy.record.repeat\n===================\n\n method\n\n record.repeat()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.repeat`](numpy.ndarray.repeat#numpy.ndarray.repeat \"numpy.ndarray.repeat\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.repeat.htmlnumpy.record.reshape\n====================\n\n method\n\n record.reshape()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.reshape.htmlnumpy.record.resize\n===================\n\n method\n\n record.resize()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.resize`](numpy.ndarray.resize#numpy.ndarray.resize \"numpy.ndarray.resize\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.resize.htmlnumpy.record.round\n==================\n\n method\n\n record.round()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.round`](numpy.ndarray.round#numpy.ndarray.round \"numpy.ndarray.round\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.round.htmlnumpy.record.searchsorted\n=========================\n\n method\n\n record.searchsorted()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.searchsorted`](numpy.ndarray.searchsorted#numpy.ndarray.searchsorted \"numpy.ndarray.searchsorted\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.searchsorted.htmlnumpy.record.setfield\n=====================\n\n method\n\n record.setfield()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.setfield`](numpy.ndarray.setfield#numpy.ndarray.setfield \"numpy.ndarray.setfield\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.setfield.htmlnumpy.record.setflags\n=====================\n\n method\n\n record.setflags()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.setflags.htmlnumpy.record.sort\n=================\n\n method\n\n record.sort()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.sort`](numpy.ndarray.sort#numpy.ndarray.sort \"numpy.ndarray.sort\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.sort.htmlnumpy.record.squeeze\n====================\n\n method\n\n record.squeeze()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.squeeze`](numpy.ndarray.squeeze#numpy.ndarray.squeeze \"numpy.ndarray.squeeze\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.squeeze.htmlnumpy.record.std\n================\n\n method\n\n record.std()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.std`](numpy.ndarray.std#numpy.ndarray.std \"numpy.ndarray.std\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.std.htmlnumpy.record.sum\n================\n\n method\n\n record.sum()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.sum`](numpy.ndarray.sum#numpy.ndarray.sum \"numpy.ndarray.sum\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.sum.htmlnumpy.record.swapaxes\n=====================\n\n method\n\n record.swapaxes()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.swapaxes`](numpy.ndarray.swapaxes#numpy.ndarray.swapaxes \"numpy.ndarray.swapaxes\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.swapaxes.htmlnumpy.record.take\n=================\n\n method\n\n record.take()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.take`](numpy.ndarray.take#numpy.ndarray.take \"numpy.ndarray.take\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.take.htmlnumpy.record.tofile\n===================\n\n method\n\n record.tofile()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.tofile`](numpy.ndarray.tofile#numpy.ndarray.tofile \"numpy.ndarray.tofile\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.tofile.htmlnumpy.record.tolist\n===================\n\n method\n\n record.tolist()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.tolist`](numpy.ndarray.tolist#numpy.ndarray.tolist \"numpy.ndarray.tolist\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.tolist.htmlnumpy.record.tostring\n=====================\n\n method\n\n record.tostring()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.tostring`](numpy.ndarray.tostring#numpy.ndarray.tostring \"numpy.ndarray.tostring\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.tostring.htmlnumpy.record.trace\n==================\n\n method\n\n record.trace()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.trace`](numpy.ndarray.trace#numpy.ndarray.trace \"numpy.ndarray.trace\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.trace.htmlnumpy.record.transpose\n======================\n\n method\n\n record.transpose()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.transpose`](numpy.ndarray.transpose#numpy.ndarray.transpose \"numpy.ndarray.transpose\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.transpose.htmlnumpy.record.var\n================\n\n method\n\n record.var()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.var`](numpy.ndarray.var#numpy.ndarray.var \"numpy.ndarray.var\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.var.htmlnumpy.record.view\n=================\n\n method\n\n record.view()\n \nScalar method identical to the corresponding array attribute.\n\n Please see [`ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.view.htmlnumpy.record.T\n==============\n\n attribute\n\n record.T\n \nScalar attribute identical to the corresponding array attribute.\n\n Please see [`ndarray.T`](numpy.ndarray.t#numpy.ndarray.T \"numpy.ndarray.T\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.T.htmlnumpy.record.base\n=================\n\n attribute\n\n record.base\n \nbase object\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.base.htmlnumpy.record.data\n=================\n\n attribute\n\n record.data\n \nPointer to start of data.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.data.htmlnumpy.record.flags\n==================\n\n attribute\n\n record.flags\n \ninteger value of flags\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.flags.htmlnumpy.record.flat\n=================\n\n attribute\n\n record.flat\n \nA 1-D view of the scalar.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.flat.htmlnumpy.record.itemsize\n=====================\n\n attribute\n\n record.itemsize\n \nThe length of one element in bytes.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.itemsize.htmlnumpy.record.nbytes\n===================\n\n attribute\n\n record.nbytes\n \nThe length of the scalar in bytes.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.nbytes.htmlnumpy.record.ndim\n=================\n\n attribute\n\n record.ndim\n \nThe number of array dimensions.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.ndim.htmlnumpy.record.size\n=================\n\n attribute\n\n record.size\n \nThe number of elements in the gentype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.size.htmlnumpy.record.strides\n====================\n\n attribute\n\n record.strides\n \nTuple of bytes steps in each dimension.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.record.strides.htmlnumpy.broadcast.index\n=====================\n\n attribute\n\n broadcast.index\n \ncurrent index in broadcasted result\n\n #### Examples\n\n \n```\n>>> x = np.array([[1], [2], [3]])\n>>> y = np.array([4, 5, 6])\n>>> b = np.broadcast(x, y)\n>>> b.index\n0\n>>> next(b), next(b), next(b)\n((1, 4), (1, 5), (1, 6))\n>>> b.index\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.index.htmlnumpy.broadcast.iters\n=====================\n\n attribute\n\n broadcast.iters\n \ntuple of iterators along `self`’s “components.”\n\n Returns a tuple of [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\") objects, one for each “component” of `self`.\n\n See also\n\n [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> y = np.array([[4], [5], [6]])\n>>> b = np.broadcast(x, y)\n>>> row, col = b.iters\n>>> next(row), next(col)\n(1, 4)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.iters.htmlnumpy.broadcast.nd\n==================\n\n attribute\n\n broadcast.nd\n \nNumber of dimensions of broadcasted result. For code intended for NumPy 1.12.0 and later the more consistent [`ndim`](numpy.broadcast.ndim#numpy.broadcast.ndim \"numpy.broadcast.ndim\") is preferred.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> y = np.array([[4], [5], [6]])\n>>> b = np.broadcast(x, y)\n>>> b.nd\n2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.nd.htmlnumpy.broadcast.ndim\n====================\n\n attribute\n\n broadcast.ndim\n \nNumber of dimensions of broadcasted result. Alias for [`nd`](numpy.broadcast.nd#numpy.broadcast.nd \"numpy.broadcast.nd\").\n\n New in version 1.12.0.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> y = np.array([[4], [5], [6]])\n>>> b = np.broadcast(x, y)\n>>> b.ndim\n2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.ndim.htmlnumpy.broadcast.numiter\n=======================\n\n attribute\n\n broadcast.numiter\n \nNumber of iterators possessed by the broadcasted result.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> y = np.array([[4], [5], [6]])\n>>> b = np.broadcast(x, y)\n>>> b.numiter\n2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.numiter.htmlnumpy.broadcast.size\n====================\n\n attribute\n\n broadcast.size\n \nTotal size of broadcasted result.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> y = np.array([[4], [5], [6]])\n>>> b = np.broadcast(x, y)\n>>> b.size\n9\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.broadcast.size.htmlnumpy.busdaycalendar.weekmask\n=============================\n\n attribute\n\n busdaycalendar.weekmask\n \nA copy of the seven-element boolean mask indicating valid days.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.busdaycalendar.weekmask.htmlnumpy.busdaycalendar.holidays\n=============================\n\n attribute\n\n busdaycalendar.holidays\n \nA copy of the holiday array indicating additional invalid days.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.busdaycalendar.holidays.htmlnumpy.polynomial.polynomial.polyvander\n======================================\n\n polynomial.polynomial.polyvander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1058-L1109)\n \nVandermonde matrix of given degree.\n\n Returns the Vandermonde matrix of degree `deg` and sample points `x`. The Vandermonde matrix is defined by\n\n \\[V[..., i] = x^i,\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the power of `x`.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the matrix `V = polyvander(x, n)`, then `np.dot(V, c)` and `polyval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of polynomials of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray.\n\nThe Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where the last index is the power of `x`. The dtype will be the same as the converted `x`.\n\n See also\n\n \n[`polyvander2d`](numpy.polynomial.polynomial.polyvander2d#numpy.polynomial.polynomial.polyvander2d \"numpy.polynomial.polynomial.polyvander2d\"), [`polyvander3d`](numpy.polynomial.polynomial.polyvander3d#numpy.polynomial.polynomial.polyvander3d \"numpy.polynomial.polynomial.polyvander3d\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyvander.htmlnumpy.char.chararray.astype\n===========================\n\n method\n\n char.chararray.astype(*dtype*, *order='K'*, *casting='unsafe'*, *subok=True*, *copy=True*)\n \nCopy of the array, cast to a specified type.\n\n Parameters \n \n**dtype**str or dtype\n\nTypecode or data-type to which the array is cast.\n\n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.\n\n \n**casting**{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional\n\nControls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.\n\n * ‘no’ means the data types should not be cast at all.\n* ‘equiv’ means only byte-order changes are allowed.\n* ‘safe’ means only casts which can preserve values are allowed.\n* ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.\n* ‘unsafe’ means any data conversions may be done.\n\n \n**subok**bool, optional\n\nIf True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.\n\n \n**copy**bool, optional\n\nBy default, astype always returns a newly allocated array. If this is set to false, and the [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy.\n\n Returns \n \n**arr_t**ndarray\n\nUnless [`copy`](numpy.copy#numpy.copy \"numpy.copy\") is False and the other conditions for returning the input array are satisfied (see description for [`copy`](numpy.copy#numpy.copy \"numpy.copy\") input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), `order`.\n\n Raises \n ComplexWarning\n\nWhen casting from complex to float or int. To avoid this, one should use `a.real.astype(t)`.\n\n #### Notes\n\n Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.\n\n Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 2.5])\n>>> x\narray([1. , 2. , 2.5])\n\n```\n \n```\n>>> x.astype(int)\narray([1, 2, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.astype.htmlnumpy.char.chararray.argsort\n============================\n\n method\n\n char.chararray.argsort(*axis=- 1*, *kind=None*, *order=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2121-L2139)\n \nReturns the indices that would sort this array.\n\n Refer to [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\") for full documentation.\n\n See also\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.argsort.htmlnumpy.char.chararray.copy\n=========================\n\n method\n\n char.chararray.copy(*order='C'*)\n \nReturn a copy of the array.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\nControls the memory layout of the copy. ‘C’ means C-order, ‘F’ means F-order, ‘A’ means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout of `a` as closely as possible. (Note that this function and [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") are very similar but have different default values for their order= arguments, and this function always passes sub-classes through.)\n\n See also\n\n [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\")\n\nSimilar function with different default behavior\n\n [`numpy.copyto`](numpy.copyto#numpy.copyto \"numpy.copyto\")\n #### Notes\n\n This function is the preferred method for creating an array copy. The function [`numpy.copy`](numpy.copy#numpy.copy \"numpy.copy\") is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.\n\n #### Examples\n\n \n```\n>>> x = np.array([[1,2,3],[4,5,6]], order='F')\n\n```\n \n```\n>>> y = x.copy()\n\n```\n \n```\n>>> x.fill(0)\n\n```\n \n```\n>>> x\narray([[0, 0, 0],\n [0, 0, 0]])\n\n```\n \n```\n>>> y\narray([[1, 2, 3],\n [4, 5, 6]])\n\n```\n \n```\n>>> y.flags['C_CONTIGUOUS']\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.copy.htmlnumpy.char.chararray.count\n==========================\n\n method\n\n char.chararray.count(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2165-L2175)\n \nReturns an array with the number of non-overlapping occurrences of substring `sub` in the range [`start`, `end`].\n\n See also\n\n [`char.count`](numpy.char.count#numpy.char.count \"numpy.char.count\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.count.htmlnumpy.char.chararray.decode\n===========================\n\n method\n\n char.chararray.decode(*encoding=None*, *errors=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2177-L2186)\n \nCalls `str.decode` element-wise.\n\n See also\n\n [`char.decode`](numpy.char.decode#numpy.char.decode \"numpy.char.decode\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.decode.htmlnumpy.char.chararray.dump\n=========================\n\n method\n\n char.chararray.dump(*file*)\n \nDump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.\n\n Parameters \n \n**file**str or Path\n\nA string naming the dump file.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.dump.htmlnumpy.char.chararray.dumps\n==========================\n\n method\n\n char.chararray.dumps()\n \nReturns the pickle of the array as a string. pickle.loads will convert the string back to an array.\n\n Parameters \n **None**\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.dumps.htmlnumpy.char.chararray.encode\n===========================\n\n method\n\n char.chararray.encode(*encoding=None*, *errors=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2188-L2197)\n \nCalls [`str.encode`](https://docs.python.org/3/library/stdtypes.html#str.encode \"(in Python v3.10)\") element-wise.\n\n See also\n\n [`char.encode`](numpy.char.encode#numpy.char.encode \"numpy.char.encode\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.encode.htmlnumpy.char.chararray.endswith\n=============================\n\n method\n\n char.chararray.endswith(*suffix*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2199-L2209)\n \nReturns a boolean array which is `True` where the string element in `self` ends with `suffix`, otherwise `False`.\n\n See also\n\n [`char.endswith`](numpy.char.endswith#numpy.char.endswith \"numpy.char.endswith\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.endswith.htmlnumpy.char.chararray.expandtabs\n===============================\n\n method\n\n char.chararray.expandtabs(*tabsize=8*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2211-L2221)\n \nReturn a copy of each string element where all tab characters are replaced by one or more spaces.\n\n See also\n\n [`char.expandtabs`](numpy.char.expandtabs#numpy.char.expandtabs \"numpy.char.expandtabs\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.expandtabs.htmlnumpy.char.chararray.fill\n=========================\n\n method\n\n char.chararray.fill(*value*)\n \nFill the array with a scalar value.\n\n Parameters \n \n**value**scalar\n\nAll elements of `a` will be assigned this value.\n\n #### Examples\n\n \n```\n>>> a = np.array([1, 2])\n>>> a.fill(0)\n>>> a\narray([0, 0])\n>>> a = np.empty(2)\n>>> a.fill(1)\n>>> a\narray([1., 1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.fill.htmlnumpy.char.chararray.find\n=========================\n\n method\n\n char.chararray.find(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2223-L2233)\n \nFor each element, return the lowest index in the string where substring `sub` is found.\n\n See also\n\n [`char.find`](numpy.char.find#numpy.char.find \"numpy.char.find\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.find.htmlnumpy.char.chararray.flatten\n============================\n\n method\n\n char.chararray.flatten(*order='C'*)\n \nReturn a copy of the array collapsed into one dimension.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’, ‘K’}, optional\n\n‘C’ means to flatten in row-major (C-style) order. ‘F’ means to flatten in column-major (Fortran- style) order. ‘A’ means to flatten in column-major order if `a` is Fortran *contiguous* in memory, row-major order otherwise. ‘K’ means to flatten `a` in the order the elements occur in memory. The default is ‘C’.\n\n Returns \n \n**y**ndarray\n\nA copy of the input array, flattened to one dimension.\n\n See also\n\n [`ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nReturn a flattened array.\n\n [`flat`](numpy.char.chararray.flat#numpy.char.chararray.flat \"numpy.char.chararray.flat\")\n\nA 1-D flat iterator over the array.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,2], [3,4]])\n>>> a.flatten()\narray([1, 2, 3, 4])\n>>> a.flatten('F')\narray([1, 3, 2, 4])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.flatten.htmlnumpy.char.chararray.getfield\n=============================\n\n method\n\n char.chararray.getfield(*dtype*, *offset=0*)\n \nReturns a field of the given array as a certain type.\n\n A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.\n\n Parameters \n \n**dtype**str or dtype\n\nThe data type of the view. The dtype size of the view can not be larger than that of the array itself.\n\n \n**offset**int\n\nNumber of bytes to skip before beginning the element view.\n\n #### Examples\n\n \n```\n>>> x = np.diag([1.+1.j]*2)\n>>> x[1, 1] = 2 + 4.j\n>>> x\narray([[1.+1.j, 0.+0.j],\n [0.+0.j, 2.+4.j]])\n>>> x.getfield(np.float64)\narray([[1., 0.],\n [0., 2.]])\n\n```\n By choosing an offset of 8 bytes we can select the complex part of the array for our view:\n\n \n```\n>>> x.getfield(np.float64, offset=8)\narray([[1., 0.],\n [0., 4.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.getfield.htmlnumpy.char.chararray.index\n==========================\n\n method\n\n char.chararray.index(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2235-L2244)\n \nLike [`find`](numpy.char.chararray.find#numpy.char.chararray.find \"numpy.char.chararray.find\"), but raises `ValueError` when the substring is not found.\n\n See also\n\n [`char.index`](numpy.char.index#numpy.char.index \"numpy.char.index\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.index.htmlnumpy.char.chararray.isalnum\n============================\n\n method\n\n char.chararray.isalnum()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2246-L2257)\n \nReturns true for each element if all characters in the string are alphanumeric and there is at least one character, false otherwise.\n\n See also\n\n [`char.isalnum`](numpy.char.isalnum#numpy.char.isalnum \"numpy.char.isalnum\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isalnum.htmlnumpy.char.chararray.isalpha\n============================\n\n method\n\n char.chararray.isalpha()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2259-L2270)\n \nReturns true for each element if all characters in the string are alphabetic and there is at least one character, false otherwise.\n\n See also\n\n [`char.isalpha`](numpy.char.isalpha#numpy.char.isalpha \"numpy.char.isalpha\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isalpha.htmlnumpy.char.chararray.isdecimal\n==============================\n\n method\n\n char.chararray.isdecimal()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2599-L2609)\n \nFor each element in `self`, return True if there are only decimal characters in the element.\n\n See also\n\n [`char.isdecimal`](numpy.char.isdecimal#numpy.char.isdecimal \"numpy.char.isdecimal\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isdecimal.htmlnumpy.char.chararray.isdigit\n============================\n\n method\n\n char.chararray.isdigit()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2272-L2282)\n \nReturns true for each element if all characters in the string are digits and there is at least one character, false otherwise.\n\n See also\n\n [`char.isdigit`](numpy.char.isdigit#numpy.char.isdigit \"numpy.char.isdigit\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isdigit.htmlnumpy.char.chararray.islower\n============================\n\n method\n\n char.chararray.islower()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2284-L2295)\n \nReturns true for each element if all cased characters in the string are lowercase and there is at least one cased character, false otherwise.\n\n See also\n\n [`char.islower`](numpy.char.islower#numpy.char.islower \"numpy.char.islower\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.islower.htmlnumpy.char.chararray.isnumeric\n==============================\n\n method\n\n char.chararray.isnumeric()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2587-L2597)\n \nFor each element in `self`, return True if there are only numeric characters in the element.\n\n See also\n\n [`char.isnumeric`](numpy.char.isnumeric#numpy.char.isnumeric \"numpy.char.isnumeric\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isnumeric.htmlnumpy.char.chararray.isspace\n============================\n\n method\n\n char.chararray.isspace()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2297-L2308)\n \nReturns true for each element if there are only whitespace characters in the string and there is at least one character, false otherwise.\n\n See also\n\n [`char.isspace`](numpy.char.isspace#numpy.char.isspace \"numpy.char.isspace\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isspace.htmlnumpy.char.chararray.istitle\n============================\n\n method\n\n char.chararray.istitle()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2310-L2320)\n \nReturns true for each element if the element is a titlecased string and there is at least one character, false otherwise.\n\n See also\n\n [`char.istitle`](numpy.char.istitle#numpy.char.istitle \"numpy.char.istitle\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.istitle.htmlnumpy.char.chararray.isupper\n============================\n\n method\n\n char.chararray.isupper()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2322-L2333)\n \nReturns true for each element if all cased characters in the string are uppercase and there is at least one character, false otherwise.\n\n See also\n\n [`char.isupper`](numpy.char.isupper#numpy.char.isupper \"numpy.char.isupper\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.isupper.htmlnumpy.char.chararray.item\n=========================\n\n method\n\n char.chararray.item(**args*)\n \nCopy an element of an array to a standard Python scalar and return it.\n\n Parameters \n \n***args**Arguments (variable number and type)\n\n* none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned.\n* int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.\n* tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.\n\n Returns \n \n**z**Standard Python scalar object\n\nA copy of the specified element of the array as a suitable Python scalar\n\n #### Notes\n\n When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.\n\n [`item`](#numpy.char.chararray.item \"numpy.char.chararray.item\") is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> x = np.random.randint(9, size=(3, 3))\n>>> x\narray([[2, 2, 6],\n [1, 3, 6],\n [1, 0, 1]])\n>>> x.item(3)\n1\n>>> x.item(7)\n0\n>>> x.item((0, 1))\n2\n>>> x.item((2, 2))\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.item.htmlnumpy.char.chararray.join\n=========================\n\n method\n\n char.chararray.join(*seq*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2335-L2345)\n \nReturn a string which is the concatenation of the strings in the sequence `seq`.\n\n See also\n\n [`char.join`](numpy.char.join#numpy.char.join \"numpy.char.join\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.join.htmlnumpy.char.chararray.ljust\n==========================\n\n method\n\n char.chararray.ljust(*width*, *fillchar=' '*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2347-L2357)\n \nReturn an array with the elements of `self` left-justified in a string of length `width`.\n\n See also\n\n [`char.ljust`](numpy.char.ljust#numpy.char.ljust \"numpy.char.ljust\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.ljust.htmlnumpy.char.chararray.lower\n==========================\n\n method\n\n char.chararray.lower()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2359-L2369)\n \nReturn an array with the elements of `self` converted to lowercase.\n\n See also\n\n [`char.lower`](numpy.char.lower#numpy.char.lower \"numpy.char.lower\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.lower.htmlnumpy.char.chararray.lstrip\n===========================\n\n method\n\n char.chararray.lstrip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2371-L2381)\n \nFor each element in `self`, return a copy with the leading characters removed.\n\n See also\n\n [`char.lstrip`](numpy.char.lstrip#numpy.char.lstrip \"numpy.char.lstrip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.lstrip.htmlnumpy.char.chararray.nonzero\n============================\n\n method\n\n char.chararray.nonzero()\n \nReturn the indices of the elements that are non-zero.\n\n Refer to [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\") for full documentation.\n\n See also\n\n [`numpy.nonzero`](numpy.nonzero#numpy.nonzero \"numpy.nonzero\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.nonzero.htmlnumpy.char.chararray.put\n========================\n\n method\n\n char.chararray.put(*indices*, *values*, *mode='raise'*)\n \nSet `a.flat[n] = values[n]` for all `n` in indices.\n\n Refer to [`numpy.put`](numpy.put#numpy.put \"numpy.put\") for full documentation.\n\n See also\n\n [`numpy.put`](numpy.put#numpy.put \"numpy.put\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.put.htmlnumpy.char.chararray.ravel\n==========================\n\n method\n\n char.chararray.ravel([*order*])\n \nReturn a flattened array.\n\n Refer to [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\") for full documentation.\n\n See also\n\n [`numpy.ravel`](numpy.ravel#numpy.ravel \"numpy.ravel\")\n\nequivalent function\n\n [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\")\n\na flat iterator on the array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.ravel.htmlnumpy.char.chararray.repeat\n===========================\n\n method\n\n char.chararray.repeat(*repeats*, *axis=None*)\n \nRepeat elements of an array.\n\n Refer to [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\") for full documentation.\n\n See also\n\n [`numpy.repeat`](numpy.repeat#numpy.repeat \"numpy.repeat\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.repeat.htmlnumpy.char.chararray.replace\n============================\n\n method\n\n char.chararray.replace(*old*, *new*, *count=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2393-L2403)\n \nFor each element in `self`, return a copy of the string with all occurrences of substring `old` replaced by `new`.\n\n See also\n\n [`char.replace`](numpy.char.replace#numpy.char.replace \"numpy.char.replace\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.replace.htmlnumpy.char.chararray.reshape\n============================\n\n method\n\n char.chararray.reshape(*shape*, *order='C'*)\n \nReturns an array containing the same data with a new shape.\n\n Refer to [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\") for full documentation.\n\n See also\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nequivalent function\n\n #### Notes\n\n Unlike the free function [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), this method on [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") allows the elements of the shape parameter to be passed in as separate arguments. For example, `a.reshape(10, 11)` is equivalent to `a.reshape((10, 11))`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.reshape.htmlnumpy.char.chararray.resize\n===========================\n\n method\n\n char.chararray.resize(*new_shape*, *refcheck=True*)\n \nChange shape and size of array in-place.\n\n Parameters \n \n**new_shape**tuple of ints, or `n` ints\n\nShape of resized array.\n\n \n**refcheck**bool, optional\n\nIf False, reference count will not be checked. Default is True.\n\n Returns \n None\n Raises \n ValueError\n\nIf `a` does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist.\n\n SystemError\n\nIf the `order` keyword argument is specified. This behaviour is a bug in NumPy.\n\n See also\n\n [`resize`](numpy.resize#numpy.resize \"numpy.resize\")\n\nReturn a new array with the specified shape.\n\n #### Notes\n\n This reallocates space for the data area if necessary.\n\n Only contiguous arrays (data elements consecutive in memory) can be resized.\n\n The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False.\n\n #### Examples\n\n Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:\n\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='C')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [1]])\n\n```\n \n```\n>>> a = np.array([[0, 1], [2, 3]], order='F')\n>>> a.resize((2, 1))\n>>> a\narray([[0],\n [2]])\n\n```\n Enlarging an array: as above, but missing entries are filled with zeros:\n\n \n```\n>>> b = np.array([[0, 1], [2, 3]])\n>>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n>>> b\narray([[0, 1, 2],\n [3, 0, 0]])\n\n```\n Referencing an array prevents resizing…\n\n \n```\n>>> c = a\n>>> a.resize((1, 1))\nTraceback (most recent call last):\n...\nValueError: cannot resize an array that references or is referenced ...\n\n```\n Unless `refcheck` is False:\n\n \n```\n>>> a.resize((1, 1), refcheck=False)\n>>> a\narray([[0]])\n>>> c\narray([[0]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.resize.htmlnumpy.char.chararray.rfind\n==========================\n\n method\n\n char.chararray.rfind(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2405-L2416)\n \nFor each element in `self`, return the highest index in the string where substring `sub` is found, such that `sub` is contained within [`start`, `end`].\n\n See also\n\n [`char.rfind`](numpy.char.rfind#numpy.char.rfind \"numpy.char.rfind\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.rfind.htmlnumpy.char.chararray.rindex\n===========================\n\n method\n\n char.chararray.rindex(*sub*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2418-L2428)\n \nLike [`rfind`](numpy.char.chararray.rfind#numpy.char.chararray.rfind \"numpy.char.chararray.rfind\"), but raises `ValueError` when the substring `sub` is not found.\n\n See also\n\n [`char.rindex`](numpy.char.rindex#numpy.char.rindex \"numpy.char.rindex\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.rindex.htmlnumpy.char.chararray.rjust\n==========================\n\n method\n\n char.chararray.rjust(*width*, *fillchar=' '*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2430-L2440)\n \nReturn an array with the elements of `self` right-justified in a string of length `width`.\n\n See also\n\n [`char.rjust`](numpy.char.rjust#numpy.char.rjust \"numpy.char.rjust\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.rjust.htmlnumpy.char.chararray.rsplit\n===========================\n\n method\n\n char.chararray.rsplit(*sep=None*, *maxsplit=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2452-L2462)\n \nFor each element in `self`, return a list of the words in the string, using `sep` as the delimiter string.\n\n See also\n\n [`char.rsplit`](numpy.char.rsplit#numpy.char.rsplit \"numpy.char.rsplit\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.rsplit.htmlnumpy.char.chararray.rstrip\n===========================\n\n method\n\n char.chararray.rstrip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2464-L2474)\n \nFor each element in `self`, return a copy with the trailing characters removed.\n\n See also\n\n [`char.rstrip`](numpy.char.rstrip#numpy.char.rstrip \"numpy.char.rstrip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.rstrip.htmlnumpy.char.chararray.searchsorted\n=================================\n\n method\n\n char.chararray.searchsorted(*v*, *side='left'*, *sorter=None*)\n \nFind indices where elements of v should be inserted in a to maintain order.\n\n For full documentation, see [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\n See also\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.searchsorted.htmlnumpy.char.chararray.setfield\n=============================\n\n method\n\n char.chararray.setfield(*val*, *dtype*, *offset=0*)\n \nPut a value into a specified place in a field defined by a data-type.\n\n Place `val` into `a`’s field defined by [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\") and beginning `offset` bytes into the field.\n\n Parameters \n \n**val**object\n\nValue to be placed in field.\n\n \n**dtype**dtype object\n\nData-type of the field in which to place `val`.\n\n \n**offset**int, optional\n\nThe number of bytes into the field at which to place `val`.\n\n Returns \n None\n See also\n\n [`getfield`](numpy.char.chararray.getfield#numpy.char.chararray.getfield \"numpy.char.chararray.getfield\")\n #### Examples\n\n \n```\n>>> x = np.eye(3)\n>>> x.getfield(np.float64)\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n>>> x.setfield(3, np.int32)\n>>> x.getfield(np.int32)\narray([[3, 3, 3],\n [3, 3, 3],\n [3, 3, 3]], dtype=int32)\n>>> x\narray([[1.0e+000, 1.5e-323, 1.5e-323],\n [1.5e-323, 1.0e+000, 1.5e-323],\n [1.5e-323, 1.5e-323, 1.0e+000]])\n>>> x.setfield(np.eye(3), np.int32)\n>>> x\narray([[1., 0., 0.],\n [0., 1., 0.],\n [0., 0., 1.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.setfield.htmlnumpy.char.chararray.setflags\n=============================\n\n method\n\n char.chararray.setflags(*write=None*, *align=None*, *uic=None*)\n \nSet array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.\n\n These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)\n\n Parameters \n \n**write**bool, optional\n\nDescribes whether or not `a` can be written to.\n\n \n**align**bool, optional\n\nDescribes whether or not `a` is aligned properly for its type.\n\n \n**uic**bool, optional\n\nDescribes whether or not `a` is a copy of another “base” array.\n\n #### Notes\n\n Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n\n WRITEABLE (W) the data area can be written to;\n\n ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);\n\n WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.\n\n All flags can be accessed using the single (upper case) letter as well as the full name.\n\n #### Examples\n\n \n```\n>>> y = np.array([[3, 1, 7],\n... [2, 0, 0],\n... [8, 5, 9]])\n>>> y\narray([[3, 1, 7],\n [2, 0, 0],\n [8, 5, 9]])\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : True\n ALIGNED : True\n WRITEBACKIFCOPY : False\n>>> y.setflags(write=0, align=0)\n>>> y.flags\n C_CONTIGUOUS : True\n F_CONTIGUOUS : False\n OWNDATA : True\n WRITEABLE : False\n ALIGNED : False\n WRITEBACKIFCOPY : False\n>>> y.setflags(uic=1)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: cannot set WRITEBACKIFCOPY flag to True\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.setflags.htmlnumpy.char.chararray.sort\n=========================\n\n method\n\n char.chararray.sort(*axis=- 1*, *kind=None*, *order=None*)\n \nSort an array in-place. Refer to [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for full documentation.\n\n Parameters \n \n**axis**int, optional\n\nAxis along which to sort. Default is -1, which means sort along the last axis.\n\n \n**kind**{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional\n\nSorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.\n\n Changed in version 1.15.0: The ‘stable’ option was added.\n\n \n**order**str or list of str, optional\n\nWhen `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.\n\n See also\n\n [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\")\n\nReturn a sorted copy of an array.\n\n [`numpy.argsort`](numpy.argsort#numpy.argsort \"numpy.argsort\")\n\nIndirect sort.\n\n [`numpy.lexsort`](numpy.lexsort#numpy.lexsort \"numpy.lexsort\")\n\nIndirect stable sort on multiple keys.\n\n [`numpy.searchsorted`](numpy.searchsorted#numpy.searchsorted \"numpy.searchsorted\")\n\nFind elements in sorted array.\n\n [`numpy.partition`](numpy.partition#numpy.partition \"numpy.partition\")\n\nPartial sort.\n\n #### Notes\n\n See [`numpy.sort`](numpy.sort#numpy.sort \"numpy.sort\") for notes on the different sorting algorithms.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1,4], [3,1]])\n>>> a.sort(axis=1)\n>>> a\narray([[1, 4],\n [1, 3]])\n>>> a.sort(axis=0)\n>>> a\narray([[1, 3],\n [1, 4]])\n\n```\n Use the `order` keyword to specify a field to use when sorting a structured array:\n\n \n```\n>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n>>> a.sort(order='y')\n>>> a\narray([(b'c', 1), (b'a', 2)],\n dtype=[('x', 'S1'), ('y', '<i8')])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.sort.htmlnumpy.char.chararray.split\n==========================\n\n method\n\n char.chararray.split(*sep=None*, *maxsplit=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2476-L2486)\n \nFor each element in `self`, return a list of the words in the string, using `sep` as the delimiter string.\n\n See also\n\n [`char.split`](numpy.char.split#numpy.char.split \"numpy.char.split\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.split.htmlnumpy.char.chararray.splitlines\n===============================\n\n method\n\n char.chararray.splitlines(*keepends=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2488-L2498)\n \nFor each element in `self`, return a list of the lines in the element, breaking at line boundaries.\n\n See also\n\n [`char.splitlines`](numpy.char.splitlines#numpy.char.splitlines \"numpy.char.splitlines\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.splitlines.htmlnumpy.char.chararray.squeeze\n============================\n\n method\n\n char.chararray.squeeze(*axis=None*)\n \nRemove axes of length one from `a`.\n\n Refer to [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\") for full documentation.\n\n See also\n\n [`numpy.squeeze`](numpy.squeeze#numpy.squeeze \"numpy.squeeze\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.squeeze.htmlnumpy.char.chararray.startswith\n===============================\n\n method\n\n char.chararray.startswith(*prefix*, *start=0*, *end=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2500-L2510)\n \nReturns a boolean array which is `True` where the string element in `self` starts with `prefix`, otherwise `False`.\n\n See also\n\n [`char.startswith`](numpy.char.startswith#numpy.char.startswith \"numpy.char.startswith\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.startswith.htmlnumpy.char.chararray.strip\n==========================\n\n method\n\n char.chararray.strip(*chars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2512-L2522)\n \nFor each element in `self`, return a copy with the leading and trailing characters removed.\n\n See also\n\n [`char.strip`](numpy.char.strip#numpy.char.strip \"numpy.char.strip\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.strip.htmlnumpy.char.chararray.swapaxes\n=============================\n\n method\n\n char.chararray.swapaxes(*axis1*, *axis2*)\n \nReturn a view of the array with `axis1` and `axis2` interchanged.\n\n Refer to [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\") for full documentation.\n\n See also\n\n [`numpy.swapaxes`](numpy.swapaxes#numpy.swapaxes \"numpy.swapaxes\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.swapaxes.htmlnumpy.char.chararray.swapcase\n=============================\n\n method\n\n char.chararray.swapcase()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2524-L2534)\n \nFor each element in `self`, return a copy of the string with uppercase characters converted to lowercase and vice versa.\n\n See also\n\n [`char.swapcase`](numpy.char.swapcase#numpy.char.swapcase \"numpy.char.swapcase\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.swapcase.htmlnumpy.char.chararray.take\n=========================\n\n method\n\n char.chararray.take(*indices*, *axis=None*, *out=None*, *mode='raise'*)\n \nReturn an array formed from the elements of `a` at the given indices.\n\n Refer to [`numpy.take`](numpy.take#numpy.take \"numpy.take\") for full documentation.\n\n See also\n\n [`numpy.take`](numpy.take#numpy.take \"numpy.take\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.take.htmlnumpy.char.chararray.title\n==========================\n\n method\n\n char.chararray.title()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2536-L2547)\n \nFor each element in `self`, return a titlecased version of the string: words start with uppercase characters, all remaining cased characters are lowercase.\n\n See also\n\n [`char.title`](numpy.char.title#numpy.char.title \"numpy.char.title\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.title.htmlnumpy.char.chararray.tofile\n===========================\n\n method\n\n char.chararray.tofile(*fid*, *sep=''*, *format='%s'*)\n \nWrite array to a file as text or binary (default).\n\n Data is always written in ‘C’ order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile().\n\n Parameters \n \n**fid**file or str or Path\n\nAn open file object, or a string containing a filename.\n\n Changed in version 1.17.0: [`pathlib.Path`](https://docs.python.org/3/library/pathlib.html#pathlib.Path \"(in Python v3.10)\") objects are now accepted.\n\n \n**sep**str\n\nSeparator between array items for text output. If “” (empty), a binary file is written, equivalent to `file.write(a.tobytes())`.\n\n \n**format**str\n\nFormat string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.\n\n #### Notes\n\n This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.\n\n When fid is a file object, array contents are directly written to the file, bypassing the file object’s `write` method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not support `fileno()` (e.g., BytesIO).\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.tofile.htmlnumpy.char.chararray.tolist\n===========================\n\n method\n\n char.chararray.tolist()\n \nReturn the array as an `a.ndim`-levels deep nested list of Python scalars.\n\n Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the [`item`](numpy.ndarray.item#numpy.ndarray.item \"numpy.ndarray.item\") function.\n\n If `a.ndim` is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.\n\n Parameters \n **none**\n Returns \n \n**y**object, or list of object, or list of list of object, or …\n\nThe possibly nested list of array elements.\n\n #### Notes\n\n The array may be recreated via `a = np.array(a.tolist())`, although this may sometimes lose precision.\n\n #### Examples\n\n For a 1D array, `a.tolist()` is almost the same as `list(a)`, except that `tolist` changes numpy scalars to Python scalars:\n\n \n```\n>>> a = np.uint32([1, 2])\n>>> a_list = list(a)\n>>> a_list\n[1, 2]\n>>> type(a_list[0])\n<class 'numpy.uint32'>\n>>> a_tolist = a.tolist()\n>>> a_tolist\n[1, 2]\n>>> type(a_tolist[0])\n<class 'int'```\n Additionally, for a 2D array, `tolist` applies recursively:\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> list(a)\n[array([1, 2]), array([3, 4])]\n>>> a.tolist()\n[[1, 2], [3, 4]]\n\n```\n The base case for this recursion is a 0D array:\n\n \n```\n>>> a = np.array(1)\n>>> list(a)\nTraceback (most recent call last):\n ...\nTypeError: iteration over a 0-d array\n>>> a.tolist()\n1\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.tolist.htmlnumpy.char.chararray.tostring\n=============================\n\n method\n\n char.chararray.tostring(*order='C'*)\n \nA compatibility alias for [`tobytes`](numpy.char.chararray.tobytes#numpy.char.chararray.tobytes \"numpy.char.chararray.tobytes\"), with exactly the same behavior.\n\n Despite its name, it returns `bytes` not [`str`](https://docs.python.org/3/library/stdtypes.html#str \"(in Python v3.10)\")s.\n\n Deprecated since version 1.19.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.tostring.htmlnumpy.char.chararray.translate\n==============================\n\n method\n\n char.chararray.translate(*table*, *deletechars=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2549-L2561)\n \nFor each element in `self`, return a copy of the string where all characters occurring in the optional argument `deletechars` are removed, and the remaining characters have been mapped through the given translation table.\n\n See also\n\n [`char.translate`](numpy.char.translate#numpy.char.translate \"numpy.char.translate\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.translate.htmlnumpy.char.chararray.transpose\n==============================\n\n method\n\n char.chararray.transpose(**axes*)\n \nReturns a view of the array with axes transposed.\n\n For a 1-D array this has no effect, as a transposed vector is simply the same vector. To convert a 1-D array into a 2D column vector, an additional dimension must be added. `np.atleast2d(a).T` achieves this, as does `a[:, np.newaxis]`. For a 2-D array, this is a standard matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and `a.shape = (i[0], i[1], ... i[n-2], i[n-1])`, then `a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])`.\n\n Parameters \n \n**axes**None, tuple of ints, or `n` ints\n\n* None or no argument: reverses the order of the axes.\n* tuple of ints: `i` in the `j`-th place in the tuple means `a`’s `i`-th axis becomes `a.transpose()`’s `j`-th axis.\n* `n` ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)\n\n Returns \n \n**out**ndarray\n\nView of `a`, with axes suitably permuted.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n\nEquivalent function\n\n [`ndarray.T`](numpy.ndarray.t#numpy.ndarray.T \"numpy.ndarray.T\")\n\nArray property returning the array transposed.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nGive a new shape to an array without changing its data.\n\n #### Examples\n\n \n```\n>>> a = np.array([[1, 2], [3, 4]])\n>>> a\narray([[1, 2],\n [3, 4]])\n>>> a.transpose()\narray([[1, 3],\n [2, 4]])\n>>> a.transpose((1, 0))\narray([[1, 3],\n [2, 4]])\n>>> a.transpose(1, 0)\narray([[1, 3],\n [2, 4]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.transpose.htmlnumpy.char.chararray.upper\n==========================\n\n method\n\n char.chararray.upper()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/defchararray.py#L2563-L2573)\n \nReturn an array with the elements of `self` converted to uppercase.\n\n See also\n\n [`char.upper`](numpy.char.upper#numpy.char.upper \"numpy.char.upper\")\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.upper.htmlnumpy.char.chararray.view\n=========================\n\n method\n\n char.chararray.view(*[dtype][, type]*)\n \nNew view of array with the same data.\n\n Note\n\n Passing None for `dtype` is different from omitting the parameter, since the former invokes `dtype(None)` which is an alias for `dtype('float_')`.\n\n Parameters \n \n**dtype**data-type or ndarray sub-class, optional\n\nData-type descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the `type` parameter).\n\n \n**type**Python type, optional\n\nType of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.\n\n #### Notes\n\n `a.view()` is used two different ways:\n\n `a.view(some_dtype)` or `a.view(dtype=some_dtype)` constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.\n\n `a.view(ndarray_subclass)` or `a.view(type=ndarray_subclass)` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.\n\n For `a.view(some_dtype)`, if `some_dtype` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis of `a` must be contiguous. This axis will be resized in the result.\n\n Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.\n\n #### Examples\n\n \n```\n>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n\n```\n Viewing array data using a different type and dtype:\n\n \n```\n>>> y = x.view(dtype=np.int16, type=np.matrix)\n>>> y\nmatrix([[513]], dtype=int16)\n>>> print(type(y))\n<class 'numpy.matrix'```\n Creating a view on a structured array so it can be used in calculations\n\n \n```\n>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n>>> xv = x.view(dtype=np.int8).reshape(-1,2)\n>>> xv\narray([[1, 2],\n [3, 4]], dtype=int8)\n>>> xv.mean(0)\narray([2., 3.])\n\n```\n Making changes to the view changes the underlying array\n\n \n```\n>>> xv[0,1] = 20\n>>> x\narray([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n\n```\n Using a view to convert an array to a recarray:\n\n \n```\n>>> z = x.view(np.recarray)\n>>> z.a\narray([1, 3], dtype=int8)\n\n```\n Views share data:\n\n \n```\n>>> x[0] = (9, 10)\n>>> z[0]\n(9, 10)\n\n```\n Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n\n \n```\n>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n>>> y = x[:, ::2]\n>>> y\narray([[1, 3],\n [4, 6]], dtype=int16)\n>>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\nTraceback (most recent call last):\n ...\nValueError: To change to a dtype of a different size, the last axis must be contiguous\n>>> z = y.copy()\n>>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\narray([[(1, 3)],\n [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n\n```\n However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:\n\n \n```\n>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n>>> x.transpose(1, 0, 2).view(np.int16)\narray([[[ 256, 770],\n [3340, 3854]],\n\n [[1284, 1798],\n [4368, 4882]],\n\n [[2312, 2826],\n [5396, 5910]]], dtype=int16)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.view.htmlnumpy.char.chararray.dtype\n==========================\n\n attribute\n\n char.chararray.dtype\n \nData-type of the array’s elements.\n\n Warning\n\n Setting `arr.dtype` is discouraged and may be deprecated in the future. Setting will replace the `dtype` without modifying the memory (see also [`ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\") and [`ndarray.astype`](numpy.ndarray.astype#numpy.ndarray.astype \"numpy.ndarray.astype\")).\n\n Parameters \n **None**\n Returns \n \n**d**numpy dtype object\n\n See also\n\n [`ndarray.astype`](numpy.ndarray.astype#numpy.ndarray.astype \"numpy.ndarray.astype\")\n\nCast the values contained in the array to a new data-type.\n\n [`ndarray.view`](numpy.ndarray.view#numpy.ndarray.view \"numpy.ndarray.view\")\n\nCreate a view of the same data but a different data-type.\n\n [`numpy.dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n #### Examples\n\n \n```\n>>> x\narray([[0, 1],\n [2, 3]])\n>>> x.dtype\ndtype('int32')\n>>> type(x.dtype)\n<type 'numpy.dtype'```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.dtype.htmlnumpy.char.chararray.strides\n============================\n\n attribute\n\n char.chararray.strides\n \nTuple of bytes to step in each dimension when traversing an array.\n\n The byte offset of element `(i[0], i[1], ..., i[n])` in an array `a` is:\n\n \n```\noffset = sum(np.array(i) * a.strides)\n\n```\n A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.\n\n Warning\n\n Setting `arr.strides` is discouraged and may be deprecated in the future. [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\") should be preferred to create a new view of the same data in a safer way.\n\n See also\n\n [`numpy.lib.stride_tricks.as_strided`](numpy.lib.stride_tricks.as_strided#numpy.lib.stride_tricks.as_strided \"numpy.lib.stride_tricks.as_strided\")\n #### Notes\n\n Imagine an array of 32-bit integers (each 4 bytes):\n\n \n```\nx = np.array([[0, 1, 2, 3, 4],\n [5, 6, 7, 8, 9]], dtype=np.int32)\n\n```\n This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be `(20, 4)`.\n\n #### Examples\n\n \n```\n>>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n>>> y\narray([[[ 0, 1, 2, 3],\n [ 4, 5, 6, 7],\n [ 8, 9, 10, 11]],\n [[12, 13, 14, 15],\n [16, 17, 18, 19],\n [20, 21, 22, 23]]])\n>>> y.strides\n(48, 16, 4)\n>>> y[1,1,1]\n17\n>>> offset=sum(y.strides * np.array((1,1,1)))\n>>> offset/y.itemsize\n17\n\n```\n \n```\n>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n>>> x.strides\n(32, 4, 224, 1344)\n>>> i = np.array([3,5,2,2])\n>>> offset = sum(i * x.strides)\n>>> x[3,5,2,2]\n813\n>>> offset / x.itemsize\n813\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.strides.htmlnumpy.char.chararray.T\n======================\n\n attribute\n\n char.chararray.T\n \nThe transposed array.\n\n Same as `self.transpose()`.\n\n See also\n\n [`transpose`](numpy.transpose#numpy.transpose \"numpy.transpose\")\n #### Examples\n\n \n```\n>>> x = np.array([[1.,2.],[3.,4.]])\n>>> x\narray([[ 1., 2.],\n [ 3., 4.]])\n>>> x.T\narray([[ 1., 3.],\n [ 2., 4.]])\n>>> x = np.array([1.,2.,3.,4.])\n>>> x\narray([ 1., 2., 3., 4.])\n>>> x.T\narray([ 1., 2., 3., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.T.htmlnumpy.char.chararray.base\n=========================\n\n attribute\n\n char.chararray.base\n \nBase object if memory is from some other object.\n\n #### Examples\n\n The base of an array that owns its memory is None:\n\n \n```\n>>> x = np.array([1,2,3,4])\n>>> x.base is None\nTrue\n\n```\n Slicing creates a view, whose memory is shared with x:\n\n \n```\n>>> y = x[2:]\n>>> y.base is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.base.htmlnumpy.char.chararray.ctypes\n===========================\n\n attribute\n\n char.chararray.ctypes\n \nAn object to simplify the interaction of the array with the ctypes module.\n\n This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.\n\n Parameters \n **None**\n Returns \n \n**c**Python object\n\nPossessing attributes data, shape, strides, etc.\n\n See also\n\n [`numpy.ctypeslib`](../routines.ctypeslib#module-numpy.ctypeslib \"numpy.ctypeslib\")\n #### Notes\n\n Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):\n\n _ctypes.data\n \nA pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as `self._array_interface_['data'][0]`.\n\n Note that unlike `data_as`, a reference will not be kept to the array: code like `ctypes.c_void_p((a + b).ctypes.data)` will result in a pointer to a deallocated array, and should be spelt `(a + b).ctypes.data_as(ctypes.c_void_p)`\n\n \n _ctypes.shape\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to `dtype('p')` on this platform (see [`c_intp`](../routines.ctypeslib#numpy.ctypeslib.c_intp \"numpy.ctypeslib.c_intp\")). This base-type could be [`ctypes.c_int`](https://docs.python.org/3/library/ctypes.html#ctypes.c_int \"(in Python v3.10)\"), [`ctypes.c_long`](https://docs.python.org/3/library/ctypes.html#ctypes.c_long \"(in Python v3.10)\"), or [`ctypes.c_longlong`](https://docs.python.org/3/library/ctypes.html#ctypes.c_longlong \"(in Python v3.10)\") depending on the platform. The ctypes array contains the shape of the underlying array.\n\n \n _ctypes.strides\n \n(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.\n\n \n _ctypes.data_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L267-L284)\n \nReturn the data pointer cast to a particular c-types object. For example, calling `self._as_parameter_` is equivalent to `self.data_as(ctypes.c_void_p)`. Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: `self.data_as(ctypes.POINTER(ctypes.c_double))`.\n\n The returned pointer will keep a reference to the array.\n\n \n _ctypes.shape_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L286-L293)\n \nReturn the shape tuple as an array of some other c-types type. For example: `self.shape_as(ctypes.c_short)`.\n\n \n _ctypes.strides_as(*obj*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/core/_internal.py#L295-L302)\n \nReturn the strides tuple as an array of some other c-types type. For example: `self.strides_as(ctypes.c_longlong)`.\n\n \n If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the `as_parameter` attribute which will return an integer equal to the data attribute.\n\n #### Examples\n\n \n```\n>>> import ctypes\n>>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n>>> x\narray([[0, 1],\n [2, 3]], dtype=int32)\n>>> x.ctypes.data\n31962608 # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n<__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\nc_uint(0)\n>>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\nc_ulong(4294967296)\n>>> x.ctypes.shape\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n>>> x.ctypes.strides\n<numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.ctypes.htmlnumpy.char.chararray.data\n=========================\n\n attribute\n\n char.chararray.data\n \nPython buffer object pointing to the start of the array’s data.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.data.htmlnumpy.char.chararray.flags\n==========================\n\n attribute\n\n char.chararray.flags\n \nInformation about the memory layout of the array.\n\n #### Notes\n\n The [`flags`](#numpy.char.chararray.flags \"numpy.char.chararray.flags\") object can be accessed dictionary-like (as in `a.flags['WRITEABLE']`), or by using lowercased attribute names (as in `a.flags.writeable`). Short flag names are only supported in dictionary access.\n\n Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling [`ndarray.setflags`](numpy.ndarray.setflags#numpy.ndarray.setflags \"numpy.ndarray.setflags\").\n\n The array flags cannot be set arbitrarily:\n\n * WRITEBACKIFCOPY can only be set `False`.\n* ALIGNED can only be set `True` if the data is truly aligned.\n* WRITEABLE can only be set `True` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.\n\n Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.\n\n Even for contiguous arrays a stride for a given dimension `arr.strides[dim]` may be *arbitrary* if `arr.shape[dim] == 1` or the array has no elements. It does *not* generally hold that `self.strides[-1] == self.itemsize` for C-style contiguous arrays or `self.strides[0] == self.itemsize` for Fortran-style contiguous arrays is true.\n\n Attributes \n **C_CONTIGUOUS (C)**\n\nThe data is in a single, C-style contiguous segment.\n\n **F_CONTIGUOUS (F)**\n\nThe data is in a single, Fortran-style contiguous segment.\n\n **OWNDATA (O)**\n\nThe array owns the memory it uses or borrows it from another object.\n\n **WRITEABLE (W)**\n\nThe data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.\n\n **ALIGNED (A)**\n\nThe data and all elements are aligned appropriately for the hardware.\n\n **WRITEBACKIFCOPY (X)**\n\nThis array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.\n\n **FNC**\n\nF_CONTIGUOUS and not C_CONTIGUOUS.\n\n **FORC**\n\nF_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n\n **BEHAVED (B)**\n\nALIGNED and WRITEABLE.\n\n **CARRAY (CA)**\n\nBEHAVED and C_CONTIGUOUS.\n\n **FARRAY (FA)**\n\nBEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.flags.htmlnumpy.char.chararray.flat\n=========================\n\n attribute\n\n char.chararray.flat\n \nA 1-D iterator over the array.\n\n This is a [`numpy.flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\") instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.\n\n See also\n\n [`flatten`](numpy.char.chararray.flatten#numpy.char.chararray.flatten \"numpy.char.chararray.flatten\")\n\nReturn a copy of the array collapsed into one dimension.\n\n [`flatiter`](numpy.flatiter#numpy.flatiter \"numpy.flatiter\")\n #### Examples\n\n \n```\n>>> x = np.arange(1, 7).reshape(2, 3)\n>>> x\narray([[1, 2, 3],\n [4, 5, 6]])\n>>> x.flat[3]\n4\n>>> x.T\narray([[1, 4],\n [2, 5],\n [3, 6]])\n>>> x.T.flat[3]\n5\n>>> type(x.flat)\n<class 'numpy.flatiter'```\n An assignment example:\n\n \n```\n>>> x.flat = 3; x\narray([[3, 3, 3],\n [3, 3, 3]])\n>>> x.flat[[1,4]] = 1; x\narray([[3, 1, 3],\n [3, 1, 3]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.flat.htmlnumpy.char.chararray.imag\n=========================\n\n attribute\n\n char.chararray.imag\n \nThe imaginary part of the array.\n\n #### Examples\n\n \n```\n>>> x = np.sqrt([1+0j, 0+1j])\n>>> x.imag\narray([ 0. , 0.70710678])\n>>> x.imag.dtype\ndtype('float64')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.imag.htmlnumpy.char.chararray.itemsize\n=============================\n\n attribute\n\n char.chararray.itemsize\n \nLength of one array element in bytes.\n\n #### Examples\n\n \n```\n>>> x = np.array([1,2,3], dtype=np.float64)\n>>> x.itemsize\n8\n>>> x = np.array([1,2,3], dtype=np.complex128)\n>>> x.itemsize\n16\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.itemsize.htmlnumpy.char.chararray.nbytes\n===========================\n\n attribute\n\n char.chararray.nbytes\n \nTotal bytes consumed by the elements of the array.\n\n #### Notes\n\n Does not include memory consumed by non-element attributes of the array object.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3,5,2), dtype=np.complex128)\n>>> x.nbytes\n480\n>>> np.prod(x.shape) * x.itemsize\n480\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.nbytes.htmlnumpy.char.chararray.ndim\n=========================\n\n attribute\n\n char.chararray.ndim\n \nNumber of array dimensions.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3])\n>>> x.ndim\n1\n>>> y = np.zeros((2, 3, 4))\n>>> y.ndim\n3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.ndim.htmlnumpy.char.chararray.real\n=========================\n\n attribute\n\n char.chararray.real\n \nThe real part of the array.\n\n See also\n\n [`numpy.real`](numpy.real#numpy.real \"numpy.real\")\n\nequivalent function\n\n #### Examples\n\n \n```\n>>> x = np.sqrt([1+0j, 0+1j])\n>>> x.real\narray([ 1. , 0.70710678])\n>>> x.real.dtype\ndtype('float64')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.real.htmlnumpy.char.chararray.shape\n==========================\n\n attribute\n\n char.chararray.shape\n \nTuple of array dimensions.\n\n The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\"), one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.\n\n Warning\n\n Setting `arr.shape` is discouraged and may be deprecated in the future. Using [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\") is the preferred approach.\n\n See also\n\n [`numpy.shape`](numpy.shape#numpy.shape \"numpy.shape\")\n\nEquivalent getter function.\n\n [`numpy.reshape`](numpy.reshape#numpy.reshape \"numpy.reshape\")\n\nFunction similar to setting `shape`.\n\n [`ndarray.reshape`](numpy.ndarray.reshape#numpy.ndarray.reshape \"numpy.ndarray.reshape\")\n\nMethod similar to setting `shape`.\n\n #### Examples\n\n \n```\n>>> x = np.array([1, 2, 3, 4])\n>>> x.shape\n(4,)\n>>> y = np.zeros((2, 3, 4))\n>>> y.shape\n(2, 3, 4)\n>>> y.shape = (3, 8)\n>>> y\narray([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n [ 0., 0., 0., 0., 0., 0., 0., 0.],\n [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n>>> y.shape = (3, 6)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nValueError: total size of new array must be unchanged\n>>> np.zeros((4,2))[::2].shape = (-1,)\nTraceback (most recent call last):\n File \"<stdin>\", line 1, in <module>\nAttributeError: Incompatible shape for in-place modification. Use\n`.reshape()` to make a copy with the desired shape.\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.shape.htmlnumpy.char.chararray.size\n=========================\n\n attribute\n\n char.chararray.size\n \nNumber of elements in the array.\n\n Equal to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.\n\n #### Notes\n\n `a.size` returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested `np.prod(a.shape)`, which returns an instance of `np.int_`), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.\n\n #### Examples\n\n \n```\n>>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n>>> x.size\n30\n>>> np.prod(x.shape)\n30\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.size.htmlnumpy.char.chararray.tobytes\n============================\n\n method\n\n char.chararray.tobytes(*order='C'*)\n \nConstruct Python bytes containing the raw data bytes in the array.\n\n Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in C-order by default. This behavior is controlled by the `order` parameter.\n\n New in version 1.9.0.\n\n Parameters \n \n**order**{‘C’, ‘F’, ‘A’}, optional\n\nControls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for *Any*) means ‘F’ if `a` is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.\n\n Returns \n \n**s**bytes\n\nPython bytes exhibiting a copy of `a`’s raw data.\n\n #### Examples\n\n \n```\n>>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n>>> x.tobytes()\nb'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n>>> x.tobytes('C') == x.tobytes()\nTrue\n>>> x.tobytes('F')\nb'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.char.chararray.tobytes.htmlnumpy.finfo.machar\n==================\n\n property\n\n *property*finfo.machar\n \nThe object which calculated these parameters and holds more detailed information.\n\n Deprecated since version 1.22.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.finfo.machar.htmlnumpy.finfo.tiny\n================\n\n property\n\n *property*finfo.tiny\n \nReturn the value for tiny, alias of smallest_normal.\n\n Returns \n \n**tiny**float\n\nValue for the smallest normal, alias of smallest_normal.\n\n Warns \n UserWarning\n\nIf the calculated value for the smallest normal is requested for double-double.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.finfo.tiny.htmlnumpy.finfo.smallest_normal\n============================\n\n property\n\n *property*finfo.smallest_normal\n \nReturn the value for the smallest normal.\n\n Returns \n \n**smallest_normal**float\n\nValue for the smallest normal.\n\n Warns \n UserWarning\n\nIf the calculated value for the smallest normal is requested for double-double.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.finfo.smallest_normal.htmlnumpy.iinfo.min\n===============\n\n property\n\n *property*iinfo.min\n \nMinimum value of given dtype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.iinfo.min.htmlnumpy.iinfo.max\n===============\n\n property\n\n *property*iinfo.max\n \nMaximum value of given dtype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.iinfo.max.htmlnumpy.errstate.__call__\n===========================\n\n method\n\n errstate.__call__(*func*)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.errstate.__call__.htmlnumpy.DataSource.abspath\n========================\n\n method\n\n DataSource.abspath(*path*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/_datasource.py#L375-L415)\n \nReturn absolute path of file in the DataSource directory.\n\n If `path` is an URL, then [`abspath`](#numpy.DataSource.abspath \"numpy.DataSource.abspath\") will return either the location the file exists locally or the location it would exist when opened using the [`open`](numpy.datasource.open#numpy.DataSource.open \"numpy.DataSource.open\") method.\n\n Parameters \n \n**path**str\n\nCan be a local file or a remote URL.\n\n Returns \n \n**out**str\n\nComplete path, including the [`DataSource`](numpy.datasource#numpy.DataSource \"numpy.DataSource\") destination directory.\n\n #### Notes\n\n The functionality is based on [`os.path.abspath`](https://docs.python.org/3/library/os.path.html#os.path.abspath \"(in Python v3.10)\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.DataSource.abspath.htmlnumpy.DataSource.exists\n=======================\n\n method\n\n DataSource.exists(*path*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/_datasource.py#L431-L485)\n \nTest if path exists.\n\n Test if `path` exists as (and in this order):\n\n * a local file.\n* a remote URL that has been downloaded and stored locally in the [`DataSource`](numpy.datasource#numpy.DataSource \"numpy.DataSource\") directory.\n* a remote URL that has not been downloaded, but is valid and accessible.\n\n Parameters \n \n**path**str\n\nCan be a local file or a remote URL.\n\n Returns \n \n**out**bool\n\nTrue if `path` exists.\n\n #### Notes\n\n When `path` is an URL, [`exists`](#numpy.DataSource.exists \"numpy.DataSource.exists\") will return True if it’s either stored locally in the [`DataSource`](numpy.datasource#numpy.DataSource \"numpy.DataSource\") directory, or is a valid remote URL. [`DataSource`](numpy.datasource#numpy.DataSource \"numpy.DataSource\") does not discriminate between the two, the file is accessible if it exists in either location.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.DataSource.exists.htmlnumpy.DataSource.open\n=====================\n\n method\n\n DataSource.open(*path*, *mode='r'*, *encoding=None*, *newline=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/_datasource.py#L487-L533)\n \nOpen and return file-like object.\n\n If `path` is an URL, it will be downloaded, stored in the [`DataSource`](numpy.datasource#numpy.DataSource \"numpy.DataSource\") directory and opened from there.\n\n Parameters \n \n**path**str\n\nLocal file path or URL to open.\n\n \n**mode**{‘r’, ‘w’, ‘a’}, optional\n\nMode to open `path`. Mode ‘r’ for reading, ‘w’ for writing, ‘a’ to append. Available modes depend on the type of object specified by `path`. Default is ‘r’.\n\n \n**encoding**{None, str}, optional\n\nOpen text file with given encoding. The default encoding will be what [`io.open`](https://docs.python.org/3/library/io.html#io.open \"(in Python v3.10)\") uses.\n\n \n**newline**{None, str}, optional\n\nNewline to use when reading text file.\n\n Returns \n \n**out**file object\n\nFile object.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.DataSource.open.htmlnumpy.lib.format.descr_to_dtype\n=================================\n\n lib.format.descr_to_dtype(*descr*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L282-L336)\n \nReturns a dtype based off the given description.\n\n This is essentially the reverse of `dtype_to_descr()`. It will remove the valueless padding fields created by, i.e. simple fields like dtype(‘float32’), and then convert the description to its corresponding dtype.\n\n Parameters \n \n**descr**object\n\nThe object retrieved by dtype.descr. Can be passed to `numpy.dtype()` in order to replicate the input dtype.\n\n Returns \n \n**dtype**dtype\n\nThe dtype constructed by the description.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.descr_to_dtype.htmlnumpy.lib.format.dtype_to_descr\n=================================\n\n lib.format.dtype_to_descr(*dtype*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L246-L280)\n \nGet a serializable descriptor from the dtype.\n\n The .descr attribute of a dtype object cannot be round-tripped through the dtype() constructor. Simple types, like dtype(‘float32’), have a descr which looks like a record array with one field with ‘’ as a name. The dtype() constructor interprets this as a request to give a default name. Instead, we construct descriptor that can be passed to dtype().\n\n Parameters \n \n**dtype**dtype\n\nThe dtype of the array that will be written to disk.\n\n Returns \n \n**descr**object\n\nAn object that can be passed to `numpy.dtype()` in order to replicate the input dtype.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.dtype_to_descr.htmlnumpy.lib.format.header_data_from_array_1_0\n================================================\n\n lib.format.header_data_from_array_1_0(*array*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L338-L363)\n \nGet the dictionary of header metadata from a numpy.ndarray.\n\n Parameters \n \n**array**numpy.ndarray\n\n Returns \n \n**d**dict\n\nThis has the appropriate entries for writing its string representation to the header of the file.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.header_data_from_array_1_0.htmlnumpy.lib.format.magic\n======================\n\n lib.format.magic(*major*, *minor*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L195-L215)\n \nReturn the magic string for the given file format version.\n\n Parameters \n \n**major**int in [0, 255]\n\n**minor**int in [0, 255]\n\n Returns \n \n**magic**str\n\n Raises \n ValueError if the version cannot be formatted.\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.magic.htmlnumpy.lib.format.read_array\n============================\n\n lib.format.read_array(*fp*, *allow_pickle=False*, *pickle_kwargs=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L697-L787)\n \nRead an array from an NPY file.\n\n Parameters \n \n**fp**file_like object\n\nIf this is not a real file object, then this may take extra memory and time.\n\n \n**allow_pickle**bool, optional\n\nWhether to allow writing pickled data. Default: False\n\n Changed in version 1.16.3: Made default False in response to CVE-2019-6446.\n\n \n**pickle_kwargs**dict\n\nAdditional keyword arguments to pass to pickle.load. These are only useful when loading object arrays saved on Python 2 when using Python 3.\n\n Returns \n \n**array**ndarray\n\nThe array from the data on disk.\n\n Raises \n ValueError\n\nIf the data is invalid, or allow_pickle=False and the file contains an object array.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.read_array.htmlnumpy.lib.format.read_array_header_1_0\n==========================================\n\n lib.format.read_array_header_1_0(*fp*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L468-L497)\n \nRead an array header from a filelike object using the 1.0 file format version.\n\n This will leave the file object located just after the header.\n\n Parameters \n \n**fp**filelike object\n\nA file object or something with a `read()` method like a file.\n\n Returns \n \n**shape**tuple of int\n\nThe shape of the array.\n\n \n**fortran_order**bool\n\nThe array data will be written out directly if it is either C-contiguous or Fortran-contiguous. Otherwise, it will be made contiguous before writing it out.\n\n \n**dtype**dtype\n\nThe dtype of the file’s data.\n\n Raises \n ValueError\n\nIf the data is invalid.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.read_array_header_1_0.htmlnumpy.lib.format.read_array_header_2_0\n==========================================\n\n lib.format.read_array_header_2_0(*fp*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L499-L530)\n \nRead an array header from a filelike object using the 2.0 file format version.\n\n This will leave the file object located just after the header.\n\n New in version 1.9.0.\n\n Parameters \n \n**fp**filelike object\n\nA file object or something with a `read()` method like a file.\n\n Returns \n \n**shape**tuple of int\n\nThe shape of the array.\n\n \n**fortran_order**bool\n\nThe array data will be written out directly if it is either C-contiguous or Fortran-contiguous. Otherwise, it will be made contiguous before writing it out.\n\n \n**dtype**dtype\n\nThe dtype of the file’s data.\n\n Raises \n ValueError\n\nIf the data is invalid.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.read_array_header_2_0.htmlnumpy.lib.format.read_magic\n============================\n\n lib.format.read_magic(*fp*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L217-L234)\n \nRead the magic string to get the version of the file format.\n\n Parameters \n \n**fp**filelike object\n\n Returns \n \n**major**int\n\n**minor**int\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.read_magic.htmlnumpy.lib.format.write_array\n=============================\n\n lib.format.write_array(*fp*, *array*, *version=None*, *allow_pickle=True*, *pickle_kwargs=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L625-L694)\n \nWrite an array to an NPY file, including a header.\n\n If the array is neither C-contiguous nor Fortran-contiguous AND the file_like object is not a real file object, this function will have to copy data in memory.\n\n Parameters \n \n**fp**file_like object\n\nAn open, writable file object, or similar object with a `.write()` method.\n\n \n**array**ndarray\n\nThe array to write to disk.\n\n \n**version**(int, int) or None, optional\n\nThe version number of the format. None means use the oldest supported version that is able to store the data. Default: None\n\n \n**allow_pickle**bool, optional\n\nWhether to allow writing pickled data. Default: True\n\n \n**pickle_kwargs**dict, optional\n\nAdditional keyword arguments to pass to pickle.dump, excluding ‘protocol’. These are only useful when pickling objects in object arrays on Python 3 to Python 2 compatible format.\n\n Raises \n ValueError\n\nIf the array cannot be persisted. This includes the case of allow_pickle=False and array being an object array.\n\n Various other errors\n\nIf the array contains Python objects as part of its dtype, the process of pickling them may raise various errors if the objects are not picklable.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.write_array.htmlnumpy.lib.format.write_array_header_1_0\n===========================================\n\n lib.format.write_array_header_1_0(*fp*, *d*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/format.py#L440-L450)\n \nWrite the header for an array using the 1.0 format.\n\n Parameters \n \n**fp**filelike object\n\n**d**dict\n\nThis has the appropriate entries for writing its string representation to the header of the file.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.lib.format.write_array_header_1_0.htmlnumpy.polymul\n=============\n\n numpy.polymul(*a1*, *a2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L909-L969)\n \nFind the product of two polynomials.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Finds the polynomial resulting from the multiplication of the two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree.\n\n Parameters \n \n**a1, a2**array_like or poly1d object\n\nInput polynomials.\n\n Returns \n \n**out**ndarray or poly1d object\n\nThe polynomial resulting from the multiplication of the inputs. If either inputs is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree.\n\n See also\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nA one-dimensional polynomial class.\n\n \n[`poly`](numpy.poly#numpy.poly \"numpy.poly\"), [`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\"), [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\n[`convolve`](numpy.convolve#numpy.convolve \"numpy.convolve\")\n\nArray convolution. Same output as polymul, but has parameter for overlap mode.\n\n #### Examples\n\n \n```\n>>> np.polymul([1, 2, 3], [9, 5, 1])\narray([ 9, 23, 38, 17, 3])\n\n```\n Using poly1d objects:\n\n \n```\n>>> p1 = np.poly1d([1, 2, 3])\n>>> p2 = np.poly1d([9, 5, 1])\n>>> print(p1)\n 2\n1 x + 2 x + 3\n>>> print(p2)\n 2\n9 x + 5 x + 1\n>>> print(np.polymul(p1, p2))\n 4 3 2\n9 x + 23 x + 38 x + 17 x + 3\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polymul.htmlnumpy.polynomial.set_default_printstyle\n=========================================\n\n polynomial.set_default_printstyle(*style*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/__init__.py#L134-L180)\n \nSet the default format for the string representation of polynomials.\n\n Values for `style` must be valid inputs to `__format__`, i.e. ‘ascii’ or ‘unicode’.\n\n Parameters \n \n**style**str\n\nFormat string for default printing style. Must be either ‘ascii’ or ‘unicode’.\n\n #### Notes\n\n The default format depends on the platform: ‘unicode’ is used on Unix-based systems and ‘ascii’ on Windows. This determination is based on default font support for the unicode superscript and subscript ranges.\n\n #### Examples\n\n \n```\n>>> p = np.polynomial.Polynomial([1, 2, 3])\n>>> c = np.polynomial.Chebyshev([1, 2, 3])\n>>> np.polynomial.set_default_printstyle('unicode')\n>>> print(p)\n1.0 + 2.0·x¹ + 3.0·x²\n>>> print(c)\n1.0 + 2.0·T₁(x) + 3.0·T₂(x)\n>>> np.polynomial.set_default_printstyle('ascii')\n>>> print(p)\n1.0 + 2.0 x**1 + 3.0 x**2\n>>> print(c)\n1.0 + 2.0 T_1(x) + 3.0 T_2(x)\n>>> # Formatting supersedes all class/package-level defaults\n>>> print(f\"{p:unicode}\")\n1.0 + 2.0·x¹ + 3.0·x²\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.set_default_printstyle.htmlnumpy.polynomial.polynomial.polydomain\n======================================\n\n polynomial.polynomial.polydomain*=array([-1, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polydomain.htmlnumpy.polynomial.polynomial.polyzero\n====================================\n\n polynomial.polynomial.polyzero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyzero.htmlnumpy.polynomial.polynomial.polyone\n===================================\n\n polynomial.polynomial.polyone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyone.htmlnumpy.polynomial.polynomial.polyx\n=================================\n\n polynomial.polynomial.polyx*=array([0, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyx.htmlnumpy.polynomial.polynomial.polyadd\n===================================\n\n polynomial.polynomial.polyadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L215-L248)\n \nAdd one polynomial to another.\n\n Returns the sum of two polynomials `c1` + `c2`. The arguments are sequences of coefficients from lowest order term to highest, i.e., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of polynomial coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nThe coefficient array representing their sum.\n\n See also\n\n \n[`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polymulx`](numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polypow`](numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> sum = P.polyadd(c1,c2); sum\narray([4., 4., 4.])\n>>> P.polyval(2, sum) # 4 + 4(2) + 4(2**2)\n28.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyadd.htmlnumpy.polynomial.polynomial.polysub\n===================================\n\n polynomial.polynomial.polysub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L251-L285)\n \nSubtract one polynomial from another.\n\n Returns the difference of two polynomials `c1` - `c2`. The arguments are sequences of coefficients from lowest order term to highest, i.e., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of polynomial coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf coefficients representing their difference.\n\n See also\n\n \n[`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polymulx`](numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polypow`](numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> P.polysub(c1,c2)\narray([-2., 0., 2.])\n>>> P.polysub(c2,c1) # -P.polysub(c1,c2)\narray([ 2., 0., -2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polysub.htmlnumpy.polynomial.polynomial.polymulx\n====================================\n\n polynomial.polynomial.polymulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L288-L325)\n \nMultiply a polynomial by x.\n\n Multiply the polynomial `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of polynomial coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n See also\n\n \n[`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polypow`](numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")\n\n #### Notes\n\n New in version 1.5.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polymulx.htmlnumpy.polynomial.polynomial.polymul\n===================================\n\n polynomial.polynomial.polymul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L328-L363)\n \nMultiply one polynomial by another.\n\n Returns the product of two polynomials `c1` * `c2`. The arguments are sequences of coefficients, from lowest order term to highest, e.g., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2.`\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of coefficients representing a polynomial, relative to the “standard” basis, and ordered from lowest order term to highest.\n\n Returns \n \n**out**ndarray\n\nOf the coefficients of their product.\n\n See also\n\n \n[`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polymulx`](numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polypow`](numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> P.polymul(c1,c2)\narray([ 3., 8., 14., 8., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polymul.htmlnumpy.polynomial.polynomial.polydiv\n===================================\n\n polynomial.polynomial.polydiv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L366-L421)\n \nDivide one polynomial by another.\n\n Returns the quotient-with-remainder of two polynomials `c1` / `c2`. The arguments are sequences of coefficients, from lowest order term to highest, e.g., [1,2,3] represents `1 + 2*x + 3*x**2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of polynomial coefficients ordered from low to high.\n\n Returns \n \n**[quo, rem]**ndarrays\n\nOf coefficient series representing the quotient and remainder.\n\n See also\n\n \n[`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polymulx`](numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polypow`](numpy.polynomial.polynomial.polypow#numpy.polynomial.polynomial.polypow \"numpy.polynomial.polynomial.polypow\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> P.polydiv(c1,c2)\n(array([3.]), array([-8., -4.]))\n>>> P.polydiv(c2,c1)\n(array([ 0.33333333]), array([ 2.66666667, 1.33333333])) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polydiv.htmlnumpy.polynomial.polynomial.polypow\n===================================\n\n polynomial.polynomial.polypow(*c*, *pow*, *maxpower=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L424-L460)\n \nRaise a polynomial to a power.\n\n Returns the polynomial `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `1 + 2*x + 3*x**2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of array of series coefficients ordered from low to high degree.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nPower series of power.\n\n See also\n\n \n[`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\"), [`polymulx`](numpy.polynomial.polynomial.polymulx#numpy.polynomial.polynomial.polymulx \"numpy.polynomial.polynomial.polymulx\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> P.polypow([1,2,3], 2)\narray([ 1., 4., 10., 12., 9.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polypow.htmlnumpy.polynomial.polynomial.polyval\n===================================\n\n polynomial.polynomial.polyval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L664-L757)\n \nEvaluate a polynomial at points x.\n\n If `c` is of length `n + 1`, this function returns the value\n\n \\[p(x) = c_0 + c_1 * x + ... + c_n * x^n\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe shape of the returned array is described above.\n\n See also\n\n \n[`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polygrid2d`](numpy.polynomial.polynomial.polygrid2d#numpy.polynomial.polynomial.polygrid2d \"numpy.polynomial.polynomial.polygrid2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\"), [`polygrid3d`](numpy.polynomial.polynomial.polygrid3d#numpy.polynomial.polynomial.polygrid3d \"numpy.polynomial.polynomial.polygrid3d\")\n\n #### Notes\n\n The evaluation uses Horner’s method.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.polynomial import polyval\n>>> polyval(1, [1,2,3])\n6.0\n>>> a = np.arange(4).reshape(2,2)\n>>> a\narray([[0, 1],\n [2, 3]])\n>>> polyval(a, [1,2,3])\narray([[ 1., 6.],\n [17., 34.]])\n>>> coef = np.arange(4).reshape(2,2) # multidimensional coefficients\n>>> coef\narray([[0, 1],\n [2, 3]])\n>>> polyval([1,2], coef, tensor=True)\narray([[2., 4.],\n [4., 7.]])\n>>> polyval([1,2], coef, tensor=False)\narray([2., 7.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyval.htmlnumpy.polynomial.polynomial.polyval2d\n=====================================\n\n polynomial.polynomial.polyval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L848-L895)\n \nEvaluate a 2-D polynomial at points (x, y).\n\n This function returns the value\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * x^i * y^j\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\"), [`polygrid2d`](numpy.polynomial.polynomial.polygrid2d#numpy.polynomial.polynomial.polygrid2d \"numpy.polynomial.polynomial.polygrid2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\"), [`polygrid3d`](numpy.polynomial.polynomial.polygrid3d#numpy.polynomial.polynomial.polygrid3d \"numpy.polynomial.polynomial.polygrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyval2d.htmlnumpy.polynomial.polynomial.polyval3d\n=====================================\n\n polynomial.polynomial.polyval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L951-L999)\n \nEvaluate a 3-D polynomial at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * x^i * y^j * z^k\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\"), [`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polygrid2d`](numpy.polynomial.polynomial.polygrid2d#numpy.polynomial.polynomial.polygrid2d \"numpy.polynomial.polynomial.polygrid2d\"), [`polygrid3d`](numpy.polynomial.polynomial.polygrid3d#numpy.polynomial.polynomial.polygrid3d \"numpy.polynomial.polynomial.polygrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyval3d.htmlnumpy.polynomial.polynomial.polygrid2d\n======================================\n\n polynomial.polynomial.polygrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L898-L948)\n \nEvaluate a 2-D polynomial on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * a^i * b^j\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\"), [`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\"), [`polygrid3d`](numpy.polynomial.polynomial.polygrid3d#numpy.polynomial.polynomial.polygrid3d \"numpy.polynomial.polynomial.polygrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polygrid2d.htmlnumpy.polynomial.polynomial.polygrid3d\n======================================\n\n polynomial.polynomial.polygrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1002-L1055)\n \nEvaluate a 3-D polynomial on the Cartesian product of x, y and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * a^i * b^j * c^k\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\"), [`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polygrid2d`](numpy.polynomial.polynomial.polygrid2d#numpy.polynomial.polynomial.polygrid2d \"numpy.polynomial.polynomial.polygrid2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polygrid3d.htmlnumpy.polynomial.polynomial.polyder\n===================================\n\n polynomial.polynomial.polyder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L463-L542)\n \nDifferentiate a polynomial.\n\n Returns the polynomial coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2` while [[1,2],[1,2]] represents `1 + 1*x + 2*y + 2*x*y` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of polynomial coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nPolynomial coefficients of the derivative.\n\n See also\n\n [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c = (1,2,3,4) # 1 + 2x + 3x**2 + 4x**3\n>>> P.polyder(c) # (d/dx)(c) = 2 + 6x + 12x**2\narray([ 2., 6., 12.])\n>>> P.polyder(c,3) # (d**3/dx**3)(c) = 24\narray([24.])\n>>> P.polyder(c,scl=-1) # (d/d(-x))(c) = -2 - 6x - 12x**2\narray([ -2., -6., -12.])\n>>> P.polyder(c,2,-1) # (d**2/d(-x)**2)(c) = 6 + 24x\narray([ 6., 24.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyder.htmlnumpy.polynomial.polynomial.polyint\n===================================\n\n polynomial.polynomial.polyint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L545-L661)\n \nIntegrate a polynomial.\n\n Returns the polynomial coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients, from low to high degree along each axis, e.g., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2` while [[1,2],[1,2]] represents `1 + 1*x + 2*y + 2*x*y` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\n1-D array of polynomial coefficients, ordered from low to high.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at zero is the first value in the list, the value of the second integral at zero is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nCoefficient array of the integral.\n\n Raises \n ValueError\n\nIf `m < 1`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\) - perhaps not what one would have first thought.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> c = (1,2,3)\n>>> P.polyint(c) # should return array([0, 1, 1, 1])\narray([0., 1., 1., 1.])\n>>> P.polyint(c,3) # should return array([0, 0, 0, 1/6, 1/12, 1/20])\n array([ 0. , 0. , 0. , 0.16666667, 0.08333333, # may vary\n 0.05 ])\n>>> P.polyint(c,k=3) # should return array([3, 1, 1, 1])\narray([3., 1., 1., 1.])\n>>> P.polyint(c,lbnd=-2) # should return array([6, 1, 1, 1])\narray([6., 1., 1., 1.])\n>>> P.polyint(c,scl=-2) # should return array([0, -2, -2, -2])\narray([ 0., -2., -2., -2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyint.htmlnumpy.polynomial.polynomial.polyfromroots\n=========================================\n\n polynomial.polynomial.polyfromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L151-L212)\n \nGenerate a monic polynomial with given roots.\n\n Return the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * x + ... + x^n\\] The coefficient of the last term is 1 for monic polynomials in this form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of the polynomial’s coefficients If all the roots are real, then `out` is also real, otherwise it is complex. (see Examples below).\n\n See also\n\n [`numpy.polynomial.chebyshev.chebfromroots`](numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")\n[`numpy.polynomial.legendre.legfromroots`](numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")\n[`numpy.polynomial.laguerre.lagfromroots`](numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")\n[`numpy.polynomial.hermite.hermfromroots`](numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")\n[`numpy.polynomial.hermite_e.hermefromroots`](numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")\n #### Notes\n\n The coefficients are determined by multiplying together linear factors of the form `(x - r_i)`, i.e.\n\n \\[p(x) = (x - r_0) (x - r_1) ... (x - r_n)\\] where `n == len(roots) - 1`; note that this implies that `1` is always returned for \\(a_n\\).\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> P.polyfromroots((-1,0,1)) # x(x - 1)(x + 1) = x^3 - x\narray([ 0., -1., 0., 1.])\n>>> j = complex(0,1)\n>>> P.polyfromroots((-j,j)) # complex returned, though values are real\narray([1.+0.j, 0.+0.j, 1.+0.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyfromroots.htmlnumpy.polynomial.polynomial.polyroots\n=====================================\n\n polynomial.polynomial.polyroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1405-L1465)\n \nCompute the roots of a polynomial.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * x^i.\\] Parameters \n \n**c**1-D array_like\n\n1-D array of polynomial coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the polynomial. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.chebyshev.chebroots`](numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")\n[`numpy.polynomial.legendre.legroots`](numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")\n[`numpy.polynomial.laguerre.lagroots`](numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")\n[`numpy.polynomial.hermite.hermroots`](numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")\n[`numpy.polynomial.hermite_e.hermeroots`](numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n #### Examples\n\n \n```\n>>> import numpy.polynomial.polynomial as poly\n>>> poly.polyroots(poly.polyfromroots((-1,0,1)))\narray([-1., 0., 1.])\n>>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype\ndtype('float64')\n>>> j = complex(0,1)\n>>> poly.polyroots(poly.polyfromroots((-j,0,j)))\narray([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyroots.htmlnumpy.polynomial.polynomial.polyvalfromroots\n============================================\n\n polynomial.polynomial.polyvalfromroots(*x*, *r*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L760-L845)\n \nEvaluate a polynomial specified by its roots at points x.\n\n If `r` is of length `N`, this function returns the value\n\n \\[p(x) = \\prod_{n=1}^{N} (x - r_n)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `r`.\n\n If `r` is a 1-D array, then `p(x)` will have the same shape as `x`. If `r` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is `True` the shape will be r.shape[1:] + x.shape; that is, each polynomial is evaluated at every value of `x`. If `tensor` is `False`, the shape will be r.shape[1:]; that is, each polynomial is evaluated only for the corresponding broadcast value of `x`. Note that scalars have shape (,).\n\n New in version 1.12.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with with themselves and with the elements of `r`.\n\n \n**r**array_like\n\nArray of roots. If `r` is multidimensional the first index is the root index, while the remaining indices enumerate multiple polynomials. For instance, in the two dimensional case the roots of each polynomial may be thought of as stored in the columns of `r`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the roots array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `r` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `r` for the evaluation. This keyword is useful when `r` is multidimensional. The default value is True.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe shape of the returned array is described above.\n\n See also\n\n \n[`polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\"), [`polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\"), [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.polynomial import polyvalfromroots\n>>> polyvalfromroots(1, [1,2,3])\n0.0\n>>> a = np.arange(4).reshape(2,2)\n>>> a\narray([[0, 1],\n [2, 3]])\n>>> polyvalfromroots(a, [-1, 0, 1])\narray([[-0., 0.],\n [ 6., 24.]])\n>>> r = np.arange(-2, 2).reshape(2,2) # multidimensional coefficients\n>>> r # each column of r defines one polynomial\narray([[-2, -1],\n [ 0, 1]])\n>>> b = [-2, 1]\n>>> polyvalfromroots(b, r, tensor=True)\narray([[-0., 3.],\n [ 3., 0.]])\n>>> polyvalfromroots(b, r, tensor=False)\narray([-0., 0.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyvalfromroots.htmlnumpy.polynomial.polynomial.polyvander2d\n========================================\n\n polynomial.polynomial.polyvander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1112-L1157)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = x^i * y^j,\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the powers of `x` and `y`.\n\n If `V = polyvander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `polyval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D polynomials of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg([1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`polyvander`](numpy.polynomial.polynomial.polyvander#numpy.polynomial.polynomial.polyvander \"numpy.polynomial.polynomial.polyvander\"), [`polyvander3d`](numpy.polynomial.polynomial.polyvander3d#numpy.polynomial.polynomial.polyvander3d \"numpy.polynomial.polynomial.polyvander3d\"), [`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyvander2d.htmlnumpy.polynomial.polynomial.polyvander3d\n========================================\n\n polynomial.polynomial.polyvander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1160-L1211)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = x^i * y^j * z^k,\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the powers of `x`, `y`, and `z`.\n\n If `V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `polyval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D polynomials of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg([1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`polyvander`](numpy.polynomial.polynomial.polyvander#numpy.polynomial.polynomial.polyvander \"numpy.polynomial.polynomial.polyvander\"), [`polyvander3d`](#numpy.polynomial.polynomial.polyvander3d \"numpy.polynomial.polynomial.polyvander3d\"), [`polyval2d`](numpy.polynomial.polynomial.polyval2d#numpy.polynomial.polynomial.polyval2d \"numpy.polynomial.polynomial.polyval2d\"), [`polyval3d`](numpy.polynomial.polynomial.polyval3d#numpy.polynomial.polynomial.polyval3d \"numpy.polynomial.polynomial.polyval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyvander3d.htmlnumpy.polynomial.polynomial.polycompanion\n=========================================\n\n polynomial.polynomial.polycompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1365-L1402)\n \nReturn the companion matrix of c.\n\n The companion matrix for power series cannot be made symmetric by scaling the basis, so this function differs from those for the orthogonal polynomials.\n\n Parameters \n \n**c**array_like\n\n1-D array of polynomial coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nCompanion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polycompanion.htmlnumpy.polynomial.polynomial.polyfit\n===================================\n\n polynomial.polynomial.polyfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L1214-L1362)\n \nLeast-squares fit of a polynomial to data.\n\n Return the coefficients of a polynomial of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * x + ... + c_n * x^n,\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (`M`,)\n\nx-coordinates of the `M` sample (data) points `(x[i], y[i])`.\n\n \n**y**array_like, shape (`M`,) or (`M`, `K`)\n\ny-coordinates of the sample points. Several sets of sample points sharing the same x-coordinates can be (independently) fit with one call to [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\") by passing in for `y` a 2-D array that contains one data set per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than `rcond`, relative to the largest singular value, will be ignored. The default value is `len(x)*eps`, where `eps` is the relative precision of the platform’s float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining the nature of the return value. When `False` (the default) just the coefficients are returned; when `True`, diagnostic information from the singular value decomposition (used to solve the fit’s matrix equation) is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n Returns \n \n**coef**ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`)\n\nPolynomial coefficients ordered from low to high. If `y` was 2-D, the coefficients in column `k` of `coef` represent the polynomial fit to the data in `y`’s `k`-th column.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Raises \n RankWarning\n\nRaised if the matrix in the least-squares fit is rank deficient. The warning is only raised if `full == False`. The warnings can be turned off by:\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.chebyshev.chebfit`](numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")\n[`numpy.polynomial.legendre.legfit`](numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")\n[`numpy.polynomial.laguerre.lagfit`](numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")\n[`numpy.polynomial.hermite.hermfit`](numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")\n[`numpy.polynomial.hermite_e.hermefit`](numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")\n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\nEvaluates a polynomial.\n\n [`polyvander`](numpy.polynomial.polynomial.polyvander#numpy.polynomial.polynomial.polyvander \"numpy.polynomial.polynomial.polyvander\")\n\nVandermonde matrix for powers.\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the polynomial `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where the \\(w_j\\) are the weights. This problem is solved by setting up the (typically) over-determined matrix equation:\n\n \\[V(x) * c = w * y,\\] where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected (and [`full`](numpy.full#numpy.full \"numpy.full\") == `False`), a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be raised. This means that the coefficient values may be poorly determined. Fitting to a lower order polynomial will usually get rid of the warning (but may not be what you want, of course; if you have independent reason(s) for choosing the degree which isn’t working, you may have to: a) reconsider those reasons, and/or b) reconsider the quality of your data). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Polynomial fits using double precision tend to “fail” at about (polynomial) degree 20. Fits using Chebyshev or Legendre series are generally better conditioned, but much can still depend on the distribution of the sample points and the smoothness of the data. If the quality of the fit is inadequate, splines may be a good alternative.\n\n #### Examples\n\n \n```\n>>> np.random.seed(123)\n>>> from numpy.polynomial import polynomial as P\n>>> x = np.linspace(-1,1,51) # x \"data\": [-1, -0.96, ..., 0.96, 1]\n>>> y = x**3 - x + np.random.randn(len(x)) # x^3 - x + N(0,1) \"noise\"\n>>> c, stats = P.polyfit(x,y,3,full=True)\n>>> np.random.seed(123)\n>>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1\narray([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) # may vary\n>>> stats # note the large SSR, explaining the rather poor results\n [array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, # may vary\n 0.28853036]), 1.1324274851176597e-014]\n\n```\n Same thing without the added noise\n\n \n```\n>>> y = x**3 - x\n>>> c, stats = P.polyfit(x,y,3,full=True)\n>>> c # c[0], c[2] should be \"very close to 0\", c[1] ~= -1, c[3] ~= 1\narray([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16, 1.00000000e+00])\n>>> stats # note the minuscule SSR\n[array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, # may vary\n 0.50443316, 0.28853036]), 1.1324274851176597e-014]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyfit.htmlnumpy.polynomial.polynomial.polytrim\n====================================\n\n polynomial.polynomial.polytrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polytrim.htmlnumpy.polynomial.polynomial.polyline\n====================================\n\n polynomial.polynomial.polyline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polynomial.py#L113-L148)\n \nReturns an array representing a linear polynomial.\n\n Parameters \n \n**off, scl**scalars\n\nThe “y-intercept” and “slope” of the line, respectively.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the linear polynomial `off +\nscl*x`.\n\n See also\n\n [`numpy.polynomial.chebyshev.chebline`](numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")\n[`numpy.polynomial.legendre.legline`](numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")\n[`numpy.polynomial.laguerre.lagline`](numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")\n[`numpy.polynomial.hermite.hermline`](numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")\n[`numpy.polynomial.hermite_e.hermeline`](numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polynomial as P\n>>> P.polyline(1,-1)\narray([ 1, -1])\n>>> P.polyval(1, P.polyline(1,-1)) # should be 0\n0.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.polyline.htmlnumpy.polynomial.chebyshev.Chebyshev\n====================================\n\n *class*numpy.polynomial.chebyshev.Chebyshev(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1994-L2075)\n \nA Chebyshev series class.\n\n The Chebyshev class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the methods listed below.\n\n Parameters \n \n**coef**array_like\n\nChebyshev coefficients in order of increasing degree, i.e., `(1, 2, 3)` gives `1*T_0(x) + 2*T_1(x) + 3*T_2(x)`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [-1, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.chebyshev.chebyshev.domain#numpy.polynomial.chebyshev.Chebyshev.domain \"numpy.polynomial.chebyshev.Chebyshev.domain\") for its use. The default value is [-1, 1].\n\n New in version 1.6.0.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.chebyshev.chebyshev.__call__#numpy.polynomial.chebyshev.Chebyshev.__call__ \"numpy.polynomial.chebyshev.Chebyshev.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.chebyshev.chebyshev.basis#numpy.polynomial.chebyshev.Chebyshev.basis \"numpy.polynomial.chebyshev.Chebyshev.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.chebyshev.chebyshev.cast#numpy.polynomial.chebyshev.Chebyshev.cast \"numpy.polynomial.chebyshev.Chebyshev.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.chebyshev.chebyshev.convert#numpy.polynomial.chebyshev.Chebyshev.convert \"numpy.polynomial.chebyshev.Chebyshev.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.chebyshev.chebyshev.copy#numpy.polynomial.chebyshev.Chebyshev.copy \"numpy.polynomial.chebyshev.Chebyshev.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.chebyshev.chebyshev.cutdeg#numpy.polynomial.chebyshev.Chebyshev.cutdeg \"numpy.polynomial.chebyshev.Chebyshev.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.chebyshev.chebyshev.degree#numpy.polynomial.chebyshev.Chebyshev.degree \"numpy.polynomial.chebyshev.Chebyshev.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.chebyshev.chebyshev.deriv#numpy.polynomial.chebyshev.Chebyshev.deriv \"numpy.polynomial.chebyshev.Chebyshev.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.chebyshev.chebyshev.fit#numpy.polynomial.chebyshev.Chebyshev.fit \"numpy.polynomial.chebyshev.Chebyshev.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.chebyshev.chebyshev.fromroots#numpy.polynomial.chebyshev.Chebyshev.fromroots \"numpy.polynomial.chebyshev.Chebyshev.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.chebyshev.chebyshev.has_samecoef#numpy.polynomial.chebyshev.Chebyshev.has_samecoef \"numpy.polynomial.chebyshev.Chebyshev.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.chebyshev.chebyshev.has_samedomain#numpy.polynomial.chebyshev.Chebyshev.has_samedomain \"numpy.polynomial.chebyshev.Chebyshev.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.chebyshev.chebyshev.has_sametype#numpy.polynomial.chebyshev.Chebyshev.has_sametype \"numpy.polynomial.chebyshev.Chebyshev.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.chebyshev.chebyshev.has_samewindow#numpy.polynomial.chebyshev.Chebyshev.has_samewindow \"numpy.polynomial.chebyshev.Chebyshev.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.chebyshev.chebyshev.identity#numpy.polynomial.chebyshev.Chebyshev.identity \"numpy.polynomial.chebyshev.Chebyshev.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.chebyshev.chebyshev.integ#numpy.polynomial.chebyshev.Chebyshev.integ \"numpy.polynomial.chebyshev.Chebyshev.integ\")([m, k, lbnd]) | Integrate. |\n| [`interpolate`](numpy.polynomial.chebyshev.chebyshev.interpolate#numpy.polynomial.chebyshev.Chebyshev.interpolate \"numpy.polynomial.chebyshev.Chebyshev.interpolate\")(func, deg[, domain, args]) | Interpolate a function at the Chebyshev points of the first kind. |\n| [`linspace`](numpy.polynomial.chebyshev.chebyshev.linspace#numpy.polynomial.chebyshev.Chebyshev.linspace \"numpy.polynomial.chebyshev.Chebyshev.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.chebyshev.chebyshev.mapparms#numpy.polynomial.chebyshev.Chebyshev.mapparms \"numpy.polynomial.chebyshev.Chebyshev.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.chebyshev.chebyshev.roots#numpy.polynomial.chebyshev.Chebyshev.roots \"numpy.polynomial.chebyshev.Chebyshev.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.chebyshev.chebyshev.trim#numpy.polynomial.chebyshev.Chebyshev.trim \"numpy.polynomial.chebyshev.Chebyshev.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.chebyshev.chebyshev.truncate#numpy.polynomial.chebyshev.Chebyshev.truncate \"numpy.polynomial.chebyshev.Chebyshev.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.htmlnumpy.polynomial.chebyshev.chebdomain\n=====================================\n\n polynomial.chebyshev.chebdomain*=array([-1, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebdomain.htmlnumpy.polynomial.chebyshev.chebzero\n===================================\n\n polynomial.chebyshev.chebzero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebzero.htmlnumpy.polynomial.chebyshev.chebone\n==================================\n\n polynomial.chebyshev.chebone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebone.htmlnumpy.polynomial.chebyshev.chebx\n================================\n\n polynomial.chebyshev.chebx*=array([0, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebx.htmlnumpy.polynomial.chebyshev.chebadd\n==================================\n\n polynomial.chebyshev.chebadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L569-L608)\n \nAdd one Chebyshev series to another.\n\n Returns the sum of two Chebyshev series `c1` + `c2`. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series `T_0 + 2*T_1 + 3*T_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Chebyshev series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the Chebyshev series of their sum.\n\n See also\n\n \n[`chebsub`](numpy.polynomial.chebyshev.chebsub#numpy.polynomial.chebyshev.chebsub \"numpy.polynomial.chebyshev.chebsub\"), [`chebmulx`](numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\"), [`chebmul`](numpy.polynomial.chebyshev.chebmul#numpy.polynomial.chebyshev.chebmul \"numpy.polynomial.chebyshev.chebmul\"), [`chebdiv`](numpy.polynomial.chebyshev.chebdiv#numpy.polynomial.chebyshev.chebdiv \"numpy.polynomial.chebyshev.chebdiv\"), [`chebpow`](numpy.polynomial.chebyshev.chebpow#numpy.polynomial.chebyshev.chebpow \"numpy.polynomial.chebyshev.chebpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the sum of two Chebyshev series is a Chebyshev series (without having to “reproject” the result onto the basis set) so addition, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> C.chebadd(c1,c2)\narray([4., 4., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebadd.htmlnumpy.polynomial.chebyshev.chebsub\n==================================\n\n polynomial.chebyshev.chebsub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L611-L652)\n \nSubtract one Chebyshev series from another.\n\n Returns the difference of two Chebyshev series `c1` - `c2`. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series `T_0 + 2*T_1 + 3*T_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Chebyshev series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Chebyshev series coefficients representing their difference.\n\n See also\n\n \n[`chebadd`](numpy.polynomial.chebyshev.chebadd#numpy.polynomial.chebyshev.chebadd \"numpy.polynomial.chebyshev.chebadd\"), [`chebmulx`](numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\"), [`chebmul`](numpy.polynomial.chebyshev.chebmul#numpy.polynomial.chebyshev.chebmul \"numpy.polynomial.chebyshev.chebmul\"), [`chebdiv`](numpy.polynomial.chebyshev.chebdiv#numpy.polynomial.chebyshev.chebdiv \"numpy.polynomial.chebyshev.chebdiv\"), [`chebpow`](numpy.polynomial.chebyshev.chebpow#numpy.polynomial.chebyshev.chebpow \"numpy.polynomial.chebyshev.chebpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the difference of two Chebyshev series is a Chebyshev series (without having to “reproject” the result onto the basis set) so subtraction, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> C.chebsub(c1,c2)\narray([-2., 0., 2.])\n>>> C.chebsub(c2,c1) # -C.chebsub(c1,c2)\narray([ 2., 0., -2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebsub.htmlnumpy.polynomial.chebyshev.chebmulx\n===================================\n\n polynomial.chebyshev.chebmulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L655-L698)\n \nMultiply a Chebyshev series by x.\n\n Multiply the polynomial `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of Chebyshev series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n #### Notes\n\n New in version 1.5.0.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> C.chebmulx([1,2,3])\narray([1. , 2.5, 1. , 1.5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebmulx.htmlnumpy.polynomial.chebyshev.chebmul\n==================================\n\n polynomial.chebyshev.chebmul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L701-L747)\n \nMultiply one Chebyshev series by another.\n\n Returns the product of two Chebyshev series `c1` * `c2`. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series `T_0 + 2*T_1 + 3*T_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Chebyshev series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Chebyshev series coefficients representing their product.\n\n See also\n\n \n[`chebadd`](numpy.polynomial.chebyshev.chebadd#numpy.polynomial.chebyshev.chebadd \"numpy.polynomial.chebyshev.chebadd\"), [`chebsub`](numpy.polynomial.chebyshev.chebsub#numpy.polynomial.chebyshev.chebsub \"numpy.polynomial.chebyshev.chebsub\"), [`chebmulx`](numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\"), [`chebdiv`](numpy.polynomial.chebyshev.chebdiv#numpy.polynomial.chebyshev.chebdiv \"numpy.polynomial.chebyshev.chebdiv\"), [`chebpow`](numpy.polynomial.chebyshev.chebpow#numpy.polynomial.chebyshev.chebpow \"numpy.polynomial.chebyshev.chebpow\")\n\n #### Notes\n\n In general, the (polynomial) product of two C-series results in terms that are not in the Chebyshev polynomial basis set. Thus, to express the product as a C-series, it is typically necessary to “reproject” the product onto said basis set, which typically produces “unintuitive live” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> C.chebmul(c1,c2) # multiplication requires \"reprojection\"\narray([ 6.5, 12. , 12. , 4. , 1.5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebmul.htmlnumpy.polynomial.chebyshev.chebdiv\n==================================\n\n polynomial.chebyshev.chebdiv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L750-L814)\n \nDivide one Chebyshev series by another.\n\n Returns the quotient-with-remainder of two Chebyshev series `c1` / `c2`. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series `T_0 + 2*T_1 + 3*T_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Chebyshev series coefficients ordered from low to high.\n\n Returns \n \n**[quo, rem]**ndarrays\n\nOf Chebyshev series coefficients representing the quotient and remainder.\n\n See also\n\n \n[`chebadd`](numpy.polynomial.chebyshev.chebadd#numpy.polynomial.chebyshev.chebadd \"numpy.polynomial.chebyshev.chebadd\"), [`chebsub`](numpy.polynomial.chebyshev.chebsub#numpy.polynomial.chebyshev.chebsub \"numpy.polynomial.chebyshev.chebsub\"), [`chebmulx`](numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\"), [`chebmul`](numpy.polynomial.chebyshev.chebmul#numpy.polynomial.chebyshev.chebmul \"numpy.polynomial.chebyshev.chebmul\"), [`chebpow`](numpy.polynomial.chebyshev.chebpow#numpy.polynomial.chebyshev.chebpow \"numpy.polynomial.chebyshev.chebpow\")\n\n #### Notes\n\n In general, the (polynomial) division of one C-series by another results in quotient and remainder terms that are not in the Chebyshev polynomial basis set. Thus, to express these results as C-series, it is typically necessary to “reproject” the results onto said basis set, which typically produces “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> C.chebdiv(c1,c2) # quotient \"intuitive,\" remainder not\n(array([3.]), array([-8., -4.]))\n>>> c2 = (0,1,2,3)\n>>> C.chebdiv(c2,c1) # neither \"intuitive\"\n(array([0., 2.]), array([-2., -4.]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebdiv.htmlnumpy.polynomial.chebyshev.chebpow\n==================================\n\n polynomial.chebyshev.chebpow(*c*, *pow*, *maxpower=16*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L817-L872)\n \nRaise a Chebyshev series to a power.\n\n Returns the Chebyshev series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `T_0 + 2*T_1 + 3*T_2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of Chebyshev series coefficients ordered from low to high.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nChebyshev series of power.\n\n See also\n\n \n[`chebadd`](numpy.polynomial.chebyshev.chebadd#numpy.polynomial.chebyshev.chebadd \"numpy.polynomial.chebyshev.chebadd\"), [`chebsub`](numpy.polynomial.chebyshev.chebsub#numpy.polynomial.chebyshev.chebsub \"numpy.polynomial.chebyshev.chebsub\"), [`chebmulx`](numpy.polynomial.chebyshev.chebmulx#numpy.polynomial.chebyshev.chebmulx \"numpy.polynomial.chebyshev.chebmulx\"), [`chebmul`](numpy.polynomial.chebyshev.chebmul#numpy.polynomial.chebyshev.chebmul \"numpy.polynomial.chebyshev.chebmul\"), [`chebdiv`](numpy.polynomial.chebyshev.chebdiv#numpy.polynomial.chebyshev.chebdiv \"numpy.polynomial.chebyshev.chebdiv\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> C.chebpow([1, 2, 3, 4], 2)\narray([15.5, 22. , 16. , ..., 12.5, 12. , 8. ])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebpow.htmlnumpy.polynomial.chebyshev.chebval\n==================================\n\n polynomial.chebyshev.chebval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1094-L1175)\n \nEvaluate a Chebyshev series at points x.\n\n If `c` is of length `n + 1`, this function returns the value:\n\n \\[p(x) = c_0 * T_0(x) + c_1 * T_1(x) + ... + c_n * T_n(x)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, algebra_like\n\nThe shape of the return value is described above.\n\n See also\n\n \n[`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebgrid2d`](numpy.polynomial.chebyshev.chebgrid2d#numpy.polynomial.chebyshev.chebgrid2d \"numpy.polynomial.chebyshev.chebgrid2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\"), [`chebgrid3d`](numpy.polynomial.chebyshev.chebgrid3d#numpy.polynomial.chebyshev.chebgrid3d \"numpy.polynomial.chebyshev.chebgrid3d\")\n\n #### Notes\n\n The evaluation uses Clenshaw recursion, aka synthetic division.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebval.htmlnumpy.polynomial.chebyshev.chebval2d\n====================================\n\n polynomial.chebyshev.chebval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1178-L1224)\n \nEvaluate a 2-D Chebyshev series at points (x, y).\n\n This function returns the values:\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * T_i(x) * T_j(y)\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than 2 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional Chebyshev series at points formed from pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`chebval`](numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\"), [`chebgrid2d`](numpy.polynomial.chebyshev.chebgrid2d#numpy.polynomial.chebyshev.chebgrid2d \"numpy.polynomial.chebyshev.chebgrid2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\"), [`chebgrid3d`](numpy.polynomial.chebyshev.chebgrid3d#numpy.polynomial.chebyshev.chebgrid3d \"numpy.polynomial.chebyshev.chebgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebval2d.htmlnumpy.polynomial.chebyshev.chebval3d\n====================================\n\n polynomial.chebyshev.chebval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1280-L1328)\n \nEvaluate a 3-D Chebyshev series at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * T_i(x) * T_j(y) * T_k(z)\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`chebval`](numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\"), [`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebgrid2d`](numpy.polynomial.chebyshev.chebgrid2d#numpy.polynomial.chebyshev.chebgrid2d \"numpy.polynomial.chebyshev.chebgrid2d\"), [`chebgrid3d`](numpy.polynomial.chebyshev.chebgrid3d#numpy.polynomial.chebyshev.chebgrid3d \"numpy.polynomial.chebyshev.chebgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebval3d.htmlnumpy.polynomial.chebyshev.chebgrid2d\n=====================================\n\n polynomial.chebyshev.chebgrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1227-L1277)\n \nEvaluate a 2-D Chebyshev series on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * T_i(a) * T_j(b),\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional Chebyshev series at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`chebval`](numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\"), [`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\"), [`chebgrid3d`](numpy.polynomial.chebyshev.chebgrid3d#numpy.polynomial.chebyshev.chebgrid3d \"numpy.polynomial.chebyshev.chebgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebgrid2d.htmlnumpy.polynomial.chebyshev.chebgrid3d\n=====================================\n\n polynomial.chebyshev.chebgrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1331-L1384)\n \nEvaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * T_i(a) * T_j(b) * T_k(c)\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`chebval`](numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\"), [`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebgrid2d`](numpy.polynomial.chebyshev.chebgrid2d#numpy.polynomial.chebyshev.chebgrid2d \"numpy.polynomial.chebyshev.chebgrid2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebgrid3d.htmlnumpy.polynomial.chebyshev.chebder\n==================================\n\n polynomial.chebyshev.chebder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L875-L964)\n \nDifferentiate a Chebyshev series.\n\n Returns the Chebyshev series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `1*T_0 + 2*T_1 + 3*T_2` while [[1,2],[1,2]] represents `1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) +\n2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Chebyshev series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nChebyshev series of the derivative.\n\n See also\n\n [`chebint`](numpy.polynomial.chebyshev.chebint#numpy.polynomial.chebyshev.chebint \"numpy.polynomial.chebyshev.chebint\")\n #### Notes\n\n In general, the result of differentiating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c = (1,2,3,4)\n>>> C.chebder(c)\narray([14., 12., 24.])\n>>> C.chebder(c,3)\narray([96.])\n>>> C.chebder(c,scl=-1)\narray([-14., -12., -24.])\n>>> C.chebder(c,2,-1)\narray([12., 96.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebder.htmlnumpy.polynomial.chebyshev.chebint\n==================================\n\n polynomial.chebyshev.chebint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L967-L1091)\n \nIntegrate a Chebyshev series.\n\n Returns the Chebyshev series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `T_0 + 2*T_1 + 3*T_2` while [[1,2],[1,2]] represents `1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) +\n2*T_1(x)*T_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Chebyshev series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at zero is the first value in the list, the value of the second integral at zero is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nC-series coefficients of the integral.\n\n Raises \n ValueError\n\nIf `m < 1`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`chebder`](numpy.polynomial.chebyshev.chebder#numpy.polynomial.chebyshev.chebder \"numpy.polynomial.chebyshev.chebder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\)- perhaps not what one would have first thought.\n\n Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import chebyshev as C\n>>> c = (1,2,3)\n>>> C.chebint(c)\narray([ 0.5, -0.5, 0.5, 0.5])\n>>> C.chebint(c,3)\narray([ 0.03125 , -0.1875 , 0.04166667, -0.05208333, 0.01041667, # may vary\n 0.00625 ])\n>>> C.chebint(c, k=3)\narray([ 3.5, -0.5, 0.5, 0.5])\n>>> C.chebint(c,lbnd=-2)\narray([ 8.5, -0.5, 0.5, 0.5])\n>>> C.chebint(c,scl=-2)\narray([-1., 1., -1., -1.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebint.htmlnumpy.polynomial.chebyshev.chebfromroots\n========================================\n\n polynomial.chebyshev.chebfromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L514-L566)\n \nGenerate a Chebyshev series with given roots.\n\n The function returns the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] in Chebyshev form, where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x)\\] The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below).\n\n See also\n\n [`numpy.polynomial.polynomial.polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")\n[`numpy.polynomial.legendre.legfromroots`](numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")\n[`numpy.polynomial.laguerre.lagfromroots`](numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")\n[`numpy.polynomial.hermite.hermfromroots`](numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")\n[`numpy.polynomial.hermite_e.hermefromroots`](numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")\n #### Examples\n\n \n```\n>>> import numpy.polynomial.chebyshev as C\n>>> C.chebfromroots((-1,0,1)) # x^3 - x relative to the standard basis\narray([ 0. , -0.25, 0. , 0.25])\n>>> j = complex(0,1)\n>>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis\narray([1.5+0.j, 0. +0.j, 0.5+0.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebfromroots.htmlnumpy.polynomial.chebyshev.chebroots\n====================================\n\n polynomial.chebyshev.chebroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1719-L1777)\n \nCompute the roots of a Chebyshev series.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * T_i(x).\\] Parameters \n \n**c**1-D array_like\n\n1-D array of coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.polynomial.polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")\n[`numpy.polynomial.legendre.legroots`](numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")\n[`numpy.polynomial.laguerre.lagroots`](numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")\n[`numpy.polynomial.hermite.hermroots`](numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")\n[`numpy.polynomial.hermite_e.hermeroots`](numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n The Chebyshev series basis polynomials aren’t powers of `x` so the results of this function may seem unintuitive.\n\n #### Examples\n\n \n```\n>>> import numpy.polynomial.chebyshev as cheb\n>>> cheb.chebroots((-1, 1,-1, 1)) # T3 - T2 + T1 - T0 has real roots\narray([ -5.00000000e-01, 2.60860684e-17, 1.00000000e+00]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebroots.htmlnumpy.polynomial.chebyshev.chebvander\n=====================================\n\n polynomial.chebyshev.chebvander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1387-L1437)\n \nPseudo-Vandermonde matrix of given degree.\n\n Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., i] = T_i(x),\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the Chebyshev polynomial.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the matrix `V = chebvander(x, n)`, then `np.dot(V, c)` and `chebval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Chebyshev series of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray\n\nThe pseudo Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding Chebyshev polynomial. The dtype will be the same as the converted `x`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebvander.htmlnumpy.polynomial.chebyshev.chebvander2d\n=======================================\n\n polynomial.chebyshev.chebvander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1440-L1490)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = T_i(x) * T_j(y),\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the Chebyshev polynomials.\n\n If `V = chebvander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `chebval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D Chebyshev series of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`chebvander`](numpy.polynomial.chebyshev.chebvander#numpy.polynomial.chebyshev.chebvander \"numpy.polynomial.chebyshev.chebvander\"), [`chebvander3d`](numpy.polynomial.chebyshev.chebvander3d#numpy.polynomial.chebyshev.chebvander3d \"numpy.polynomial.chebyshev.chebvander3d\"), [`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebvander2d.htmlnumpy.polynomial.chebyshev.chebvander3d\n=======================================\n\n polynomial.chebyshev.chebvander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1493-L1544)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = T_i(x)*T_j(y)*T_k(z),\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the Chebyshev polynomials.\n\n If `V = chebvander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `chebval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D Chebyshev series of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`chebvander`](numpy.polynomial.chebyshev.chebvander#numpy.polynomial.chebyshev.chebvander \"numpy.polynomial.chebyshev.chebvander\"), [`chebvander3d`](#numpy.polynomial.chebyshev.chebvander3d \"numpy.polynomial.chebyshev.chebvander3d\"), [`chebval2d`](numpy.polynomial.chebyshev.chebval2d#numpy.polynomial.chebyshev.chebval2d \"numpy.polynomial.chebyshev.chebval2d\"), [`chebval3d`](numpy.polynomial.chebyshev.chebval3d#numpy.polynomial.chebyshev.chebval3d \"numpy.polynomial.chebyshev.chebval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebvander3d.htmlnumpy.polynomial.chebyshev.chebgauss\n====================================\n\n polynomial.chebyshev.chebgauss(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1847-L1889)\n \nGauss-Chebyshev quadrature.\n\n Computes the sample points and weights for Gauss-Chebyshev quadrature. These sample points and weights will correctly integrate polynomials of degree \\(2*deg - 1\\) or less over the interval \\([-1, 1]\\) with the weight function \\(f(x) = 1/\\sqrt{1 - x^2}\\).\n\n Parameters \n \n**deg**int\n\nNumber of sample points and weights. It must be >= 1.\n\n Returns \n \n**x**ndarray\n\n1-D ndarray containing the sample points.\n\n \n**y**ndarray\n\n1-D ndarray containing the weights.\n\n #### Notes\n\n New in version 1.7.0.\n\n The results have only been tested up to degree 100, higher degrees may be problematic. For Gauss-Chebyshev there are closed form solutions for the sample points and weights. If n = `deg`, then\n\n \\[x_i = \\cos(\\pi (2 i - 1) / (2 n))\\] \\[w_i = \\pi / n\\] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebgauss.htmlnumpy.polynomial.chebyshev.chebweight\n=====================================\n\n polynomial.chebyshev.chebweight(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1892-L1917)\n \nThe weight function of the Chebyshev polynomials.\n\n The weight function is \\(1/\\sqrt{1 - x^2}\\) and the interval of integration is \\([-1, 1]\\). The Chebyshev polynomials are orthogonal, but not normalized, with respect to this weight function.\n\n Parameters \n \n**x**array_like\n\nValues at which the weight function will be computed.\n\n Returns \n \n**w**ndarray\n\nThe weight function at `x`.\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebweight.htmlnumpy.polynomial.chebyshev.chebcompanion\n========================================\n\n polynomial.chebyshev.chebcompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1674-L1716)\n \nReturn the scaled companion matrix of c.\n\n The basis polynomials are scaled so that the companion matrix is symmetric when `c` is a Chebyshev basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if [`numpy.linalg.eigvalsh`](numpy.linalg.eigvalsh#numpy.linalg.eigvalsh \"numpy.linalg.eigvalsh\") is used to obtain them.\n\n Parameters \n \n**c**array_like\n\n1-D array of Chebyshev series coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nScaled companion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebcompanion.htmlnumpy.polynomial.chebyshev.chebfit\n==================================\n\n polynomial.chebyshev.chebfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1547-L1671)\n \nLeast squares fit of Chebyshev series to data.\n\n Return the coefficients of a Chebyshev series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x),\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer, all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n Returns \n \n**coef**ndarray, shape (M,) or (M, K)\n\nChebyshev coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`. The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.polynomial.polyfit`](numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")\n[`numpy.polynomial.legendre.legfit`](numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")\n[`numpy.polynomial.laguerre.lagfit`](numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")\n[`numpy.polynomial.hermite.hermfit`](numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")\n[`numpy.polynomial.hermite_e.hermefit`](numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")\n[`chebval`](numpy.polynomial.chebyshev.chebval#numpy.polynomial.chebyshev.chebval \"numpy.polynomial.chebyshev.chebval\")\n\nEvaluates a Chebyshev series.\n\n [`chebvander`](numpy.polynomial.chebyshev.chebvander#numpy.polynomial.chebyshev.chebvander \"numpy.polynomial.chebyshev.chebvander\")\n\nVandermonde matrix of Chebyshev series.\n\n [`chebweight`](numpy.polynomial.chebyshev.chebweight#numpy.polynomial.chebyshev.chebweight \"numpy.polynomial.chebyshev.chebweight\")\n\nChebyshev weight function.\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the Chebyshev series `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where \\(w_j\\) are the weights. This problem is solved by setting up as the (typically) overdetermined matrix equation\n\n \\[V(x) * c = w * y,\\] where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected, then a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Fits using Chebyshev series are usually better conditioned than fits using power series, but much can depend on the distribution of the sample points and the smoothness of the data. If the quality of the fit is inadequate splines may be a good alternative.\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebfit.htmlnumpy.polynomial.chebyshev.chebpts1\n===================================\n\n polynomial.chebyshev.chebpts1(*npts*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1920-L1954)\n \nChebyshev points of the first kind.\n\n The Chebyshev points of the first kind are the points `cos(x)`, where `x = [pi*(k + .5)/npts for k in range(npts)]`.\n\n Parameters \n \n**npts**int\n\nNumber of sample points desired.\n\n Returns \n \n**pts**ndarray\n\nThe Chebyshev points of the first kind.\n\n See also\n\n [`chebpts2`](numpy.polynomial.chebyshev.chebpts2#numpy.polynomial.chebyshev.chebpts2 \"numpy.polynomial.chebyshev.chebpts2\")\n #### Notes\n\n New in version 1.5.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebpts1.htmlnumpy.polynomial.chebyshev.chebpts2\n===================================\n\n polynomial.chebyshev.chebpts2(*npts*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1957-L1987)\n \nChebyshev points of the second kind.\n\n The Chebyshev points of the second kind are the points `cos(x)`, where `x = [pi*k/(npts - 1) for k in range(npts)]`.\n\n Parameters \n \n**npts**int\n\nNumber of sample points desired.\n\n Returns \n \n**pts**ndarray\n\nThe Chebyshev points of the second kind.\n\n #### Notes\n\n New in version 1.5.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebpts2.htmlnumpy.polynomial.chebyshev.chebtrim\n===================================\n\n polynomial.chebyshev.chebtrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebtrim.htmlnumpy.polynomial.chebyshev.chebline\n===================================\n\n polynomial.chebyshev.chebline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L476-L511)\n \nChebyshev series whose graph is a straight line.\n\n Parameters \n \n**off, scl**scalars\n\nThe specified line is given by `off + scl*x`.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the Chebyshev series for `off + scl*x`.\n\n See also\n\n [`numpy.polynomial.polynomial.polyline`](numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")\n[`numpy.polynomial.legendre.legline`](numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")\n[`numpy.polynomial.laguerre.lagline`](numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")\n[`numpy.polynomial.hermite.hermline`](numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")\n[`numpy.polynomial.hermite_e.hermeline`](numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")\n #### Examples\n\n \n```\n>>> import numpy.polynomial.chebyshev as C\n>>> C.chebline(3,2)\narray([3, 2])\n>>> C.chebval(-3, C.chebline(3,2)) # should be -3\n-3.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebline.htmlnumpy.polynomial.chebyshev.cheb2poly\n====================================\n\n polynomial.chebyshev.cheb2poly(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L397-L455)\n \nConvert a Chebyshev series to a polynomial.\n\n Convert an array representing the coefficients of a Chebyshev series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.\n\n Parameters \n \n**c**array_like\n\n1-D array containing the Chebyshev series coefficients, ordered from lowest order term to highest.\n\n Returns \n \n**pol**ndarray\n\n1-D array containing the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest order term to highest.\n\n See also\n\n [`poly2cheb`](numpy.polynomial.chebyshev.poly2cheb#numpy.polynomial.chebyshev.poly2cheb \"numpy.polynomial.chebyshev.poly2cheb\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy import polynomial as P\n>>> c = P.Chebyshev(range(4))\n>>> c\nChebyshev([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1])\n>>> p = c.convert(kind=P.Polynomial)\n>>> p\nPolynomial([-2., -8., 4., 12.], domain=[-1., 1.], window=[-1., 1.])\n>>> P.chebyshev.cheb2poly(range(4))\narray([-2., -8., 4., 12.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.cheb2poly.htmlnumpy.polynomial.chebyshev.poly2cheb\n====================================\n\n polynomial.chebyshev.poly2cheb(*pol*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L347-L394)\n \nConvert a polynomial to a Chebyshev series.\n\n Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Chebyshev series, ordered from lowest to highest degree.\n\n Parameters \n \n**pol**array_like\n\n1-D array containing the polynomial coefficients\n\n Returns \n \n**c**ndarray\n\n1-D array containing the coefficients of the equivalent Chebyshev series.\n\n See also\n\n [`cheb2poly`](numpy.polynomial.chebyshev.cheb2poly#numpy.polynomial.chebyshev.cheb2poly \"numpy.polynomial.chebyshev.cheb2poly\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy import polynomial as P\n>>> p = P.Polynomial(range(4))\n>>> p\nPolynomial([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1])\n>>> c = p.convert(kind=P.Chebyshev)\n>>> c\nChebyshev([1. , 3.25, 1. , 0.75], domain=[-1., 1.], window=[-1., 1.])\n>>> P.chebyshev.poly2cheb(range(4))\narray([1. , 3.25, 1. , 0.75])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.poly2cheb.htmlnumpy.polynomial.chebyshev.chebinterpolate\n==========================================\n\n polynomial.chebyshev.chebinterpolate(*func*, *deg*, *args=()*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L1780-L1844)\n \nInterpolate a function at the Chebyshev points of the first kind.\n\n Returns the Chebyshev series that interpolates `func` at the Chebyshev points of the first kind in the interval [-1, 1]. The interpolating series tends to a minmax approximation to `func` with increasing `deg` if the function is continuous in the interval.\n\n New in version 1.14.0.\n\n Parameters \n \n**func**function\n\nThe function to be approximated. It must be a function of a single variable of the form `f(x, a, b, c...)`, where `a, b, c...` are extra arguments passed in the `args` parameter.\n\n \n**deg**int\n\nDegree of the interpolating polynomial\n\n \n**args**tuple, optional\n\nExtra arguments to be used in the function call. Default is no extra arguments.\n\n Returns \n \n**coef**ndarray, shape (deg + 1,)\n\nChebyshev coefficients of the interpolating series ordered from low to high.\n\n #### Notes\n\n The Chebyshev polynomials used in the interpolation are orthogonal when sampled at the Chebyshev points of the first kind. If it is desired to constrain some of the coefficients they can simply be set to the desired value after the interpolation, no new interpolation or fit is needed. This is especially useful if it is known apriori that some of coefficients are zero. For instance, if the function is even then the coefficients of the terms of odd degree in the result can be set to zero.\n\n #### Examples\n\n \n```\n>>> import numpy.polynomial.chebyshev as C\n>>> C.chebfromfunction(lambda x: np.tanh(x) + 0.5, 8)\narray([ 5.00000000e-01, 8.11675684e-01, -9.86864911e-17,\n -5.42457905e-02, -2.71387850e-16, 4.51658839e-03,\n 2.46716228e-17, -3.79694221e-04, -3.26899002e-16])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.chebinterpolate.htmlnumpy.polynomial.hermite.Hermite\n================================\n\n *class*numpy.polynomial.hermite.Hermite(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1658-L1697)\n \nAn Hermite series class.\n\n The Hermite class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the `ABCPolyBase` documentation.\n\n Parameters \n \n**coef**array_like\n\nHermite coefficients in order of increasing degree, i.e, `(1, 2, 3)` gives `1*H_0(x) + 2*H_1(X) + 3*H_2(x)`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [-1, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.hermite.hermite.domain#numpy.polynomial.hermite.Hermite.domain \"numpy.polynomial.hermite.Hermite.domain\") for its use. The default value is [-1, 1].\n\n New in version 1.6.0.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.hermite.hermite.__call__#numpy.polynomial.hermite.Hermite.__call__ \"numpy.polynomial.hermite.Hermite.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.hermite.hermite.basis#numpy.polynomial.hermite.Hermite.basis \"numpy.polynomial.hermite.Hermite.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.hermite.hermite.cast#numpy.polynomial.hermite.Hermite.cast \"numpy.polynomial.hermite.Hermite.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.hermite.hermite.convert#numpy.polynomial.hermite.Hermite.convert \"numpy.polynomial.hermite.Hermite.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.hermite.hermite.copy#numpy.polynomial.hermite.Hermite.copy \"numpy.polynomial.hermite.Hermite.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.hermite.hermite.cutdeg#numpy.polynomial.hermite.Hermite.cutdeg \"numpy.polynomial.hermite.Hermite.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.hermite.hermite.degree#numpy.polynomial.hermite.Hermite.degree \"numpy.polynomial.hermite.Hermite.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.hermite.hermite.deriv#numpy.polynomial.hermite.Hermite.deriv \"numpy.polynomial.hermite.Hermite.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.hermite.hermite.fit#numpy.polynomial.hermite.Hermite.fit \"numpy.polynomial.hermite.Hermite.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.hermite.hermite.fromroots#numpy.polynomial.hermite.Hermite.fromroots \"numpy.polynomial.hermite.Hermite.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.hermite.hermite.has_samecoef#numpy.polynomial.hermite.Hermite.has_samecoef \"numpy.polynomial.hermite.Hermite.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.hermite.hermite.has_samedomain#numpy.polynomial.hermite.Hermite.has_samedomain \"numpy.polynomial.hermite.Hermite.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.hermite.hermite.has_sametype#numpy.polynomial.hermite.Hermite.has_sametype \"numpy.polynomial.hermite.Hermite.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.hermite.hermite.has_samewindow#numpy.polynomial.hermite.Hermite.has_samewindow \"numpy.polynomial.hermite.Hermite.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.hermite.hermite.identity#numpy.polynomial.hermite.Hermite.identity \"numpy.polynomial.hermite.Hermite.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.hermite.hermite.integ#numpy.polynomial.hermite.Hermite.integ \"numpy.polynomial.hermite.Hermite.integ\")([m, k, lbnd]) | Integrate. |\n| [`linspace`](numpy.polynomial.hermite.hermite.linspace#numpy.polynomial.hermite.Hermite.linspace \"numpy.polynomial.hermite.Hermite.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.hermite.hermite.mapparms#numpy.polynomial.hermite.Hermite.mapparms \"numpy.polynomial.hermite.Hermite.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.hermite.hermite.roots#numpy.polynomial.hermite.Hermite.roots \"numpy.polynomial.hermite.Hermite.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.hermite.hermite.trim#numpy.polynomial.hermite.Hermite.trim \"numpy.polynomial.hermite.Hermite.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.hermite.hermite.truncate#numpy.polynomial.hermite.Hermite.truncate \"numpy.polynomial.hermite.Hermite.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.htmlnumpy.polynomial.hermite.hermdomain\n===================================\n\n polynomial.hermite.hermdomain*=array([-1, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermdomain.htmlnumpy.polynomial.hermite.hermzero\n=================================\n\n polynomial.hermite.hermzero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermzero.htmlnumpy.polynomial.hermite.hermone\n================================\n\n polynomial.hermite.hermone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermone.htmlnumpy.polynomial.hermite.hermx\n==============================\n\n polynomial.hermite.hermx*=array([0. , 0.5])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermx.htmlnumpy.polynomial.hermite.hermadd\n================================\n\n polynomial.hermite.hermadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L313-L350)\n \nAdd one Hermite series to another.\n\n Returns the sum of two Hermite series `c1` + `c2`. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the Hermite series of their sum.\n\n See also\n\n \n[`hermsub`](numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\"), [`hermmulx`](numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\"), [`hermmul`](numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\"), [`hermdiv`](numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\"), [`hermpow`](numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the sum of two Hermite series is a Hermite series (without having to “reproject” the result onto the basis set) so addition, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermadd\n>>> hermadd([1, 2, 3], [1, 2, 3, 4])\narray([2., 4., 6., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermadd.htmlnumpy.polynomial.hermite.hermsub\n================================\n\n polynomial.hermite.hermsub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L353-L390)\n \nSubtract one Hermite series from another.\n\n Returns the difference of two Hermite series `c1` - `c2`. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Hermite series coefficients representing their difference.\n\n See also\n\n \n[`hermadd`](numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\"), [`hermmulx`](numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\"), [`hermmul`](numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\"), [`hermdiv`](numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\"), [`hermpow`](numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the difference of two Hermite series is a Hermite series (without having to “reproject” the result onto the basis set) so subtraction, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermsub\n>>> hermsub([1, 2, 3, 4], [1, 2, 3])\narray([0., 0., 0., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermsub.htmlnumpy.polynomial.hermite.hermmulx\n=================================\n\n polynomial.hermite.hermmulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L393-L443)\n \nMultiply a Hermite series by x.\n\n Multiply the Hermite series `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n See also\n\n \n[`hermadd`](numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\"), [`hermsub`](numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\"), [`hermmul`](numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\"), [`hermdiv`](numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\"), [`hermpow`](numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")\n\n #### Notes\n\n The multiplication uses the recursion relationship for Hermite polynomials in the form\n\n \\[xP_i(x) = (P_{i + 1}(x)/2 + i*P_{i - 1}(x))\\] #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermmulx\n>>> hermmulx([1, 2, 3])\narray([2. , 6.5, 1. , 1.5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermmulx.htmlnumpy.polynomial.hermite.hermmul\n================================\n\n polynomial.hermite.hermmul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L446-L509)\n \nMultiply one Hermite series by another.\n\n Returns the product of two Hermite series `c1` * `c2`. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Hermite series coefficients representing their product.\n\n See also\n\n \n[`hermadd`](numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\"), [`hermsub`](numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\"), [`hermmulx`](numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\"), [`hermdiv`](numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\"), [`hermpow`](numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")\n\n #### Notes\n\n In general, the (polynomial) product of two C-series results in terms that are not in the Hermite polynomial basis set. Thus, to express the product as a Hermite series, it is necessary to “reproject” the product onto said basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermmul\n>>> hermmul([1, 2, 3], [0, 1, 2])\narray([52., 29., 52., 7., 6.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermmul.htmlnumpy.polynomial.hermite.hermdiv\n================================\n\n polynomial.hermite.hermdiv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L512-L557)\n \nDivide one Hermite series by another.\n\n Returns the quotient-with-remainder of two Hermite series `c1` / `c2`. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**[quo, rem]**ndarrays\n\nOf Hermite series coefficients representing the quotient and remainder.\n\n See also\n\n \n[`hermadd`](numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\"), [`hermsub`](numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\"), [`hermmulx`](numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\"), [`hermmul`](numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\"), [`hermpow`](numpy.polynomial.hermite.hermpow#numpy.polynomial.hermite.hermpow \"numpy.polynomial.hermite.hermpow\")\n\n #### Notes\n\n In general, the (polynomial) division of one Hermite series by another results in quotient and remainder terms that are not in the Hermite polynomial basis set. Thus, to express these results as a Hermite series, it is necessary to “reproject” the results onto the Hermite basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermdiv\n>>> hermdiv([ 52., 29., 52., 7., 6.], [0, 1, 2])\n(array([1., 2., 3.]), array([0.]))\n>>> hermdiv([ 54., 31., 52., 7., 6.], [0, 1, 2])\n(array([1., 2., 3.]), array([2., 2.]))\n>>> hermdiv([ 53., 30., 52., 7., 6.], [0, 1, 2])\n(array([1., 2., 3.]), array([1., 1.]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermdiv.htmlnumpy.polynomial.hermite.hermpow\n================================\n\n polynomial.hermite.hermpow(*c*, *pow*, *maxpower=16*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L560-L594)\n \nRaise a Hermite series to a power.\n\n Returns the Hermite series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `P_0 + 2*P_1 + 3*P_2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of Hermite series coefficients ordered from low to high.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nHermite series of power.\n\n See also\n\n \n[`hermadd`](numpy.polynomial.hermite.hermadd#numpy.polynomial.hermite.hermadd \"numpy.polynomial.hermite.hermadd\"), [`hermsub`](numpy.polynomial.hermite.hermsub#numpy.polynomial.hermite.hermsub \"numpy.polynomial.hermite.hermsub\"), [`hermmulx`](numpy.polynomial.hermite.hermmulx#numpy.polynomial.hermite.hermmulx \"numpy.polynomial.hermite.hermmulx\"), [`hermmul`](numpy.polynomial.hermite.hermmul#numpy.polynomial.hermite.hermmul \"numpy.polynomial.hermite.hermmul\"), [`hermdiv`](numpy.polynomial.hermite.hermdiv#numpy.polynomial.hermite.hermdiv \"numpy.polynomial.hermite.hermdiv\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermpow\n>>> hermpow([1, 2, 3], 2)\narray([81., 52., 82., 12., 9.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermpow.htmlnumpy.polynomial.hermite.hermval\n================================\n\n polynomial.hermite.hermval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L802-L895)\n \nEvaluate an Hermite series at points x.\n\n If `c` is of length `n + 1`, this function returns the value:\n\n \\[p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, algebra_like\n\nThe shape of the return value is described above.\n\n See also\n\n \n[`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermgrid2d`](numpy.polynomial.hermite.hermgrid2d#numpy.polynomial.hermite.hermgrid2d \"numpy.polynomial.hermite.hermgrid2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\"), [`hermgrid3d`](numpy.polynomial.hermite.hermgrid3d#numpy.polynomial.hermite.hermgrid3d \"numpy.polynomial.hermite.hermgrid3d\")\n\n #### Notes\n\n The evaluation uses Clenshaw recursion, aka synthetic division.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermval\n>>> coef = [1,2,3]\n>>> hermval(1, coef)\n11.0\n>>> hermval([[1,2],[3,4]], coef)\narray([[ 11., 51.],\n [115., 203.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermval.htmlnumpy.polynomial.hermite.hermval2d\n==================================\n\n polynomial.hermite.hermval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L898-L944)\n \nEvaluate a 2-D Hermite series at points (x, y).\n\n This function returns the values:\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * H_i(x) * H_j(y)\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`hermval`](numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\"), [`hermgrid2d`](numpy.polynomial.hermite.hermgrid2d#numpy.polynomial.hermite.hermgrid2d \"numpy.polynomial.hermite.hermgrid2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\"), [`hermgrid3d`](numpy.polynomial.hermite.hermgrid3d#numpy.polynomial.hermite.hermgrid3d \"numpy.polynomial.hermite.hermgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermval2d.htmlnumpy.polynomial.hermite.hermval3d\n==================================\n\n polynomial.hermite.hermval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1000-L1048)\n \nEvaluate a 3-D Hermite series at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * H_i(x) * H_j(y) * H_k(z)\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`hermval`](numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\"), [`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermgrid2d`](numpy.polynomial.hermite.hermgrid2d#numpy.polynomial.hermite.hermgrid2d \"numpy.polynomial.hermite.hermgrid2d\"), [`hermgrid3d`](numpy.polynomial.hermite.hermgrid3d#numpy.polynomial.hermite.hermgrid3d \"numpy.polynomial.hermite.hermgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermval3d.htmlnumpy.polynomial.hermite.hermgrid2d\n===================================\n\n polynomial.hermite.hermgrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L947-L997)\n \nEvaluate a 2-D Hermite series on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b)\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`hermval`](numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\"), [`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\"), [`hermgrid3d`](numpy.polynomial.hermite.hermgrid3d#numpy.polynomial.hermite.hermgrid3d \"numpy.polynomial.hermite.hermgrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermgrid2d.htmlnumpy.polynomial.hermite.hermgrid3d\n===================================\n\n polynomial.hermite.hermgrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1051-L1104)\n \nEvaluate a 3-D Hermite series on the Cartesian product of x, y, and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * H_i(a) * H_j(b) * H_k(c)\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`hermval`](numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\"), [`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermgrid2d`](numpy.polynomial.hermite.hermgrid2d#numpy.polynomial.hermite.hermgrid2d \"numpy.polynomial.hermite.hermgrid2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermgrid3d.htmlnumpy.polynomial.hermite.hermder\n================================\n\n polynomial.hermite.hermder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L597-L677)\n \nDifferentiate a Hermite series.\n\n Returns the Hermite series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `1*H_0 + 2*H_1 + 3*H_2` while [[1,2],[1,2]] represents `1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) +\n2*H_0(x)*H_1(y) + 2*H_1(x)*H_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Hermite series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nHermite series of the derivative.\n\n See also\n\n [`hermint`](numpy.polynomial.hermite.hermint#numpy.polynomial.hermite.hermint \"numpy.polynomial.hermite.hermint\")\n #### Notes\n\n In general, the result of differentiating a Hermite series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermder\n>>> hermder([ 1. , 0.5, 0.5, 0.5])\narray([1., 2., 3.])\n>>> hermder([-0.5, 1./2., 1./8., 1./12., 1./16.], m=2)\narray([1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermder.htmlnumpy.polynomial.hermite.hermint\n================================\n\n polynomial.hermite.hermint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L680-L799)\n \nIntegrate a Hermite series.\n\n Returns the Hermite series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `H_0 + 2*H_1 + 3*H_2` while [[1,2],[1,2]] represents `1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) +\n2*H_1(x)*H_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Hermite series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at `lbnd` is the first value in the list, the value of the second integral at `lbnd` is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nHermite series coefficients of the integral.\n\n Raises \n ValueError\n\nIf `m < 0`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`hermder`](numpy.polynomial.hermite.hermder#numpy.polynomial.hermite.hermder \"numpy.polynomial.hermite.hermder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\) - perhaps not what one would have first thought.\n\n Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermint\n>>> hermint([1,2,3]) # integrate once, value 0 at 0.\narray([1. , 0.5, 0.5, 0.5])\n>>> hermint([1,2,3], m=2) # integrate twice, value & deriv 0 at 0\narray([-0.5 , 0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary\n>>> hermint([1,2,3], k=1) # integrate once, value 1 at 0.\narray([2. , 0.5, 0.5, 0.5])\n>>> hermint([1,2,3], lbnd=-1) # integrate once, value 0 at -1\narray([-2. , 0.5, 0.5, 0.5])\n>>> hermint([1,2,3], m=2, k=[1,2], lbnd=-1)\narray([ 1.66666667, -0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermint.htmlnumpy.polynomial.hermite.hermfromroots\n======================================\n\n polynomial.hermite.hermfromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L257-L310)\n \nGenerate a Hermite series with given roots.\n\n The function returns the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] in Hermite form, where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x)\\] The coefficient of the last term is not generally 1 for monic polynomials in Hermite form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below).\n\n See also\n\n [`numpy.polynomial.polynomial.polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")\n[`numpy.polynomial.legendre.legfromroots`](numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")\n[`numpy.polynomial.laguerre.lagfromroots`](numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")\n[`numpy.polynomial.chebyshev.chebfromroots`](numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")\n[`numpy.polynomial.hermite_e.hermefromroots`](numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermfromroots, hermval\n>>> coef = hermfromroots((-1, 0, 1))\n>>> hermval((-1, 0, 1), coef)\narray([0., 0., 0.])\n>>> coef = hermfromroots((-1j, 1j))\n>>> hermval((-1j, 1j), coef)\narray([0.+0.j, 0.+0.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermfromroots.htmlnumpy.polynomial.hermite.hermroots\n==================================\n\n polynomial.hermite.hermroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1452-L1513)\n \nCompute the roots of a Hermite series.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * H_i(x).\\] Parameters \n \n**c**1-D array_like\n\n1-D array of coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.polynomial.polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")\n[`numpy.polynomial.legendre.legroots`](numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")\n[`numpy.polynomial.laguerre.lagroots`](numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")\n[`numpy.polynomial.chebyshev.chebroots`](numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")\n[`numpy.polynomial.hermite_e.hermeroots`](numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n The Hermite series basis polynomials aren’t powers of `x` so the results of this function may seem unintuitive.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermroots, hermfromroots\n>>> coef = hermfromroots([-1, 0, 1])\n>>> coef\narray([0. , 0.25 , 0. , 0.125])\n>>> hermroots(coef)\narray([-1.00000000e+00, -1.38777878e-17, 1.00000000e+00])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermroots.htmlnumpy.polynomial.hermite.hermvander\n===================================\n\n polynomial.hermite.hermvander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1107-L1165)\n \nPseudo-Vandermonde matrix of given degree.\n\n Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., i] = H_i(x),\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the Hermite polynomial.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the array `V = hermvander(x, n)`, then `np.dot(V, c)` and `hermval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Hermite series of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray\n\nThe pseudo-Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted `x`.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermvander\n>>> x = np.array([-1, 0, 1])\n>>> hermvander(x, 3)\narray([[ 1., -2., 2., 4.],\n [ 1., 0., -2., -0.],\n [ 1., 2., 2., -4.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermvander.htmlnumpy.polynomial.hermite.hermvander2d\n=====================================\n\n polynomial.hermite.hermvander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1168-L1218)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = H_i(x) * H_j(y),\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the Hermite polynomials.\n\n If `V = hermvander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `hermval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D Hermite series of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`hermvander`](numpy.polynomial.hermite.hermvander#numpy.polynomial.hermite.hermvander \"numpy.polynomial.hermite.hermvander\"), [`hermvander3d`](numpy.polynomial.hermite.hermvander3d#numpy.polynomial.hermite.hermvander3d \"numpy.polynomial.hermite.hermvander3d\"), [`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermvander2d.htmlnumpy.polynomial.hermite.hermvander3d\n=====================================\n\n polynomial.hermite.hermvander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1221-L1272)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = H_i(x)*H_j(y)*H_k(z),\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the Hermite polynomials.\n\n If `V = hermvander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `hermval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D Hermite series of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`hermvander`](numpy.polynomial.hermite.hermvander#numpy.polynomial.hermite.hermvander \"numpy.polynomial.hermite.hermvander\"), [`hermvander3d`](#numpy.polynomial.hermite.hermvander3d \"numpy.polynomial.hermite.hermvander3d\"), [`hermval2d`](numpy.polynomial.hermite.hermval2d#numpy.polynomial.hermite.hermval2d \"numpy.polynomial.hermite.hermval2d\"), [`hermval3d`](numpy.polynomial.hermite.hermval3d#numpy.polynomial.hermite.hermval3d \"numpy.polynomial.hermite.hermval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermvander3d.htmlnumpy.polynomial.hermite.hermgauss\n==================================\n\n polynomial.hermite.hermgauss(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1559-L1623)\n \nGauss-Hermite quadrature.\n\n Computes the sample points and weights for Gauss-Hermite quadrature. These sample points and weights will correctly integrate polynomials of degree \\(2*deg - 1\\) or less over the interval \\([-\\inf, \\inf]\\) with the weight function \\(f(x) = \\exp(-x^2)\\).\n\n Parameters \n \n**deg**int\n\nNumber of sample points and weights. It must be >= 1.\n\n Returns \n \n**x**ndarray\n\n1-D ndarray containing the sample points.\n\n \n**y**ndarray\n\n1-D ndarray containing the weights.\n\n #### Notes\n\n New in version 1.7.0.\n\n The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that\n\n \\[w_k = c / (H'_n(x_k) * H_{n-1}(x_k))\\] where \\(c\\) is a constant independent of \\(k\\) and \\(x_k\\) is the k’th root of \\(H_n\\), and then scaling the results to get the right value when integrating 1.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermgauss.htmlnumpy.polynomial.hermite.hermweight\n===================================\n\n polynomial.hermite.hermweight(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1626-L1651)\n \nWeight function of the Hermite polynomials.\n\n The weight function is \\(\\exp(-x^2)\\) and the interval of integration is \\([-\\inf, \\inf]\\). the Hermite polynomials are orthogonal, but not normalized, with respect to this weight function.\n\n Parameters \n \n**x**array_like\n\nValues at which the weight function will be computed.\n\n Returns \n \n**w**ndarray\n\nThe weight function at `x`.\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermweight.htmlnumpy.polynomial.hermite.hermcompanion\n======================================\n\n polynomial.hermite.hermcompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1407-L1449)\n \nReturn the scaled companion matrix of c.\n\n The basis polynomials are scaled so that the companion matrix is symmetric when `c` is an Hermite basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if [`numpy.linalg.eigvalsh`](numpy.linalg.eigvalsh#numpy.linalg.eigvalsh \"numpy.linalg.eigvalsh\") is used to obtain them.\n\n Parameters \n \n**c**array_like\n\n1-D array of Hermite series coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nScaled companion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermcompanion.htmlnumpy.polynomial.hermite.hermfit\n================================\n\n polynomial.hermite.hermfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L1275-L1404)\n \nLeast squares fit of Hermite series to data.\n\n Return the coefficients of a Hermite series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x),\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n Returns \n \n**coef**ndarray, shape (M,) or (M, K)\n\nHermite coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`. The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.chebyshev.chebfit`](numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")\n[`numpy.polynomial.legendre.legfit`](numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")\n[`numpy.polynomial.laguerre.lagfit`](numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")\n[`numpy.polynomial.polynomial.polyfit`](numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")\n[`numpy.polynomial.hermite_e.hermefit`](numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")\n[`hermval`](numpy.polynomial.hermite.hermval#numpy.polynomial.hermite.hermval \"numpy.polynomial.hermite.hermval\")\n\nEvaluates a Hermite series.\n\n [`hermvander`](numpy.polynomial.hermite.hermvander#numpy.polynomial.hermite.hermvander \"numpy.polynomial.hermite.hermvander\")\n\nVandermonde matrix of Hermite series.\n\n [`hermweight`](numpy.polynomial.hermite.hermweight#numpy.polynomial.hermite.hermweight \"numpy.polynomial.hermite.hermweight\")\n\nHermite weight function\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the Hermite series `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where the \\(w_j\\) are the weights. This problem is solved by setting up the (typically) overdetermined matrix equation\n\n \\[V(x) * c = w * y,\\] where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected, then a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Fits using Hermite series are probably most useful when the data can be approximated by `sqrt(w(x)) * p(x)`, where `w(x)` is the Hermite weight. In that case the weight `sqrt(w(x[i]))` should be used together with data values `y[i]/sqrt(w(x[i]))`. The weight function is available as [`hermweight`](numpy.polynomial.hermite.hermweight#numpy.polynomial.hermite.hermweight \"numpy.polynomial.hermite.hermweight\").\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermfit, hermval\n>>> x = np.linspace(-10, 10)\n>>> err = np.random.randn(len(x))/10\n>>> y = hermval(x, [1, 2, 3]) + err\n>>> hermfit(x, y, 2)\narray([1.0218, 1.9986, 2.9999]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermfit.htmlnumpy.polynomial.hermite.hermtrim\n=================================\n\n polynomial.hermite.hermtrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermtrim.htmlnumpy.polynomial.hermite.hermline\n=================================\n\n polynomial.hermite.hermline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L217-L254)\n \nHermite series whose graph is a straight line.\n\n Parameters \n \n**off, scl**scalars\n\nThe specified line is given by `off + scl*x`.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the Hermite series for `off + scl*x`.\n\n See also\n\n [`numpy.polynomial.polynomial.polyline`](numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")\n[`numpy.polynomial.chebyshev.chebline`](numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")\n[`numpy.polynomial.legendre.legline`](numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")\n[`numpy.polynomial.laguerre.lagline`](numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")\n[`numpy.polynomial.hermite_e.hermeline`](numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import hermline, hermval\n>>> hermval(0,hermline(3, 2))\n3.0\n>>> hermval(1,hermline(3, 2))\n5.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.hermline.htmlnumpy.polynomial.hermite.herm2poly\n==================================\n\n polynomial.hermite.herm2poly(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L142-L197)\n \nConvert a Hermite series to a polynomial.\n\n Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.\n\n Parameters \n \n**c**array_like\n\n1-D array containing the Hermite series coefficients, ordered from lowest order term to highest.\n\n Returns \n \n**pol**ndarray\n\n1-D array containing the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest order term to highest.\n\n See also\n\n [`poly2herm`](numpy.polynomial.hermite.poly2herm#numpy.polynomial.hermite.poly2herm \"numpy.polynomial.hermite.poly2herm\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import herm2poly\n>>> herm2poly([ 1. , 2.75 , 0.5 , 0.375])\narray([0., 1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.herm2poly.htmlnumpy.polynomial.hermite.poly2herm\n==================================\n\n polynomial.hermite.poly2herm(*pol*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite.py#L96-L139)\n \nConvert a polynomial to a Hermite series.\n\n Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Hermite series, ordered from lowest to highest degree.\n\n Parameters \n \n**pol**array_like\n\n1-D array containing the polynomial coefficients\n\n Returns \n \n**c**ndarray\n\n1-D array containing the coefficients of the equivalent Hermite series.\n\n See also\n\n [`herm2poly`](numpy.polynomial.hermite.herm2poly#numpy.polynomial.hermite.herm2poly \"numpy.polynomial.hermite.herm2poly\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite import poly2herm\n>>> poly2herm(np.arange(4))\narray([1. , 2.75 , 0.5 , 0.375])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.poly2herm.htmlnumpy.polynomial.hermite_e.HermiteE\n====================================\n\n *class*numpy.polynomial.hermite_e.HermiteE(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1650-L1689)\n \nAn HermiteE series class.\n\n The HermiteE class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the `ABCPolyBase` documentation.\n\n Parameters \n \n**coef**array_like\n\nHermiteE coefficients in order of increasing degree, i.e, `(1, 2, 3)` gives `1*He_0(x) + 2*He_1(X) + 3*He_2(x)`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [-1, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.hermite_e.hermitee.domain#numpy.polynomial.hermite_e.HermiteE.domain \"numpy.polynomial.hermite_e.HermiteE.domain\") for its use. The default value is [-1, 1].\n\n New in version 1.6.0.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.hermite_e.hermitee.__call__#numpy.polynomial.hermite_e.HermiteE.__call__ \"numpy.polynomial.hermite_e.HermiteE.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.hermite_e.hermitee.basis#numpy.polynomial.hermite_e.HermiteE.basis \"numpy.polynomial.hermite_e.HermiteE.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.hermite_e.hermitee.cast#numpy.polynomial.hermite_e.HermiteE.cast \"numpy.polynomial.hermite_e.HermiteE.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.hermite_e.hermitee.convert#numpy.polynomial.hermite_e.HermiteE.convert \"numpy.polynomial.hermite_e.HermiteE.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.hermite_e.hermitee.copy#numpy.polynomial.hermite_e.HermiteE.copy \"numpy.polynomial.hermite_e.HermiteE.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.hermite_e.hermitee.cutdeg#numpy.polynomial.hermite_e.HermiteE.cutdeg \"numpy.polynomial.hermite_e.HermiteE.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.hermite_e.hermitee.degree#numpy.polynomial.hermite_e.HermiteE.degree \"numpy.polynomial.hermite_e.HermiteE.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.hermite_e.hermitee.deriv#numpy.polynomial.hermite_e.HermiteE.deriv \"numpy.polynomial.hermite_e.HermiteE.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.hermite_e.hermitee.fit#numpy.polynomial.hermite_e.HermiteE.fit \"numpy.polynomial.hermite_e.HermiteE.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.hermite_e.hermitee.fromroots#numpy.polynomial.hermite_e.HermiteE.fromroots \"numpy.polynomial.hermite_e.HermiteE.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.hermite_e.hermitee.has_samecoef#numpy.polynomial.hermite_e.HermiteE.has_samecoef \"numpy.polynomial.hermite_e.HermiteE.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.hermite_e.hermitee.has_samedomain#numpy.polynomial.hermite_e.HermiteE.has_samedomain \"numpy.polynomial.hermite_e.HermiteE.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.hermite_e.hermitee.has_sametype#numpy.polynomial.hermite_e.HermiteE.has_sametype \"numpy.polynomial.hermite_e.HermiteE.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.hermite_e.hermitee.has_samewindow#numpy.polynomial.hermite_e.HermiteE.has_samewindow \"numpy.polynomial.hermite_e.HermiteE.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.hermite_e.hermitee.identity#numpy.polynomial.hermite_e.HermiteE.identity \"numpy.polynomial.hermite_e.HermiteE.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.hermite_e.hermitee.integ#numpy.polynomial.hermite_e.HermiteE.integ \"numpy.polynomial.hermite_e.HermiteE.integ\")([m, k, lbnd]) | Integrate. |\n| [`linspace`](numpy.polynomial.hermite_e.hermitee.linspace#numpy.polynomial.hermite_e.HermiteE.linspace \"numpy.polynomial.hermite_e.HermiteE.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.hermite_e.hermitee.mapparms#numpy.polynomial.hermite_e.HermiteE.mapparms \"numpy.polynomial.hermite_e.HermiteE.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.hermite_e.hermitee.roots#numpy.polynomial.hermite_e.HermiteE.roots \"numpy.polynomial.hermite_e.HermiteE.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.hermite_e.hermitee.trim#numpy.polynomial.hermite_e.HermiteE.trim \"numpy.polynomial.hermite_e.HermiteE.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.hermite_e.hermitee.truncate#numpy.polynomial.hermite_e.HermiteE.truncate \"numpy.polynomial.hermite_e.HermiteE.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.htmlnumpy.polynomial.hermite_e.hermedomain\n=======================================\n\n polynomial.hermite_e.hermedomain*=array([-1, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermedomain.htmlnumpy.polynomial.hermite_e.hermezero\n=====================================\n\n polynomial.hermite_e.hermezero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermezero.htmlnumpy.polynomial.hermite_e.hermeone\n====================================\n\n polynomial.hermite_e.hermeone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeone.htmlnumpy.polynomial.hermite_e.hermex\n==================================\n\n polynomial.hermite_e.hermex*=array([0, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermex.htmlnumpy.polynomial.hermite_e.hermeadd\n====================================\n\n polynomial.hermite_e.hermeadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L312-L349)\n \nAdd one Hermite series to another.\n\n Returns the sum of two Hermite series `c1` + `c2`. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the Hermite series of their sum.\n\n See also\n\n \n[`hermesub`](numpy.polynomial.hermite_e.hermesub#numpy.polynomial.hermite_e.hermesub \"numpy.polynomial.hermite_e.hermesub\"), [`hermemulx`](numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\"), [`hermemul`](numpy.polynomial.hermite_e.hermemul#numpy.polynomial.hermite_e.hermemul \"numpy.polynomial.hermite_e.hermemul\"), [`hermediv`](numpy.polynomial.hermite_e.hermediv#numpy.polynomial.hermite_e.hermediv \"numpy.polynomial.hermite_e.hermediv\"), [`hermepow`](numpy.polynomial.hermite_e.hermepow#numpy.polynomial.hermite_e.hermepow \"numpy.polynomial.hermite_e.hermepow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the sum of two Hermite series is a Hermite series (without having to “reproject” the result onto the basis set) so addition, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeadd\n>>> hermeadd([1, 2, 3], [1, 2, 3, 4])\narray([2., 4., 6., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeadd.htmlnumpy.polynomial.hermite_e.hermesub\n====================================\n\n polynomial.hermite_e.hermesub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L352-L389)\n \nSubtract one Hermite series from another.\n\n Returns the difference of two Hermite series `c1` - `c2`. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Hermite series coefficients representing their difference.\n\n See also\n\n \n[`hermeadd`](numpy.polynomial.hermite_e.hermeadd#numpy.polynomial.hermite_e.hermeadd \"numpy.polynomial.hermite_e.hermeadd\"), [`hermemulx`](numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\"), [`hermemul`](numpy.polynomial.hermite_e.hermemul#numpy.polynomial.hermite_e.hermemul \"numpy.polynomial.hermite_e.hermemul\"), [`hermediv`](numpy.polynomial.hermite_e.hermediv#numpy.polynomial.hermite_e.hermediv \"numpy.polynomial.hermite_e.hermediv\"), [`hermepow`](numpy.polynomial.hermite_e.hermepow#numpy.polynomial.hermite_e.hermepow \"numpy.polynomial.hermite_e.hermepow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the difference of two Hermite series is a Hermite series (without having to “reproject” the result onto the basis set) so subtraction, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermesub\n>>> hermesub([1, 2, 3, 4], [1, 2, 3])\narray([0., 0., 0., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermesub.htmlnumpy.polynomial.hermite_e.hermemulx\n=====================================\n\n polynomial.hermite_e.hermemulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L392-L438)\n \nMultiply a Hermite series by x.\n\n Multiply the Hermite series `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n #### Notes\n\n The multiplication uses the recursion relationship for Hermite polynomials in the form\n\n \\[xP_i(x) = (P_{i + 1}(x) + iP_{i - 1}(x)))\\] #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermemulx\n>>> hermemulx([1, 2, 3])\narray([2., 7., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermemulx.htmlnumpy.polynomial.hermite_e.hermemul\n====================================\n\n polynomial.hermite_e.hermemul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L441-L504)\n \nMultiply one Hermite series by another.\n\n Returns the product of two Hermite series `c1` * `c2`. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Hermite series coefficients representing their product.\n\n See also\n\n \n[`hermeadd`](numpy.polynomial.hermite_e.hermeadd#numpy.polynomial.hermite_e.hermeadd \"numpy.polynomial.hermite_e.hermeadd\"), [`hermesub`](numpy.polynomial.hermite_e.hermesub#numpy.polynomial.hermite_e.hermesub \"numpy.polynomial.hermite_e.hermesub\"), [`hermemulx`](numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\"), [`hermediv`](numpy.polynomial.hermite_e.hermediv#numpy.polynomial.hermite_e.hermediv \"numpy.polynomial.hermite_e.hermediv\"), [`hermepow`](numpy.polynomial.hermite_e.hermepow#numpy.polynomial.hermite_e.hermepow \"numpy.polynomial.hermite_e.hermepow\")\n\n #### Notes\n\n In general, the (polynomial) product of two C-series results in terms that are not in the Hermite polynomial basis set. Thus, to express the product as a Hermite series, it is necessary to “reproject” the product onto said basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermemul\n>>> hermemul([1, 2, 3], [0, 1, 2])\narray([14., 15., 28., 7., 6.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermemul.htmlnumpy.polynomial.hermite_e.hermediv\n====================================\n\n polynomial.hermite_e.hermediv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L507-L550)\n \nDivide one Hermite series by another.\n\n Returns the quotient-with-remainder of two Hermite series `c1` / `c2`. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Hermite series coefficients ordered from low to high.\n\n Returns \n \n**[quo, rem]**ndarrays\n\nOf Hermite series coefficients representing the quotient and remainder.\n\n See also\n\n \n[`hermeadd`](numpy.polynomial.hermite_e.hermeadd#numpy.polynomial.hermite_e.hermeadd \"numpy.polynomial.hermite_e.hermeadd\"), [`hermesub`](numpy.polynomial.hermite_e.hermesub#numpy.polynomial.hermite_e.hermesub \"numpy.polynomial.hermite_e.hermesub\"), [`hermemulx`](numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\"), [`hermemul`](numpy.polynomial.hermite_e.hermemul#numpy.polynomial.hermite_e.hermemul \"numpy.polynomial.hermite_e.hermemul\"), [`hermepow`](numpy.polynomial.hermite_e.hermepow#numpy.polynomial.hermite_e.hermepow \"numpy.polynomial.hermite_e.hermepow\")\n\n #### Notes\n\n In general, the (polynomial) division of one Hermite series by another results in quotient and remainder terms that are not in the Hermite polynomial basis set. Thus, to express these results as a Hermite series, it is necessary to “reproject” the results onto the Hermite basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermediv\n>>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2])\n(array([1., 2., 3.]), array([0.]))\n>>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2])\n(array([1., 2., 3.]), array([1., 2.]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermediv.htmlnumpy.polynomial.hermite_e.hermepow\n====================================\n\n polynomial.hermite_e.hermepow(*c*, *pow*, *maxpower=16*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L553-L587)\n \nRaise a Hermite series to a power.\n\n Returns the Hermite series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `P_0 + 2*P_1 + 3*P_2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of Hermite series coefficients ordered from low to high.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nHermite series of power.\n\n See also\n\n \n[`hermeadd`](numpy.polynomial.hermite_e.hermeadd#numpy.polynomial.hermite_e.hermeadd \"numpy.polynomial.hermite_e.hermeadd\"), [`hermesub`](numpy.polynomial.hermite_e.hermesub#numpy.polynomial.hermite_e.hermesub \"numpy.polynomial.hermite_e.hermesub\"), [`hermemulx`](numpy.polynomial.hermite_e.hermemulx#numpy.polynomial.hermite_e.hermemulx \"numpy.polynomial.hermite_e.hermemulx\"), [`hermemul`](numpy.polynomial.hermite_e.hermemul#numpy.polynomial.hermite_e.hermemul \"numpy.polynomial.hermite_e.hermemul\"), [`hermediv`](numpy.polynomial.hermite_e.hermediv#numpy.polynomial.hermite_e.hermediv \"numpy.polynomial.hermite_e.hermediv\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermepow\n>>> hermepow([1, 2, 3], 2)\narray([23., 28., 46., 12., 9.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermepow.htmlnumpy.polynomial.hermite_e.hermeval\n====================================\n\n polynomial.hermite_e.hermeval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L795-L887)\n \nEvaluate an HermiteE series at points x.\n\n If `c` is of length `n + 1`, this function returns the value:\n\n \\[p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, algebra_like\n\nThe shape of the return value is described above.\n\n See also\n\n \n[`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermegrid2d`](numpy.polynomial.hermite_e.hermegrid2d#numpy.polynomial.hermite_e.hermegrid2d \"numpy.polynomial.hermite_e.hermegrid2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\"), [`hermegrid3d`](numpy.polynomial.hermite_e.hermegrid3d#numpy.polynomial.hermite_e.hermegrid3d \"numpy.polynomial.hermite_e.hermegrid3d\")\n\n #### Notes\n\n The evaluation uses Clenshaw recursion, aka synthetic division.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeval\n>>> coef = [1,2,3]\n>>> hermeval(1, coef)\n3.0\n>>> hermeval([[1,2],[3,4]], coef)\narray([[ 3., 14.],\n [31., 54.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeval.htmlnumpy.polynomial.hermite_e.hermeval2d\n======================================\n\n polynomial.hermite_e.hermeval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L890-L936)\n \nEvaluate a 2-D HermiteE series at points (x, y).\n\n This function returns the values:\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * He_i(x) * He_j(y)\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`hermeval`](numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\"), [`hermegrid2d`](numpy.polynomial.hermite_e.hermegrid2d#numpy.polynomial.hermite_e.hermegrid2d \"numpy.polynomial.hermite_e.hermegrid2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\"), [`hermegrid3d`](numpy.polynomial.hermite_e.hermegrid3d#numpy.polynomial.hermite_e.hermegrid3d \"numpy.polynomial.hermite_e.hermegrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeval2d.htmlnumpy.polynomial.hermite_e.hermeval3d\n======================================\n\n polynomial.hermite_e.hermeval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L992-L1040)\n \nEvaluate a 3-D Hermite_e series at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * He_i(x) * He_j(y) * He_k(z)\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`hermeval`](numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\"), [`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermegrid2d`](numpy.polynomial.hermite_e.hermegrid2d#numpy.polynomial.hermite_e.hermegrid2d \"numpy.polynomial.hermite_e.hermegrid2d\"), [`hermegrid3d`](numpy.polynomial.hermite_e.hermegrid3d#numpy.polynomial.hermite_e.hermegrid3d \"numpy.polynomial.hermite_e.hermegrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeval3d.htmlnumpy.polynomial.hermite_e.hermegrid2d\n=======================================\n\n polynomial.hermite_e.hermegrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L939-L989)\n \nEvaluate a 2-D HermiteE series on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b)\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`hermeval`](numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\"), [`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\"), [`hermegrid3d`](numpy.polynomial.hermite_e.hermegrid3d#numpy.polynomial.hermite_e.hermegrid3d \"numpy.polynomial.hermite_e.hermegrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermegrid2d.htmlnumpy.polynomial.hermite_e.hermegrid3d\n=======================================\n\n polynomial.hermite_e.hermegrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1043-L1096)\n \nEvaluate a 3-D HermiteE series on the Cartesian product of x, y, and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c)\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`hermeval`](numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\"), [`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermegrid2d`](numpy.polynomial.hermite_e.hermegrid2d#numpy.polynomial.hermite_e.hermegrid2d \"numpy.polynomial.hermite_e.hermegrid2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermegrid3d.htmlnumpy.polynomial.hermite_e.hermeder\n====================================\n\n polynomial.hermite_e.hermeder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L590-L670)\n \nDifferentiate a Hermite_e series.\n\n Returns the series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `1*He_0 + 2*He_1 + 3*He_2` while [[1,2],[1,2]] represents `1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y)\n+ 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Hermite_e series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nHermite series of the derivative.\n\n See also\n\n [`hermeint`](numpy.polynomial.hermite_e.hermeint#numpy.polynomial.hermite_e.hermeint \"numpy.polynomial.hermite_e.hermeint\")\n #### Notes\n\n In general, the result of differentiating a Hermite series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeder\n>>> hermeder([ 1., 1., 1., 1.])\narray([1., 2., 3.])\n>>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2)\narray([1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeder.htmlnumpy.polynomial.hermite_e.hermeint\n====================================\n\n polynomial.hermite_e.hermeint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L673-L792)\n \nIntegrate a Hermite_e series.\n\n Returns the Hermite_e series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `H_0 + 2*H_1 + 3*H_2` while [[1,2],[1,2]] represents `1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) +\n2*H_1(x)*H_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at `lbnd` is the first value in the list, the value of the second integral at `lbnd` is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nHermite_e series coefficients of the integral.\n\n Raises \n ValueError\n\nIf `m < 0`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`hermeder`](numpy.polynomial.hermite_e.hermeder#numpy.polynomial.hermite_e.hermeder \"numpy.polynomial.hermite_e.hermeder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\) - perhaps not what one would have first thought.\n\n Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeint\n>>> hermeint([1, 2, 3]) # integrate once, value 0 at 0.\narray([1., 1., 1., 1.])\n>>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0\narray([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary\n>>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0.\narray([2., 1., 1., 1.])\n>>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1\narray([-1., 1., 1., 1.])\n>>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1)\narray([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeint.htmlnumpy.polynomial.hermite_e.hermefromroots\n==========================================\n\n polynomial.hermite_e.hermefromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L256-L309)\n \nGenerate a HermiteE series with given roots.\n\n The function returns the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] in HermiteE form, where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x)\\] The coefficient of the last term is not generally 1 for monic polynomials in HermiteE form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below).\n\n See also\n\n [`numpy.polynomial.polynomial.polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")\n[`numpy.polynomial.legendre.legfromroots`](numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")\n[`numpy.polynomial.laguerre.lagfromroots`](numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")\n[`numpy.polynomial.hermite.hermfromroots`](numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")\n[`numpy.polynomial.chebyshev.chebfromroots`](numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermefromroots, hermeval\n>>> coef = hermefromroots((-1, 0, 1))\n>>> hermeval((-1, 0, 1), coef)\narray([0., 0., 0.])\n>>> coef = hermefromroots((-1j, 1j))\n>>> hermeval((-1j, 1j), coef)\narray([0.+0.j, 0.+0.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermefromroots.htmlnumpy.polynomial.hermite_e.hermeroots\n======================================\n\n polynomial.hermite_e.hermeroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1445-L1506)\n \nCompute the roots of a HermiteE series.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * He_i(x).\\] Parameters \n \n**c**1-D array_like\n\n1-D array of coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.polynomial.polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")\n[`numpy.polynomial.legendre.legroots`](numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")\n[`numpy.polynomial.laguerre.lagroots`](numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")\n[`numpy.polynomial.hermite.hermroots`](numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")\n[`numpy.polynomial.chebyshev.chebroots`](numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n The HermiteE series basis polynomials aren’t powers of `x` so the results of this function may seem unintuitive.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots\n>>> coef = hermefromroots([-1, 0, 1])\n>>> coef\narray([0., 2., 0., 1.])\n>>> hermeroots(coef)\narray([-1., 0., 1.]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeroots.htmlnumpy.polynomial.hermite_e.hermevander\n=======================================\n\n polynomial.hermite_e.hermevander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1099-L1156)\n \nPseudo-Vandermonde matrix of given degree.\n\n Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., i] = He_i(x),\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the HermiteE polynomial.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the array `V = hermevander(x, n)`, then `np.dot(V, c)` and `hermeval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of HermiteE series of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray\n\nThe pseudo-Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding HermiteE polynomial. The dtype will be the same as the converted `x`.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermevander\n>>> x = np.array([-1, 0, 1])\n>>> hermevander(x, 3)\narray([[ 1., -1., 0., 2.],\n [ 1., 0., -1., -0.],\n [ 1., 1., 0., -2.]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermevander.htmlnumpy.polynomial.hermite_e.hermevander2d\n=========================================\n\n polynomial.hermite_e.hermevander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1159-L1209)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = He_i(x) * He_j(y),\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the HermiteE polynomials.\n\n If `V = hermevander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `hermeval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D HermiteE series of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`hermevander`](numpy.polynomial.hermite_e.hermevander#numpy.polynomial.hermite_e.hermevander \"numpy.polynomial.hermite_e.hermevander\"), [`hermevander3d`](numpy.polynomial.hermite_e.hermevander3d#numpy.polynomial.hermite_e.hermevander3d \"numpy.polynomial.hermite_e.hermevander3d\"), [`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermevander2d.htmlnumpy.polynomial.hermite_e.hermevander3d\n=========================================\n\n polynomial.hermite_e.hermevander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1212-L1263)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then Hehe pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z),\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the HermiteE polynomials.\n\n If `V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `hermeval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D HermiteE series of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`hermevander`](numpy.polynomial.hermite_e.hermevander#numpy.polynomial.hermite_e.hermevander \"numpy.polynomial.hermite_e.hermevander\"), [`hermevander3d`](#numpy.polynomial.hermite_e.hermevander3d \"numpy.polynomial.hermite_e.hermevander3d\"), [`hermeval2d`](numpy.polynomial.hermite_e.hermeval2d#numpy.polynomial.hermite_e.hermeval2d \"numpy.polynomial.hermite_e.hermeval2d\"), [`hermeval3d`](numpy.polynomial.hermite_e.hermeval3d#numpy.polynomial.hermite_e.hermeval3d \"numpy.polynomial.hermite_e.hermeval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermevander3d.htmlnumpy.polynomial.hermite_e.hermegauss\n======================================\n\n polynomial.hermite_e.hermegauss(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1552-L1616)\n \nGauss-HermiteE quadrature.\n\n Computes the sample points and weights for Gauss-HermiteE quadrature. These sample points and weights will correctly integrate polynomials of degree \\(2*deg - 1\\) or less over the interval \\([-\\inf, \\inf]\\) with the weight function \\(f(x) = \\exp(-x^2/2)\\).\n\n Parameters \n \n**deg**int\n\nNumber of sample points and weights. It must be >= 1.\n\n Returns \n \n**x**ndarray\n\n1-D ndarray containing the sample points.\n\n \n**y**ndarray\n\n1-D ndarray containing the weights.\n\n #### Notes\n\n New in version 1.7.0.\n\n The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that\n\n \\[w_k = c / (He'_n(x_k) * He_{n-1}(x_k))\\] where \\(c\\) is a constant independent of \\(k\\) and \\(x_k\\) is the k’th root of \\(He_n\\), and then scaling the results to get the right value when integrating 1.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermegauss.htmlnumpy.polynomial.hermite_e.hermeweight\n=======================================\n\n polynomial.hermite_e.hermeweight(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1619-L1643)\n \nWeight function of the Hermite_e polynomials.\n\n The weight function is \\(\\exp(-x^2/2)\\) and the interval of integration is \\([-\\inf, \\inf]\\). the HermiteE polynomials are orthogonal, but not normalized, with respect to this weight function.\n\n Parameters \n \n**x**array_like\n\nValues at which the weight function will be computed.\n\n Returns \n \n**w**ndarray\n\nThe weight function at `x`.\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeweight.htmlnumpy.polynomial.hermite_e.hermecompanion\n==========================================\n\n polynomial.hermite_e.hermecompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1399-L1442)\n \nReturn the scaled companion matrix of c.\n\n The basis polynomials are scaled so that the companion matrix is symmetric when `c` is an HermiteE basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if [`numpy.linalg.eigvalsh`](numpy.linalg.eigvalsh#numpy.linalg.eigvalsh \"numpy.linalg.eigvalsh\") is used to obtain them.\n\n Parameters \n \n**c**array_like\n\n1-D array of HermiteE series coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nScaled companion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermecompanion.htmlnumpy.polynomial.hermite_e.hermefit\n====================================\n\n polynomial.hermite_e.hermefit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L1266-L1396)\n \nLeast squares fit of Hermite series to data.\n\n Return the coefficients of a HermiteE series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x),\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n Returns \n \n**coef**ndarray, shape (M,) or (M, K)\n\nHermite coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full = False`. The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.chebyshev.chebfit`](numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")\n[`numpy.polynomial.legendre.legfit`](numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")\n[`numpy.polynomial.polynomial.polyfit`](numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")\n[`numpy.polynomial.hermite.hermfit`](numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")\n[`numpy.polynomial.laguerre.lagfit`](numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")\n[`hermeval`](numpy.polynomial.hermite_e.hermeval#numpy.polynomial.hermite_e.hermeval \"numpy.polynomial.hermite_e.hermeval\")\n\nEvaluates a Hermite series.\n\n [`hermevander`](numpy.polynomial.hermite_e.hermevander#numpy.polynomial.hermite_e.hermevander \"numpy.polynomial.hermite_e.hermevander\")\n\npseudo Vandermonde matrix of Hermite series.\n\n [`hermeweight`](numpy.polynomial.hermite_e.hermeweight#numpy.polynomial.hermite_e.hermeweight \"numpy.polynomial.hermite_e.hermeweight\")\n\nHermiteE weight function.\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the HermiteE series `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where the \\(w_j\\) are the weights. This problem is solved by setting up the (typically) overdetermined matrix equation\n\n \\[V(x) * c = w * y,\\] where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c` are the coefficients to be solved for, and the elements of `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected, then a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Fits using HermiteE series are probably most useful when the data can be approximated by `sqrt(w(x)) * p(x)`, where `w(x)` is the HermiteE weight. In that case the weight `sqrt(w(x[i]))` should be used together with data values `y[i]/sqrt(w(x[i]))`. The weight function is available as [`hermeweight`](numpy.polynomial.hermite_e.hermeweight#numpy.polynomial.hermite_e.hermeweight \"numpy.polynomial.hermite_e.hermeweight\").\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermefit, hermeval\n>>> x = np.linspace(-10, 10)\n>>> np.random.seed(123)\n>>> err = np.random.randn(len(x))/10\n>>> y = hermeval(x, [1, 2, 3]) + err\n>>> hermefit(x, y, 2)\narray([ 1.01690445, 1.99951418, 2.99948696]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermefit.htmlnumpy.polynomial.hermite_e.hermetrim\n=====================================\n\n polynomial.hermite_e.hermetrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermetrim.htmlnumpy.polynomial.hermite_e.hermeline\n=====================================\n\n polynomial.hermite_e.hermeline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L217-L253)\n \nHermite series whose graph is a straight line.\n\n Parameters \n \n**off, scl**scalars\n\nThe specified line is given by `off + scl*x`.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the Hermite series for `off + scl*x`.\n\n See also\n\n [`numpy.polynomial.polynomial.polyline`](numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")\n[`numpy.polynomial.chebyshev.chebline`](numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")\n[`numpy.polynomial.legendre.legline`](numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")\n[`numpy.polynomial.laguerre.lagline`](numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")\n[`numpy.polynomial.hermite.hermline`](numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import hermeline\n>>> from numpy.polynomial.hermite_e import hermeline, hermeval\n>>> hermeval(0,hermeline(3, 2))\n3.0\n>>> hermeval(1,hermeline(3, 2))\n5.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.hermeline.htmlnumpy.polynomial.hermite_e.herme2poly\n======================================\n\n polynomial.hermite_e.herme2poly(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L143-L197)\n \nConvert a Hermite series to a polynomial.\n\n Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.\n\n Parameters \n \n**c**array_like\n\n1-D array containing the Hermite series coefficients, ordered from lowest order term to highest.\n\n Returns \n \n**pol**ndarray\n\n1-D array containing the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest order term to highest.\n\n See also\n\n [`poly2herme`](numpy.polynomial.hermite_e.poly2herme#numpy.polynomial.hermite_e.poly2herme \"numpy.polynomial.hermite_e.poly2herme\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import herme2poly\n>>> herme2poly([ 2., 10., 2., 3.])\narray([0., 1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.herme2poly.htmlnumpy.polynomial.hermite_e.poly2herme\n======================================\n\n polynomial.hermite_e.poly2herme(*pol*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/hermite_e.py#L97-L140)\n \nConvert a polynomial to a Hermite series.\n\n Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Hermite series, ordered from lowest to highest degree.\n\n Parameters \n \n**pol**array_like\n\n1-D array containing the polynomial coefficients\n\n Returns \n \n**c**ndarray\n\n1-D array containing the coefficients of the equivalent Hermite series.\n\n See also\n\n [`herme2poly`](numpy.polynomial.hermite_e.herme2poly#numpy.polynomial.hermite_e.herme2poly \"numpy.polynomial.hermite_e.herme2poly\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.hermite_e import poly2herme\n>>> poly2herme(np.arange(4))\narray([ 2., 10., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.poly2herme.htmlnumpy.polynomial.laguerre.Laguerre\n==================================\n\n *class*numpy.polynomial.laguerre.Laguerre(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1606-L1645)\n \nA Laguerre series class.\n\n The Laguerre class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the `ABCPolyBase` documentation.\n\n Parameters \n \n**coef**array_like\n\nLaguerre coefficients in order of increasing degree, i.e, `(1, 2, 3)` gives `1*L_0(x) + 2*L_1(X) + 3*L_2(x)`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [0, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.laguerre.laguerre.domain#numpy.polynomial.laguerre.Laguerre.domain \"numpy.polynomial.laguerre.Laguerre.domain\") for its use. The default value is [0, 1].\n\n New in version 1.6.0.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.laguerre.laguerre.__call__#numpy.polynomial.laguerre.Laguerre.__call__ \"numpy.polynomial.laguerre.Laguerre.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.laguerre.laguerre.basis#numpy.polynomial.laguerre.Laguerre.basis \"numpy.polynomial.laguerre.Laguerre.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.laguerre.laguerre.cast#numpy.polynomial.laguerre.Laguerre.cast \"numpy.polynomial.laguerre.Laguerre.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.laguerre.laguerre.convert#numpy.polynomial.laguerre.Laguerre.convert \"numpy.polynomial.laguerre.Laguerre.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.laguerre.laguerre.copy#numpy.polynomial.laguerre.Laguerre.copy \"numpy.polynomial.laguerre.Laguerre.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.laguerre.laguerre.cutdeg#numpy.polynomial.laguerre.Laguerre.cutdeg \"numpy.polynomial.laguerre.Laguerre.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.laguerre.laguerre.degree#numpy.polynomial.laguerre.Laguerre.degree \"numpy.polynomial.laguerre.Laguerre.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.laguerre.laguerre.deriv#numpy.polynomial.laguerre.Laguerre.deriv \"numpy.polynomial.laguerre.Laguerre.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.laguerre.laguerre.fit#numpy.polynomial.laguerre.Laguerre.fit \"numpy.polynomial.laguerre.Laguerre.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.laguerre.laguerre.fromroots#numpy.polynomial.laguerre.Laguerre.fromroots \"numpy.polynomial.laguerre.Laguerre.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.laguerre.laguerre.has_samecoef#numpy.polynomial.laguerre.Laguerre.has_samecoef \"numpy.polynomial.laguerre.Laguerre.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.laguerre.laguerre.has_samedomain#numpy.polynomial.laguerre.Laguerre.has_samedomain \"numpy.polynomial.laguerre.Laguerre.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.laguerre.laguerre.has_sametype#numpy.polynomial.laguerre.Laguerre.has_sametype \"numpy.polynomial.laguerre.Laguerre.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.laguerre.laguerre.has_samewindow#numpy.polynomial.laguerre.Laguerre.has_samewindow \"numpy.polynomial.laguerre.Laguerre.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.laguerre.laguerre.identity#numpy.polynomial.laguerre.Laguerre.identity \"numpy.polynomial.laguerre.Laguerre.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.laguerre.laguerre.integ#numpy.polynomial.laguerre.Laguerre.integ \"numpy.polynomial.laguerre.Laguerre.integ\")([m, k, lbnd]) | Integrate. |\n| [`linspace`](numpy.polynomial.laguerre.laguerre.linspace#numpy.polynomial.laguerre.Laguerre.linspace \"numpy.polynomial.laguerre.Laguerre.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.laguerre.laguerre.mapparms#numpy.polynomial.laguerre.Laguerre.mapparms \"numpy.polynomial.laguerre.Laguerre.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.laguerre.laguerre.roots#numpy.polynomial.laguerre.Laguerre.roots \"numpy.polynomial.laguerre.Laguerre.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.laguerre.laguerre.trim#numpy.polynomial.laguerre.Laguerre.trim \"numpy.polynomial.laguerre.Laguerre.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.laguerre.laguerre.truncate#numpy.polynomial.laguerre.Laguerre.truncate \"numpy.polynomial.laguerre.Laguerre.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.htmlnumpy.polynomial.laguerre.lagdomain\n===================================\n\n polynomial.laguerre.lagdomain*=array([0, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagdomain.htmlnumpy.polynomial.laguerre.lagzero\n=================================\n\n polynomial.laguerre.lagzero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagzero.htmlnumpy.polynomial.laguerre.lagone\n================================\n\n polynomial.laguerre.lagone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagone.htmlnumpy.polynomial.laguerre.lagx\n==============================\n\n polynomial.laguerre.lagx*=array([ 1, -1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagx.htmlnumpy.polynomial.laguerre.lagadd\n================================\n\n polynomial.laguerre.lagadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L307-L345)\n \nAdd one Laguerre series to another.\n\n Returns the sum of two Laguerre series `c1` + `c2`. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Laguerre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the Laguerre series of their sum.\n\n See also\n\n \n[`lagsub`](numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\"), [`lagmulx`](numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\"), [`lagmul`](numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\"), [`lagdiv`](numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\"), [`lagpow`](numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the sum of two Laguerre series is a Laguerre series (without having to “reproject” the result onto the basis set) so addition, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagadd\n>>> lagadd([1, 2, 3], [1, 2, 3, 4])\narray([2., 4., 6., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagadd.htmlnumpy.polynomial.laguerre.lagsub\n================================\n\n polynomial.laguerre.lagsub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L348-L385)\n \nSubtract one Laguerre series from another.\n\n Returns the difference of two Laguerre series `c1` - `c2`. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Laguerre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Laguerre series coefficients representing their difference.\n\n See also\n\n \n[`lagadd`](numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\"), [`lagmulx`](numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\"), [`lagmul`](numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\"), [`lagdiv`](numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\"), [`lagpow`](numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the difference of two Laguerre series is a Laguerre series (without having to “reproject” the result onto the basis set) so subtraction, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagsub\n>>> lagsub([1, 2, 3, 4], [1, 2, 3])\narray([0., 0., 0., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagsub.htmlnumpy.polynomial.laguerre.lagmulx\n=================================\n\n polynomial.laguerre.lagmulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L388-L439)\n \nMultiply a Laguerre series by x.\n\n Multiply the Laguerre series `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of Laguerre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n See also\n\n \n[`lagadd`](numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\"), [`lagsub`](numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\"), [`lagmul`](numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\"), [`lagdiv`](numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\"), [`lagpow`](numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")\n\n #### Notes\n\n The multiplication uses the recursion relationship for Laguerre polynomials in the form\n\n \\[xP_i(x) = (-(i + 1)*P_{i + 1}(x) + (2i + 1)P_{i}(x) - iP_{i - 1}(x))\\] #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagmulx\n>>> lagmulx([1, 2, 3])\narray([-1., -1., 11., -9.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagmulx.htmlnumpy.polynomial.laguerre.lagmul\n================================\n\n polynomial.laguerre.lagmul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L442-L505)\n \nMultiply one Laguerre series by another.\n\n Returns the product of two Laguerre series `c1` * `c2`. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Laguerre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Laguerre series coefficients representing their product.\n\n See also\n\n \n[`lagadd`](numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\"), [`lagsub`](numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\"), [`lagmulx`](numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\"), [`lagdiv`](numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\"), [`lagpow`](numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")\n\n #### Notes\n\n In general, the (polynomial) product of two C-series results in terms that are not in the Laguerre polynomial basis set. Thus, to express the product as a Laguerre series, it is necessary to “reproject” the product onto said basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagmul\n>>> lagmul([1, 2, 3], [0, 1, 2])\narray([ 8., -13., 38., -51., 36.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagmul.htmlnumpy.polynomial.laguerre.lagdiv\n================================\n\n polynomial.laguerre.lagdiv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L508-L551)\n \nDivide one Laguerre series by another.\n\n Returns the quotient-with-remainder of two Laguerre series `c1` / `c2`. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Laguerre series coefficients ordered from low to high.\n\n Returns \n \n**[quo, rem]**ndarrays\n\nOf Laguerre series coefficients representing the quotient and remainder.\n\n See also\n\n \n[`lagadd`](numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\"), [`lagsub`](numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\"), [`lagmulx`](numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\"), [`lagmul`](numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\"), [`lagpow`](numpy.polynomial.laguerre.lagpow#numpy.polynomial.laguerre.lagpow \"numpy.polynomial.laguerre.lagpow\")\n\n #### Notes\n\n In general, the (polynomial) division of one Laguerre series by another results in quotient and remainder terms that are not in the Laguerre polynomial basis set. Thus, to express these results as a Laguerre series, it is necessary to “reproject” the results onto the Laguerre basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagdiv\n>>> lagdiv([ 8., -13., 38., -51., 36.], [0, 1, 2])\n(array([1., 2., 3.]), array([0.]))\n>>> lagdiv([ 9., -12., 38., -51., 36.], [0, 1, 2])\n(array([1., 2., 3.]), array([1., 1.]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagdiv.htmlnumpy.polynomial.laguerre.lagpow\n================================\n\n polynomial.laguerre.lagpow(*c*, *pow*, *maxpower=16*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L554-L588)\n \nRaise a Laguerre series to a power.\n\n Returns the Laguerre series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `P_0 + 2*P_1 + 3*P_2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of Laguerre series coefficients ordered from low to high.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nLaguerre series of power.\n\n See also\n\n \n[`lagadd`](numpy.polynomial.laguerre.lagadd#numpy.polynomial.laguerre.lagadd \"numpy.polynomial.laguerre.lagadd\"), [`lagsub`](numpy.polynomial.laguerre.lagsub#numpy.polynomial.laguerre.lagsub \"numpy.polynomial.laguerre.lagsub\"), [`lagmulx`](numpy.polynomial.laguerre.lagmulx#numpy.polynomial.laguerre.lagmulx \"numpy.polynomial.laguerre.lagmulx\"), [`lagmul`](numpy.polynomial.laguerre.lagmul#numpy.polynomial.laguerre.lagmul \"numpy.polynomial.laguerre.lagmul\"), [`lagdiv`](numpy.polynomial.laguerre.lagdiv#numpy.polynomial.laguerre.lagdiv \"numpy.polynomial.laguerre.lagdiv\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagpow\n>>> lagpow([1, 2, 3], 2)\narray([ 14., -16., 56., -72., 54.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagpow.htmlnumpy.polynomial.laguerre.lagval\n================================\n\n polynomial.laguerre.lagval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L801-L893)\n \nEvaluate a Laguerre series at points x.\n\n If `c` is of length `n + 1`, this function returns the value:\n\n \\[p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, algebra_like\n\nThe shape of the return value is described above.\n\n See also\n\n \n[`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`laggrid2d`](numpy.polynomial.laguerre.laggrid2d#numpy.polynomial.laguerre.laggrid2d \"numpy.polynomial.laguerre.laggrid2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\"), [`laggrid3d`](numpy.polynomial.laguerre.laggrid3d#numpy.polynomial.laguerre.laggrid3d \"numpy.polynomial.laguerre.laggrid3d\")\n\n #### Notes\n\n The evaluation uses Clenshaw recursion, aka synthetic division.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagval\n>>> coef = [1,2,3]\n>>> lagval(1, coef)\n-0.5\n>>> lagval([[1,2],[3,4]], coef)\narray([[-0.5, -4. ],\n [-4.5, -2. ]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagval.htmlnumpy.polynomial.laguerre.lagval2d\n==================================\n\n polynomial.laguerre.lagval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L896-L942)\n \nEvaluate a 2-D Laguerre series at points (x, y).\n\n This function returns the values:\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y)\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`lagval`](numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\"), [`laggrid2d`](numpy.polynomial.laguerre.laggrid2d#numpy.polynomial.laguerre.laggrid2d \"numpy.polynomial.laguerre.laggrid2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\"), [`laggrid3d`](numpy.polynomial.laguerre.laggrid3d#numpy.polynomial.laguerre.laggrid3d \"numpy.polynomial.laguerre.laggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagval2d.htmlnumpy.polynomial.laguerre.lagval3d\n==================================\n\n polynomial.laguerre.lagval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L998-L1046)\n \nEvaluate a 3-D Laguerre series at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z)\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`lagval`](numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\"), [`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`laggrid2d`](numpy.polynomial.laguerre.laggrid2d#numpy.polynomial.laguerre.laggrid2d \"numpy.polynomial.laguerre.laggrid2d\"), [`laggrid3d`](numpy.polynomial.laguerre.laggrid3d#numpy.polynomial.laguerre.laggrid3d \"numpy.polynomial.laguerre.laggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagval3d.htmlnumpy.polynomial.laguerre.laggrid2d\n===================================\n\n polynomial.laguerre.laggrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L945-L995)\n \nEvaluate a 2-D Laguerre series on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * L_i(a) * L_j(b)\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional Chebyshev series at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`lagval`](numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\"), [`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\"), [`laggrid3d`](numpy.polynomial.laguerre.laggrid3d#numpy.polynomial.laguerre.laggrid3d \"numpy.polynomial.laguerre.laggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.laggrid2d.htmlnumpy.polynomial.laguerre.laggrid3d\n===================================\n\n polynomial.laguerre.laggrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1049-L1102)\n \nEvaluate a 3-D Laguerre series on the Cartesian product of x, y, and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`lagval`](numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\"), [`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`laggrid2d`](numpy.polynomial.laguerre.laggrid2d#numpy.polynomial.laguerre.laggrid2d \"numpy.polynomial.laguerre.laggrid2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.laggrid3d.htmlnumpy.polynomial.laguerre.lagder\n================================\n\n polynomial.laguerre.lagder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L591-L674)\n \nDifferentiate a Laguerre series.\n\n Returns the Laguerre series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `1*L_0 + 2*L_1 + 3*L_2` while [[1,2],[1,2]] represents `1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) +\n2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Laguerre series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nLaguerre series of the derivative.\n\n See also\n\n [`lagint`](numpy.polynomial.laguerre.lagint#numpy.polynomial.laguerre.lagint \"numpy.polynomial.laguerre.lagint\")\n #### Notes\n\n In general, the result of differentiating a Laguerre series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagder\n>>> lagder([ 1., 1., 1., -3.])\narray([1., 2., 3.])\n>>> lagder([ 1., 0., 0., -4., 3.], m=2)\narray([1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagder.htmlnumpy.polynomial.laguerre.lagint\n================================\n\n polynomial.laguerre.lagint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L677-L798)\n \nIntegrate a Laguerre series.\n\n Returns the Laguerre series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `L_0 + 2*L_1 + 3*L_2` while [[1,2],[1,2]] represents `1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) +\n2*L_1(x)*L_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Laguerre series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at `lbnd` is the first value in the list, the value of the second integral at `lbnd` is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nLaguerre series coefficients of the integral.\n\n Raises \n ValueError\n\nIf `m < 0`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`lagder`](numpy.polynomial.laguerre.lagder#numpy.polynomial.laguerre.lagder \"numpy.polynomial.laguerre.lagder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\) - perhaps not what one would have first thought.\n\n Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagint\n>>> lagint([1,2,3])\narray([ 1., 1., 1., -3.])\n>>> lagint([1,2,3], m=2)\narray([ 1., 0., 0., -4., 3.])\n>>> lagint([1,2,3], k=1)\narray([ 2., 1., 1., -3.])\n>>> lagint([1,2,3], lbnd=-1)\narray([11.5, 1. , 1. , -3. ])\n>>> lagint([1,2], m=2, k=[1,2], lbnd=-1)\narray([ 11.16666667, -5. , -3. , 2. ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagint.htmlnumpy.polynomial.laguerre.lagfromroots\n======================================\n\n polynomial.laguerre.lagfromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L251-L304)\n \nGenerate a Laguerre series with given roots.\n\n The function returns the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] in Laguerre form, where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x)\\] The coefficient of the last term is not generally 1 for monic polynomials in Laguerre form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below).\n\n See also\n\n [`numpy.polynomial.polynomial.polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")\n[`numpy.polynomial.legendre.legfromroots`](numpy.polynomial.legendre.legfromroots#numpy.polynomial.legendre.legfromroots \"numpy.polynomial.legendre.legfromroots\")\n[`numpy.polynomial.chebyshev.chebfromroots`](numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")\n[`numpy.polynomial.hermite.hermfromroots`](numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")\n[`numpy.polynomial.hermite_e.hermefromroots`](numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagfromroots, lagval\n>>> coef = lagfromroots((-1, 0, 1))\n>>> lagval((-1, 0, 1), coef)\narray([0., 0., 0.])\n>>> coef = lagfromroots((-1j, 1j))\n>>> lagval((-1j, 1j), coef)\narray([0.+0.j, 0.+0.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagfromroots.htmlnumpy.polynomial.laguerre.lagroots\n==================================\n\n polynomial.laguerre.lagroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1448-L1509)\n \nCompute the roots of a Laguerre series.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * L_i(x).\\] Parameters \n \n**c**1-D array_like\n\n1-D array of coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.polynomial.polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")\n[`numpy.polynomial.legendre.legroots`](numpy.polynomial.legendre.legroots#numpy.polynomial.legendre.legroots \"numpy.polynomial.legendre.legroots\")\n[`numpy.polynomial.chebyshev.chebroots`](numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")\n[`numpy.polynomial.hermite.hermroots`](numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")\n[`numpy.polynomial.hermite_e.hermeroots`](numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n The Laguerre series basis polynomials aren’t powers of `x` so the results of this function may seem unintuitive.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagroots, lagfromroots\n>>> coef = lagfromroots([0, 1, 2])\n>>> coef\narray([ 2., -8., 12., -6.])\n>>> lagroots(coef)\narray([-4.4408921e-16, 1.0000000e+00, 2.0000000e+00])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagroots.htmlnumpy.polynomial.laguerre.lagvander\n===================================\n\n polynomial.laguerre.lagvander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1105-L1162)\n \nPseudo-Vandermonde matrix of given degree.\n\n Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., i] = L_i(x)\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the Laguerre polynomial.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the array `V = lagvander(x, n)`, then `np.dot(V, c)` and `lagval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Laguerre series of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray\n\nThe pseudo-Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted `x`.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagvander\n>>> x = np.array([0, 1, 2])\n>>> lagvander(x, 3)\narray([[ 1. , 1. , 1. , 1. ],\n [ 1. , 0. , -0.5 , -0.66666667],\n [ 1. , -1. , -1. , -0.33333333]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagvander.htmlnumpy.polynomial.laguerre.lagvander2d\n=====================================\n\n polynomial.laguerre.lagvander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1165-L1215)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y),\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the Laguerre polynomials.\n\n If `V = lagvander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `lagval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D Laguerre series of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`lagvander`](numpy.polynomial.laguerre.lagvander#numpy.polynomial.laguerre.lagvander \"numpy.polynomial.laguerre.lagvander\"), [`lagvander3d`](numpy.polynomial.laguerre.lagvander3d#numpy.polynomial.laguerre.lagvander3d \"numpy.polynomial.laguerre.lagvander3d\"), [`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagvander2d.htmlnumpy.polynomial.laguerre.lagvander3d\n=====================================\n\n polynomial.laguerre.lagvander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1218-L1269)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = L_i(x)*L_j(y)*L_k(z),\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the Laguerre polynomials.\n\n If `V = lagvander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `lagval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D Laguerre series of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`lagvander`](numpy.polynomial.laguerre.lagvander#numpy.polynomial.laguerre.lagvander \"numpy.polynomial.laguerre.lagvander\"), [`lagvander3d`](#numpy.polynomial.laguerre.lagvander3d \"numpy.polynomial.laguerre.lagvander3d\"), [`lagval2d`](numpy.polynomial.laguerre.lagval2d#numpy.polynomial.laguerre.lagval2d \"numpy.polynomial.laguerre.lagval2d\"), [`lagval3d`](numpy.polynomial.laguerre.lagval3d#numpy.polynomial.laguerre.lagval3d \"numpy.polynomial.laguerre.lagval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagvander3d.htmlnumpy.polynomial.laguerre.laggauss\n==================================\n\n polynomial.laguerre.laggauss(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1512-L1573)\n \nGauss-Laguerre quadrature.\n\n Computes the sample points and weights for Gauss-Laguerre quadrature. These sample points and weights will correctly integrate polynomials of degree \\(2*deg - 1\\) or less over the interval \\([0, \\inf]\\) with the weight function \\(f(x) = \\exp(-x)\\).\n\n Parameters \n \n**deg**int\n\nNumber of sample points and weights. It must be >= 1.\n\n Returns \n \n**x**ndarray\n\n1-D ndarray containing the sample points.\n\n \n**y**ndarray\n\n1-D ndarray containing the weights.\n\n #### Notes\n\n New in version 1.7.0.\n\n The results have only been tested up to degree 100 higher degrees may be problematic. The weights are determined by using the fact that\n\n \\[w_k = c / (L'_n(x_k) * L_{n-1}(x_k))\\] where \\(c\\) is a constant independent of \\(k\\) and \\(x_k\\) is the k’th root of \\(L_n\\), and then scaling the results to get the right value when integrating 1.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.laggauss.htmlnumpy.polynomial.laguerre.lagweight\n===================================\n\n polynomial.laguerre.lagweight(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1576-L1600)\n \nWeight function of the Laguerre polynomials.\n\n The weight function is \\(exp(-x)\\) and the interval of integration is \\([0, \\inf]\\). The Laguerre polynomials are orthogonal, but not normalized, with respect to this weight function.\n\n Parameters \n \n**x**array_like\n\nValues at which the weight function will be computed.\n\n Returns \n \n**w**ndarray\n\nThe weight function at `x`.\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagweight.htmlnumpy.polynomial.laguerre.lagcompanion\n======================================\n\n polynomial.laguerre.lagcompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1404-L1445)\n \nReturn the companion matrix of c.\n\n The usual companion matrix of the Laguerre polynomials is already symmetric when `c` is a basis Laguerre polynomial, so no scaling is applied.\n\n Parameters \n \n**c**array_like\n\n1-D array of Laguerre series coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nCompanion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagcompanion.htmlnumpy.polynomial.laguerre.lagfit\n================================\n\n polynomial.laguerre.lagfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L1272-L1401)\n \nLeast squares fit of Laguerre series to data.\n\n Return the coefficients of a Laguerre series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x),\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n Returns \n \n**coef**ndarray, shape (M,) or (M, K)\n\nLaguerre coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`. The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.polynomial.polyfit`](numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")\n[`numpy.polynomial.legendre.legfit`](numpy.polynomial.legendre.legfit#numpy.polynomial.legendre.legfit \"numpy.polynomial.legendre.legfit\")\n[`numpy.polynomial.chebyshev.chebfit`](numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")\n[`numpy.polynomial.hermite.hermfit`](numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")\n[`numpy.polynomial.hermite_e.hermefit`](numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")\n[`lagval`](numpy.polynomial.laguerre.lagval#numpy.polynomial.laguerre.lagval \"numpy.polynomial.laguerre.lagval\")\n\nEvaluates a Laguerre series.\n\n [`lagvander`](numpy.polynomial.laguerre.lagvander#numpy.polynomial.laguerre.lagvander \"numpy.polynomial.laguerre.lagvander\")\n\npseudo Vandermonde matrix of Laguerre series.\n\n [`lagweight`](numpy.polynomial.laguerre.lagweight#numpy.polynomial.laguerre.lagweight \"numpy.polynomial.laguerre.lagweight\")\n\nLaguerre weight function.\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the Laguerre series `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where the \\(w_j\\) are the weights. This problem is solved by setting up as the (typically) overdetermined matrix equation\n\n \\[V(x) * c = w * y,\\] where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected, then a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Fits using Laguerre series are probably most useful when the data can be approximated by `sqrt(w(x)) * p(x)`, where `w(x)` is the Laguerre weight. In that case the weight `sqrt(w(x[i]))` should be used together with data values `y[i]/sqrt(w(x[i]))`. The weight function is available as [`lagweight`](numpy.polynomial.laguerre.lagweight#numpy.polynomial.laguerre.lagweight \"numpy.polynomial.laguerre.lagweight\").\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagfit, lagval\n>>> x = np.linspace(0, 10)\n>>> err = np.random.randn(len(x))/10\n>>> y = lagval(x, [1, 2, 3]) + err\n>>> lagfit(x, y, 2)\narray([ 0.96971004, 2.00193749, 3.00288744]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagfit.htmlnumpy.polynomial.laguerre.lagtrim\n=================================\n\n polynomial.laguerre.lagtrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagtrim.htmlnumpy.polynomial.laguerre.lagline\n=================================\n\n polynomial.laguerre.lagline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L213-L248)\n \nLaguerre series whose graph is a straight line.\n\n Parameters \n \n**off, scl**scalars\n\nThe specified line is given by `off + scl*x`.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the Laguerre series for `off + scl*x`.\n\n See also\n\n [`numpy.polynomial.polynomial.polyline`](numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")\n[`numpy.polynomial.chebyshev.chebline`](numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")\n[`numpy.polynomial.legendre.legline`](numpy.polynomial.legendre.legline#numpy.polynomial.legendre.legline \"numpy.polynomial.legendre.legline\")\n[`numpy.polynomial.hermite.hermline`](numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")\n[`numpy.polynomial.hermite_e.hermeline`](numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lagline, lagval\n>>> lagval(0,lagline(3, 2))\n3.0\n>>> lagval(1,lagline(3, 2))\n5.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lagline.htmlnumpy.polynomial.laguerre.lag2poly\n==================================\n\n polynomial.laguerre.lag2poly(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L141-L193)\n \nConvert a Laguerre series to a polynomial.\n\n Convert an array representing the coefficients of a Laguerre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.\n\n Parameters \n \n**c**array_like\n\n1-D array containing the Laguerre series coefficients, ordered from lowest order term to highest.\n\n Returns \n \n**pol**ndarray\n\n1-D array containing the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest order term to highest.\n\n See also\n\n [`poly2lag`](numpy.polynomial.laguerre.poly2lag#numpy.polynomial.laguerre.poly2lag \"numpy.polynomial.laguerre.poly2lag\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import lag2poly\n>>> lag2poly([ 23., -63., 58., -18.])\narray([0., 1., 2., 3.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.lag2poly.htmlnumpy.polynomial.laguerre.poly2lag\n==================================\n\n polynomial.laguerre.poly2lag(*pol*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/laguerre.py#L96-L138)\n \nConvert a polynomial to a Laguerre series.\n\n Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Laguerre series, ordered from lowest to highest degree.\n\n Parameters \n \n**pol**array_like\n\n1-D array containing the polynomial coefficients\n\n Returns \n \n**c**ndarray\n\n1-D array containing the coefficients of the equivalent Laguerre series.\n\n See also\n\n [`lag2poly`](numpy.polynomial.laguerre.lag2poly#numpy.polynomial.laguerre.lag2poly \"numpy.polynomial.laguerre.lag2poly\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial.laguerre import poly2lag\n>>> poly2lag(np.arange(4))\narray([ 23., -63., 58., -18.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.poly2lag.htmlnumpy.polynomial.legendre.Legendre\n==================================\n\n *class*numpy.polynomial.legendre.Legendre(*coef*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1619-L1658)\n \nA Legendre series class.\n\n The Legendre class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed in the `ABCPolyBase` documentation.\n\n Parameters \n \n**coef**array_like\n\nLegendre coefficients in order of increasing degree, i.e., `(1, 2, 3)` gives `1*P_0(x) + 2*P_1(x) + 3*P_2(x)`.\n\n \n**domain**(2,) array_like, optional\n\nDomain to use. The interval `[domain[0], domain[1]]` is mapped to the interval `[window[0], window[1]]` by shifting and scaling. The default value is [-1, 1].\n\n \n**window**(2,) array_like, optional\n\nWindow, see [`domain`](numpy.polynomial.legendre.legendre.domain#numpy.polynomial.legendre.Legendre.domain \"numpy.polynomial.legendre.Legendre.domain\") for its use. The default value is [-1, 1].\n\n New in version 1.6.0.\n\n #### Methods\n\n \n\n| | |\n| --- | --- |\n| [`__call__`](numpy.polynomial.legendre.legendre.__call__#numpy.polynomial.legendre.Legendre.__call__ \"numpy.polynomial.legendre.Legendre.__call__\")(arg) | Call self as a function. |\n| [`basis`](numpy.polynomial.legendre.legendre.basis#numpy.polynomial.legendre.Legendre.basis \"numpy.polynomial.legendre.Legendre.basis\")(deg[, domain, window]) | Series basis polynomial of degree `deg`. |\n| [`cast`](numpy.polynomial.legendre.legendre.cast#numpy.polynomial.legendre.Legendre.cast \"numpy.polynomial.legendre.Legendre.cast\")(series[, domain, window]) | Convert series to series of this class. |\n| [`convert`](numpy.polynomial.legendre.legendre.convert#numpy.polynomial.legendre.Legendre.convert \"numpy.polynomial.legendre.Legendre.convert\")([domain, kind, window]) | Convert series to a different kind and/or domain and/or window. |\n| [`copy`](numpy.polynomial.legendre.legendre.copy#numpy.polynomial.legendre.Legendre.copy \"numpy.polynomial.legendre.Legendre.copy\")() | Return a copy. |\n| [`cutdeg`](numpy.polynomial.legendre.legendre.cutdeg#numpy.polynomial.legendre.Legendre.cutdeg \"numpy.polynomial.legendre.Legendre.cutdeg\")(deg) | Truncate series to the given degree. |\n| [`degree`](numpy.polynomial.legendre.legendre.degree#numpy.polynomial.legendre.Legendre.degree \"numpy.polynomial.legendre.Legendre.degree\")() | The degree of the series. |\n| [`deriv`](numpy.polynomial.legendre.legendre.deriv#numpy.polynomial.legendre.Legendre.deriv \"numpy.polynomial.legendre.Legendre.deriv\")([m]) | Differentiate. |\n| [`fit`](numpy.polynomial.legendre.legendre.fit#numpy.polynomial.legendre.Legendre.fit \"numpy.polynomial.legendre.Legendre.fit\")(x, y, deg[, domain, rcond, full, w, window]) | Least squares fit to data. |\n| [`fromroots`](numpy.polynomial.legendre.legendre.fromroots#numpy.polynomial.legendre.Legendre.fromroots \"numpy.polynomial.legendre.Legendre.fromroots\")(roots[, domain, window]) | Return series instance that has the specified roots. |\n| [`has_samecoef`](numpy.polynomial.legendre.legendre.has_samecoef#numpy.polynomial.legendre.Legendre.has_samecoef \"numpy.polynomial.legendre.Legendre.has_samecoef\")(other) | Check if coefficients match. |\n| [`has_samedomain`](numpy.polynomial.legendre.legendre.has_samedomain#numpy.polynomial.legendre.Legendre.has_samedomain \"numpy.polynomial.legendre.Legendre.has_samedomain\")(other) | Check if domains match. |\n| [`has_sametype`](numpy.polynomial.legendre.legendre.has_sametype#numpy.polynomial.legendre.Legendre.has_sametype \"numpy.polynomial.legendre.Legendre.has_sametype\")(other) | Check if types match. |\n| [`has_samewindow`](numpy.polynomial.legendre.legendre.has_samewindow#numpy.polynomial.legendre.Legendre.has_samewindow \"numpy.polynomial.legendre.Legendre.has_samewindow\")(other) | Check if windows match. |\n| [`identity`](numpy.polynomial.legendre.legendre.identity#numpy.polynomial.legendre.Legendre.identity \"numpy.polynomial.legendre.Legendre.identity\")([domain, window]) | Identity function. |\n| [`integ`](numpy.polynomial.legendre.legendre.integ#numpy.polynomial.legendre.Legendre.integ \"numpy.polynomial.legendre.Legendre.integ\")([m, k, lbnd]) | Integrate. |\n| [`linspace`](numpy.polynomial.legendre.legendre.linspace#numpy.polynomial.legendre.Legendre.linspace \"numpy.polynomial.legendre.Legendre.linspace\")([n, domain]) | Return x, y values at equally spaced points in domain. |\n| [`mapparms`](numpy.polynomial.legendre.legendre.mapparms#numpy.polynomial.legendre.Legendre.mapparms \"numpy.polynomial.legendre.Legendre.mapparms\")() | Return the mapping parameters. |\n| [`roots`](numpy.polynomial.legendre.legendre.roots#numpy.polynomial.legendre.Legendre.roots \"numpy.polynomial.legendre.Legendre.roots\")() | Return the roots of the series polynomial. |\n| [`trim`](numpy.polynomial.legendre.legendre.trim#numpy.polynomial.legendre.Legendre.trim \"numpy.polynomial.legendre.Legendre.trim\")([tol]) | Remove trailing coefficients |\n| [`truncate`](numpy.polynomial.legendre.legendre.truncate#numpy.polynomial.legendre.Legendre.truncate \"numpy.polynomial.legendre.Legendre.truncate\")(size) | Truncate series to length `size`. |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.htmlnumpy.polynomial.legendre.legdomain\n===================================\n\n polynomial.legendre.legdomain*=array([-1, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legdomain.htmlnumpy.polynomial.legendre.legzero\n=================================\n\n polynomial.legendre.legzero*=array([0])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legzero.htmlnumpy.polynomial.legendre.legone\n================================\n\n polynomial.legendre.legone*=array([1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legone.htmlnumpy.polynomial.legendre.legx\n==============================\n\n polynomial.legendre.legx*=array([0, 1])*\n \nAn array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.)\n\n Arrays should be constructed using [`array`](numpy.array#numpy.array \"numpy.array\"), [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\") or [`empty`](numpy.empty#numpy.empty \"numpy.empty\") (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(…)`) for instantiating an array.\n\n For more information, refer to the [`numpy`](../index#module-numpy \"numpy\") module and examine the methods and attributes of an array.\n\n Parameters \n **(for the __new__ method; see Notes below)**\n\n**shape**tuple of ints\n\nShape of created array.\n\n \n**dtype**data-type, optional\n\nAny object that can be interpreted as a numpy data type.\n\n \n**buffer**object exposing buffer interface, optional\n\nUsed to fill the array with data.\n\n \n**offset**int, optional\n\nOffset of array data in buffer.\n\n \n**strides**tuple of ints, optional\n\nStrides of data in memory.\n\n \n**order**{‘C’, ‘F’}, optional\n\nRow-major (C-style) or column-major (Fortran-style) order.\n\n See also\n\n [`array`](numpy.array#numpy.array \"numpy.array\")\n\nConstruct an array.\n\n [`zeros`](numpy.zeros#numpy.zeros \"numpy.zeros\")\n\nCreate an array, each element of which is zero.\n\n [`empty`](numpy.empty#numpy.empty \"numpy.empty\")\n\nCreate an array, but leave its allocated memory unchanged (i.e., it contains “garbage”).\n\n [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\")\n\nCreate a data-type.\n\n [`numpy.typing.NDArray`](../typing#numpy.typing.NDArray \"numpy.typing.NDArray\")\n\nAn ndarray alias [generic](https://docs.python.org/3/glossary.html#term-generic-type \"(in Python v3.10)\") w.r.t. its [`dtype.type`](numpy.dtype.type#numpy.dtype.type \"numpy.dtype.type\").\n\n #### Notes\n\n There are two modes of creating an array using `__new__`:\n\n 1. If `buffer` is None, then only [`shape`](numpy.shape#numpy.shape \"numpy.shape\"), [`dtype`](numpy.dtype#numpy.dtype \"numpy.dtype\"), and `order` are used.\n2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted.\n\n No `__init__` method is needed because the array is fully initialized after the `__new__` method.\n\n #### Examples\n\n These examples illustrate the low-level [`ndarray`](numpy.ndarray#numpy.ndarray \"numpy.ndarray\") constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray.\n\n First mode, `buffer` is None:\n\n \n```\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n [ nan, 2.5e-323]])\n\n```\n Second mode:\n\n \n```\n>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n... offset=np.int_().itemsize,\n... dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n\n```\n Attributes \n \n**T**ndarray\n\nTranspose of the array.\n\n \n**data**buffer\n\nThe array’s elements, in memory.\n\n \n**dtype**dtype object\n\nDescribes the format of the elements in the array.\n\n \n**flags**dict\n\nDictionary containing information related to memory use, e.g., ‘C_CONTIGUOUS’, ‘OWNDATA’, ‘WRITEABLE’, etc.\n\n \n**flat**numpy.flatiter object\n\nFlattened version of the array as an iterator. The iterator allows assignments, e.g., `x.flat = 3` (See [`ndarray.flat`](numpy.ndarray.flat#numpy.ndarray.flat \"numpy.ndarray.flat\") for assignment examples; TODO).\n\n \n**imag**ndarray\n\nImaginary part of the array.\n\n \n**real**ndarray\n\nReal part of the array.\n\n \n**size**int\n\nNumber of elements in the array.\n\n \n**itemsize**int\n\nThe memory use of each array element in bytes.\n\n \n**nbytes**int\n\nThe total number of bytes required to store the array data, i.e., `itemsize * size`.\n\n \n**ndim**int\n\nThe array’s number of dimensions.\n\n \n**shape**tuple of ints\n\nShape of the array.\n\n \n**strides**tuple of ints\n\nThe step-size required to move from one element to the next in memory. For example, a contiguous `(3, 4)` array of type `int16` in C-order has strides `(8, 2)`. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (`2 * 4`).\n\n \n**ctypes**ctypes object\n\nClass containing properties of the array needed for interaction with ctypes.\n\n \n**base**ndarray\n\nIf the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legx.htmlnumpy.polynomial.legendre.legadd\n================================\n\n polynomial.legendre.legadd(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L322-L361)\n \nAdd one Legendre series to another.\n\n Returns the sum of two Legendre series `c1` + `c2`. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Legendre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the Legendre series of their sum.\n\n See also\n\n \n[`legsub`](numpy.polynomial.legendre.legsub#numpy.polynomial.legendre.legsub \"numpy.polynomial.legendre.legsub\"), [`legmulx`](numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\"), [`legmul`](numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\"), [`legdiv`](numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\"), [`legpow`](numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the sum of two Legendre series is a Legendre series (without having to “reproject” the result onto the basis set) so addition, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> L.legadd(c1,c2)\narray([4., 4., 4.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legadd.htmlnumpy.polynomial.legendre.legsub\n================================\n\n polynomial.legendre.legsub(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L364-L405)\n \nSubtract one Legendre series from another.\n\n Returns the difference of two Legendre series `c1` - `c2`. The sequences of coefficients are from lowest order term to highest, i.e., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Legendre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Legendre series coefficients representing their difference.\n\n See also\n\n \n[`legadd`](numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\"), [`legmulx`](numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\"), [`legmul`](numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\"), [`legdiv`](numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\"), [`legpow`](numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")\n\n #### Notes\n\n Unlike multiplication, division, etc., the difference of two Legendre series is a Legendre series (without having to “reproject” the result onto the basis set) so subtraction, just like that of “standard” polynomials, is simply “component-wise.”\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> L.legsub(c1,c2)\narray([-2., 0., 2.])\n>>> L.legsub(c2,c1) # -C.legsub(c1,c2)\narray([ 2., 0., -2.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legsub.htmlnumpy.polynomial.legendre.legmulx\n=================================\n\n polynomial.legendre.legmulx(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L408-L461)\n \nMultiply a Legendre series by x.\n\n Multiply the Legendre series `c` by x, where x is the independent variable.\n\n Parameters \n \n**c**array_like\n\n1-D array of Legendre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nArray representing the result of the multiplication.\n\n See also\n\n \n[`legadd`](numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\"), [`legmul`](numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\"), [`legdiv`](numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\"), [`legpow`](numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")\n\n #### Notes\n\n The multiplication uses the recursion relationship for Legendre polynomials in the form\n\n \\[xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1)\\] #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> L.legmulx([1,2,3])\narray([ 0.66666667, 2.2, 1.33333333, 1.8]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legmulx.htmlnumpy.polynomial.legendre.legmul\n================================\n\n polynomial.legendre.legmul(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L464-L529)\n \nMultiply one Legendre series by another.\n\n Returns the product of two Legendre series `c1` * `c2`. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Legendre series coefficients ordered from low to high.\n\n Returns \n \n**out**ndarray\n\nOf Legendre series coefficients representing their product.\n\n See also\n\n \n[`legadd`](numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\"), [`legsub`](numpy.polynomial.legendre.legsub#numpy.polynomial.legendre.legsub \"numpy.polynomial.legendre.legsub\"), [`legmulx`](numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\"), [`legdiv`](numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\"), [`legpow`](numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")\n\n #### Notes\n\n In general, the (polynomial) product of two C-series results in terms that are not in the Legendre polynomial basis set. Thus, to express the product as a Legendre series, it is necessary to “reproject” the product onto said basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c1 = (1,2,3)\n>>> c2 = (3,2)\n>>> L.legmul(c1,c2) # multiplication requires \"reprojection\"\narray([ 4.33333333, 10.4 , 11.66666667, 3.6 ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legmul.htmlnumpy.polynomial.legendre.legdiv\n================================\n\n polynomial.legendre.legdiv(*c1*, *c2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L532-L578)\n \nDivide one Legendre series by another.\n\n Returns the quotient-with-remainder of two Legendre series `c1` / `c2`. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series `P_0 + 2*P_1 + 3*P_2`.\n\n Parameters \n \n**c1, c2**array_like\n\n1-D arrays of Legendre series coefficients ordered from low to high.\n\n Returns \n \n**quo, rem**ndarrays\n\nOf Legendre series coefficients representing the quotient and remainder.\n\n See also\n\n \n[`legadd`](numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\"), [`legsub`](numpy.polynomial.legendre.legsub#numpy.polynomial.legendre.legsub \"numpy.polynomial.legendre.legsub\"), [`legmulx`](numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\"), [`legmul`](numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\"), [`legpow`](numpy.polynomial.legendre.legpow#numpy.polynomial.legendre.legpow \"numpy.polynomial.legendre.legpow\")\n\n #### Notes\n\n In general, the (polynomial) division of one Legendre series by another results in quotient and remainder terms that are not in the Legendre polynomial basis set. Thus, to express these results as a Legendre series, it is necessary to “reproject” the results onto the Legendre basis set, which may produce “unintuitive” (but correct) results; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c1 = (1,2,3)\n>>> c2 = (3,2,1)\n>>> L.legdiv(c1,c2) # quotient \"intuitive,\" remainder not\n(array([3.]), array([-8., -4.]))\n>>> c2 = (0,1,2,3)\n>>> L.legdiv(c2,c1) # neither \"intuitive\"\n(array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852])) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legdiv.htmlnumpy.polynomial.legendre.legpow\n================================\n\n polynomial.legendre.legpow(*c*, *pow*, *maxpower=16*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L581-L609)\n \nRaise a Legendre series to a power.\n\n Returns the Legendre series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series `P_0 + 2*P_1 + 3*P_2.`\n\n Parameters \n \n**c**array_like\n\n1-D array of Legendre series coefficients ordered from low to high.\n\n \n**pow**integer\n\nPower to which the series will be raised\n\n \n**maxpower**integer, optional\n\nMaximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16\n\n Returns \n \n**coef**ndarray\n\nLegendre series of power.\n\n See also\n\n \n[`legadd`](numpy.polynomial.legendre.legadd#numpy.polynomial.legendre.legadd \"numpy.polynomial.legendre.legadd\"), [`legsub`](numpy.polynomial.legendre.legsub#numpy.polynomial.legendre.legsub \"numpy.polynomial.legendre.legsub\"), [`legmulx`](numpy.polynomial.legendre.legmulx#numpy.polynomial.legendre.legmulx \"numpy.polynomial.legendre.legmulx\"), [`legmul`](numpy.polynomial.legendre.legmul#numpy.polynomial.legendre.legmul \"numpy.polynomial.legendre.legmul\"), [`legdiv`](numpy.polynomial.legendre.legdiv#numpy.polynomial.legendre.legdiv \"numpy.polynomial.legendre.legdiv\")\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legpow.htmlnumpy.polynomial.legendre.legval\n================================\n\n polynomial.legendre.legval(*x*, *c*, *tensor=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L832-L914)\n \nEvaluate a Legendre series at points x.\n\n If `c` is of length `n + 1`, this function returns the value:\n\n \\[p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x)\\] The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either `x` or its elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If `c` is multidimensional, then the shape of the result depends on the value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that scalars have shape (,).\n\n Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.\n\n Parameters \n \n**x**array_like, compatible object\n\nIf `x` is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, `x` or its elements must support addition and multiplication with themselves and with the elements of `c`.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If `c` is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of `c`.\n\n \n**tensor**boolean, optional\n\nIf True, the shape of the coefficient array is extended with ones on the right, one for each dimension of `x`. Scalars have dimension 0 for this action. The result is that every column of coefficients in `c` is evaluated for every element of `x`. If False, `x` is broadcast over the columns of `c` for the evaluation. This keyword is useful when `c` is multidimensional. The default value is True.\n\n New in version 1.7.0.\n\n Returns \n \n**values**ndarray, algebra_like\n\nThe shape of the return value is described above.\n\n See also\n\n \n[`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`leggrid2d`](numpy.polynomial.legendre.leggrid2d#numpy.polynomial.legendre.leggrid2d \"numpy.polynomial.legendre.leggrid2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\"), [`leggrid3d`](numpy.polynomial.legendre.leggrid3d#numpy.polynomial.legendre.leggrid3d \"numpy.polynomial.legendre.leggrid3d\")\n\n #### Notes\n\n The evaluation uses Clenshaw recursion, aka synthetic division.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legval.htmlnumpy.polynomial.legendre.legval2d\n==================================\n\n polynomial.legendre.legval2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L917-L963)\n \nEvaluate a 2-D Legendre series at points (x, y).\n\n This function returns the values:\n\n \\[p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y)\\] The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional Legendre series at points formed from pairs of corresponding values from `x` and `y`.\n\n See also\n\n \n[`legval`](numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\"), [`leggrid2d`](numpy.polynomial.legendre.leggrid2d#numpy.polynomial.legendre.leggrid2d \"numpy.polynomial.legendre.leggrid2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\"), [`leggrid3d`](numpy.polynomial.legendre.leggrid3d#numpy.polynomial.legendre.leggrid3d \"numpy.polynomial.legendre.leggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legval2d.htmlnumpy.polynomial.legendre.legval3d\n==================================\n\n polynomial.legendre.legval3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1019-L1067)\n \nEvaluate a 3-D Legendre series at points (x, y, z).\n\n This function returns the values:\n\n \\[p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z)\\] The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible object\n\nThe three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in `c[i,j,k]`. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`.\n\n See also\n\n \n[`legval`](numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\"), [`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`leggrid2d`](numpy.polynomial.legendre.leggrid2d#numpy.polynomial.legendre.leggrid2d \"numpy.polynomial.legendre.leggrid2d\"), [`leggrid3d`](numpy.polynomial.legendre.leggrid3d#numpy.polynomial.legendre.leggrid3d \"numpy.polynomial.legendre.leggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legval3d.htmlnumpy.polynomial.legendre.leggrid2d\n===================================\n\n polynomial.legendre.leggrid2d(*x*, *y*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L966-L1016)\n \nEvaluate a 2-D Legendre series on the Cartesian product of x and y.\n\n This function returns the values:\n\n \\[p(a,b) = \\sum_{i,j} c_{i,j} * L_i(a) * L_j(b)\\] where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second.\n\n The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape + y.shape.\n\n Parameters \n \n**x, y**array_like, compatible objects\n\nThe two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional Chebyshev series at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`legval`](numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\"), [`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\"), [`leggrid3d`](numpy.polynomial.legendre.leggrid3d#numpy.polynomial.legendre.leggrid3d \"numpy.polynomial.legendre.leggrid3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.leggrid2d.htmlnumpy.polynomial.legendre.leggrid3d\n===================================\n\n polynomial.legendre.leggrid3d(*x*, *y*, *z*, *c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1070-L1123)\n \nEvaluate a 3-D Legendre series on the Cartesian product of x, y, and z.\n\n This function returns the values:\n\n \\[p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\\] where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third.\n\n The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`.\n\n If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.\n\n Parameters \n \n**x, y, z**array_like, compatible objects\n\nThe three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.\n\n \n**c**array_like\n\nArray of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients.\n\n Returns \n \n**values**ndarray, compatible object\n\nThe values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`.\n\n See also\n\n \n[`legval`](numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\"), [`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`leggrid2d`](numpy.polynomial.legendre.leggrid2d#numpy.polynomial.legendre.leggrid2d \"numpy.polynomial.legendre.leggrid2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.leggrid3d.htmlnumpy.polynomial.legendre.legder\n================================\n\n polynomial.legendre.legder(*c*, *m=1*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L612-L701)\n \nDifferentiate a Legendre series.\n\n Returns the Legendre series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `1*L_0 + 2*L_1 + 3*L_2` while [[1,2],[1,2]] represents `1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) +\n2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nNumber of derivatives taken, must be non-negative. (Default: 1)\n\n \n**scl**scalar, optional\n\nEach differentiation is multiplied by `scl`. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the derivative is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**der**ndarray\n\nLegendre series of the derivative.\n\n See also\n\n [`legint`](numpy.polynomial.legendre.legint#numpy.polynomial.legendre.legint \"numpy.polynomial.legendre.legint\")\n #### Notes\n\n In general, the result of differentiating a Legendre series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c = (1,2,3,4)\n>>> L.legder(c)\narray([ 6., 9., 20.])\n>>> L.legder(c, 3)\narray([60.])\n>>> L.legder(c, scl=-1)\narray([ -6., -9., -20.])\n>>> L.legder(c, 2,-1)\narray([ 9., 60.])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legder.htmlnumpy.polynomial.legendre.legint\n================================\n\n polynomial.legendre.legint(*c*, *m=1*, *k=[]*, *lbnd=0*, *scl=1*, *axis=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L704-L829)\n \nIntegrate a Legendre series.\n\n Returns the Legendre series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series `L_0 + 2*L_1 + 3*L_2` while [[1,2],[1,2]] represents `1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) +\n2*L_1(x)*L_1(y)` if axis=0 is `x` and axis=1 is `y`.\n\n Parameters \n \n**c**array_like\n\nArray of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.\n\n \n**m**int, optional\n\nOrder of integration, must be positive. (Default: 1)\n\n \n**k**{[], list, scalar}, optional\n\nIntegration constant(s). The value of the first integral at `lbnd` is the first value in the list, the value of the second integral at `lbnd` is the second value, etc. If `k == []` (the default), all constants are set to zero. If `m == 1`, a single scalar can be given instead of a list.\n\n \n**lbnd**scalar, optional\n\nThe lower bound of the integral. (Default: 0)\n\n \n**scl**scalar, optional\n\nFollowing each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1)\n\n \n**axis**int, optional\n\nAxis over which the integral is taken. (Default: 0).\n\n New in version 1.7.0.\n\n Returns \n \n**S**ndarray\n\nLegendre series coefficient array of the integral.\n\n Raises \n ValueError\n\nIf `m < 0`, `len(k) > m`, `np.ndim(lbnd) != 0`, or `np.ndim(scl) != 0`.\n\n See also\n\n [`legder`](numpy.polynomial.legendre.legder#numpy.polynomial.legendre.legder \"numpy.polynomial.legendre.legder\")\n #### Notes\n\n Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable \\(u = ax + b\\) in an integral relative to `x`. Then \\(dx = du/a\\), so one will need to set `scl` equal to \\(1/a\\) - perhaps not what one would have first thought.\n\n Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import legendre as L\n>>> c = (1,2,3)\n>>> L.legint(c)\narray([ 0.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary\n>>> L.legint(c, 3)\narray([ 1.66666667e-02, -1.78571429e-02, 4.76190476e-02, # may vary\n -1.73472348e-18, 1.90476190e-02, 9.52380952e-03])\n>>> L.legint(c, k=3)\n array([ 3.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary\n>>> L.legint(c, lbnd=-2)\narray([ 7.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary\n>>> L.legint(c, scl=2)\narray([ 0.66666667, 0.8 , 1.33333333, 1.2 ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legint.htmlnumpy.polynomial.legendre.legfromroots\n======================================\n\n polynomial.legendre.legfromroots(*roots*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L267-L319)\n \nGenerate a Legendre series with given roots.\n\n The function returns the coefficients of the polynomial\n\n \\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\\] in Legendre form, where the `r_n` are the roots specified in [`roots`](numpy.roots#numpy.roots \"numpy.roots\"). If a zero has multiplicity n, then it must appear in [`roots`](numpy.roots#numpy.roots \"numpy.roots\") n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then [`roots`](numpy.roots#numpy.roots \"numpy.roots\") looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.\n\n If the returned coefficients are `c`, then\n\n \\[p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x)\\] The coefficient of the last term is not generally 1 for monic polynomials in Legendre form.\n\n Parameters \n \n**roots**array_like\n\nSequence containing the roots.\n\n Returns \n \n**out**ndarray\n\n1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below).\n\n See also\n\n [`numpy.polynomial.polynomial.polyfromroots`](numpy.polynomial.polynomial.polyfromroots#numpy.polynomial.polynomial.polyfromroots \"numpy.polynomial.polynomial.polyfromroots\")\n[`numpy.polynomial.chebyshev.chebfromroots`](numpy.polynomial.chebyshev.chebfromroots#numpy.polynomial.chebyshev.chebfromroots \"numpy.polynomial.chebyshev.chebfromroots\")\n[`numpy.polynomial.laguerre.lagfromroots`](numpy.polynomial.laguerre.lagfromroots#numpy.polynomial.laguerre.lagfromroots \"numpy.polynomial.laguerre.lagfromroots\")\n[`numpy.polynomial.hermite.hermfromroots`](numpy.polynomial.hermite.hermfromroots#numpy.polynomial.hermite.hermfromroots \"numpy.polynomial.hermite.hermfromroots\")\n[`numpy.polynomial.hermite_e.hermefromroots`](numpy.polynomial.hermite_e.hermefromroots#numpy.polynomial.hermite_e.hermefromroots \"numpy.polynomial.hermite_e.hermefromroots\")\n #### Examples\n\n \n```\n>>> import numpy.polynomial.legendre as L\n>>> L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis\narray([ 0. , -0.4, 0. , 0.4])\n>>> j = complex(0,1)\n>>> L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis\narray([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legfromroots.htmlnumpy.polynomial.legendre.legroots\n==================================\n\n polynomial.legendre.legroots(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1459-L1517)\n \nCompute the roots of a Legendre series.\n\n Return the roots (a.k.a. “zeros”) of the polynomial\n\n \\[p(x) = \\sum_i c[i] * L_i(x).\\] Parameters \n \n**c**1-D array_like\n\n1-D array of coefficients.\n\n Returns \n \n**out**ndarray\n\nArray of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex.\n\n See also\n\n [`numpy.polynomial.polynomial.polyroots`](numpy.polynomial.polynomial.polyroots#numpy.polynomial.polynomial.polyroots \"numpy.polynomial.polynomial.polyroots\")\n[`numpy.polynomial.chebyshev.chebroots`](numpy.polynomial.chebyshev.chebroots#numpy.polynomial.chebyshev.chebroots \"numpy.polynomial.chebyshev.chebroots\")\n[`numpy.polynomial.laguerre.lagroots`](numpy.polynomial.laguerre.lagroots#numpy.polynomial.laguerre.lagroots \"numpy.polynomial.laguerre.lagroots\")\n[`numpy.polynomial.hermite.hermroots`](numpy.polynomial.hermite.hermroots#numpy.polynomial.hermite.hermroots \"numpy.polynomial.hermite.hermroots\")\n[`numpy.polynomial.hermite_e.hermeroots`](numpy.polynomial.hermite_e.hermeroots#numpy.polynomial.hermite_e.hermeroots \"numpy.polynomial.hermite_e.hermeroots\")\n #### Notes\n\n The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.\n\n The Legendre series basis polynomials aren’t powers of `x` so the results of this function may seem unintuitive.\n\n #### Examples\n\n \n```\n>>> import numpy.polynomial.legendre as leg\n>>> leg.legroots((1, 2, 3, 4)) # 4L_3 + 3L_2 + 2L_1 + 1L_0, all real roots\narray([-0.85099543, -0.11407192, 0.51506735]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legroots.htmlnumpy.polynomial.legendre.legvander\n===================================\n\n polynomial.legendre.legvander(*x*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1126-L1176)\n \nPseudo-Vandermonde matrix of given degree.\n\n Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., i] = L_i(x)\\] where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the Legendre polynomial.\n\n If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the array `V = legvander(x, n)`, then `np.dot(V, c)` and `legval(x, c)` are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Legendre series of the same degree and sample points.\n\n Parameters \n \n**x**array_like\n\nArray of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array.\n\n \n**deg**int\n\nDegree of the resulting matrix.\n\n Returns \n \n**vander**ndarray\n\nThe pseudo-Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding Legendre polynomial. The dtype will be the same as the converted `x`.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legvander.htmlnumpy.polynomial.legendre.legvander2d\n=====================================\n\n polynomial.legendre.legvander2d(*x*, *y*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1179-L1229)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y),\\] where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the Legendre polynomials.\n\n If `V = legvander2d(x, y, [xdeg, ydeg])`, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order\n\n \\[c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...\\] and `np.dot(V, c.flat)` and `legval2d(x, y, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D Legendre series of the same degrees and sample points.\n\n Parameters \n \n**x, y**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg].\n\n Returns \n \n**vander2d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)\\). The dtype will be the same as the converted `x` and `y`.\n\n See also\n\n \n[`legvander`](numpy.polynomial.legendre.legvander#numpy.polynomial.legendre.legvander \"numpy.polynomial.legendre.legvander\"), [`legvander3d`](numpy.polynomial.legendre.legvander3d#numpy.polynomial.legendre.legvander3d \"numpy.polynomial.legendre.legvander3d\"), [`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legvander2d.htmlnumpy.polynomial.legendre.legvander3d\n=====================================\n\n polynomial.legendre.legvander3d(*x*, *y*, *z*, *deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1232-L1283)\n \nPseudo-Vandermonde matrix of given degrees.\n\n Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then The pseudo-Vandermonde matrix is defined by\n\n \\[V[..., (m+1)(n+1)i + (n+1)j + k] = L_i(x)*L_j(y)*L_k(z),\\] where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the Legendre polynomials.\n\n If `V = legvander3d(x, y, z, [xdeg, ydeg, zdeg])`, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order\n\n \\[c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...\\] and `np.dot(V, c.flat)` and `legval3d(x, y, z, c)` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D Legendre series of the same degrees and sample points.\n\n Parameters \n \n**x, y, z**array_like\n\nArrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays.\n\n \n**deg**list of ints\n\nList of maximum degrees of the form [x_deg, y_deg, z_deg].\n\n Returns \n \n**vander3d**ndarray\n\nThe shape of the returned matrix is `x.shape + (order,)`, where \\(order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)\\). The dtype will be the same as the converted `x`, `y`, and `z`.\n\n See also\n\n \n[`legvander`](numpy.polynomial.legendre.legvander#numpy.polynomial.legendre.legvander \"numpy.polynomial.legendre.legvander\"), [`legvander3d`](#numpy.polynomial.legendre.legvander3d \"numpy.polynomial.legendre.legvander3d\"), [`legval2d`](numpy.polynomial.legendre.legval2d#numpy.polynomial.legendre.legval2d \"numpy.polynomial.legendre.legval2d\"), [`legval3d`](numpy.polynomial.legendre.legval3d#numpy.polynomial.legendre.legval3d \"numpy.polynomial.legendre.legval3d\")\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legvander3d.htmlnumpy.polynomial.legendre.leggauss\n==================================\n\n polynomial.legendre.leggauss(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1520-L1585)\n \nGauss-Legendre quadrature.\n\n Computes the sample points and weights for Gauss-Legendre quadrature. These sample points and weights will correctly integrate polynomials of degree \\(2*deg - 1\\) or less over the interval \\([-1, 1]\\) with the weight function \\(f(x) = 1\\).\n\n Parameters \n \n**deg**int\n\nNumber of sample points and weights. It must be >= 1.\n\n Returns \n \n**x**ndarray\n\n1-D ndarray containing the sample points.\n\n \n**y**ndarray\n\n1-D ndarray containing the weights.\n\n #### Notes\n\n New in version 1.7.0.\n\n The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that\n\n \\[w_k = c / (L'_n(x_k) * L_{n-1}(x_k))\\] where \\(c\\) is a constant independent of \\(k\\) and \\(x_k\\) is the k’th root of \\(L_n\\), and then scaling the results to get the right value when integrating 1.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.leggauss.htmlnumpy.polynomial.legendre.legweight\n===================================\n\n polynomial.legendre.legweight(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1588-L1613)\n \nWeight function of the Legendre polynomials.\n\n The weight function is \\(1\\) and the interval of integration is \\([-1, 1]\\). The Legendre polynomials are orthogonal, but not normalized, with respect to this weight function.\n\n Parameters \n \n**x**array_like\n\nValues at which the weight function will be computed.\n\n Returns \n \n**w**ndarray\n\nThe weight function at `x`.\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legweight.htmlnumpy.polynomial.legendre.legcompanion\n======================================\n\n polynomial.legendre.legcompanion(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1415-L1456)\n \nReturn the scaled companion matrix of c.\n\n The basis polynomials are scaled so that the companion matrix is symmetric when `c` is an Legendre basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if [`numpy.linalg.eigvalsh`](numpy.linalg.eigvalsh#numpy.linalg.eigvalsh \"numpy.linalg.eigvalsh\") is used to obtain them.\n\n Parameters \n \n**c**array_like\n\n1-D array of Legendre series coefficients ordered from low to high degree.\n\n Returns \n \n**mat**ndarray\n\nScaled companion matrix of dimensions (deg, deg).\n\n #### Notes\n\n New in version 1.7.0.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legcompanion.htmlnumpy.polynomial.legendre.legfit\n================================\n\n polynomial.legendre.legfit(*x*, *y*, *deg*, *rcond=None*, *full=False*, *w=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L1286-L1412)\n \nLeast squares fit of Legendre series to data.\n\n Return the coefficients of a Legendre series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form\n\n \\[p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x),\\] where `n` is `deg`.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,) or (M, K)\n\ny-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (`M`,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n Returns \n \n**coef**ndarray, shape (M,) or (M, K)\n\nLegendre coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`. If `deg` is specified as a list, coefficients for terms not included in the fit are set equal to zero in the returned `coef`.\n\n \n**[residuals, rank, singular_values, rcond]**list\n\nThese values are only returned if `full == True`\n\n * residuals – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* singular_values – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n Warns \n RankWarning\n\nThe rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full == False`. The warnings can be turned off by\n\n \n```\n>>> import warnings\n>>> warnings.simplefilter('ignore', np.RankWarning)\n\n```\n See also\n\n [`numpy.polynomial.polynomial.polyfit`](numpy.polynomial.polynomial.polyfit#numpy.polynomial.polynomial.polyfit \"numpy.polynomial.polynomial.polyfit\")\n[`numpy.polynomial.chebyshev.chebfit`](numpy.polynomial.chebyshev.chebfit#numpy.polynomial.chebyshev.chebfit \"numpy.polynomial.chebyshev.chebfit\")\n[`numpy.polynomial.laguerre.lagfit`](numpy.polynomial.laguerre.lagfit#numpy.polynomial.laguerre.lagfit \"numpy.polynomial.laguerre.lagfit\")\n[`numpy.polynomial.hermite.hermfit`](numpy.polynomial.hermite.hermfit#numpy.polynomial.hermite.hermfit \"numpy.polynomial.hermite.hermfit\")\n[`numpy.polynomial.hermite_e.hermefit`](numpy.polynomial.hermite_e.hermefit#numpy.polynomial.hermite_e.hermefit \"numpy.polynomial.hermite_e.hermefit\")\n[`legval`](numpy.polynomial.legendre.legval#numpy.polynomial.legendre.legval \"numpy.polynomial.legendre.legval\")\n\nEvaluates a Legendre series.\n\n [`legvander`](numpy.polynomial.legendre.legvander#numpy.polynomial.legendre.legvander \"numpy.polynomial.legendre.legvander\")\n\nVandermonde matrix of Legendre series.\n\n [`legweight`](numpy.polynomial.legendre.legweight#numpy.polynomial.legendre.legweight \"numpy.polynomial.legendre.legweight\")\n\nLegendre weight function (= 1).\n\n [`numpy.linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\")\n\nComputes a least-squares fit from the matrix.\n\n [`scipy.interpolate.UnivariateSpline`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html#scipy.interpolate.UnivariateSpline \"(in SciPy v1.8.1)\")\n\nComputes spline fits.\n\n #### Notes\n\n The solution is the coefficients of the Legendre series `p` that minimizes the sum of the weighted squared errors\n\n \\[E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,\\] where \\(w_j\\) are the weights. This problem is solved by setting up as the (typically) overdetermined matrix equation\n\n \\[V(x) * c = w * y,\\] where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`.\n\n If some of the singular values of `V` are so small that they are neglected, then a [`RankWarning`](numpy.rankwarning#numpy.RankWarning \"numpy.RankWarning\") will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error.\n\n Fits using Legendre series are usually better conditioned than fits using power series, but much can depend on the distribution of the sample points and the smoothness of the data. If the quality of the fit is inadequate splines may be a good alternative.\n\n #### References\n\n 1 \nWikipedia, “Curve fitting”, <https://en.wikipedia.org/wiki/Curve_fitting © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legfit.htmlnumpy.polynomial.legendre.legtrim\n=================================\n\n polynomial.legendre.legtrim(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n `trimseq`\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legtrim.htmlnumpy.polynomial.legendre.legline\n=================================\n\n polynomial.legendre.legline(*off*, *scl*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L227-L264)\n \nLegendre series whose graph is a straight line.\n\n Parameters \n \n**off, scl**scalars\n\nThe specified line is given by `off + scl*x`.\n\n Returns \n \n**y**ndarray\n\nThis module’s representation of the Legendre series for `off + scl*x`.\n\n See also\n\n [`numpy.polynomial.polynomial.polyline`](numpy.polynomial.polynomial.polyline#numpy.polynomial.polynomial.polyline \"numpy.polynomial.polynomial.polyline\")\n[`numpy.polynomial.chebyshev.chebline`](numpy.polynomial.chebyshev.chebline#numpy.polynomial.chebyshev.chebline \"numpy.polynomial.chebyshev.chebline\")\n[`numpy.polynomial.laguerre.lagline`](numpy.polynomial.laguerre.lagline#numpy.polynomial.laguerre.lagline \"numpy.polynomial.laguerre.lagline\")\n[`numpy.polynomial.hermite.hermline`](numpy.polynomial.hermite.hermline#numpy.polynomial.hermite.hermline \"numpy.polynomial.hermite.hermline\")\n[`numpy.polynomial.hermite_e.hermeline`](numpy.polynomial.hermite_e.hermeline#numpy.polynomial.hermite_e.hermeline \"numpy.polynomial.hermite_e.hermeline\")\n #### Examples\n\n \n```\n>>> import numpy.polynomial.legendre as L\n>>> L.legline(3,2)\narray([3, 2])\n>>> L.legval(-3, L.legline(3,2)) # should be -3\n-3.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.legline.htmlnumpy.polynomial.legendre.leg2poly\n==================================\n\n polynomial.legendre.leg2poly(*c*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L148-L207)\n \nConvert a Legendre series to a polynomial.\n\n Convert an array representing the coefficients of a Legendre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.\n\n Parameters \n \n**c**array_like\n\n1-D array containing the Legendre series coefficients, ordered from lowest order term to highest.\n\n Returns \n \n**pol**ndarray\n\n1-D array containing the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest order term to highest.\n\n See also\n\n [`poly2leg`](numpy.polynomial.legendre.poly2leg#numpy.polynomial.legendre.poly2leg \"numpy.polynomial.legendre.poly2leg\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy import polynomial as P\n>>> c = P.Legendre(range(4))\n>>> c\nLegendre([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1])\n>>> p = c.convert(kind=P.Polynomial)\n>>> p\nPolynomial([-1. , -3.5, 3. , 7.5], domain=[-1., 1.], window=[-1., 1.])\n>>> P.legendre.leg2poly(range(4))\narray([-1. , -3.5, 3. , 7.5])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.leg2poly.htmlnumpy.polynomial.legendre.poly2leg\n==================================\n\n polynomial.legendre.poly2leg(*pol*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/legendre.py#L100-L145)\n \nConvert a polynomial to a Legendre series.\n\n Convert an array representing the coefficients of a polynomial (relative to the “standard” basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Legendre series, ordered from lowest to highest degree.\n\n Parameters \n \n**pol**array_like\n\n1-D array containing the polynomial coefficients\n\n Returns \n \n**c**ndarray\n\n1-D array containing the coefficients of the equivalent Legendre series.\n\n See also\n\n [`leg2poly`](numpy.polynomial.legendre.leg2poly#numpy.polynomial.legendre.leg2poly \"numpy.polynomial.legendre.leg2poly\")\n #### Notes\n\n The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance.\n\n #### Examples\n\n \n```\n>>> from numpy import polynomial as P\n>>> p = P.Polynomial(np.arange(4))\n>>> p\nPolynomial([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1])\n>>> c = P.Legendre(P.legendre.poly2leg(p.coef))\n>>> c\nLegendre([ 1. , 3.25, 1. , 0.75], domain=[-1, 1], window=[-1, 1]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.poly2leg.htmlnumpy.polynomial.polyutils.RankWarning\n======================================\n\n *exception*polynomial.polyutils.RankWarning[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L43-L45)\n \nIssued by chebfit when the design matrix is rank deficient.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.RankWarning.htmlnumpy.polynomial.polyutils.as_series\n=====================================\n\n polynomial.polyutils.as_series(*alist*, *trim=True*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L80-L153)\n \nReturn argument as a list of 1-d arrays.\n\n The returned list contains array(s) of dtype double, complex double, or object. A 1-d argument of shape `(N,)` is parsed into `N` arrays of size one; a 2-d argument of shape `(M,N)` is parsed into `M` arrays of size `N` (i.e., is “parsed by row”); and a higher dimensional array raises a Value Error if it is not first reshaped into either a 1-d or 2-d array.\n\n Parameters \n \n**alist**array_like\n\nA 1- or 2-d array_like\n\n \n**trim**boolean, optional\n\nWhen True, trailing zeros are removed from the inputs. When False, the inputs are passed through intact.\n\n Returns \n \n**[a1, a2,…]**list of 1-D arrays\n\nA copy of the input data as a list of 1-d arrays.\n\n Raises \n ValueError\n\nRaised when [`as_series`](#numpy.polynomial.polyutils.as_series \"numpy.polynomial.polyutils.as_series\") cannot convert its input to 1-d arrays, or at least one of the resulting arrays is empty.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> a = np.arange(4)\n>>> pu.as_series(a)\n[array([0.]), array([1.]), array([2.]), array([3.])]\n>>> b = np.arange(6).reshape((2,3))\n>>> pu.as_series(b)\n[array([0., 1., 2.]), array([3., 4., 5.])]\n\n```\n \n```\n>>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16)))\n[array([1.]), array([0., 1., 2.]), array([0., 1.])]\n\n```\n \n```\n>>> pu.as_series([2, [1.1, 0.]])\n[array([2.]), array([1.1])]\n\n```\n \n```\n>>> pu.as_series([2, [1.1, 0.]], trim=False)\n[array([2.]), array([1.1, 0. ])]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.as_series.htmlnumpy.polynomial.polyutils.trimseq\n==================================\n\n polynomial.polyutils.trimseq(*seq*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L50-L77)\n \nRemove small Poly series coefficients.\n\n Parameters \n \n**seq**sequence\n\nSequence of Poly series coefficients. This routine fails for empty sequences.\n\n Returns \n \n**series**sequence\n\nSubsequence with trailing zeros removed. If the resulting sequence would be empty, return the first element. The returned sequence may or may not be a view.\n\n #### Notes\n\n Do not lose the type info if the sequence contains unknown objects.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.trimseq.htmlnumpy.polynomial.polyutils.trimcoef\n===================================\n\n polynomial.polyutils.trimcoef(*c*, *tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L156-L208)\n \nRemove “small” “trailing” coefficients from a polynomial.\n\n “Small” means “small in absolute value” and is controlled by the parameter `tol`; “trailing” means highest order coefficient(s), e.g., in `[0, 1, 1, 0, 0]` (which represents `0 + x + x**2 + 0*x**3 + 0*x**4`) both the 3-rd and 4-th order coefficients would be “trimmed.”\n\n Parameters \n \n**c**array_like\n\n1-d array of coefficients, ordered from lowest order to highest.\n\n \n**tol**number, optional\n\nTrailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed.\n\n Returns \n \n**trimmed**ndarray\n\n1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.\n\n Raises \n ValueError\n\nIf `tol` < 0\n\n See also\n\n [`trimseq`](numpy.polynomial.polyutils.trimseq#numpy.polynomial.polyutils.trimseq \"numpy.polynomial.polyutils.trimseq\")\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.trimcoef((0,0,3,0,5,0,0))\narray([0., 0., 3., 0., 5.])\n>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed\narray([0.])\n>>> i = complex(0,1) # works for complex\n>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)\narray([0.0003+0.j , 0.001 -0.001j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.trimcoef.htmlnumpy.polynomial.polyutils.getdomain\n====================================\n\n polynomial.polyutils.getdomain(*x*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L210-L254)\n \nReturn a domain suitable for given abscissae.\n\n Find a domain suitable for a polynomial or Chebyshev series defined at the values supplied.\n\n Parameters \n \n**x**array_like\n\n1-d array of abscissae whose domain will be determined.\n\n Returns \n \n**domain**ndarray\n\n1-d array containing two values. If the inputs are complex, then the two returned points are the lower left and upper right corners of the smallest rectangle (aligned with the axes) in the complex plane containing the points `x`. If the inputs are real, then the two points are the ends of the smallest interval containing the points `x`.\n\n See also\n\n \n[`mapparms`](numpy.polynomial.polyutils.mapparms#numpy.polynomial.polyutils.mapparms \"numpy.polynomial.polyutils.mapparms\"), [`mapdomain`](numpy.polynomial.polyutils.mapdomain#numpy.polynomial.polyutils.mapdomain \"numpy.polynomial.polyutils.mapdomain\")\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> points = np.arange(4)**2 - 5; points\narray([-5, -4, -1, 4])\n>>> pu.getdomain(points)\narray([-5., 4.])\n>>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle\n>>> pu.getdomain(c)\narray([-1.-1.j, 1.+1.j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.getdomain.htmlnumpy.polynomial.polyutils.mapdomain\n====================================\n\n polynomial.polyutils.mapdomain(*x*, *old*, *new*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L303-L368)\n \nApply linear map to input points.\n\n The linear map `offset + scale*x` that maps the domain `old` to the domain `new` is applied to the points `x`.\n\n Parameters \n \n**x**array_like\n\nPoints to be mapped. If `x` is a subtype of ndarray the subtype will be preserved.\n\n \n**old, new**array_like\n\nThe two domains that determine the map. Each must (successfully) convert to 1-d arrays containing precisely two values.\n\n Returns \n \n**x_out**ndarray\n\nArray of points of the same shape as `x`, after application of the linear map between the two domains.\n\n See also\n\n \n[`getdomain`](numpy.polynomial.polyutils.getdomain#numpy.polynomial.polyutils.getdomain \"numpy.polynomial.polyutils.getdomain\"), [`mapparms`](numpy.polynomial.polyutils.mapparms#numpy.polynomial.polyutils.mapparms \"numpy.polynomial.polyutils.mapparms\")\n\n #### Notes\n\n Effectively, this implements:\n\n \\[x\\_out = new[0] + m(x - old[0])\\] where\n\n \\[m = \\frac{new[1]-new[0]}{old[1]-old[0]}\\] #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> old_domain = (-1,1)\n>>> new_domain = (0,2*np.pi)\n>>> x = np.linspace(-1,1,6); x\narray([-1. , -0.6, -0.2, 0.2, 0.6, 1. ])\n>>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out\narray([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary\n 6.28318531])\n>>> x - pu.mapdomain(x_out, new_domain, old_domain)\narray([0., 0., 0., 0., 0., 0.])\n\n```\n Also works for complex numbers (and thus can be used to map any line in the complex plane to any other line therein).\n\n \n```\n>>> i = complex(0,1)\n>>> old = (-1 - i, 1 + i)\n>>> new = (-1 + i, 1 - i)\n>>> z = np.linspace(old[0], old[1], 6); z\narray([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ])\n>>> new_z = pu.mapdomain(z, old, new); new_z\narray([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.mapdomain.htmlnumpy.polynomial.polyutils.mapparms\n===================================\n\n polynomial.polyutils.mapparms(*old*, *new*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/polyutils.py#L256-L301)\n \nLinear map parameters between domains.\n\n Return the parameters of the linear map `offset + scale*x` that maps `old` to `new` such that `old[i] -> new[i]`, `i = 0, 1`.\n\n Parameters \n \n**old, new**array_like\n\nDomains. Each domain must (successfully) convert to a 1-d array containing precisely two values.\n\n Returns \n \n**offset, scale**scalars\n\nThe map `L(x) = offset + scale*x` maps the first domain to the second.\n\n See also\n\n \n[`getdomain`](numpy.polynomial.polyutils.getdomain#numpy.polynomial.polyutils.getdomain \"numpy.polynomial.polyutils.getdomain\"), [`mapdomain`](numpy.polynomial.polyutils.mapdomain#numpy.polynomial.polyutils.mapdomain \"numpy.polynomial.polyutils.mapdomain\")\n\n #### Notes\n\n Also works for complex numbers, and thus can be used to calculate the parameters required to map any line in the complex plane to any other line therein.\n\n #### Examples\n\n \n```\n>>> from numpy.polynomial import polyutils as pu\n>>> pu.mapparms((-1,1),(-1,1))\n(0.0, 1.0)\n>>> pu.mapparms((1,-1),(-1,1))\n(-0.0, -1.0)\n>>> i = complex(0,1)\n>>> pu.mapparms((-i,-1),(1,i))\n((1+1j), (1-0j))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polyutils.mapparms.htmlnumpy.roots\n===========\n\n numpy.roots(*p*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L171-L260)\n \nReturn the roots of a polynomial with coefficients given in p.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n The values in the rank-1 array `p` are coefficients of a polynomial. If the length of `p` is n+1 then the polynomial is described by:\n\n \n```\np[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]\n\n```\n Parameters \n \n**p**array_like\n\nRank-1 array of polynomial coefficients.\n\n Returns \n \n**out**ndarray\n\nAn array containing the roots of the polynomial.\n\n Raises \n ValueError\n\nWhen `p` cannot be converted to a rank-1 array.\n\n See also\n\n [`poly`](numpy.poly#numpy.poly \"numpy.poly\")\n\nFind the coefficients of a polynomial with a given sequence of roots.\n\n [`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n\nCompute polynomial values.\n\n [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\")\n\nLeast squares polynomial fit.\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nA one-dimensional polynomial class.\n\n #### Notes\n\n The algorithm relies on computing the eigenvalues of the companion matrix [[1]](#r01a8f58ef25b-1).\n\n #### References\n\n [1](#id1) \n<NAME> & <NAME>, *Matrix Analysis*. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.\n\n #### Examples\n\n \n```\n>>> coeff = [3.2, 2, 1]\n>>> np.roots(coeff)\narray([-0.3125+0.46351241j, -0.3125-0.46351241j])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.roots.htmlnumpy.polyder\n=============\n\n numpy.polyder(*p*, *m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L372-L445)\n \nReturn the derivative of the specified order of a polynomial.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Parameters \n \n**p**poly1d or sequence\n\nPolynomial to differentiate. A sequence is interpreted as polynomial coefficients, see [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\").\n\n \n**m**int, optional\n\nOrder of differentiation (default: 1)\n\n Returns \n \n**der**poly1d\n\nA new polynomial representing the derivative.\n\n See also\n\n [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\")\n\nAnti-derivative of a polynomial.\n\n [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\")\n\nClass for one-dimensional polynomials.\n\n #### Examples\n\n The derivative of the polynomial \\(x^3 + x^2 + x^1 + 1\\) is:\n\n \n```\n>>> p = np.poly1d([1,1,1,1])\n>>> p2 = np.polyder(p)\n>>> p2\npoly1d([3, 2, 1])\n\n```\n which evaluates to:\n\n \n```\n>>> p2(2.)\n17.0\n\n```\n We can verify this, approximating the derivative with `(f(x + h) - f(x))/h`:\n\n \n```\n>>> (p(2. + 0.001) - p(2.)) / 0.001\n17.007000999997857\n\n```\n The fourth-order derivative of a 3rd-order polynomial is zero:\n\n \n```\n>>> np.polyder(p, 2)\npoly1d([6, 2])\n>>> np.polyder(p, 3)\npoly1d([6])\n>>> np.polyder(p, 4)\npoly1d([0])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polyder.htmlnumpy.polyint\n=============\n\n numpy.polyint(*p*, *m=1*, *k=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L267-L365)\n \nReturn an antiderivative (indefinite integral) of a polynomial.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n The returned order `m` antiderivative `P` of polynomial `p` satisfies \\(\\frac{d^m}{dx^m}P(x) = p(x)\\) and is defined up to `m - 1` integration constants `k`. The constants determine the low-order polynomial part\n\n \\[\\frac{k_{m-1}}{0!} x^0 + \\ldots + \\frac{k_0}{(m-1)!}x^{m-1}\\] of `P` so that \\(P^{(j)}(0) = k_{m-j-1}\\).\n\n Parameters \n \n**p**array_like or poly1d\n\nPolynomial to integrate. A sequence is interpreted as polynomial coefficients, see [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\").\n\n \n**m**int, optional\n\nOrder of the antiderivative. (Default: 1)\n\n \n**k**list of `m` scalars or scalar, optional\n\nIntegration constants. They are given in the order of integration: those corresponding to highest-order terms come first.\n\n If `None` (default), all constants are assumed to be zero. If `m = 1`, a single scalar can be given instead of a list.\n\n See also\n\n [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\")\n\nderivative of a polynomial\n\n [`poly1d.integ`](numpy.poly1d.integ#numpy.poly1d.integ \"numpy.poly1d.integ\")\n\nequivalent method\n\n #### Examples\n\n The defining property of the antiderivative:\n\n \n```\n>>> p = np.poly1d([1,1,1])\n>>> P = np.polyint(p)\n>>> P\n poly1d([ 0.33333333, 0.5 , 1. , 0. ]) # may vary\n>>> np.polyder(P) == p\nTrue\n\n```\n The integration constants default to zero, but can be specified:\n\n \n```\n>>> P = np.polyint(p, 3)\n>>> P(0)\n0.0\n>>> np.polyder(P)(0)\n0.0\n>>> np.polyder(P, 2)(0)\n0.0\n>>> P = np.polyint(p, 3, k=[6,5,3])\n>>> P\npoly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) # may vary\n\n```\n Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first:\n\n \n```\n>>> np.polyder(P, 2)(0)\n6.0\n>>> np.polyder(P, 1)(0)\n5.0\n>>> P(0)\n3.0\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polyint.htmlnumpy.polydiv\n=============\n\n numpy.polydiv(*u*, *v*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L976-L1046)\n \nReturns the quotient and remainder of polynomial division.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n The input arrays are the coefficients (including any coefficients equal to zero) of the “numerator” (dividend) and “denominator” (divisor) polynomials, respectively.\n\n Parameters \n \n**u**array_like or poly1d\n\nDividend polynomial’s coefficients.\n\n \n**v**array_like or poly1d\n\nDivisor polynomial’s coefficients.\n\n Returns \n \n**q**ndarray\n\nCoefficients, including those equal to zero, of the quotient.\n\n \n**r**ndarray\n\nCoefficients, including those equal to zero, of the remainder.\n\n See also\n\n \n[`poly`](numpy.poly#numpy.poly \"numpy.poly\"), [`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\"), [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\"), [`polydiv`](#numpy.polydiv \"numpy.polydiv\"), [`polyfit`](numpy.polyfit#numpy.polyfit \"numpy.polyfit\"), [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polysub`](numpy.polysub#numpy.polysub \"numpy.polysub\")\n\n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\")\n #### Notes\n\n Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need not equal `v.ndim`. In other words, all four possible combinations - `u.ndim = v.ndim = 0`, `u.ndim = v.ndim = 1`, `u.ndim = 1, v.ndim = 0`, and `u.ndim = 0, v.ndim = 1` - work.\n\n #### Examples\n\n \\[\\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25\\] \n```\n>>> x = np.array([3.0, 5.0, 2.0])\n>>> y = np.array([2.0, 1.0])\n>>> np.polydiv(x, y)\n(array([1.5 , 1.75]), array([0.25]))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polydiv.htmlnumpy.polysub\n=============\n\n numpy.polysub(*a1*, *a2*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L855-L906)\n \nDifference (subtraction) of two polynomials.\n\n Note\n\n This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in [`numpy.polynomial`](../routines.polynomials.package#module-numpy.polynomial \"numpy.polynomial\") is preferred. A summary of the differences can be found in the [transition guide](../routines.polynomials).\n\n Given two polynomials `a1` and `a2`, returns `a1 - a2`. `a1` and `a2` can be either array_like sequences of the polynomials’ coefficients (including coefficients equal to zero), or [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\") objects.\n\n Parameters \n \n**a1, a2**array_like or poly1d\n\nMinuend and subtrahend polynomials, respectively.\n\n Returns \n \n**out**ndarray or poly1d\n\nArray or [`poly1d`](numpy.poly1d#numpy.poly1d \"numpy.poly1d\") object of the difference polynomial’s coefficients.\n\n See also\n\n \n[`polyval`](numpy.polyval#numpy.polyval \"numpy.polyval\"), [`polydiv`](numpy.polydiv#numpy.polydiv \"numpy.polydiv\"), [`polymul`](numpy.polymul#numpy.polymul \"numpy.polymul\"), [`polyadd`](numpy.polyadd#numpy.polyadd \"numpy.polyadd\")\n\n #### Examples\n\n \\[(2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2)\\] \n```\n>>> np.polysub([2, 10, -2], [3, 10, -4])\narray([-1, 0, 2])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polysub.htmlnumpy.polynomial.chebyshev.Chebyshev.fit\n========================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.fit.htmlnumpy.poly1d.variable\n=====================\n\n property\n\n *property*poly1d.variable\n \nThe name of the polynomial variable\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.variable.htmlnumpy.poly1d.c\n==============\n\n property\n\n *property*poly1d.c\n \nThe polynomial coefficients\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.c.htmlnumpy.poly1d.coef\n=================\n\n property\n\n *property*poly1d.coef\n \nThe polynomial coefficients\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.coef.htmlnumpy.poly1d.coefficients\n=========================\n\n property\n\n *property*poly1d.coefficients\n \nThe polynomial coefficients\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.coefficients.htmlnumpy.poly1d.coeffs\n===================\n\n property\n\n *property*poly1d.coeffs\n \nThe polynomial coefficients\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.coeffs.htmlnumpy.poly1d.o\n==============\n\n property\n\n *property*poly1d.o\n \nThe order or degree of the polynomial\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.o.htmlnumpy.poly1d.order\n==================\n\n property\n\n *property*poly1d.order\n \nThe order or degree of the polynomial\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.order.htmlnumpy.poly1d.r\n==============\n\n property\n\n *property*poly1d.r\n \nThe roots of the polynomial, where self(x) == 0\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.r.htmlnumpy.poly1d.__call__\n=========================\n\n method\n\n poly1d.__call__(*val*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L1324-L1325)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.__call__.htmlnumpy.poly1d.deriv\n==================\n\n method\n\n poly1d.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L1437-L1448)\n \nReturn a derivative of this polynomial.\n\n Refer to [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\") for full documentation.\n\n See also\n\n [`polyder`](numpy.polyder#numpy.polyder \"numpy.polyder\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.deriv.htmlnumpy.poly1d.integ\n==================\n\n method\n\n poly1d.integ(*m=1*, *k=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/lib/polynomial.py#L1424-L1435)\n \nReturn an antiderivative (indefinite integral) of this polynomial.\n\n Refer to [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\") for full documentation.\n\n See also\n\n [`polyint`](numpy.polyint#numpy.polyint \"numpy.polyint\")\n\nequivalent function\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.poly1d.integ.htmlnumpy.polynomial.polynomial.Polynomial.domain\n=============================================\n\n attribute\n\n polynomial.polynomial.Polynomial.domain*=array([-1, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.domain.htmlnumpy.polynomial.polynomial.Polynomial.__call__\n===================================================\n\n method\n\n polynomial.polynomial.Polynomial.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.__call__.htmlnumpy.polynomial.polynomial.Polynomial.basis\n============================================\n\n method\n\n *classmethod*polynomial.polynomial.Polynomial.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.basis.htmlnumpy.polynomial.polynomial.Polynomial.cast\n===========================================\n\n method\n\n *classmethod*polynomial.polynomial.Polynomial.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.polynomial.polynomial.convert#numpy.polynomial.polynomial.Polynomial.convert \"numpy.polynomial.polynomial.Polynomial.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.cast.htmlnumpy.polynomial.polynomial.Polynomial.copy\n===========================================\n\n method\n\n polynomial.polynomial.Polynomial.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.copy.htmlnumpy.polynomial.polynomial.Polynomial.cutdeg\n=============================================\n\n method\n\n polynomial.polynomial.Polynomial.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.cutdeg.htmlnumpy.polynomial.polynomial.Polynomial.degree\n=============================================\n\n method\n\n polynomial.polynomial.Polynomial.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.degree.htmlnumpy.polynomial.polynomial.Polynomial.deriv\n============================================\n\n method\n\n polynomial.polynomial.Polynomial.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.deriv.htmlnumpy.polynomial.polynomial.Polynomial.fromroots\n================================================\n\n method\n\n *classmethod*polynomial.polynomial.Polynomial.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.fromroots.htmlnumpy.polynomial.polynomial.Polynomial.has_samecoef\n====================================================\n\n method\n\n polynomial.polynomial.Polynomial.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.has_samecoef.htmlnumpy.polynomial.polynomial.Polynomial.has_samedomain\n======================================================\n\n method\n\n polynomial.polynomial.Polynomial.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.has_samedomain.htmlnumpy.polynomial.polynomial.Polynomial.has_sametype\n====================================================\n\n method\n\n polynomial.polynomial.Polynomial.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.has_sametype.htmlnumpy.polynomial.polynomial.Polynomial.has_samewindow\n======================================================\n\n method\n\n polynomial.polynomial.Polynomial.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.has_samewindow.htmlnumpy.polynomial.polynomial.Polynomial.identity\n===============================================\n\n method\n\n *classmethod*polynomial.polynomial.Polynomial.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.identity.htmlnumpy.polynomial.polynomial.Polynomial.integ\n============================================\n\n method\n\n polynomial.polynomial.Polynomial.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.integ.htmlnumpy.polynomial.polynomial.Polynomial.linspace\n===============================================\n\n method\n\n polynomial.polynomial.Polynomial.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.linspace.htmlnumpy.polynomial.polynomial.Polynomial.mapparms\n===============================================\n\n method\n\n polynomial.polynomial.Polynomial.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.mapparms.htmlnumpy.polynomial.polynomial.Polynomial.roots\n============================================\n\n method\n\n polynomial.polynomial.Polynomial.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.roots.htmlnumpy.polynomial.polynomial.Polynomial.trim\n===========================================\n\n method\n\n polynomial.polynomial.Polynomial.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.trim.htmlnumpy.polynomial.polynomial.Polynomial.truncate\n===============================================\n\n method\n\n polynomial.polynomial.Polynomial.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.polynomial.Polynomial.truncate.htmlnumpy.random.Generator.bit_generator\n=====================================\n\n attribute\n\n random.Generator.bit_generator\n \nGets the bit generator instance used by the generator\n\n Returns \n \n**bit_generator**BitGenerator\n\nThe bit generator instance used by the generator\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.bit_generator.htmlnumpy.random.Generator.bytes\n============================\n\n method\n\n random.Generator.bytes(*length*)\n \nReturn random bytes.\n\n Parameters \n \n**length**int\n\nNumber of random bytes.\n\n Returns \n \n**out**bytes\n\nString of length `length`.\n\n #### Examples\n\n \n```\n>>> np.random.default_rng().bytes(10)\nb'\\xfeC\\x9b\\x86\\x17\\xf2\\xa1\\xafcp' # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.bytes.htmlnumpy.random.Generator.permuted\n===============================\n\n method\n\n random.Generator.permuted(*x*, *axis=None*, *out=None*)\n \nRandomly permute `x` along axis `axis`.\n\n Unlike [`shuffle`](numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\"), each slice along the given axis is shuffled independently of the others.\n\n Parameters \n \n**x**array_like, at least one-dimensional\n\nArray to be shuffled.\n\n \n**axis**int, optional\n\nSlices of `x` in this axis are shuffled. Each slice is shuffled independently of the others. If `axis` is None, the flattened array is shuffled.\n\n \n**out**ndarray, optional\n\nIf given, this is the destinaton of the shuffled array. If `out` is None, a shuffled copy of the array is returned.\n\n Returns \n ndarray\n\nIf `out` is None, a shuffled copy of `x` is returned. Otherwise, the shuffled array is stored in `out`, and `out` is returned\n\n See also\n\n [`shuffle`](numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\")\n[`permutation`](numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")\n #### Notes\n\n An important distinction between methods `shuffle` and `permuted` is how they both treat the `axis` parameter which can be found at [Handling the axis parameter](../generator#generator-handling-axis-parameter).\n\n #### Examples\n\n Create a [`numpy.random.Generator`](../generator#numpy.random.Generator \"numpy.random.Generator\") instance:\n\n \n```\n>>> rng = np.random.default_rng()\n\n```\n Create a test array:\n\n \n```\n>>> x = np.arange(24).reshape(3, 8)\n>>> x\narray([[ 0, 1, 2, 3, 4, 5, 6, 7],\n [ 8, 9, 10, 11, 12, 13, 14, 15],\n [16, 17, 18, 19, 20, 21, 22, 23]])\n\n```\n Shuffle the rows of `x`:\n\n \n```\n>>> y = rng.permuted(x, axis=1)\n>>> y\narray([[ 4, 3, 6, 7, 1, 2, 5, 0], # random\n [15, 10, 14, 9, 12, 11, 8, 13],\n [17, 16, 20, 21, 18, 22, 23, 19]])\n\n```\n `x` has not been modified:\n\n \n```\n>>> x\narray([[ 0, 1, 2, 3, 4, 5, 6, 7],\n [ 8, 9, 10, 11, 12, 13, 14, 15],\n [16, 17, 18, 19, 20, 21, 22, 23]])\n\n```\n To shuffle the rows of `x` in-place, pass `x` as the `out` parameter:\n\n \n```\n>>> y = rng.permuted(x, axis=1, out=x)\n>>> x\narray([[ 3, 0, 4, 7, 1, 6, 2, 5], # random\n [ 8, 14, 13, 9, 12, 11, 15, 10],\n [17, 18, 16, 22, 19, 23, 20, 21]])\n\n```\n Note that when the `out` parameter is given, the return value is `out`:\n\n \n```\n>>> y is x\nTrue\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.permuted.htmlnumpy.random.Generator.beta\n===========================\n\n method\n\n random.Generator.beta(*a*, *b*, *size=None*)\n \nDraw samples from a Beta distribution.\n\n The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function\n\n \\[f(x; a,b) = \\frac{1}{B(\\alpha, \\beta)} x^{\\alpha - 1} (1 - x)^{\\beta - 1},\\] where the normalization, B, is the beta function,\n\n \\[B(\\alpha, \\beta) = \\int_0^1 t^{\\alpha - 1} (1 - t)^{\\beta - 1} dt.\\] It is often seen in Bayesian inference and order statistics.\n\n Parameters \n \n**a**float or array_like of floats\n\nAlpha, positive (>0).\n\n \n**b**float or array_like of floats\n\nBeta, positive (>0).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` and `b` are both scalars. Otherwise, `np.broadcast(a, b).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized beta distribution.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.beta.htmlnumpy.random.Generator.binomial\n===============================\n\n method\n\n random.Generator.binomial(*n*, *p*, *size=None*)\n \nDraw samples from a binomial distribution.\n\n Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use)\n\n Parameters \n \n**n**int or array_like of ints\n\nParameter of the distribution, >= 0. Floats are also accepted, but they will be truncated to integers.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution, >= 0 and <=1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized binomial distribution, where each sample is equal to the number of successes over the n trials.\n\n See also\n\n [`scipy.stats.binom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html#scipy.stats.binom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the binomial distribution is\n\n \\[P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\\] where \\(n\\) is the number of trials, \\(p\\) is the probability of success, and \\(N\\) is the number of successes.\n\n When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case.\n\n #### References\n\n 1 \nDalgaard, Peter, “Introductory Statistics with R”, Springer-Verlag, 2002.\n\n 2 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 3 \nLentner, Marvin, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 4 \nWeisstein, <NAME>. “Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/BinomialDistribution.html 5 \nWikipedia, “Binomial distribution”, <https://en.wikipedia.org/wiki/Binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> n, p = 10, .5 # number of trials, probability of each trial\n>>> s = rng.binomial(n, p, 1000)\n# result of flipping a coin 10 times, tested 1000 times.\n\n```\n A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening?\n\n Let’s do 20,000 trials of the model, and count the number that generate zero positive results.\n\n \n```\n>>> sum(rng.binomial(9, 0.1, 20000) == 0)/20000.\n# answer = 0.38885, or 39%.\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.binomial.htmlnumpy.random.Generator.chisquare\n================================\n\n method\n\n random.Generator.chisquare(*df*, *size=None*)\n \nDraw samples from a chi-square distribution.\n\n When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing.\n\n Parameters \n \n**df**float or array_like of floats\n\nNumber of degrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized chi-square distribution.\n\n Raises \n ValueError\n\nWhen `df` <= 0 or when an inappropriate `size` (e.g. `size=-1`) is given.\n\n #### Notes\n\n The variable obtained by summing the squares of `df` independent, standard normally distributed random variables:\n\n \\[Q = \\sum_{i=0}^{\\mathtt{df}} X^2_i\\] is chi-square distributed, denoted\n\n \\[Q \\sim \\chi^2_k.\\] The probability density function of the chi-squared distribution is\n\n \\[p(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)} x^{k/2 - 1} e^{-x/2},\\] where \\(\\Gamma\\) is the gamma function,\n\n \\[\\Gamma(x) = \\int_0^{-\\infty} t^{x - 1} e^{-t} dt.\\] #### References\n\n 1 \nNIST “Engineering Statistics Handbook” <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm #### Examples\n\n \n```\n>>> np.random.default_rng().chisquare(2,4)\narray([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.chisquare.htmlnumpy.random.Generator.dirichlet\n================================\n\n method\n\n random.Generator.dirichlet(*alpha*, *size=None*)\n \nDraw samples from the Dirichlet distribution.\n\n Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference.\n\n Parameters \n \n**alpha**sequence of floats, length k\n\nParameter of the distribution (length `k` for sample of length `k`).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n)`, then `m * n * k` samples are drawn. Default is None, in which case a vector of length `k` is returned.\n\n Returns \n \n**samples**ndarray,\n\nThe drawn samples, of shape `(size, k)`.\n\n Raises \n ValueError\n\nIf any value in `alpha` is less than or equal to zero\n\n #### Notes\n\n The Dirichlet distribution is a distribution over vectors \\(x\\) that fulfil the conditions \\(x_i>0\\) and \\(\\sum_{i=1}^k x_i = 1\\).\n\n The probability density function \\(p\\) of a Dirichlet-distributed random vector \\(X\\) is proportional to\n\n \\[p(x) \\propto \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i},\\] where \\(\\alpha\\) is a vector containing the positive concentration parameters.\n\n The method uses the following property for computation: let \\(Y\\) be a random vector which has components that follow a standard gamma distribution, then \\(X = \\frac{1}{\\sum_{i=1}^k{Y_i}} Y\\) is Dirichlet-distributed\n\n #### References\n\n 1 \n<NAME>, “Information Theory, Inference and Learning Algorithms,” chapter 23, <http://www.inference.org.uk/mackay/itila/ 2 \nWikipedia, “Dirichlet distribution”, <https://en.wikipedia.org/wiki/Dirichlet_distribution #### Examples\n\n Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.\n\n \n```\n>>> s = np.random.default_rng().dirichlet((10, 5, 3), 20).transpose()\n\n```\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.barh(range(20), s[0])\n>>> plt.barh(range(20), s[1], left=s[0], color='g')\n>>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')\n>>> plt.title(\"Lengths of Strings\")\n\n```\n ![../../../_images/numpy-random-Generator-dirichlet-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.dirichlet.htmlnumpy.random.Generator.exponential\n==================================\n\n method\n\n random.Generator.exponential(*scale=1.0*, *size=None*)\n \nDraw samples from an exponential distribution.\n\n Its probability density function is\n\n \\[f(x; \\frac{1}{\\beta}) = \\frac{1}{\\beta} \\exp(-\\frac{x}{\\beta}),\\] for `x > 0` and 0 elsewhere. \\(\\beta\\) is the scale parameter, which is the inverse of the rate parameter \\(\\lambda = 1/\\beta\\). The rate parameter is an alternative, widely used parameterization of the exponential distribution [[3]](#r0dbb9b01ef9c-3).\n\n The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [[1]](#r0dbb9b01ef9c-1), or the time between page requests to Wikipedia [[2]](#r0dbb9b01ef9c-2).\n\n Parameters \n \n**scale**float or array_like of floats\n\nThe scale parameter, \\(\\beta = 1/\\lambda\\). Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized exponential distribution.\n\n #### References\n\n [1](#id2) \n<NAME>., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.\n\n [2](#id3) \nWikipedia, “Poisson process”, <https://en.wikipedia.org/wiki/Poisson_process [3](#id1) \nWikipedia, “Exponential distribution”, <https://en.wikipedia.org/wiki/Exponential_distribution © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.exponential.htmlnumpy.random.Generator.f\n========================\n\n method\n\n random.Generator.f(*dfnum*, *dfden*, *size=None*)\n \nDraw samples from an F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters must be greater than zero.\n\n The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates.\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nDegrees of freedom in numerator, must be > 0.\n\n \n**dfden**float or array_like of float\n\nDegrees of freedom in denominator, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum` and `dfden` are both scalars. Otherwise, `np.broadcast(dfnum, dfden).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Fisher distribution.\n\n See also\n\n [`scipy.stats.f`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f.html#scipy.stats.f \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups.\n\n #### References\n\n 1 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 2 \nWikipedia, “F-distribution”, <https://en.wikipedia.org/wiki/F-distribution #### Examples\n\n An example from Glantz[1], pp 47-40:\n\n Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children’s blood glucose levels? Calculating the F statistic from the data gives a value of 36.01.\n\n Draw samples from the distribution:\n\n \n```\n>>> dfnum = 1. # between group degrees of freedom\n>>> dfden = 48. # within groups degrees of freedom\n>>> s = np.random.default_rng().f(dfnum, dfden, 1000)\n\n```\n The lower bound for the top 1% of the samples is :\n\n \n```\n>>> np.sort(s)[-10]\n7.61988120985 # random\n\n```\n So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.f.htmlnumpy.random.Generator.gamma\n============================\n\n method\n\n random.Generator.gamma(*shape*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, [`shape`](../../generated/numpy.shape#numpy.shape \"numpy.shape\") (sometimes designated “k”) and `scale` (sometimes designated “theta”), where both parameters are > 0.\n\n Parameters \n \n**shape**float or array_like of floats\n\nThe shape of the gamma distribution. Must be non-negative.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale of the gamma distribution. Must be non-negative. Default is equal to 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` and `scale` are both scalars. Otherwise, `np.broadcast(shape, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2)\n>>> s = np.random.default_rng().gamma(shape, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1)*(np.exp(-bins/scale) / \n... (sps.gamma(shape)*scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.gamma.htmlnumpy.random.Generator.geometric\n================================\n\n method\n\n random.Generator.geometric(*p*, *size=None*)\n \nDraw samples from the geometric distribution.\n\n Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, `k = 1, 2, ...`.\n\n The probability mass function of the geometric distribution is\n\n \\[f(k) = (1 - p)^{k - 1} p\\] where `p` is the probability of success of an individual trial.\n\n Parameters \n \n**p**float or array_like of floats\n\nThe probability of success of an individual trial.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized geometric distribution.\n\n #### Examples\n\n Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35:\n\n \n```\n>>> z = np.random.default_rng().geometric(p=0.35, size=10000)\n\n```\n How many trials succeeded after a single run?\n\n \n```\n>>> (z == 1).sum() / 10000.\n0.34889999999999999 # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.geometric.htmlnumpy.random.Generator.gumbel\n=============================\n\n method\n\n random.Generator.gumbel(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gumbel distribution.\n\n Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below.\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe location of the mode of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale parameter of the distribution. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Gumbel distribution.\n\n See also\n\n [`scipy.stats.gumbel_l`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_l.html#scipy.stats.gumbel_l \"(in SciPy v1.8.1)\")\n[`scipy.stats.gumbel_r`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`weibull`](numpy.random.generator.weibull#numpy.random.Generator.weibull \"numpy.random.Generator.weibull\")\n #### Notes\n\n The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with “exponential-like” tails.\n\n The probability density for the Gumbel distribution is\n\n \\[p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/ \\beta}},\\] where \\(\\mu\\) is the mode, a location parameter, and \\(\\beta\\) is the scale parameter.\n\n The Gumbel (named for German mathematician <NAME>) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a “fat-tailed” distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events.\n\n It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet.\n\n The function has a mean of \\(\\mu + 0.57721\\beta\\) and a variance of \\(\\frac{\\pi^2}{6}\\beta^2\\).\n\n #### References\n\n 1 \n<NAME>., “Statistics of Extremes,” New York: Columbia University Press, 1958.\n\n 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields,” Basel: Birkhauser Verlag, 2001.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> mu, beta = 0, 0.1 # location and scale\n>>> s = rng.gumbel(mu, beta, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp( -np.exp( -(bins - mu) /beta) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-gumbel-1_00_00.png] Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian:\n\n \n```\n>>> means = []\n>>> maxima = []\n>>> for i in range(0,1000) :\n... a = rng.normal(mu, beta, 1000)\n... means.append(a.mean())\n... maxima.append(a.max())\n>>> count, bins, ignored = plt.hist(maxima, 30, density=True)\n>>> beta = np.std(maxima) * np.sqrt(6) / np.pi\n>>> mu = np.mean(maxima) - 0.57721*beta\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp(-np.exp(-(bins - mu)/beta)),\n... linewidth=2, color='r')\n>>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))\n... * np.exp(-(bins - mu)**2 / (2 * beta**2)),\n... linewidth=2, color='g')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-gumbel-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.gumbel.htmlnumpy.random.Generator.hypergeometric\n=====================================\n\n method\n\n random.Generator.hypergeometric(*ngood*, *nbad*, *nsample*, *size=None*)\n \nDraw samples from a Hypergeometric distribution.\n\n Samples are drawn from a hypergeometric distribution with specified parameters, `ngood` (ways to make a good selection), `nbad` (ways to make a bad selection), and `nsample` (number of items sampled, which is less than or equal to the sum `ngood + nbad`).\n\n Parameters \n \n**ngood**int or array_like of ints\n\nNumber of ways to make a good selection. Must be nonnegative and less than 10**9.\n\n \n**nbad**int or array_like of ints\n\nNumber of ways to make a bad selection. Must be nonnegative and less than 10**9.\n\n \n**nsample**int or array_like of ints\n\nNumber of items sampled. Must be nonnegative and less than `ngood + nbad`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `ngood`, `nbad`, and `nsample` are all scalars. Otherwise, `np.broadcast(ngood, nbad, nsample).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized hypergeometric distribution. Each sample is the number of good items within a randomly selected subset of size `nsample` taken from a set of `ngood` good items and `nbad` bad items.\n\n See also\n\n [`multivariate_hypergeometric`](numpy.random.generator.multivariate_hypergeometric#numpy.random.Generator.multivariate_hypergeometric \"numpy.random.Generator.multivariate_hypergeometric\")\n\nDraw samples from the multivariate hypergeometric distribution.\n\n [`scipy.stats.hypergeom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hypergeom.html#scipy.stats.hypergeom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Hypergeometric distribution is\n\n \\[P(x) = \\frac{\\binom{g}{x}\\binom{b}{n-x}}{\\binom{g+b}{n}},\\] where \\(0 \\le x \\le n\\) and \\(n-b \\le x \\le g\\)\n\n for P(x) the probability of `x` good results in the drawn sample, g = `ngood`, b = `nbad`, and n = `nsample`.\n\n Consider an urn with black and white marbles in it, `ngood` of them are black and `nbad` are white. If you draw `nsample` balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample.\n\n Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial.\n\n The arguments `ngood` and `nbad` each must be less than `10**9`. For extremely large arguments, the algorithm that is used to compute the samples [[4]](#r688e4aa3bfc3-4) breaks down because of loss of precision in floating point calculations. For such large values, if `nsample` is not also large, the distribution can be approximated with the binomial distribution, `binomial(n=nsample, p=ngood/(ngood + nbad))`.\n\n #### References\n\n 1 \n<NAME>, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 2 \nWeisstein, <NAME>. “Hypergeometric Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/HypergeometricDistribution.html 3 \nWikipedia, “Hypergeometric distribution”, <https://en.wikipedia.org/wiki/Hypergeometric_distribution [4](#id1) \n<NAME>, “The ratio of uniforms approach for generating discrete random variates”, Journal of Computational and Applied Mathematics, 31, pp. 181-189 (1990).\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> ngood, nbad, nsamp = 100, 2, 10\n# number of good, number of bad, and number of samples\n>>> s = rng.hypergeometric(ngood, nbad, nsamp, 1000)\n>>> from matplotlib.pyplot import hist\n>>> hist(s)\n# note that it is very unlikely to grab both bad items\n\n```\n Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color?\n\n \n```\n>>> s = rng.hypergeometric(15, 15, 15, 100000)\n>>> sum(s>=12)/100000. + sum(s<=3)/100000.\n# answer = 0.003 ... pretty unlikely!\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.hypergeometric.htmlnumpy.random.Generator.laplace\n==============================\n\n method\n\n random.Generator.laplace(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).\n\n The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables.\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe position, \\(\\mu\\), of the distribution peak. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\n\\(\\lambda\\), the exponential decay. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Laplace distribution.\n\n #### Notes\n\n It has the probability density function\n\n \\[f(x; \\mu, \\lambda) = \\frac{1}{2\\lambda} \\exp\\left(-\\frac{|x - \\mu|}{\\lambda}\\right).\\] The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \n<NAME>, et. al. “The Laplace Distribution and Generalizations, ” Birkhauser, 2001.\n\n 3 \nWeisstein, <NAME>. “Laplace Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LaplaceDistribution.html 4 \nWikipedia, “Laplace distribution”, <https://en.wikipedia.org/wiki/Laplace_distribution #### Examples\n\n Draw samples from the distribution\n\n \n```\n>>> loc, scale = 0., 1.\n>>> s = np.random.default_rng().laplace(loc, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> x = np.arange(-8., 8., .01)\n>>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)\n>>> plt.plot(x, pdf)\n\n```\n Plot Gaussian for comparison:\n\n \n```\n>>> g = (1/(scale * np.sqrt(2 * np.pi)) *\n... np.exp(-(x - loc)**2 / (2 * scale**2)))\n>>> plt.plot(x,g)\n\n```\n ![../../../_images/numpy-random-Generator-laplace-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.laplace.htmlnumpy.random.Generator.logistic\n===============================\n\n method\n\n random.Generator.logistic(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a logistic distribution.\n\n Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nParameter of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nParameter of the distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logistic distribution.\n\n See also\n\n [`scipy.stats.logistic`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logistic.html#scipy.stats.logistic \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Logistic distribution is\n\n \\[P(x) = P(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2},\\] where \\(\\mu\\) = location and \\(s\\) = scale.\n\n The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (2001), “Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,” Birkhauser Verlag, Basel, pp 132-133.\n\n 2 \nWeisstein, <NAME>. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LogisticDistribution.html 3 \nWikipedia, “Logistic-distribution”, <https://en.wikipedia.org/wiki/Logistic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> loc, scale = 10, 1\n>>> s = np.random.default_rng().logistic(loc, scale, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=50)\n\n```\n # plot against distribution\n\n \n```\n>>> def logist(x, loc, scale):\n... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)\n>>> lgst_val = logist(bins, loc, scale)\n>>> plt.plot(bins, lgst_val * count.max() / lgst_val.max())\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-logistic-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.logistic.htmlnumpy.random.Generator.lognormal\n================================\n\n method\n\n random.Generator.lognormal(*mean=0.0*, *sigma=1.0*, *size=None*)\n \nDraw samples from a log-normal distribution.\n\n Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.\n\n Parameters \n \n**mean**float or array_like of floats, optional\n\nMean value of the underlying normal distribution. Default is 0.\n\n \n**sigma**float or array_like of floats, optional\n\nStandard deviation of the underlying normal distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `sigma` are both scalars. Otherwise, `np.broadcast(mean, sigma).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized log-normal distribution.\n\n See also\n\n [`scipy.stats.lognorm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, cumulative density function, etc.\n\n #### Notes\n\n A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is:\n\n \\[p(x) = \\frac{1}{\\sigma x \\sqrt{2\\pi}} e^{(-\\frac{(ln(x)-\\mu)^2}{2\\sigma^2})}\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables.\n\n #### References\n\n 1 \n<NAME>., <NAME>., and <NAME>., “Log-normal Distributions across the Sciences: Keys and Clues,” BioScience, Vol. 51, No. 5, May, 2001. <https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values,” Basel: Birkhauser Verlag, 2001, pp. 31-32.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> mu, sigma = 3., 1. # mean and standard deviation\n>>> s = rng.lognormal(mu, sigma, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 100, density=True, align='mid')\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, linewidth=2, color='r')\n>>> plt.axis('tight')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-lognormal-1_00_00.png] Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function.\n\n \n```\n>>> # Generate a thousand samples: each is the product of 100 random\n>>> # values, drawn from a normal distribution.\n>>> rng = rng\n>>> b = []\n>>> for i in range(1000):\n... a = 10. + rng.standard_normal(100)\n... b.append(np.product(a))\n\n```\n \n```\n>>> b = np.array(b) / np.min(b) # scale values to be positive\n>>> count, bins, ignored = plt.hist(b, 100, density=True, align='mid')\n>>> sigma = np.std(np.log(b))\n>>> mu = np.mean(np.log(b))\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, color='r', linewidth=2)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-lognormal-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.lognormal.htmlnumpy.random.Generator.logseries\n================================\n\n method\n\n random.Generator.logseries(*p*, *size=None*)\n \nDraw samples from a logarithmic series distribution.\n\n Samples are drawn from a log series distribution with specified shape parameter, 0 < `p` < 1.\n\n Parameters \n \n**p**float or array_like of floats\n\nShape parameter for the distribution. Must be in the range (0, 1).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logarithmic series distribution.\n\n See also\n\n [`scipy.stats.logser`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logser.html#scipy.stats.logser \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability mass function for the Log Series distribution is\n\n \\[P(k) = \\frac{-p^k}{k \\ln(1-p)},\\] where p = probability.\n\n The log series distribution is frequently used to represent species richness and occurrence, first proposed by <NAME>, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3].\n\n #### References\n\n 1 \n<NAME>.; Culver, <NAME>., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9).\n\n 2 \n<NAME>,, <NAME>, and <NAME>. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58.\n\n 3 \n<NAME>, <NAME>, <NAME>, <NAME>, A Handbook of Small Data Sets, CRC Press, 1994.\n\n 4 \nWikipedia, “Logarithmic distribution”, <https://en.wikipedia.org/wiki/Logarithmic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = .6\n>>> s = np.random.default_rng().logseries(a, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s)\n\n```\n # plot against distribution\n\n \n```\n>>> def logseries(k, p):\n... return -p**k/(k*np.log(1-p))\n>>> plt.plot(bins, logseries(bins, a) * count.max()/\n... logseries(bins, a).max(), 'r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-logseries-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.logseries.htmlnumpy.random.Generator.multinomial\n==================================\n\n method\n\n random.Generator.multinomial(*n*, *pvals*, *size=None*)\n \nDraw samples from a multinomial distribution.\n\n The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of `p` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, `X_i = [X_0, X_1, ..., X_p]`, represent the number of times the outcome was `i`.\n\n Parameters \n \n**n**int or array-like of ints\n\nNumber of experiments.\n\n \n**pvals**array-like of floats\n\nProbabilities of each of the `p` different outcomes with shape `(k0, k1, ..., kn, p)`. Each element `pvals[i,j,...,:]` must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as `sum(pvals[..., :-1], axis=-1) <= 1.0`. Must have at least 1 dimension where pvals.shape[-1] > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn each with `p` elements. Default is None where the output size is determined by the broadcast shape of `n` and all by the final dimension of `pvals`, which is denoted as `b=(b0, b1, ..., bq)`. If size is not None, then it must be compatible with the broadcast shape `b`. Specifically, size must have `q` or more elements and size[-(q-j):] must equal `bj`.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape size, if provided. When size is provided, the output shape is size + (p,) If not specified, the shape is determined by the broadcast shape of `n` and `pvals`, `(b0, b1, ..., bq)` augmented with the dimension of the multinomial, `p`, so that that output shape is `(b0, b1, ..., bq, p)`.\n\n Each entry `out[i,j,...,:]` is a `p`-dimensional value drawn from the distribution.\n\n #### Examples\n\n Throw a dice 20 times:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.multinomial(20, [1/6.]*6, size=1)\narray([[4, 1, 7, 5, 2, 1]]) # random\n\n```\n It landed 4 times on 1, once on 2, etc.\n\n Now, throw the dice 20 times, and 20 times again:\n\n \n```\n>>> rng.multinomial(20, [1/6.]*6, size=2)\narray([[3, 4, 3, 3, 4, 3],\n [2, 4, 3, 4, 0, 7]]) # random\n\n```\n For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc.\n\n Now, do one experiment throwing the dice 10 time, and 10 times again, and another throwing the dice 20 times, and 20 times again:\n\n \n```\n>>> rng.multinomial([[10], [20]], [1/6.]*6, size=(2, 2))\narray([[[2, 4, 0, 1, 2, 1],\n [1, 3, 0, 3, 1, 2]],\n [[1, 4, 4, 4, 4, 3],\n [3, 3, 2, 5, 5, 2]]]) # random\n\n```\n The first array shows the outcomes of throwing the dice 10 times, and the second shows the outcomes from throwing the dice 20 times.\n\n A loaded die is more likely to land on number 6:\n\n \n```\n>>> rng.multinomial(100, [1/7.]*5 + [2/7.])\narray([11, 16, 14, 17, 16, 26]) # random\n\n```\n Simulate 10 throws of a 4-sided die and 20 throws of a 6-sided die\n\n \n```\n>>> rng.multinomial([10, 20],[[1/4]*4 + [0]*2, [1/6]*6])\narray([[2, 1, 4, 3, 0, 0],\n [3, 3, 3, 6, 1, 4]], dtype=int64) # random\n\n```\n Generate categorical random variates from two categories where the first has 3 outcomes and the second has 2.\n\n \n```\n>>> rng.multinomial(1, [[.1, .5, .4 ], [.3, .7, .0]])\narray([[0, 0, 1],\n [0, 1, 0]], dtype=int64) # random\n\n```\n `argmax(axis=-1)` is then used to return the categories.\n\n \n```\n>>> pvals = [[.1, .5, .4 ], [.3, .7, .0]]\n>>> rvs = rng.multinomial(1, pvals, size=(4,2))\n>>> rvs.argmax(axis=-1)\narray([[0, 1],\n [2, 0],\n [2, 1],\n [2, 0]], dtype=int64) # random\n\n```\n The same output dimension can be produced using broadcasting.\n\n \n```\n>>> rvs = rng.multinomial([[1]] * 4, pvals)\n>>> rvs.argmax(axis=-1)\narray([[0, 1],\n [2, 0],\n [2, 1],\n [2, 0]], dtype=int64) # random\n\n```\n The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so:\n\n \n```\n>>> rng.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT\narray([38, 62]) # random\n\n```\n not like:\n\n \n```\n>>> rng.multinomial(100, [1.0, 2.0]) # WRONG\nTraceback (most recent call last):\nValueError: pvals < 0, pvals > 1 or pvals contains NaNs\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.multinomial.htmlnumpy.random.Generator.multivariate_hypergeometric\n===================================================\n\n method\n\n random.Generator.multivariate_hypergeometric(*colors*, *nsample*, *size=None*, *method='marginals'*)\n \nGenerate variates from a multivariate hypergeometric distribution.\n\n The multivariate hypergeometric distribution is a generalization of the hypergeometric distribution.\n\n Choose `nsample` items at random without replacement from a collection with `N` distinct types. `N` is the length of `colors`, and the values in `colors` are the number of occurrences of that type in the collection. The total number of items in the collection is `sum(colors)`. Each random variate generated by this function is a vector of length `N` holding the counts of the different types that occurred in the `nsample` items.\n\n The name `colors` comes from a common description of the distribution: it is the probability distribution of the number of marbles of each color selected without replacement from an urn containing marbles of different colors; `colors[i]` is the number of marbles in the urn with color `i`.\n\n Parameters \n \n**colors**sequence of integers\n\nThe number of each type of item in the collection from which a sample is drawn. The values in `colors` must be nonnegative. To avoid loss of precision in the algorithm, `sum(colors)` must be less than `10**9` when `method` is “marginals”.\n\n \n**nsample**int\n\nThe number of items selected. `nsample` must not be greater than `sum(colors)`.\n\n \n**size**int or tuple of ints, optional\n\nThe number of variates to generate, either an integer or a tuple holding the shape of the array of variates. If the given size is, e.g., `(k, m)`, then `k * m` variates are drawn, where one variate is a vector of length `len(colors)`, and the return value has shape `(k, m, len(colors))`. If `size` is an integer, the output has shape `(size, len(colors))`. Default is None, in which case a single variate is returned as an array with shape `(len(colors),)`.\n\n \n**method**string, optional\n\nSpecify the algorithm that is used to generate the variates. Must be ‘count’ or ‘marginals’ (the default). See the Notes for a description of the methods.\n\n Returns \n \n**variates**ndarray\n\nArray of variates drawn from the multivariate hypergeometric distribution.\n\n See also\n\n [`hypergeometric`](numpy.random.generator.hypergeometric#numpy.random.Generator.hypergeometric \"numpy.random.Generator.hypergeometric\")\n\nDraw samples from the (univariate) hypergeometric distribution.\n\n #### Notes\n\n The two methods do not return the same sequence of variates.\n\n The “count” algorithm is roughly equivalent to the following numpy code:\n\n \n```\nchoices = np.repeat(np.arange(len(colors)), colors)\nselection = np.random.choice(choices, nsample, replace=False)\nvariate = np.bincount(selection, minlength=len(colors))\n\n```\n The “count” algorithm uses a temporary array of integers with length `sum(colors)`.\n\n The “marginals” algorithm generates a variate by using repeated calls to the univariate hypergeometric sampler. It is roughly equivalent to:\n\n \n```\nvariate = np.zeros(len(colors), dtype=np.int64)\n# `remaining` is the cumulative sum of `colors` from the last\n# element to the first; e.g. if `colors` is [3, 1, 5], then\n# `remaining` is [9, 6, 5].\nremaining = np.cumsum(colors[::-1])[::-1]\nfor i in range(len(colors)-1):\n if nsample < 1:\n break\n variate[i] = hypergeometric(colors[i], remaining[i+1],\n nsample)\n nsample -= variate[i]\nvariate[-1] = nsample\n\n```\n The default method is “marginals”. For some cases (e.g. when `colors` contains relatively small integers), the “count” method can be significantly faster than the “marginals” method. If performance of the algorithm is important, test the two methods with typical inputs to decide which works best.\n\n New in version 1.18.0.\n\n #### Examples\n\n \n```\n>>> colors = [16, 8, 4]\n>>> seed = 4861946401452\n>>> gen = np.random.Generator(np.random.PCG64(seed))\n>>> gen.multivariate_hypergeometric(colors, 6)\narray([5, 0, 1])\n>>> gen.multivariate_hypergeometric(colors, 6, size=3)\narray([[5, 0, 1],\n [2, 2, 2],\n [3, 3, 0]])\n>>> gen.multivariate_hypergeometric(colors, 6, size=(2, 2))\narray([[[3, 2, 1],\n [3, 2, 1]],\n [[4, 1, 1],\n [3, 2, 1]]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.multivariate_hypergeometric.htmlnumpy.random.Generator.multivariate_normal\n===========================================\n\n method\n\n random.Generator.multivariate_normal(*mean*, *cov*, *size=None*, *check_valid='warn'*, *tol=1e-8*, ***, *method='svd'*)\n \nDraw random samples from a multivariate normal distribution.\n\n The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or “center”) and variance (standard deviation, or “width,” squared) of the one-dimensional normal distribution.\n\n Parameters \n \n**mean**1-D array_like, of length N\n\nMean of the N-dimensional distribution.\n\n \n**cov**2-D array_like, of shape (N, N)\n\nCovariance matrix of the distribution. It must be symmetric and positive-semidefinite for proper sampling.\n\n \n**size**int or tuple of ints, optional\n\nGiven a shape of, for example, `(m,n,k)`, `m*n*k` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is `(m,n,k,N)`. If no shape is specified, a single (`N`-D) sample is returned.\n\n \n**check_valid**{ ‘warn’, ‘raise’, ‘ignore’ }, optional\n\nBehavior when the covariance matrix is not positive semidefinite.\n\n \n**tol**float, optional\n\nTolerance when checking the singular values in covariance matrix. cov is cast to double before the check.\n\n \n**method**{ ‘svd’, ‘eigh’, ‘cholesky’}, optional\n\nThe cov input is used to compute a factor matrix A such that `A @ A.T = cov`. This argument is used to select the method used to compute the factor matrix A. The default method ‘svd’ is the slowest, while ‘cholesky’ is the fastest but less robust than the slowest method. The method `eigh` uses eigen decomposition to compute A and is faster than svd but slower than cholesky.\n\n New in version 1.18.0.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape *size*, if that was provided. If not, the shape is `(N,)`.\n\n In other words, each entry `out[i,j,...,:]` is an N-dimensional value drawn from the distribution.\n\n #### Notes\n\n The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution.\n\n Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, \\(X = [x_1, x_2, ... x_N]\\). The covariance matrix element \\(C_{ij}\\) is the covariance of \\(x_i\\) and \\(x_j\\). The element \\(C_{ii}\\) is the variance of \\(x_i\\) (i.e. its “spread”).\n\n Instead of specifying the full covariance matrix, popular approximations include:\n\n * Spherical covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") is a multiple of the identity matrix)\n* Diagonal covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") has non-negative elements, and only on the diagonal)\n\n This geometrical property can be seen in two dimensions by plotting generated data-points:\n\n \n```\n>>> mean = [0, 0]\n>>> cov = [[1, 0], [0, 100]] # diagonal covariance\n\n```\n Diagonal covariance means that points are oriented along x or y-axis:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x, y = np.random.default_rng().multivariate_normal(mean, cov, 5000).T\n>>> plt.plot(x, y, 'x')\n>>> plt.axis('equal')\n>>> plt.show()\n\n```\n Note that the covariance matrix must be positive semidefinite (a.k.a. nonnegative-definite). Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed.\n\n #### References\n\n 1 \n<NAME>., “Probability, Random Variables, and Stochastic Processes,” 3rd ed., New York: McGraw-Hill, 1991.\n\n 2 \n<NAME>., <NAME>., and <NAME>., “Pattern Classification,” 2nd ed., New York: Wiley, 2001.\n\n #### Examples\n\n \n```\n>>> mean = (1, 2)\n>>> cov = [[1, 0], [0, 1]]\n>>> rng = np.random.default_rng()\n>>> x = rng.multivariate_normal(mean, cov, (3, 3))\n>>> x.shape\n(3, 3, 2)\n\n```\n We can use a different method other than the default to factorize cov:\n\n \n```\n>>> y = rng.multivariate_normal(mean, cov, (3, 3), method='cholesky')\n>>> y.shape\n(3, 3, 2)\n\n```\n Here we generate 800 samples from the bivariate normal distribution with mean [0, 0] and covariance matrix [[6, -3], [-3, 3.5]]. The expected variances of the first and second components of the sample are 6 and 3.5, respectively, and the expected correlation coefficient is -3/sqrt(6*3.5) ≈ -0.65465.\n\n \n```\n>>> cov = np.array([[6, -3], [-3, 3.5]])\n>>> pts = rng.multivariate_normal([0, 0], cov, size=800)\n\n```\n Check that the mean, covariance, and correlation coefficient of the sample are close to the expected values:\n\n \n```\n>>> pts.mean(axis=0)\narray([ 0.0326911 , -0.01280782]) # may vary\n>>> np.cov(pts.T)\narray([[ 5.96202397, -2.85602287],\n [-2.85602287, 3.47613949]]) # may vary\n>>> np.corrcoef(pts.T)[0, 1]\n-0.6273591314603949 # may vary\n\n```\n We can visualize this data with a scatter plot. The orientation of the point cloud illustrates the negative correlation of the components of this sample.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(pts[:, 0], pts[:, 1], '.', alpha=0.5)\n>>> plt.axis('equal')\n>>> plt.grid()\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-multivariate_normal-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.multivariate_normal.htmlnumpy.random.Generator.negative_binomial\n=========================================\n\n method\n\n random.Generator.negative_binomial(*n*, *p*, *size=None*)\n \nDraw samples from a negative binomial distribution.\n\n Samples are drawn from a negative binomial distribution with specified parameters, `n` successes and `p` probability of success where `n` is > 0 and `p` is in the interval (0, 1].\n\n Parameters \n \n**n**float or array_like of floats\n\nParameter of the distribution, > 0.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution. Must satisfy 0 < p <= 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached.\n\n #### Notes\n\n The probability mass function of the negative binomial distribution is\n\n \\[P(N;n,p) = \\frac{\\Gamma(N+n)}{N!\\Gamma(n)}p^{n}(1-p)^{N},\\] where \\(n\\) is the number of successes, \\(p\\) is the probability of success, \\(N+n\\) is the number of trials, and \\(\\Gamma\\) is the gamma function. When \\(n\\) is an integer, \\(\\frac{\\Gamma(N+n)}{N!\\Gamma(n)} = \\binom{N+n-1}{N}\\), which is the more common form of this term in the the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial.\n\n If one throws a die repeatedly until the third time a “1” appears, then the probability distribution of the number of non-“1”s that appear before the third “1” is a negative binomial distribution.\n\n Because this method internally calls `Generator.poisson` with an intermediate random value, a ValueError is raised when the choice of \\(n\\) and \\(p\\) would result in the mean + 10 sigma of the sampled intermediate distribution exceeding the max acceptable value of the `Generator.poisson` method. This happens when \\(p\\) is too low (a lot of failures happen for every success) and \\(n\\) is too big ( a lot of sucesses are allowed). Therefore, the \\(n\\) and \\(p\\) values must satisfy the constraint:\n\n \\[n\\frac{1-p}{p}+10n\\sqrt{n}\\frac{1-p}{p}<2^{63}-1-10\\sqrt{2^{63}-1},\\] Where the left side of the equation is the derived mean + 10 sigma of a sample from the gamma distribution internally used as the \\(lam\\) parameter of a poisson sample, and the right side of the equation is the constraint for maximum value of \\(lam\\) in `Generator.poisson`.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Negative Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NegativeBinomialDistribution.html 2 \nWikipedia, “Negative binomial distribution”, <https://en.wikipedia.org/wiki/Negative_binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.?\n\n \n```\n>>> s = np.random.default_rng().negative_binomial(1, 0.1, 100000)\n>>> for i in range(1, 11): \n... probability = sum(s<i) / 100000.\n... print(i, \"wells drilled, probability of one success =\", probability)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.negative_binomial.htmlnumpy.random.Generator.noncentral_chisquare\n============================================\n\n method\n\n random.Generator.noncentral_chisquare(*df*, *nonc*, *size=None*)\n \nDraw samples from a noncentral chi-square distribution.\n\n The noncentral \\(\\chi^2\\) distribution is a generalization of the \\(\\chi^2\\) distribution.\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n Changed in version 1.10.0: Earlier NumPy versions required dfnum > 1.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` and `nonc` are both scalars. Otherwise, `np.broadcast(df, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral chi-square distribution.\n\n #### Notes\n\n The probability density function for the noncentral Chi-square distribution is\n\n \\[P(x;df,nonc) = \\sum^{\\infty}_{i=0} \\frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x),\\] where \\(Y_{q}\\) is the Chi-square with q degrees of freedom.\n\n #### References\n\n 1 \nWikipedia, “Noncentral chi-squared distribution” <https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> rng = np.random.default_rng()\n>>> import matplotlib.pyplot as plt\n>>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-noncentral_chisquare-1_00_00.png] Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(rng.noncentral_chisquare(3, .0000001, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> values2 = plt.hist(rng.chisquare(3, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-noncentral_chisquare-1_01_00.png] Demonstrate how large values of non-centrality lead to a more symmetric distribution.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-noncentral_chisquare-1_02_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.noncentral_chisquare.htmlnumpy.random.Generator.noncentral_f\n====================================\n\n method\n\n random.Generator.noncentral_f(*dfnum*, *dfden*, *nonc*, *size=None*)\n \nDraw samples from the noncentral F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter.\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nNumerator degrees of freedom, must be > 0.\n\n Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.\n\n \n**dfden**float or array_like of floats\n\nDenominator degrees of freedom, must be > 0.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality parameter, the sum of the squares of the numerator means, must be >= 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum`, `dfden`, and `nonc` are all scalars. Otherwise, `np.broadcast(dfnum, dfden, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral Fisher distribution.\n\n #### Notes\n\n When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NoncentralF-Distribution.html 2 \nWikipedia, “Noncentral F-distribution”, <https://en.wikipedia.org/wiki/Noncentral_F-distribution #### Examples\n\n In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We’ll plot the two probability distributions for comparison.\n\n \n```\n>>> rng = np.random.default_rng()\n>>> dfnum = 3 # between group deg of freedom\n>>> dfden = 20 # within groups degrees of freedom\n>>> nonc = 3.0\n>>> nc_vals = rng.noncentral_f(dfnum, dfden, nonc, 1000000)\n>>> NF = np.histogram(nc_vals, bins=50, density=True)\n>>> c_vals = rng.f(dfnum, dfden, 1000000)\n>>> F = np.histogram(c_vals, bins=50, density=True)\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(F[1][1:], F[0])\n>>> plt.plot(NF[1][1:], NF[0])\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-noncentral_f-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.noncentral_f.htmlnumpy.random.Generator.normal\n=============================\n\n method\n\n random.Generator.normal(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw random samples from a normal (Gaussian) distribution.\n\n The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [[2]](#r1536f9c044a3-2), is often called the bell curve because of its characteristic shape (see the example below).\n\n The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [[2]](#r1536f9c044a3-2).\n\n Parameters \n \n**loc**float or array_like of floats\n\nMean (“centre”) of the distribution.\n\n \n**scale**float or array_like of floats\n\nStandard deviation (spread or “width”) of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized normal distribution.\n\n See also\n\n [`scipy.stats.norm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Gaussian distribution is\n\n \\[p(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }} e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) the standard deviation. The square of the standard deviation, \\(\\sigma^2\\), is called the variance.\n\n The function has its peak at the mean, and its “spread” increases with the standard deviation (the function reaches 0.607 times its maximum at \\(x + \\sigma\\) and \\(x - \\sigma\\) [[2]](#r1536f9c044a3-2)). This implies that [`normal`](#numpy.random.Generator.normal \"numpy.random.Generator.normal\") is more likely to return samples lying close to the mean, rather than those far away.\n\n #### References\n\n 1 \nWikipedia, “Normal distribution”, <https://en.wikipedia.org/wiki/Normal_distribution2([1](#id1),[2](#id2),[3](#id3))\n \n<NAME>., “Central Limit Theorem” in “Probability, Random Variables and Random Signal Principles”, 4th ed., 2001, pp. 51, 51, 125.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, sigma = 0, 0.1 # mean and standard deviation\n>>> s = np.random.default_rng().normal(mu, sigma, 1000)\n\n```\n Verify the mean and the variance:\n\n \n```\n>>> abs(mu - np.mean(s))\n0.0 # may vary\n\n```\n \n```\n>>> abs(sigma - np.std(s, ddof=1))\n0.0 # may vary\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-normal-1_00_00.png]:\n\n \n```\n>>> np.random.default_rng().normal(3, 2.5, size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.normal.htmlnumpy.random.Generator.pareto\n=============================\n\n method\n\n random.Generator.pareto(*a*, *size=None*)\n \nDraw samples from a Pareto II or Lomax distribution with specified shape.\n\n The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding 1 and multiplying by the scale parameter `m` (see Notes). The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is `mu`, where the standard Pareto distribution has location `mu = 1`. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero.\n\n The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the “80-20 rule”. In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range.\n\n Parameters \n \n**a**float or array_like of floats\n\nShape of the distribution. Must be positive.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Pareto distribution.\n\n See also\n\n [`scipy.stats.lomax`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lomax.html#scipy.stats.lomax \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`scipy.stats.genpareto`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Pareto distribution is\n\n \\[p(x) = \\frac{am^a}{x^{a+1}}\\] where \\(a\\) is the shape and \\(m\\) the scale.\n\n The Pareto distribution, named after the Italian economist <NAME>, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [[1]](#rc338d9f74bfc-1). It is one of the so-called “fat-tailed” distributions.\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, On the Pareto Distribution of Sourceforge projects.\n\n 2 \n<NAME>. (1896). Course of Political Economy. Lausanne.\n\n 3 \n<NAME>., <NAME>.(2001), Statistical Analysis of Extreme Values, <NAME>, Basel, pp 23-30.\n\n 4 \nWikipedia, “Pareto distribution”, <https://en.wikipedia.org/wiki/Pareto_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a, m = 3., 2. # shape and mode\n>>> s = (np.random.default_rng().pareto(a, 1000) + 1) * m\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, _ = plt.hist(s, 100, density=True)\n>>> fit = a*m**a / bins**(a+1)\n>>> plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-pareto-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.pareto.htmlnumpy.random.Generator.poisson\n==============================\n\n method\n\n random.Generator.poisson(*lam=1.0*, *size=None*)\n \nDraw samples from a Poisson distribution.\n\n The Poisson distribution is the limit of the binomial distribution for large N.\n\n Parameters \n \n**lam**float or array_like of floats\n\nExpected number of events occurring in a fixed-time interval, must be >= 0. A sequence must be broadcastable over the requested size.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `lam` is a scalar. Otherwise, `np.array(lam).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Poisson distribution.\n\n #### Notes\n\n The Poisson distribution\n\n \\[f(k; \\lambda)=\\frac{\\lambda^k e^{-\\lambda}}{k!}\\] For events with an expected separation \\(\\lambda\\) the Poisson distribution \\(f(k; \\lambda)\\) describes the probability of \\(k\\) events occurring within the observed interval \\(\\lambda\\).\n\n Because the output is limited to the range of the C int64 type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/PoissonDistribution.html 2 \nWikipedia, “Poisson distribution”, <https://en.wikipedia.org/wiki/Poisson_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> import numpy as np\n>>> rng = np.random.default_rng()\n>>> s = rng.poisson(5, 10000)\n\n```\n Display histogram of the sample:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 14, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-poisson-1_00_00.png] Draw each 100 values for lambda 100 and 500:\n\n \n```\n>>> s = rng.poisson(lam=(100., 500.), size=(100, 2))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.poisson.htmlnumpy.random.Generator.power\n============================\n\n method\n\n random.Generator.power(*a*, *size=None*)\n \nDraws samples in [0, 1] from a power distribution with positive exponent a - 1.\n\n Also known as the power function distribution.\n\n Parameters \n \n**a**float or array_like of floats\n\nParameter of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized power distribution.\n\n Raises \n ValueError\n\nIf a <= 0.\n\n #### Notes\n\n The probability density function is\n\n \\[P(x; a) = ax^{a-1}, 0 \\le x \\le 1, a>0.\\] The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution.\n\n It is used, for example, in modeling the over-reporting of insurance claims.\n\n #### References\n\n 1 \n<NAME>, <NAME>, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.\n\n 2 \n<NAME>. and Filliben, <NAME>. “NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions”, National Institute of Standards and Technology Handbook Series, June 2003. <https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> a = 5. # shape\n>>> samples = 1000\n>>> s = rng.power(a, samples)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=30)\n>>> x = np.linspace(0, 1, 100)\n>>> y = a*x**(a-1.)\n>>> normed_y = samples*np.diff(bins)[0]*y\n>>> plt.plot(x, normed_y)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-power-1_00_00.png] Compare the power function distribution to the inverse of the Pareto.\n\n \n```\n>>> from scipy import stats \n>>> rvs = rng.power(5, 1000000)\n>>> rvsp = rng.pareto(5, 1000000)\n>>> xx = np.linspace(0,1,100)\n>>> powpdf = stats.powerlaw.pdf(xx,5) \n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(rvs, bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('power(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of 1 + Generator.pareto(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of stats.pareto(5)')\n\n```\n ![../../../_images/numpy-random-Generator-power-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.power.htmlnumpy.random.Generator.rayleigh\n===============================\n\n method\n\n random.Generator.rayleigh(*scale=1.0*, *size=None*)\n \nDraw samples from a Rayleigh distribution.\n\n The \\(\\chi\\) and Weibull distributions are generalizations of the Rayleigh.\n\n Parameters \n \n**scale**float or array_like of floats, optional\n\nScale, also equals the mode. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Rayleigh distribution.\n\n #### Notes\n\n The probability density function for the Rayleigh distribution is\n\n \\[P(x;scale) = \\frac{x}{scale^2}e^{\\frac{-x^2}{2 \\cdotp scale^2}}\\] The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.\n\n #### References\n\n 1 \nBrighton Webs Ltd., “Rayleigh Distribution,” <https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp 2 \nWikipedia, “Rayleigh distribution” <https://en.wikipedia.org/wiki/Rayleigh_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> from matplotlib.pyplot import hist\n>>> rng = np.random.default_rng()\n>>> values = hist(rng.rayleigh(3, 100000), bins=200, density=True)\n\n```\n Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters?\n\n \n```\n>>> meanvalue = 1\n>>> modevalue = np.sqrt(2 / np.pi) * meanvalue\n>>> s = rng.rayleigh(modevalue, 1000000)\n\n```\n The percentage of waves larger than 3 meters is:\n\n \n```\n>>> 100.*sum(s>3)/1000000.\n0.087300000000000003 # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.rayleigh.htmlnumpy.random.Generator.standard_cauchy\n=======================================\n\n method\n\n random.Generator.standard_cauchy(*size=None*)\n \nDraw samples from a standard Cauchy distribution with mode = 0.\n\n Also known as the Lorentz distribution.\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**samples**ndarray or scalar\n\nThe drawn samples.\n\n #### Notes\n\n The probability density function for the full Cauchy distribution is\n\n \\[P(x; x_0, \\gamma) = \\frac{1}{\\pi \\gamma \\bigl[ 1+ (\\frac{x-x_0}{\\gamma})^2 \\bigr] }\\] and the Standard Cauchy distribution just sets \\(x_0=0\\) and \\(\\gamma=1\\)\n\n The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis.\n\n When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails.\n\n #### References\n\n 1 \nNIST/SEMATECH e-Handbook of Statistical Methods, “Cauchy Distribution”, <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm 2 \nWeisstein, <NAME>. “Cauchy Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/CauchyDistribution.html 3 \nWikipedia, “Cauchy distribution” <https://en.wikipedia.org/wiki/Cauchy_distribution #### Examples\n\n Draw samples and plot the distribution:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.default_rng().standard_cauchy(1000000)\n>>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well\n>>> plt.hist(s, bins=100)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-standard_cauchy-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.standard_cauchy.htmlnumpy.random.Generator.standard_exponential\n============================================\n\n method\n\n random.Generator.standard_exponential(*size=None*, *dtype=np.float64*, *method='zig'*, *out=None*)\n \nDraw samples from the standard exponential distribution.\n\n [`standard_exponential`](#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\") is identical to the exponential distribution with a scale parameter of 1.\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result, only [`float64`](../../arrays.scalars#numpy.float64 \"numpy.float64\") and [`float32`](../../arrays.scalars#numpy.float32 \"numpy.float32\") are supported. Byteorder must be native. The default value is np.float64.\n\n \n**method**str, optional\n\nEither ‘inv’ or ‘zig’. ‘inv’ uses the default inverse CDF method. ‘zig’ uses the much faster Ziggurat method of Marsaglia and Tsang.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.\n\n Returns \n \n**out**float or ndarray\n\nDrawn samples.\n\n #### Examples\n\n Output a 3x8000 array:\n\n \n```\n>>> n = np.random.default_rng().standard_exponential((3, 8000))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.standard_exponential.htmlnumpy.random.Generator.standard_gamma\n======================================\n\n method\n\n random.Generator.standard_gamma(*shape*, *size=None*, *dtype=np.float64*, *out=None*)\n \nDraw samples from a standard Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.\n\n Parameters \n \n**shape**float or array_like of floats\n\nParameter, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` is a scalar. Otherwise, `np.array(shape).size` samples are drawn.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result, only [`float64`](../../arrays.scalars#numpy.float64 \"numpy.float64\") and [`float32`](../../arrays.scalars#numpy.float32 \"numpy.float32\") are supported. Byteorder must be native. The default value is np.float64.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 1. # mean and width\n>>> s = np.random.default_rng().standard_gamma(shape, 1000000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \n... (sps.gamma(shape) * scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-standard_gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.standard_gamma.htmlnumpy.random.Generator.standard_normal\n=======================================\n\n method\n\n random.Generator.standard_normal(*size=None*, *dtype=np.float64*, *out=None*)\n \nDraw samples from a standard Normal distribution (mean=0, stdev=1).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result, only [`float64`](../../arrays.scalars#numpy.float64 \"numpy.float64\") and [`float32`](../../arrays.scalars#numpy.float32 \"numpy.float32\") are supported. Byteorder must be native. The default value is np.float64.\n\n \n**out**ndarray, optional\n\nAlternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.\n\n Returns \n \n**out**float or ndarray\n\nA floating-point array of shape `size` of drawn samples, or a single sample if `size` was not specified.\n\n See also\n\n [`normal`](numpy.random.generator.normal#numpy.random.Generator.normal \"numpy.random.Generator.normal\")\n\nEquivalent function with additional `loc` and `scale` arguments for setting the mean and standard deviation.\n\n #### Notes\n\n For random samples from \\(N(\\mu, \\sigma^2)\\), use one of:\n\n \n```\nmu + sigma * rng.standard_normal(size=...)\nrng.normal(mu, sigma, size=...)\n\n```\n #### Examples\n\n \n```\n>>> rng = np.random.default_rng()\n>>> rng.standard_normal()\n2.1923875335537315 # random\n\n```\n \n```\n>>> s = rng.standard_normal(8000)\n>>> s\narray([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, # random\n -0.38672696, -0.4685006 ]) # random\n>>> s.shape\n(8000,)\n>>> s = rng.standard_normal(size=(3, 4, 2))\n>>> s.shape\n(3, 4, 2)\n\n```\n Two-by-four array of samples from \\(N(3, 6.25)\\):\n\n \n```\n>>> 3 + 2.5 * rng.standard_normal(size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.standard_normal.htmlnumpy.random.Generator.standard_t\n==================================\n\n method\n\n random.Generator.standard_t(*df*, *size=None*)\n \nDraw samples from a standard Student’s t distribution with `df` degrees of freedom.\n\n A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution ([`standard_normal`](numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")).\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard Student’s t distribution.\n\n #### Notes\n\n The probability density function for the t distribution is\n\n \\[P(x, df) = \\frac{\\Gamma(\\frac{df+1}{2})}{\\sqrt{\\pi df} \\Gamma(\\frac{df}{2})}\\Bigl( 1+\\frac{x^2}{df} \\Bigr)^{-(df+1)/2}\\] The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean.\n\n The derivation of the t-distribution was first published in 1908 by <NAME> while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student.\n\n #### References\n\n [1](#id3) \nDalgaard, Peter, “Introductory Statistics With R”, Springer, 2002.\n\n 2 \nWikipedia, “Student’s t-distribution” [https://en.wikipedia.org/wiki/Student’s_t-distribution](https://en.wikipedia.org/wiki/Student's_t-distribution)\n\n #### Examples\n\n From Dalgaard page 83 [[1]](#rb7c952f3992e-1), suppose the daily energy intake for 11 women in kilojoules (kJ) is:\n\n \n```\n>>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \\\n... 7515, 8230, 8770])\n\n```\n Does their energy intake deviate systematically from the recommended value of 7725 kJ? Our null hypothesis will be the absence of deviation, and the alternate hypothesis will be the presence of an effect that could be either positive or negative, hence making our test 2-tailed.\n\n Because we are estimating the mean and we have N=11 values in our sample, we have N-1=10 degrees of freedom. We set our significance level to 95% and compute the t statistic using the empirical mean and empirical standard deviation of our intake. We use a ddof of 1 to base the computation of our empirical standard deviation on an unbiased estimate of the variance (note: the final estimate is not unbiased due to the concave nature of the square root).\n\n \n```\n>>> np.mean(intake)\n6753.636363636364\n>>> intake.std(ddof=1)\n1142.1232221373727\n>>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake)))\n>>> t\n-2.8207540608310198\n\n```\n We draw 1000000 samples from Student’s t distribution with the adequate degrees of freedom.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.default_rng().standard_t(10, size=1000000)\n>>> h = plt.hist(s, bins=100, density=True)\n\n```\n Does our t statistic land in one of the two critical regions found at both tails of the distribution?\n\n \n```\n>>> np.sum(np.abs(t) < np.abs(s)) / float(len(s))\n0.018318 #random < 0.05, statistic is in critical region\n\n```\n The probability value for this 2-tailed test is about 1.83%, which is lower than the 5% pre-determined significance threshold.\n\n Therefore, the probability of observing values as extreme as our intake conditionally on the null hypothesis being true is too low, and we reject the null hypothesis of no deviation.\n\n ![../../../_images/numpy-random-Generator-standard_t-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.standard_t.htmlnumpy.random.Generator.triangular\n=================================\n\n method\n\n random.Generator.triangular(*left*, *mode*, *right*, *size=None*)\n \nDraw samples from the triangular distribution over the interval `[left, right]`.\n\n The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf.\n\n Parameters \n \n**left**float or array_like of floats\n\nLower limit.\n\n \n**mode**float or array_like of floats\n\nThe value where the peak of the distribution occurs. The value must fulfill the condition `left <= mode <= right`.\n\n \n**right**float or array_like of floats\n\nUpper limit, must be larger than `left`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `left`, `mode`, and `right` are all scalars. Otherwise, `np.broadcast(left, mode, right).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized triangular distribution.\n\n #### Notes\n\n The probability density function for the triangular distribution is\n\n \\[\\begin{split}P(x;l, m, r) = \\begin{cases} \\frac{2(x-l)}{(r-l)(m-l)}& \\text{for $l \\leq x \\leq m$},\\\\ \\frac{2(r-x)}{(r-l)(r-m)}& \\text{for $m \\leq x \\leq r$},\\\\ 0& \\text{otherwise}. \\end{cases}\\end{split}\\] The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations.\n\n #### References\n\n 1 \nWikipedia, “Triangular distribution” <https://en.wikipedia.org/wiki/Triangular_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.default_rng().triangular(-3, 0, 8, 100000), bins=200,\n... density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-triangular-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.triangular.htmlnumpy.random.Generator.uniform\n==============================\n\n method\n\n random.Generator.uniform(*low=0.0*, *high=1.0*, *size=None*)\n \nDraw samples from a uniform distribution.\n\n Samples are uniformly distributed over the half-open interval `[low, high)` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by [`uniform`](#numpy.random.Generator.uniform \"numpy.random.Generator.uniform\").\n\n Parameters \n \n**low**float or array_like of floats, optional\n\nLower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0.\n\n \n**high**float or array_like of floats\n\nUpper boundary of the output interval. All values generated will be less than high. The high limit may be included in the returned array of floats due to floating-point rounding in the equation `low + (high-low) * random_sample()`. high - low must be non-negative. The default value is 1.0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `low` and `high` are both scalars. Otherwise, `np.broadcast(low, high).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized uniform distribution.\n\n See also\n\n [`integers`](numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\")\n\nDiscrete uniform distribution, yielding integers.\n\n [`random`](../index#module-numpy.random \"numpy.random\")\n\nFloats uniformly distributed over `[0, 1)`.\n\n #### Notes\n\n The probability density function of the uniform distribution is\n\n \\[p(x) = \\frac{1}{b - a}\\] anywhere within the interval `[a, b)`, and zero elsewhere.\n\n When `high` == `low`, values of `low` will be returned.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> s = np.random.default_rng().uniform(-1,0,1000)\n\n```\n All values are within the given interval:\n\n \n```\n>>> np.all(s >= -1)\nTrue\n>>> np.all(s < 0)\nTrue\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 15, density=True)\n>>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-uniform-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.uniform.htmlnumpy.random.Generator.vonmises\n===============================\n\n method\n\n random.Generator.vonmises(*mu*, *kappa*, *size=None*)\n \nDraw samples from a von Mises distribution.\n\n Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi].\n\n The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution.\n\n Parameters \n \n**mu**float or array_like of floats\n\nMode (“center”) of the distribution.\n\n \n**kappa**float or array_like of floats\n\nDispersion of the distribution, has to be >=0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mu` and `kappa` are both scalars. Otherwise, `np.broadcast(mu, kappa).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized von Mises distribution.\n\n See also\n\n [`scipy.stats.vonmises`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html#scipy.stats.vonmises \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the von Mises distribution is\n\n \\[p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},\\] where \\(\\mu\\) is the mode and \\(\\kappa\\) the dispersion, and \\(I_0(\\kappa)\\) is the modified Bessel function of order 0.\n\n The von Mises is named for <NAME>, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \nvon <NAME>., “Mathematical Theory of Probability and Statistics”, New York: Academic Press, 1964.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, kappa = 0.0, 4.0 # mean and dispersion\n>>> s = np.random.default_rng().vonmises(mu, kappa, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import i0 \n>>> plt.hist(s, 50, density=True)\n>>> x = np.linspace(-np.pi, np.pi, num=51)\n>>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) \n>>> plt.plot(x, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-vonmises-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.vonmises.htmlnumpy.random.Generator.wald\n===========================\n\n method\n\n random.Generator.wald(*mean*, *scale*, *size=None*)\n \nDraw samples from a Wald, or inverse Gaussian, distribution.\n\n As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an inverse Gaussian with mean equal to 1, but this is by no means universal.\n\n The inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 <NAME> used the name inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time.\n\n Parameters \n \n**mean**float or array_like of floats\n\nDistribution mean, must be > 0.\n\n \n**scale**float or array_like of floats\n\nScale parameter, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `scale` are both scalars. Otherwise, `np.broadcast(mean, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Wald distribution.\n\n #### Notes\n\n The probability density function for the Wald distribution is\n\n \\[P(x;mean,scale) = \\sqrt{\\frac{scale}{2\\pi x^3}}e^ \\frac{-scale(x-mean)^2}{2\\cdotp mean^2x}\\] As noted above the inverse Gaussian distribution first arise from attempts to model Brownian motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes.\n\n #### References\n\n 1 \nBrighton Webs Ltd., Wald Distribution, <https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp 2 \n<NAME>., and <NAME>, “The Inverse Gaussian Distribution: Theory : Methodology, and Applications”, CRC Press, 1988.\n\n 3 \nWikipedia, “Inverse Gaussian distribution” <https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.default_rng().wald(3, 2, 100000), bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-wald-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.wald.htmlnumpy.random.Generator.weibull\n==============================\n\n method\n\n random.Generator.weibull(*a*, *size=None*)\n \nDraw samples from a Weibull distribution.\n\n Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`.\n\n \\[X = (-ln(U))^{1/a}\\] Here, U is drawn from the uniform distribution over (0,1].\n\n The more common 2-parameter Weibull, including a scale parameter \\(\\lambda\\) is just \\(X = \\lambda(-ln(U))^{1/a}\\).\n\n Parameters \n \n**a**float or array_like of floats\n\nShape parameter of the distribution. Must be nonnegative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Weibull distribution.\n\n See also\n\n [`scipy.stats.weibull_max`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_max.html#scipy.stats.weibull_max \"(in SciPy v1.8.1)\")\n[`scipy.stats.weibull_min`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`gumbel`](numpy.random.generator.gumbel#numpy.random.Generator.gumbel \"numpy.random.Generator.gumbel\")\n #### Notes\n\n The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions.\n\n The probability density for the Weibull distribution is\n\n \\[p(x) = \\frac{a} {\\lambda}(\\frac{x}{\\lambda})^{a-1}e^{-(x/\\lambda)^a},\\] where \\(a\\) is the shape and \\(\\lambda\\) the scale.\n\n The function has its peak (the mode) at \\(\\lambda(\\frac{a-1}{a})^{1/a}\\).\n\n When `a = 1`, the Weibull distribution reduces to the exponential distribution.\n\n #### References\n\n 1 \n<NAME>, Royal Technical University, Stockholm, 1939 “A Statistical Theory Of The Strength Of Materials”, Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm.\n\n 2 \n<NAME>, “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper 1951.\n\n 3 \nWikipedia, “Weibull distribution”, <https://en.wikipedia.org/wiki/Weibull_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> rng = np.random.default_rng()\n>>> a = 5. # shape\n>>> s = rng.weibull(a, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x = np.arange(1,100.)/50.\n>>> def weib(x,n,a):\n... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)\n\n```\n \n```\n>>> count, bins, ignored = plt.hist(rng.weibull(5.,1000))\n>>> x = np.arange(1,100.)/50.\n>>> scale = count.max()/weib(x, 1., 5.).max()\n>>> plt.plot(x, weib(x, 1., 5.)*scale)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-weibull-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.weibull.htmlnumpy.random.Generator.zipf\n===========================\n\n method\n\n random.Generator.zipf(*a*, *size=None*)\n \nDraw samples from a Zipf distribution.\n\n Samples are drawn from a Zipf distribution with specified parameter `a` > 1.\n\n The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf’s law: the frequency of an item is inversely proportional to its rank in a frequency table.\n\n Parameters \n \n**a**float or array_like of floats\n\nDistribution parameter. Must be greater than 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Zipf distribution.\n\n See also\n\n [`scipy.stats.zipf`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zipf.html#scipy.stats.zipf \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n #### Notes\n\n The probability density for the Zipf distribution is\n\n \\[p(k) = \\frac{k^{-a}}{\\zeta(a)},\\] for integers \\(k \\geq 1\\), where \\(\\zeta\\) is the Riemann Zeta function.\n\n It is named for the American linguist <NAME>, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table.\n\n #### References\n\n 1 \n<NAME>., “Selected Studies of the Principle of Relative Frequency in Language,” Cambridge, MA: Harvard Univ. Press, 1932.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 4.0\n>>> n = 20000\n>>> s = np.random.default_rng().zipf(a, size=n)\n\n```\n Display the histogram of the samples, along with the expected histogram based on the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import zeta \n\n```\n [`bincount`](../../generated/numpy.bincount#numpy.bincount \"numpy.bincount\") provides a fast histogram for small integers.\n\n \n```\n>>> count = np.bincount(s)\n>>> k = np.arange(1, s.max() + 1)\n\n```\n \n```\n>>> plt.bar(k, count[1:], alpha=0.5, label='sample count')\n>>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5,\n... label='expected count') \n>>> plt.semilogy()\n>>> plt.grid(alpha=0.4)\n>>> plt.legend()\n>>> plt.title(f'Zipf sample, a={a}, size={n}')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-Generator-zipf-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.Generator.zipf.htmlnumpy.random.random\n===================\n\n random.random(*size=None*)\n \nReturn random floats in the half-open interval [0.0, 1.0). Alias for [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\") to ease forward-porting to the new random API.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.random.htmlnumpy.random.RandomState.get_state\n===================================\n\n method\n\n random.RandomState.get_state()\n \nReturn a tuple representing the internal state of the generator.\n\n For more details, see [`set_state`](numpy.random.randomstate.set_state#numpy.random.RandomState.set_state \"numpy.random.RandomState.set_state\").\n\n Parameters \n \n**legacy**bool, optional\n\nFlag indicating to return a legacy tuple state when the BitGenerator is MT19937, instead of a dict.\n\n Returns \n \n**out**{tuple(str, ndarray of 624 uints, int, int, float), dict}\n\nThe returned tuple has the following items:\n\n 1. the string ‘MT19937’.\n2. a 1-D array of 624 unsigned integer keys.\n3. an integer `pos`.\n4. an integer `has_gauss`.\n5. a float `cached_gaussian`.\n\n If `legacy` is False, or the BitGenerator is not MT19937, then state is returned as a dictionary.\n\n See also\n\n [`set_state`](numpy.random.randomstate.set_state#numpy.random.RandomState.set_state \"numpy.random.RandomState.set_state\")\n #### Notes\n\n [`set_state`](numpy.random.randomstate.set_state#numpy.random.RandomState.set_state \"numpy.random.RandomState.set_state\") and [`get_state`](#numpy.random.RandomState.get_state \"numpy.random.RandomState.get_state\") are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.get_state.htmlnumpy.random.RandomState.set_state\n===================================\n\n method\n\n random.RandomState.set_state(*state*)\n \nSet the internal state of the generator from a tuple.\n\n For use if one has reason to manually (re-)set the internal state of the bit generator used by the RandomState instance. By default, RandomState uses the “Mersenne Twister”[[1]](#rd62dfb5ffa26-1) pseudo-random number generating algorithm.\n\n Parameters \n \n**state**{tuple(str, ndarray of 624 uints, int, int, float), dict}\n\nThe `state` tuple has the following items:\n\n 1. the string ‘MT19937’, specifying the Mersenne Twister algorithm.\n2. a 1-D array of 624 unsigned integers `keys`.\n3. an integer `pos`.\n4. an integer `has_gauss`.\n5. a float `cached_gaussian`.\n\n If state is a dictionary, it is directly set using the BitGenerators `state` property.\n\n Returns \n \n**out**None\n\nReturns ‘None’ on success.\n\n See also\n\n [`get_state`](numpy.random.randomstate.get_state#numpy.random.RandomState.get_state \"numpy.random.RandomState.get_state\")\n #### Notes\n\n [`set_state`](#numpy.random.RandomState.set_state \"numpy.random.RandomState.set_state\") and [`get_state`](numpy.random.randomstate.get_state#numpy.random.RandomState.get_state \"numpy.random.RandomState.get_state\") are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing.\n\n For backwards compatibility, the form (str, array of 624 uints, int) is also accepted although it is missing some information about the cached Gaussian value: `state = ('MT19937', keys, pos)`.\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” *ACM Trans. on Modeling and Computer Simulation*, Vol. 8, No. 1, pp. 3-30, Jan. 1998.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.set_state.htmlnumpy.random.RandomState.seed\n=============================\n\n method\n\n random.RandomState.seed(*self*, *seed=None*)\n \nReseed a legacy MT19937 BitGenerator\n\n #### Notes\n\n This is a convenience, legacy function.\n\n The best practice is to **not** reseed a BitGenerator, rather to recreate a new one. This method is here for legacy reasons. This example demonstrates best practice.\n\n \n```\n>>> from numpy.random import MT19937\n>>> from numpy.random import RandomState, SeedSequence\n>>> rs = RandomState(MT19937(SeedSequence(123456789)))\n# Later, you want to restart the stream\n>>> rs = RandomState(MT19937(SeedSequence(987654321)))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.seed.htmlnumpy.random.RandomState.randint\n================================\n\n method\n\n random.RandomState.randint(*low*, *high=None*, *size=None*, *dtype=int*)\n \nReturn random integers from `low` (inclusive) to `high` (exclusive).\n\n Return random integers from the “discrete uniform” distribution of the specified dtype in the “half-open” interval [`low`, `high`). If `high` is None (the default), then results are from [0, `low`).\n\n Note\n\n New code should use the `integers` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**low**int or array-like of ints\n\nLowest (signed) integers to be drawn from the distribution (unless `high=None`, in which case this parameter is one above the *highest* such integer).\n\n \n**high**int or array-like of ints, optional\n\nIf provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if `high=None`). If array-like, must contain integer values\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result. Byteorder must be native. The default value is int.\n\n New in version 1.11.0.\n\n Returns \n \n**out**int or ndarray of ints\n\n`size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided.\n\n See also\n\n [`random_integers`](numpy.random.randomstate.random_integers#numpy.random.RandomState.random_integers \"numpy.random.RandomState.random_integers\")\n\nsimilar to [`randint`](#numpy.random.RandomState.randint \"numpy.random.RandomState.randint\"), only for the closed interval [`low`, `high`], and 1 is the lowest value if `high` is omitted.\n\n [`random.Generator.integers`](numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.randint(2, size=10)\narray([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random\n>>> np.random.randint(1, size=10)\narray([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n\n```\n Generate a 2 x 4 array of ints between 0 and 4, inclusive:\n\n \n```\n>>> np.random.randint(5, size=(2, 4))\narray([[4, 0, 2, 1], # random\n [3, 2, 2, 0]])\n\n```\n Generate a 1 x 3 array with 3 different upper bounds\n\n \n```\n>>> np.random.randint(1, [3, 5, 10])\narray([2, 2, 9]) # random\n\n```\n Generate a 1 by 3 array with 3 different lower bounds\n\n \n```\n>>> np.random.randint([1, 5, 7], 10)\narray([9, 8, 7]) # random\n\n```\n Generate a 2 by 4 array using broadcasting with dtype of uint8\n\n \n```\n>>> np.random.randint([1, 3, 5, 7], [[10], [20]], dtype=np.uint8)\narray([[ 8, 6, 9, 7], # random\n [ 1, 16, 9, 12]], dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.randint.htmlnumpy.random.RandomState.random_integers\n=========================================\n\n method\n\n random.RandomState.random_integers(*low*, *high=None*, *size=None*)\n \nRandom integers of type `np.int_` between `low` and `high`, inclusive.\n\n Return random integers of type `np.int_` from the “discrete uniform” distribution in the closed interval [`low`, `high`]. If `high` is None (the default), then results are from [1, `low`]. The `np.int_` type translates to the C long integer type and its precision is platform dependent.\n\n This function has been deprecated. Use randint instead.\n\n Deprecated since version 1.11.0.\n\n Parameters \n \n**low**int\n\nLowest (signed) integer to be drawn from the distribution (unless `high=None`, in which case this parameter is the *highest* such integer).\n\n \n**high**int, optional\n\nIf provided, the largest (signed) integer to be drawn from the distribution (see above for behavior if `high=None`).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**int or ndarray of ints\n\n`size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided.\n\n See also\n\n [`randint`](numpy.random.randomstate.randint#numpy.random.RandomState.randint \"numpy.random.RandomState.randint\")\n\nSimilar to [`random_integers`](#numpy.random.RandomState.random_integers \"numpy.random.RandomState.random_integers\"), only for the half-open interval [`low`, `high`), and 0 is the lowest value if `high` is omitted.\n\n #### Notes\n\n To sample from N evenly spaced floating-point numbers between a and b, use:\n\n \n```\na + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)\n\n```\n #### Examples\n\n \n```\n>>> np.random.random_integers(5)\n4 # random\n>>> type(np.random.random_integers(5))\n<class 'numpy.int64'>\n>>> np.random.random_integers(5, size=(3,2))\narray([[5, 4], # random\n [3, 3],\n [4, 5]])\n\n```\n Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (*i.e.*, from the set \\({0, 5/8, 10/8, 15/8, 20/8}\\)):\n\n \n```\n>>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4.\narray([ 0.625, 1.25 , 0.625, 0.625, 2.5 ]) # random\n\n```\n Roll two six sided dice 1000 times and sum the results:\n\n \n```\n>>> d1 = np.random.random_integers(1, 6, 1000)\n>>> d2 = np.random.random_integers(1, 6, 1000)\n>>> dsums = d1 + d2\n\n```\n Display results as a histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(dsums, 11, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-random_integers-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.random_integers.htmlnumpy.random.RandomState.choice\n===============================\n\n method\n\n random.RandomState.choice(*a*, *size=None*, *replace=True*, *p=None*)\n \nGenerates a random sample from a given 1-D array\n\n New in version 1.7.0.\n\n Note\n\n New code should use the `choice` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**1-D array-like or int\n\nIf an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if it were `np.arange(a)`\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**replace**boolean, optional\n\nWhether the sample is with or without replacement. Default is True, meaning that a value of `a` can be selected multiple times.\n\n \n**p**1-D array-like, optional\n\nThe probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in `a`.\n\n Returns \n \n**samples**single item or ndarray\n\nThe generated random samples\n\n Raises \n ValueError\n\nIf a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size\n\n See also\n\n \n[`randint`](numpy.random.randomstate.randint#numpy.random.RandomState.randint \"numpy.random.RandomState.randint\"), [`shuffle`](numpy.random.randomstate.shuffle#numpy.random.RandomState.shuffle \"numpy.random.RandomState.shuffle\"), [`permutation`](numpy.random.randomstate.permutation#numpy.random.RandomState.permutation \"numpy.random.RandomState.permutation\")\n\n[`random.Generator.choice`](numpy.random.generator.choice#numpy.random.Generator.choice \"numpy.random.Generator.choice\")\n\nwhich should be used in new code\n\n #### Notes\n\n Setting user-specified probabilities through `p` uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of `p` is 1 / len(a).\n\n Sampling random rows from a 2-D array is not possible with this function, but is possible with `Generator.choice` through its `axis` keyword.\n\n #### Examples\n\n Generate a uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> np.random.choice(5, 3)\narray([0, 3, 4]) # random\n>>> #This is equivalent to np.random.randint(0,5,3)\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])\narray([3, 3, 0]) # random\n\n```\n Generate a uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> np.random.choice(5, 3, replace=False)\narray([3,1,0]) # random\n>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])\narray([2, 3, 0]) # random\n\n```\n Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:\n\n \n```\n>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']\n>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])\narray(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random\n dtype='<U11')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.choice.htmlnumpy.random.RandomState.bytes\n==============================\n\n method\n\n random.RandomState.bytes(*length*)\n \nReturn random bytes.\n\n Note\n\n New code should use the `bytes` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**length**int\n\nNumber of random bytes.\n\n Returns \n \n**out**bytes\n\nString of length `length`.\n\n See also\n\n [`random.Generator.bytes`](numpy.random.generator.bytes#numpy.random.Generator.bytes \"numpy.random.Generator.bytes\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.bytes(10)\nb' eh\\x85\\x022SZ\\xbf\\xa4' #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.bytes.htmlnumpy.random.RandomState.shuffle\n================================\n\n method\n\n random.RandomState.shuffle(*x*)\n \nModify a sequence in-place by shuffling its contents.\n\n This function only shuffles the array along the first axis of a multi-dimensional array. The order of sub-arrays is changed but their contents remains the same.\n\n Note\n\n New code should use the `shuffle` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**x**ndarray or MutableSequence\n\nThe array, list or mutable sequence to be shuffled.\n\n Returns \n None\n See also\n\n [`random.Generator.shuffle`](numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> arr = np.arange(10)\n>>> np.random.shuffle(arr)\n>>> arr\n[1 7 5 2 9 4 3 6 0 8] # random\n\n```\n Multi-dimensional arrays are only shuffled along the first axis:\n\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> np.random.shuffle(arr)\n>>> arr\narray([[3, 4, 5], # random\n [6, 7, 8],\n [0, 1, 2]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.shuffle.htmlnumpy.random.RandomState.permutation\n====================================\n\n method\n\n random.RandomState.permutation(*x*)\n \nRandomly permute a sequence, or return a permuted range.\n\n If `x` is a multi-dimensional array, it is only shuffled along its first index.\n\n Note\n\n New code should use the `permutation` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**x**int or array_like\n\nIf `x` is an integer, randomly permute `np.arange(x)`. If `x` is an array, make a copy and shuffle the elements randomly.\n\n Returns \n \n**out**ndarray\n\nPermuted sequence or array range.\n\n See also\n\n [`random.Generator.permutation`](numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.permutation(10)\narray([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) # random\n\n```\n \n```\n>>> np.random.permutation([1, 4, 9, 12, 15])\narray([15, 1, 9, 4, 12]) # random\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> np.random.permutation(arr)\narray([[6, 7, 8], # random\n [0, 1, 2],\n [3, 4, 5]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.permutation.htmlnumpy.random.RandomState.beta\n=============================\n\n method\n\n random.RandomState.beta(*a*, *b*, *size=None*)\n \nDraw samples from a Beta distribution.\n\n The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function\n\n \\[f(x; a,b) = \\frac{1}{B(\\alpha, \\beta)} x^{\\alpha - 1} (1 - x)^{\\beta - 1},\\] where the normalization, B, is the beta function,\n\n \\[B(\\alpha, \\beta) = \\int_0^1 t^{\\alpha - 1} (1 - t)^{\\beta - 1} dt.\\] It is often seen in Bayesian inference and order statistics.\n\n Note\n\n New code should use the `beta` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nAlpha, positive (>0).\n\n \n**b**float or array_like of floats\n\nBeta, positive (>0).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` and `b` are both scalars. Otherwise, `np.broadcast(a, b).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized beta distribution.\n\n See also\n\n [`random.Generator.beta`](numpy.random.generator.beta#numpy.random.Generator.beta \"numpy.random.Generator.beta\")\n\nwhich should be used for new code.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.beta.htmlnumpy.random.RandomState.binomial\n=================================\n\n method\n\n random.RandomState.binomial(*n*, *p*, *size=None*)\n \nDraw samples from a binomial distribution.\n\n Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use)\n\n Note\n\n New code should use the `binomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**int or array_like of ints\n\nParameter of the distribution, >= 0. Floats are also accepted, but they will be truncated to integers.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution, >= 0 and <=1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized binomial distribution, where each sample is equal to the number of successes over the n trials.\n\n See also\n\n [`scipy.stats.binom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html#scipy.stats.binom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.binomial`](numpy.random.generator.binomial#numpy.random.Generator.binomial \"numpy.random.Generator.binomial\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the binomial distribution is\n\n \\[P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\\] where \\(n\\) is the number of trials, \\(p\\) is the probability of success, and \\(N\\) is the number of successes.\n\n When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case.\n\n #### References\n\n 1 \n<NAME>, “Introductory Statistics with R”, Springer-Verlag, 2002.\n\n 2 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 3 \nLentner, Marvin, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 4 \nWeisstein, <NAME>. “Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/BinomialDistribution.html 5 \nWikipedia, “Binomial distribution”, <https://en.wikipedia.org/wiki/Binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> n, p = 10, .5 # number of trials, probability of each trial\n>>> s = np.random.binomial(n, p, 1000)\n# result of flipping a coin 10 times, tested 1000 times.\n\n```\n A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening?\n\n Let’s do 20,000 trials of the model, and count the number that generate zero positive results.\n\n \n```\n>>> sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.\n# answer = 0.38885, or 38%.\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.binomial.htmlnumpy.random.RandomState.chisquare\n==================================\n\n method\n\n random.RandomState.chisquare(*df*, *size=None*)\n \nDraw samples from a chi-square distribution.\n\n When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing.\n\n Note\n\n New code should use the `chisquare` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nNumber of degrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized chi-square distribution.\n\n Raises \n ValueError\n\nWhen `df` <= 0 or when an inappropriate `size` (e.g. `size=-1`) is given.\n\n See also\n\n [`random.Generator.chisquare`](numpy.random.generator.chisquare#numpy.random.Generator.chisquare \"numpy.random.Generator.chisquare\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The variable obtained by summing the squares of `df` independent, standard normally distributed random variables:\n\n \\[Q = \\sum_{i=0}^{\\mathtt{df}} X^2_i\\] is chi-square distributed, denoted\n\n \\[Q \\sim \\chi^2_k.\\] The probability density function of the chi-squared distribution is\n\n \\[p(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)} x^{k/2 - 1} e^{-x/2},\\] where \\(\\Gamma\\) is the gamma function,\n\n \\[\\Gamma(x) = \\int_0^{-\\infty} t^{x - 1} e^{-t} dt.\\] #### References\n\n 1 \nNIST “Engineering Statistics Handbook” <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm #### Examples\n\n \n```\n>>> np.random.chisquare(2,4)\narray([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.chisquare.htmlnumpy.random.RandomState.dirichlet\n==================================\n\n method\n\n random.RandomState.dirichlet(*alpha*, *size=None*)\n \nDraw samples from the Dirichlet distribution.\n\n Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference.\n\n Note\n\n New code should use the `dirichlet` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**alpha**sequence of floats, length k\n\nParameter of the distribution (length `k` for sample of length `k`).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n)`, then `m * n * k` samples are drawn. Default is None, in which case a vector of length `k` is returned.\n\n Returns \n \n**samples**ndarray,\n\nThe drawn samples, of shape `(size, k)`.\n\n Raises \n ValueError\n\nIf any value in `alpha` is less than or equal to zero\n\n See also\n\n [`random.Generator.dirichlet`](numpy.random.generator.dirichlet#numpy.random.Generator.dirichlet \"numpy.random.Generator.dirichlet\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Dirichlet distribution is a distribution over vectors \\(x\\) that fulfil the conditions \\(x_i>0\\) and \\(\\sum_{i=1}^k x_i = 1\\).\n\n The probability density function \\(p\\) of a Dirichlet-distributed random vector \\(X\\) is proportional to\n\n \\[p(x) \\propto \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i},\\] where \\(\\alpha\\) is a vector containing the positive concentration parameters.\n\n The method uses the following property for computation: let \\(Y\\) be a random vector which has components that follow a standard gamma distribution, then \\(X = \\frac{1}{\\sum_{i=1}^k{Y_i}} Y\\) is Dirichlet-distributed\n\n #### References\n\n 1 \n<NAME>, “Information Theory, Inference and Learning Algorithms,” chapter 23, <http://www.inference.org.uk/mackay/itila/ 2 \nWikipedia, “Dirichlet distribution”, <https://en.wikipedia.org/wiki/Dirichlet_distribution #### Examples\n\n Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.\n\n \n```\n>>> s = np.random.dirichlet((10, 5, 3), 20).transpose()\n\n```\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.barh(range(20), s[0])\n>>> plt.barh(range(20), s[1], left=s[0], color='g')\n>>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')\n>>> plt.title(\"Lengths of Strings\")\n\n```\n ![../../../_images/numpy-random-RandomState-dirichlet-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.dirichlet.htmlnumpy.random.RandomState.exponential\n====================================\n\n method\n\n random.RandomState.exponential(*scale=1.0*, *size=None*)\n \nDraw samples from an exponential distribution.\n\n Its probability density function is\n\n \\[f(x; \\frac{1}{\\beta}) = \\frac{1}{\\beta} \\exp(-\\frac{x}{\\beta}),\\] for `x > 0` and 0 elsewhere. \\(\\beta\\) is the scale parameter, which is the inverse of the rate parameter \\(\\lambda = 1/\\beta\\). The rate parameter is an alternative, widely used parameterization of the exponential distribution [[3]](#rcfd3e98ffb09-3).\n\n The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [[1]](#rcfd3e98ffb09-1), or the time between page requests to Wikipedia [[2]](#rcfd3e98ffb09-2).\n\n Note\n\n New code should use the `exponential` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**scale**float or array_like of floats\n\nThe scale parameter, \\(\\beta = 1/\\lambda\\). Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized exponential distribution.\n\n See also\n\n [`random.Generator.exponential`](numpy.random.generator.exponential#numpy.random.Generator.exponential \"numpy.random.Generator.exponential\")\n\nwhich should be used for new code.\n\n #### References\n\n [1](#id2) \n<NAME>r., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.\n\n [2](#id3) \nWikipedia, “Poisson process”, <https://en.wikipedia.org/wiki/Poisson_process [3](#id1) \nWikipedia, “Exponential distribution”, <https://en.wikipedia.org/wiki/Exponential_distribution © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.exponential.htmlnumpy.random.RandomState.f\n==========================\n\n method\n\n random.RandomState.f(*dfnum*, *dfden*, *size=None*)\n \nDraw samples from an F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters must be greater than zero.\n\n The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates.\n\n Note\n\n New code should use the `f` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nDegrees of freedom in numerator, must be > 0.\n\n \n**dfden**float or array_like of float\n\nDegrees of freedom in denominator, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum` and `dfden` are both scalars. Otherwise, `np.broadcast(dfnum, dfden).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Fisher distribution.\n\n See also\n\n [`scipy.stats.f`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f.html#scipy.stats.f \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.f`](numpy.random.generator.f#numpy.random.Generator.f \"numpy.random.Generator.f\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups.\n\n #### References\n\n 1 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 2 \nWikipedia, “F-distribution”, <https://en.wikipedia.org/wiki/F-distribution #### Examples\n\n An example from Glantz[1], pp 47-40:\n\n Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children’s blood glucose levels? Calculating the F statistic from the data gives a value of 36.01.\n\n Draw samples from the distribution:\n\n \n```\n>>> dfnum = 1. # between group degrees of freedom\n>>> dfden = 48. # within groups degrees of freedom\n>>> s = np.random.f(dfnum, dfden, 1000)\n\n```\n The lower bound for the top 1% of the samples is :\n\n \n```\n>>> np.sort(s)[-10]\n7.61988120985 # random\n\n```\n So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.f.htmlnumpy.random.RandomState.geometric\n==================================\n\n method\n\n random.RandomState.geometric(*p*, *size=None*)\n \nDraw samples from the geometric distribution.\n\n Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, `k = 1, 2, ...`.\n\n The probability mass function of the geometric distribution is\n\n \\[f(k) = (1 - p)^{k - 1} p\\] where `p` is the probability of success of an individual trial.\n\n Note\n\n New code should use the `geometric` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**p**float or array_like of floats\n\nThe probability of success of an individual trial.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized geometric distribution.\n\n See also\n\n [`random.Generator.geometric`](numpy.random.generator.geometric#numpy.random.Generator.geometric \"numpy.random.Generator.geometric\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35:\n\n \n```\n>>> z = np.random.geometric(p=0.35, size=10000)\n\n```\n How many trials succeeded after a single run?\n\n \n```\n>>> (z == 1).sum() / 10000.\n0.34889999999999999 #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.geometric.htmlnumpy.random.RandomState.gumbel\n===============================\n\n method\n\n random.RandomState.gumbel(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gumbel distribution.\n\n Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below.\n\n Note\n\n New code should use the `gumbel` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe location of the mode of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale parameter of the distribution. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Gumbel distribution.\n\n See also\n\n [`scipy.stats.gumbel_l`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_l.html#scipy.stats.gumbel_l \"(in SciPy v1.8.1)\")\n[`scipy.stats.gumbel_r`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`weibull`](numpy.random.randomstate.weibull#numpy.random.RandomState.weibull \"numpy.random.RandomState.weibull\")\n[`random.Generator.gumbel`](numpy.random.generator.gumbel#numpy.random.Generator.gumbel \"numpy.random.Generator.gumbel\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with “exponential-like” tails.\n\n The probability density for the Gumbel distribution is\n\n \\[p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/ \\beta}},\\] where \\(\\mu\\) is the mode, a location parameter, and \\(\\beta\\) is the scale parameter.\n\n The Gumbel (named for German mathematician Emil <NAME>) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a “fat-tailed” distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events.\n\n It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet.\n\n The function has a mean of \\(\\mu + 0.57721\\beta\\) and a variance of \\(\\frac{\\pi^2}{6}\\beta^2\\).\n\n #### References\n\n 1 \n<NAME>., “Statistics of Extremes,” New York: Columbia University Press, 1958.\n\n 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields,” Basel: Birkhauser Verlag, 2001.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, beta = 0, 0.1 # location and scale\n>>> s = np.random.gumbel(mu, beta, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp( -np.exp( -(bins - mu) /beta) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-gumbel-1_00_00.png] Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian:\n\n \n```\n>>> means = []\n>>> maxima = []\n>>> for i in range(0,1000) :\n... a = np.random.normal(mu, beta, 1000)\n... means.append(a.mean())\n... maxima.append(a.max())\n>>> count, bins, ignored = plt.hist(maxima, 30, density=True)\n>>> beta = np.std(maxima) * np.sqrt(6) / np.pi\n>>> mu = np.mean(maxima) - 0.57721*beta\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp(-np.exp(-(bins - mu)/beta)),\n... linewidth=2, color='r')\n>>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))\n... * np.exp(-(bins - mu)**2 / (2 * beta**2)),\n... linewidth=2, color='g')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-gumbel-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.gumbel.htmlnumpy.random.RandomState.hypergeometric\n=======================================\n\n method\n\n random.RandomState.hypergeometric(*ngood*, *nbad*, *nsample*, *size=None*)\n \nDraw samples from a Hypergeometric distribution.\n\n Samples are drawn from a hypergeometric distribution with specified parameters, `ngood` (ways to make a good selection), `nbad` (ways to make a bad selection), and `nsample` (number of items sampled, which is less than or equal to the sum `ngood + nbad`).\n\n Note\n\n New code should use the `hypergeometric` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**ngood**int or array_like of ints\n\nNumber of ways to make a good selection. Must be nonnegative.\n\n \n**nbad**int or array_like of ints\n\nNumber of ways to make a bad selection. Must be nonnegative.\n\n \n**nsample**int or array_like of ints\n\nNumber of items sampled. Must be at least 1 and at most `ngood + nbad`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `ngood`, `nbad`, and `nsample` are all scalars. Otherwise, `np.broadcast(ngood, nbad, nsample).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized hypergeometric distribution. Each sample is the number of good items within a randomly selected subset of size `nsample` taken from a set of `ngood` good items and `nbad` bad items.\n\n See also\n\n [`scipy.stats.hypergeom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hypergeom.html#scipy.stats.hypergeom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.hypergeometric`](numpy.random.generator.hypergeometric#numpy.random.Generator.hypergeometric \"numpy.random.Generator.hypergeometric\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Hypergeometric distribution is\n\n \\[P(x) = \\frac{\\binom{g}{x}\\binom{b}{n-x}}{\\binom{g+b}{n}},\\] where \\(0 \\le x \\le n\\) and \\(n-b \\le x \\le g\\)\n\n for P(x) the probability of `x` good results in the drawn sample, g = `ngood`, b = `nbad`, and n = `nsample`.\n\n Consider an urn with black and white marbles in it, `ngood` of them are black and `nbad` are white. If you draw `nsample` balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample.\n\n Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial.\n\n #### References\n\n 1 \n<NAME>, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 2 \nWeisstein, <NAME>. “Hypergeometric Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/HypergeometricDistribution.html 3 \nWikipedia, “Hypergeometric distribution”, <https://en.wikipedia.org/wiki/Hypergeometric_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> ngood, nbad, nsamp = 100, 2, 10\n# number of good, number of bad, and number of samples\n>>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)\n>>> from matplotlib.pyplot import hist\n>>> hist(s)\n# note that it is very unlikely to grab both bad items\n\n```\n Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color?\n\n \n```\n>>> s = np.random.hypergeometric(15, 15, 15, 100000)\n>>> sum(s>=12)/100000. + sum(s<=3)/100000.\n# answer = 0.003 ... pretty unlikely!\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.hypergeometric.htmlnumpy.random.RandomState.laplace\n================================\n\n method\n\n random.RandomState.laplace(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).\n\n The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables.\n\n Note\n\n New code should use the `laplace` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe position, \\(\\mu\\), of the distribution peak. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\n\\(\\lambda\\), the exponential decay. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Laplace distribution.\n\n See also\n\n [`random.Generator.laplace`](numpy.random.generator.laplace#numpy.random.Generator.laplace \"numpy.random.Generator.laplace\")\n\nwhich should be used for new code.\n\n #### Notes\n\n It has the probability density function\n\n \\[f(x; \\mu, \\lambda) = \\frac{1}{2\\lambda} \\exp\\left(-\\frac{|x - \\mu|}{\\lambda}\\right).\\] The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution.\n\n #### References\n\n 1 \n<NAME> <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \n<NAME>, et. al. “The Laplace Distribution and Generalizations, ” Birkhauser, 2001.\n\n 3 \nWeisstein, <NAME>. “Laplace Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LaplaceDistribution.html 4 \nWikipedia, “Laplace distribution”, <https://en.wikipedia.org/wiki/Laplace_distribution #### Examples\n\n Draw samples from the distribution\n\n \n```\n>>> loc, scale = 0., 1.\n>>> s = np.random.laplace(loc, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> x = np.arange(-8., 8., .01)\n>>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)\n>>> plt.plot(x, pdf)\n\n```\n Plot Gaussian for comparison:\n\n \n```\n>>> g = (1/(scale * np.sqrt(2 * np.pi)) *\n... np.exp(-(x - loc)**2 / (2 * scale**2)))\n>>> plt.plot(x,g)\n\n```\n ![../../../_images/numpy-random-RandomState-laplace-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.laplace.htmlnumpy.random.RandomState.logistic\n=================================\n\n method\n\n random.RandomState.logistic(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a logistic distribution.\n\n Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).\n\n Note\n\n New code should use the `logistic` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nParameter of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nParameter of the distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logistic distribution.\n\n See also\n\n [`scipy.stats.logistic`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logistic.html#scipy.stats.logistic \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.logistic`](numpy.random.generator.logistic#numpy.random.Generator.logistic \"numpy.random.Generator.logistic\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Logistic distribution is\n\n \\[P(x) = P(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2},\\] where \\(\\mu\\) = location and \\(s\\) = scale.\n\n The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (2001), “Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,” <NAME>, Basel, pp 132-133.\n\n 2 \nWeisstein, <NAME>. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LogisticDistribution.html 3 \nWikipedia, “Logistic-distribution”, <https://en.wikipedia.org/wiki/Logistic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> loc, scale = 10, 1\n>>> s = np.random.logistic(loc, scale, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=50)\n\n```\n # plot against distribution\n\n \n```\n>>> def logist(x, loc, scale):\n... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)\n>>> lgst_val = logist(bins, loc, scale)\n>>> plt.plot(bins, lgst_val * count.max() / lgst_val.max())\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-logistic-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.logistic.htmlnumpy.random.RandomState.lognormal\n==================================\n\n method\n\n random.RandomState.lognormal(*mean=0.0*, *sigma=1.0*, *size=None*)\n \nDraw samples from a log-normal distribution.\n\n Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.\n\n Note\n\n New code should use the `lognormal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**float or array_like of floats, optional\n\nMean value of the underlying normal distribution. Default is 0.\n\n \n**sigma**float or array_like of floats, optional\n\nStandard deviation of the underlying normal distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `sigma` are both scalars. Otherwise, `np.broadcast(mean, sigma).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized log-normal distribution.\n\n See also\n\n [`scipy.stats.lognorm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, cumulative density function, etc.\n\n [`random.Generator.lognormal`](numpy.random.generator.lognormal#numpy.random.Generator.lognormal \"numpy.random.Generator.lognormal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is:\n\n \\[p(x) = \\frac{1}{\\sigma x \\sqrt{2\\pi}} e^{(-\\frac{(ln(x)-\\mu)^2}{2\\sigma^2})}\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables.\n\n #### References\n\n 1 \n<NAME>., <NAME>., and <NAME>., “Log-normal Distributions across the Sciences: Keys and Clues,” BioScience, Vol. 51, No. 5, May, 2001. <https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values,” Basel: B<NAME>, 2001, pp. 31-32.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, sigma = 3., 1. # mean and standard deviation\n>>> s = np.random.lognormal(mu, sigma, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 100, density=True, align='mid')\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, linewidth=2, color='r')\n>>> plt.axis('tight')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-lognormal-1_00_00.png] Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function.\n\n \n```\n>>> # Generate a thousand samples: each is the product of 100 random\n>>> # values, drawn from a normal distribution.\n>>> b = []\n>>> for i in range(1000):\n... a = 10. + np.random.standard_normal(100)\n... b.append(np.product(a))\n\n```\n \n```\n>>> b = np.array(b) / np.min(b) # scale values to be positive\n>>> count, bins, ignored = plt.hist(b, 100, density=True, align='mid')\n>>> sigma = np.std(np.log(b))\n>>> mu = np.mean(np.log(b))\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, color='r', linewidth=2)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-lognormal-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.lognormal.htmlnumpy.random.RandomState.logseries\n==================================\n\n method\n\n random.RandomState.logseries(*p*, *size=None*)\n \nDraw samples from a logarithmic series distribution.\n\n Samples are drawn from a log series distribution with specified shape parameter, 0 < `p` < 1.\n\n Note\n\n New code should use the `logseries` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**p**float or array_like of floats\n\nShape parameter for the distribution. Must be in the range (0, 1).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logarithmic series distribution.\n\n See also\n\n [`scipy.stats.logser`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logser.html#scipy.stats.logser \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.logseries`](numpy.random.generator.logseries#numpy.random.Generator.logseries \"numpy.random.Generator.logseries\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Log Series distribution is\n\n \\[P(k) = \\frac{-p^k}{k \\ln(1-p)},\\] where p = probability.\n\n The log series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3].\n\n #### References\n\n 1 \n<NAME>.; <NAME>., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9).\n\n 2 \n<NAME>,, <NAME>, and <NAME>. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58.\n\n 3 \n<NAME>, <NAME>, <NAME>, <NAME>, A Handbook of Small Data Sets, CRC Press, 1994.\n\n 4 \nWikipedia, “Logarithmic distribution”, <https://en.wikipedia.org/wiki/Logarithmic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = .6\n>>> s = np.random.logseries(a, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s)\n\n```\n # plot against distribution\n\n \n```\n>>> def logseries(k, p):\n... return -p**k/(k*np.log(1-p))\n>>> plt.plot(bins, logseries(bins, a)*count.max()/\n... logseries(bins, a).max(), 'r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-logseries-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.logseries.htmlnumpy.random.RandomState.multinomial\n====================================\n\n method\n\n random.RandomState.multinomial(*n*, *pvals*, *size=None*)\n \nDraw samples from a multinomial distribution.\n\n The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of `p` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, `X_i = [X_0, X_1, ..., X_p]`, represent the number of times the outcome was `i`.\n\n Note\n\n New code should use the `multinomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**int\n\nNumber of experiments.\n\n \n**pvals**sequence of floats, length p\n\nProbabilities of each of the `p` different outcomes. These must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as `sum(pvals[:-1]) <= 1)`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape *size*, if that was provided. If not, the shape is `(N,)`.\n\n In other words, each entry `out[i,j,...,:]` is an N-dimensional value drawn from the distribution.\n\n See also\n\n [`random.Generator.multinomial`](numpy.random.generator.multinomial#numpy.random.Generator.multinomial \"numpy.random.Generator.multinomial\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Throw a dice 20 times:\n\n \n```\n>>> np.random.multinomial(20, [1/6.]*6, size=1)\narray([[4, 1, 7, 5, 2, 1]]) # random\n\n```\n It landed 4 times on 1, once on 2, etc.\n\n Now, throw the dice 20 times, and 20 times again:\n\n \n```\n>>> np.random.multinomial(20, [1/6.]*6, size=2)\narray([[3, 4, 3, 3, 4, 3], # random\n [2, 4, 3, 4, 0, 7]])\n\n```\n For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc.\n\n A loaded die is more likely to land on number 6:\n\n \n```\n>>> np.random.multinomial(100, [1/7.]*5 + [2/7.])\narray([11, 16, 14, 17, 16, 26]) # random\n\n```\n The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so:\n\n \n```\n>>> np.random.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT\narray([38, 62]) # random\n\n```\n not like:\n\n \n```\n>>> np.random.multinomial(100, [1.0, 2.0]) # WRONG\nTraceback (most recent call last):\nValueError: pvals < 0, pvals > 1 or pvals contains NaNs\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.multinomial.htmlnumpy.random.RandomState.multivariate_normal\n=============================================\n\n method\n\n random.RandomState.multivariate_normal(*mean*, *cov*, *size=None*, *check_valid='warn'*, *tol=1e-8*)\n \nDraw random samples from a multivariate normal distribution.\n\n The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or “center”) and variance (standard deviation, or “width,” squared) of the one-dimensional normal distribution.\n\n Note\n\n New code should use the `multivariate_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**1-D array_like, of length N\n\nMean of the N-dimensional distribution.\n\n \n**cov**2-D array_like, of shape (N, N)\n\nCovariance matrix of the distribution. It must be symmetric and positive-semidefinite for proper sampling.\n\n \n**size**int or tuple of ints, optional\n\nGiven a shape of, for example, `(m,n,k)`, `m*n*k` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is `(m,n,k,N)`. If no shape is specified, a single (`N`-D) sample is returned.\n\n \n**check_valid**{ ‘warn’, ‘raise’, ‘ignore’ }, optional\n\nBehavior when the covariance matrix is not positive semidefinite.\n\n \n**tol**float, optional\n\nTolerance when checking the singular values in covariance matrix. cov is cast to double before the check.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape *size*, if that was provided. If not, the shape is `(N,)`.\n\n In other words, each entry `out[i,j,...,:]` is an N-dimensional value drawn from the distribution.\n\n See also\n\n [`random.Generator.multivariate_normal`](numpy.random.generator.multivariate_normal#numpy.random.Generator.multivariate_normal \"numpy.random.Generator.multivariate_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution.\n\n Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, \\(X = [x_1, x_2, ... x_N]\\). The covariance matrix element \\(C_{ij}\\) is the covariance of \\(x_i\\) and \\(x_j\\). The element \\(C_{ii}\\) is the variance of \\(x_i\\) (i.e. its “spread”).\n\n Instead of specifying the full covariance matrix, popular approximations include:\n\n * Spherical covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") is a multiple of the identity matrix)\n* Diagonal covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") has non-negative elements, and only on the diagonal)\n\n This geometrical property can be seen in two dimensions by plotting generated data-points:\n\n \n```\n>>> mean = [0, 0]\n>>> cov = [[1, 0], [0, 100]] # diagonal covariance\n\n```\n Diagonal covariance means that points are oriented along x or y-axis:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x, y = np.random.multivariate_normal(mean, cov, 5000).T\n>>> plt.plot(x, y, 'x')\n>>> plt.axis('equal')\n>>> plt.show()\n\n```\n Note that the covariance matrix must be positive semidefinite (a.k.a. nonnegative-definite). Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed.\n\n #### References\n\n 1 \n<NAME>., “Probability, Random Variables, and Stochastic Processes,” 3rd ed., New York: McGraw-Hill, 1991.\n\n 2 \n<NAME>., <NAME>., and <NAME>., “Pattern Classification,” 2nd ed., New York: Wiley, 2001.\n\n #### Examples\n\n \n```\n>>> mean = (1, 2)\n>>> cov = [[1, 0], [0, 1]]\n>>> x = np.random.multivariate_normal(mean, cov, (3, 3))\n>>> x.shape\n(3, 3, 2)\n\n```\n Here we generate 800 samples from the bivariate normal distribution with mean [0, 0] and covariance matrix [[6, -3], [-3, 3.5]]. The expected variances of the first and second components of the sample are 6 and 3.5, respectively, and the expected correlation coefficient is -3/sqrt(6*3.5) ≈ -0.65465.\n\n \n```\n>>> cov = np.array([[6, -3], [-3, 3.5]])\n>>> pts = np.random.multivariate_normal([0, 0], cov, size=800)\n\n```\n Check that the mean, covariance, and correlation coefficient of the sample are close to the expected values:\n\n \n```\n>>> pts.mean(axis=0)\narray([ 0.0326911 , -0.01280782]) # may vary\n>>> np.cov(pts.T)\narray([[ 5.96202397, -2.85602287],\n [-2.85602287, 3.47613949]]) # may vary\n>>> np.corrcoef(pts.T)[0, 1]\n-0.6273591314603949 # may vary\n\n```\n We can visualize this data with a scatter plot. The orientation of the point cloud illustrates the negative correlation of the components of this sample.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(pts[:, 0], pts[:, 1], '.', alpha=0.5)\n>>> plt.axis('equal')\n>>> plt.grid()\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-multivariate_normal-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.multivariate_normal.htmlnumpy.random.RandomState.negative_binomial\n===========================================\n\n method\n\n random.RandomState.negative_binomial(*n*, *p*, *size=None*)\n \nDraw samples from a negative binomial distribution.\n\n Samples are drawn from a negative binomial distribution with specified parameters, `n` successes and `p` probability of success where `n` is > 0 and `p` is in the interval [0, 1].\n\n Note\n\n New code should use the `negative_binomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**float or array_like of floats\n\nParameter of the distribution, > 0.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution, >= 0 and <=1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached.\n\n See also\n\n [`random.Generator.negative_binomial`](numpy.random.generator.negative_binomial#numpy.random.Generator.negative_binomial \"numpy.random.Generator.negative_binomial\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability mass function of the negative binomial distribution is\n\n \\[P(N;n,p) = \\frac{\\Gamma(N+n)}{N!\\Gamma(n)}p^{n}(1-p)^{N},\\] where \\(n\\) is the number of successes, \\(p\\) is the probability of success, \\(N+n\\) is the number of trials, and \\(\\Gamma\\) is the gamma function. When \\(n\\) is an integer, \\(\\frac{\\Gamma(N+n)}{N!\\Gamma(n)} = \\binom{N+n-1}{N}\\), which is the more common form of this term in the the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial.\n\n If one throws a die repeatedly until the third time a “1” appears, then the probability distribution of the number of non-“1”s that appear before the third “1” is a negative binomial distribution.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Negative Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NegativeBinomialDistribution.html 2 \nWikipedia, “Negative binomial distribution”, <https://en.wikipedia.org/wiki/Negative_binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.?\n\n \n```\n>>> s = np.random.negative_binomial(1, 0.1, 100000)\n>>> for i in range(1, 11): \n... probability = sum(s<i) / 100000.\n... print(i, \"wells drilled, probability of one success =\", probability)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.negative_binomial.htmlnumpy.random.RandomState.noncentral_chisquare\n==============================================\n\n method\n\n random.RandomState.noncentral_chisquare(*df*, *nonc*, *size=None*)\n \nDraw samples from a noncentral chi-square distribution.\n\n The noncentral \\(\\chi^2\\) distribution is a generalization of the \\(\\chi^2\\) distribution.\n\n Note\n\n New code should use the `noncentral_chisquare` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n Changed in version 1.10.0: Earlier NumPy versions required dfnum > 1.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` and `nonc` are both scalars. Otherwise, `np.broadcast(df, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral chi-square distribution.\n\n See also\n\n [`random.Generator.noncentral_chisquare`](numpy.random.generator.noncentral_chisquare#numpy.random.Generator.noncentral_chisquare \"numpy.random.Generator.noncentral_chisquare\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the noncentral Chi-square distribution is\n\n \\[P(x;df,nonc) = \\sum^{\\infty}_{i=0} \\frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x),\\] where \\(Y_{q}\\) is the Chi-square with q degrees of freedom.\n\n #### References\n\n 1 \nWikipedia, “Noncentral chi-squared distribution” <https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-noncentral_chisquare-1_00_00.png] Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> values2 = plt.hist(np.random.chisquare(3, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-noncentral_chisquare-1_01_00.png] Demonstrate how large values of non-centrality lead to a more symmetric distribution.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-noncentral_chisquare-1_02_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.noncentral_chisquare.htmlnumpy.random.RandomState.noncentral_f\n======================================\n\n method\n\n random.RandomState.noncentral_f(*dfnum*, *dfden*, *nonc*, *size=None*)\n \nDraw samples from the noncentral F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter.\n\n Note\n\n New code should use the `noncentral_f` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nNumerator degrees of freedom, must be > 0.\n\n Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.\n\n \n**dfden**float or array_like of floats\n\nDenominator degrees of freedom, must be > 0.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality parameter, the sum of the squares of the numerator means, must be >= 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum`, `dfden`, and `nonc` are all scalars. Otherwise, `np.broadcast(dfnum, dfden, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral Fisher distribution.\n\n See also\n\n [`random.Generator.noncentral_f`](numpy.random.generator.noncentral_f#numpy.random.Generator.noncentral_f \"numpy.random.Generator.noncentral_f\")\n\nwhich should be used for new code.\n\n #### Notes\n\n When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NoncentralF-Distribution.html 2 \nWikipedia, “Noncentral F-distribution”, <https://en.wikipedia.org/wiki/Noncentral_F-distribution #### Examples\n\n In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We’ll plot the two probability distributions for comparison.\n\n \n```\n>>> dfnum = 3 # between group deg of freedom\n>>> dfden = 20 # within groups degrees of freedom\n>>> nonc = 3.0\n>>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)\n>>> NF = np.histogram(nc_vals, bins=50, density=True)\n>>> c_vals = np.random.f(dfnum, dfden, 1000000)\n>>> F = np.histogram(c_vals, bins=50, density=True)\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(F[1][1:], F[0])\n>>> plt.plot(NF[1][1:], NF[0])\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-noncentral_f-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.noncentral_f.htmlnumpy.random.RandomState.normal\n===============================\n\n method\n\n random.RandomState.normal(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw random samples from a normal (Gaussian) distribution.\n\n The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [[2]](#ra2e838c5ea87-2), is often called the bell curve because of its characteristic shape (see the example below).\n\n The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [[2]](#ra2e838c5ea87-2).\n\n Note\n\n New code should use the `normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats\n\nMean (“centre”) of the distribution.\n\n \n**scale**float or array_like of floats\n\nStandard deviation (spread or “width”) of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized normal distribution.\n\n See also\n\n [`scipy.stats.norm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.normal`](numpy.random.generator.normal#numpy.random.Generator.normal \"numpy.random.Generator.normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gaussian distribution is\n\n \\[p(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }} e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) the standard deviation. The square of the standard deviation, \\(\\sigma^2\\), is called the variance.\n\n The function has its peak at the mean, and its “spread” increases with the standard deviation (the function reaches 0.607 times its maximum at \\(x + \\sigma\\) and \\(x - \\sigma\\) [[2]](#ra2e838c5ea87-2)). This implies that normal is more likely to return samples lying close to the mean, rather than those far away.\n\n #### References\n\n 1 \nWikipedia, “Normal distribution”, <https://en.wikipedia.org/wiki/Normal_distribution2([1](#id1),[2](#id2),[3](#id3))\n \n<NAME>., “Central Limit Theorem” in “Probability, Random Variables and Random Signal Principles”, 4th ed., 2001, pp. 51, 51, 125.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, sigma = 0, 0.1 # mean and standard deviation\n>>> s = np.random.normal(mu, sigma, 1000)\n\n```\n Verify the mean and the variance:\n\n \n```\n>>> abs(mu - np.mean(s))\n0.0 # may vary\n\n```\n \n```\n>>> abs(sigma - np.std(s, ddof=1))\n0.1 # may vary\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-normal-1_00_00.png]:\n\n \n```\n>>> np.random.normal(3, 2.5, size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.normal.htmlnumpy.random.RandomState.pareto\n===============================\n\n method\n\n random.RandomState.pareto(*a*, *size=None*)\n \nDraw samples from a Pareto II or Lomax distribution with specified shape.\n\n The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding 1 and multiplying by the scale parameter `m` (see Notes). The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is `mu`, where the standard Pareto distribution has location `mu = 1`. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero.\n\n The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the “80-20 rule”. In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range.\n\n Note\n\n New code should use the `pareto` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nShape of the distribution. Must be positive.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Pareto distribution.\n\n See also\n\n [`scipy.stats.lomax`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lomax.html#scipy.stats.lomax \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`scipy.stats.genpareto`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.pareto`](numpy.random.generator.pareto#numpy.random.Generator.pareto \"numpy.random.Generator.pareto\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Pareto distribution is\n\n \\[p(x) = \\frac{am^a}{x^{a+1}}\\] where \\(a\\) is the shape and \\(m\\) the scale.\n\n The Pareto distribution, named after the Italian economist <NAME>, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [[1]](#r4338a4b3d731-1). It is one of the so-called “fat-tailed” distributions.\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, On the Pareto Distribution of Sourceforge projects.\n\n 2 \n<NAME>. (1896). Course of Political Economy. Lausanne.\n\n 3 \n<NAME>., <NAME>.(2001), Statistical Analysis of Extreme Values, <NAME>, pp 23-30.\n\n 4 \nWikipedia, “Pareto distribution”, <https://en.wikipedia.org/wiki/Pareto_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a, m = 3., 2. # shape and mode\n>>> s = (np.random.pareto(a, 1000) + 1) * m\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, _ = plt.hist(s, 100, density=True)\n>>> fit = a*m**a / bins**(a+1)\n>>> plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-pareto-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.pareto.htmlnumpy.random.RandomState.poisson\n================================\n\n method\n\n random.RandomState.poisson(*lam=1.0*, *size=None*)\n \nDraw samples from a Poisson distribution.\n\n The Poisson distribution is the limit of the binomial distribution for large N.\n\n Note\n\n New code should use the `poisson` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**lam**float or array_like of floats\n\nExpected number of events occurring in a fixed-time interval, must be >= 0. A sequence must be broadcastable over the requested size.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `lam` is a scalar. Otherwise, `np.array(lam).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Poisson distribution.\n\n See also\n\n [`random.Generator.poisson`](numpy.random.generator.poisson#numpy.random.Generator.poisson \"numpy.random.Generator.poisson\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Poisson distribution\n\n \\[f(k; \\lambda)=\\frac{\\lambda^k e^{-\\lambda}}{k!}\\] For events with an expected separation \\(\\lambda\\) the Poisson distribution \\(f(k; \\lambda)\\) describes the probability of \\(k\\) events occurring within the observed interval \\(\\lambda\\).\n\n Because the output is limited to the range of the C int64 type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/PoissonDistribution.html 2 \nWikipedia, “Poisson distribution”, <https://en.wikipedia.org/wiki/Poisson_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> import numpy as np\n>>> s = np.random.poisson(5, 10000)\n\n```\n Display histogram of the sample:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 14, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-poisson-1_00_00.png] Draw each 100 values for lambda 100 and 500:\n\n \n```\n>>> s = np.random.poisson(lam=(100., 500.), size=(100, 2))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.poisson.htmlnumpy.random.RandomState.power\n==============================\n\n method\n\n random.RandomState.power(*a*, *size=None*)\n \nDraws samples in [0, 1] from a power distribution with positive exponent a - 1.\n\n Also known as the power function distribution.\n\n Note\n\n New code should use the `power` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nParameter of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized power distribution.\n\n Raises \n ValueError\n\nIf a <= 0.\n\n See also\n\n [`random.Generator.power`](numpy.random.generator.power#numpy.random.Generator.power \"numpy.random.Generator.power\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function is\n\n \\[P(x; a) = ax^{a-1}, 0 \\le x \\le 1, a>0.\\] The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution.\n\n It is used, for example, in modeling the over-reporting of insurance claims.\n\n #### References\n\n 1 \n<NAME>, <NAME>, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.\n\n 2 \n<NAME>. and Filliben, <NAME>. “NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions”, National Institute of Standards and Technology Handbook Series, June 2003. <https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 5. # shape\n>>> samples = 1000\n>>> s = np.random.power(a, samples)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=30)\n>>> x = np.linspace(0, 1, 100)\n>>> y = a*x**(a-1.)\n>>> normed_y = samples*np.diff(bins)[0]*y\n>>> plt.plot(x, normed_y)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-power-1_00_00.png] Compare the power function distribution to the inverse of the Pareto.\n\n \n```\n>>> from scipy import stats \n>>> rvs = np.random.power(5, 1000000)\n>>> rvsp = np.random.pareto(5, 1000000)\n>>> xx = np.linspace(0,1,100)\n>>> powpdf = stats.powerlaw.pdf(xx,5) \n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(rvs, bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('np.random.power(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of 1 + np.random.pareto(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of stats.pareto(5)')\n\n```\n ![../../../_images/numpy-random-RandomState-power-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.power.htmlnumpy.random.RandomState.rayleigh\n=================================\n\n method\n\n random.RandomState.rayleigh(*scale=1.0*, *size=None*)\n \nDraw samples from a Rayleigh distribution.\n\n The \\(\\chi\\) and Weibull distributions are generalizations of the Rayleigh.\n\n Note\n\n New code should use the `rayleigh` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**scale**float or array_like of floats, optional\n\nScale, also equals the mode. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Rayleigh distribution.\n\n See also\n\n [`random.Generator.rayleigh`](numpy.random.generator.rayleigh#numpy.random.Generator.rayleigh \"numpy.random.Generator.rayleigh\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the Rayleigh distribution is\n\n \\[P(x;scale) = \\frac{x}{scale^2}e^{\\frac{-x^2}{2 \\cdotp scale^2}}\\] The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.\n\n #### References\n\n 1 \nBrighton Webs Ltd., “Rayleigh Distribution,” <https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp 2 \nWikipedia, “Rayleigh distribution” <https://en.wikipedia.org/wiki/Rayleigh_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> from matplotlib.pyplot import hist\n>>> values = hist(np.random.rayleigh(3, 100000), bins=200, density=True)\n\n```\n Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters?\n\n \n```\n>>> meanvalue = 1\n>>> modevalue = np.sqrt(2 / np.pi) * meanvalue\n>>> s = np.random.rayleigh(modevalue, 1000000)\n\n```\n The percentage of waves larger than 3 meters is:\n\n \n```\n>>> 100.*sum(s>3)/1000000.\n0.087300000000000003 # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.rayleigh.htmlnumpy.random.RandomState.standard_cauchy\n=========================================\n\n method\n\n random.RandomState.standard_cauchy(*size=None*)\n \nDraw samples from a standard Cauchy distribution with mode = 0.\n\n Also known as the Lorentz distribution.\n\n Note\n\n New code should use the `standard_cauchy` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**samples**ndarray or scalar\n\nThe drawn samples.\n\n See also\n\n [`random.Generator.standard_cauchy`](numpy.random.generator.standard_cauchy#numpy.random.Generator.standard_cauchy \"numpy.random.Generator.standard_cauchy\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the full Cauchy distribution is\n\n \\[P(x; x_0, \\gamma) = \\frac{1}{\\pi \\gamma \\bigl[ 1+ (\\frac{x-x_0}{\\gamma})^2 \\bigr] }\\] and the Standard Cauchy distribution just sets \\(x_0=0\\) and \\(\\gamma=1\\)\n\n The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis.\n\n When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails.\n\n #### References\n\n 1 \nNIST/SEMATECH e-Handbook of Statistical Methods, “Cauchy Distribution”, <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm 2 \nWeisstein, <NAME>. “Cauchy Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/CauchyDistribution.html 3 \nWikipedia, “Cauchy distribution” <https://en.wikipedia.org/wiki/Cauchy_distribution #### Examples\n\n Draw samples and plot the distribution:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.standard_cauchy(1000000)\n>>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well\n>>> plt.hist(s, bins=100)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-standard_cauchy-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.standard_cauchy.htmlnumpy.random.RandomState.standard_exponential\n==============================================\n\n method\n\n random.RandomState.standard_exponential(*size=None*)\n \nDraw samples from the standard exponential distribution.\n\n [`standard_exponential`](#numpy.random.RandomState.standard_exponential \"numpy.random.RandomState.standard_exponential\") is identical to the exponential distribution with a scale parameter of 1.\n\n Note\n\n New code should use the `standard_exponential` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray\n\nDrawn samples.\n\n See also\n\n [`random.Generator.standard_exponential`](numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Output a 3x8000 array:\n\n \n```\n>>> n = np.random.standard_exponential((3, 8000))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.standard_exponential.htmlnumpy.random.RandomState.standard_gamma\n========================================\n\n method\n\n random.RandomState.standard_gamma(*shape*, *size=None*)\n \nDraw samples from a standard Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.\n\n Note\n\n New code should use the `standard_gamma` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**shape**float or array_like of floats\n\nParameter, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` is a scalar. Otherwise, `np.array(shape).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.standard_gamma`](numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 1. # mean and width\n>>> s = np.random.standard_gamma(shape, 1000000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \n... (sps.gamma(shape) * scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-standard_gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.standard_gamma.htmlnumpy.random.RandomState.standard_normal\n=========================================\n\n method\n\n random.RandomState.standard_normal(*size=None*)\n \nDraw samples from a standard Normal distribution (mean=0, stdev=1).\n\n Note\n\n New code should use the `standard_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray\n\nA floating-point array of shape `size` of drawn samples, or a single sample if `size` was not specified.\n\n See also\n\n [`normal`](numpy.random.randomstate.normal#numpy.random.RandomState.normal \"numpy.random.RandomState.normal\")\n\nEquivalent function with additional `loc` and `scale` arguments for setting the mean and standard deviation.\n\n [`random.Generator.standard_normal`](numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n For random samples from \\(N(\\mu, \\sigma^2)\\), use one of:\n\n \n```\nmu + sigma * np.random.standard_normal(size=...)\nnp.random.normal(mu, sigma, size=...)\n\n```\n #### Examples\n\n \n```\n>>> np.random.standard_normal()\n2.1923875335537315 #random\n\n```\n \n```\n>>> s = np.random.standard_normal(8000)\n>>> s\narray([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, # random\n -0.38672696, -0.4685006 ]) # random\n>>> s.shape\n(8000,)\n>>> s = np.random.standard_normal(size=(3, 4, 2))\n>>> s.shape\n(3, 4, 2)\n\n```\n Two-by-four array of samples from \\(N(3, 6.25)\\):\n\n \n```\n>>> 3 + 2.5 * np.random.standard_normal(size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.standard_normal.htmlnumpy.random.RandomState.triangular\n===================================\n\n method\n\n random.RandomState.triangular(*left*, *mode*, *right*, *size=None*)\n \nDraw samples from the triangular distribution over the interval `[left, right]`.\n\n The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf.\n\n Note\n\n New code should use the `triangular` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**left**float or array_like of floats\n\nLower limit.\n\n \n**mode**float or array_like of floats\n\nThe value where the peak of the distribution occurs. The value must fulfill the condition `left <= mode <= right`.\n\n \n**right**float or array_like of floats\n\nUpper limit, must be larger than `left`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `left`, `mode`, and `right` are all scalars. Otherwise, `np.broadcast(left, mode, right).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized triangular distribution.\n\n See also\n\n [`random.Generator.triangular`](numpy.random.generator.triangular#numpy.random.Generator.triangular \"numpy.random.Generator.triangular\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the triangular distribution is\n\n \\[\\begin{split}P(x;l, m, r) = \\begin{cases} \\frac{2(x-l)}{(r-l)(m-l)}& \\text{for $l \\leq x \\leq m$},\\\\ \\frac{2(r-x)}{(r-l)(r-m)}& \\text{for $m \\leq x \\leq r$},\\\\ 0& \\text{otherwise}. \\end{cases}\\end{split}\\] The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations.\n\n #### References\n\n 1 \nWikipedia, “Triangular distribution” <https://en.wikipedia.org/wiki/Triangular_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200,\n... density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-triangular-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.triangular.htmlnumpy.random.RandomState.uniform\n================================\n\n method\n\n random.RandomState.uniform(*low=0.0*, *high=1.0*, *size=None*)\n \nDraw samples from a uniform distribution.\n\n Samples are uniformly distributed over the half-open interval `[low, high)` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by [`uniform`](#numpy.random.RandomState.uniform \"numpy.random.RandomState.uniform\").\n\n Note\n\n New code should use the `uniform` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**low**float or array_like of floats, optional\n\nLower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0.\n\n \n**high**float or array_like of floats\n\nUpper boundary of the output interval. All values generated will be less than or equal to high. The high limit may be included in the returned array of floats due to floating-point rounding in the equation `low + (high-low) * random_sample()`. The default value is 1.0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `low` and `high` are both scalars. Otherwise, `np.broadcast(low, high).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized uniform distribution.\n\n See also\n\n [`randint`](numpy.random.randomstate.randint#numpy.random.RandomState.randint \"numpy.random.RandomState.randint\")\n\nDiscrete uniform distribution, yielding integers.\n\n [`random_integers`](numpy.random.randomstate.random_integers#numpy.random.RandomState.random_integers \"numpy.random.RandomState.random_integers\")\n\nDiscrete uniform distribution over the closed interval `[low, high]`.\n\n [`random_sample`](numpy.random.randomstate.random_sample#numpy.random.RandomState.random_sample \"numpy.random.RandomState.random_sample\")\n\nFloats uniformly distributed over `[0, 1)`.\n\n [`random`](../index#module-numpy.random \"numpy.random\")\n\nAlias for [`random_sample`](numpy.random.randomstate.random_sample#numpy.random.RandomState.random_sample \"numpy.random.RandomState.random_sample\").\n\n [`rand`](numpy.random.randomstate.rand#numpy.random.RandomState.rand \"numpy.random.RandomState.rand\")\n\nConvenience function that accepts dimensions as input, e.g., `rand(2,2)` would generate a 2-by-2 array of floats, uniformly distributed over `[0, 1)`.\n\n [`random.Generator.uniform`](numpy.random.generator.uniform#numpy.random.Generator.uniform \"numpy.random.Generator.uniform\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function of the uniform distribution is\n\n \\[p(x) = \\frac{1}{b - a}\\] anywhere within the interval `[a, b)`, and zero elsewhere.\n\n When `high` == `low`, values of `low` will be returned. If `high` < `low`, the results are officially undefined and may eventually raise an error, i.e. do not rely on this function to behave when passed arguments satisfying that inequality condition. The `high` limit may be included in the returned array of floats due to floating-point rounding in the equation `low + (high-low) * random_sample()`. For example:\n\n \n```\n>>> x = np.float32(5*0.99999999)\n>>> x\n5.0\n\n```\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> s = np.random.uniform(-1,0,1000)\n\n```\n All values are within the given interval:\n\n \n```\n>>> np.all(s >= -1)\nTrue\n>>> np.all(s < 0)\nTrue\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 15, density=True)\n>>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-uniform-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.uniform.htmlnumpy.random.RandomState.vonmises\n=================================\n\n method\n\n random.RandomState.vonmises(*mu*, *kappa*, *size=None*)\n \nDraw samples from a von Mises distribution.\n\n Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi].\n\n The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution.\n\n Note\n\n New code should use the `vonmises` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mu**float or array_like of floats\n\nMode (“center”) of the distribution.\n\n \n**kappa**float or array_like of floats\n\nDispersion of the distribution, has to be >=0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mu` and `kappa` are both scalars. Otherwise, `np.broadcast(mu, kappa).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized von Mises distribution.\n\n See also\n\n [`scipy.stats.vonmises`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html#scipy.stats.vonmises \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n [`random.Generator.vonmises`](numpy.random.generator.vonmises#numpy.random.Generator.vonmises \"numpy.random.Generator.vonmises\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the von Mises distribution is\n\n \\[p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},\\] where \\(\\mu\\) is the mode and \\(\\kappa\\) the dispersion, and \\(I_0(\\kappa)\\) is the modified Bessel function of order 0.\n\n The von Mises is named for <NAME>, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \nvon <NAME>., “Mathematical Theory of Probability and Statistics”, New York: Academic Press, 1964.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, kappa = 0.0, 4.0 # mean and dispersion\n>>> s = np.random.vonmises(mu, kappa, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import i0 \n>>> plt.hist(s, 50, density=True)\n>>> x = np.linspace(-np.pi, np.pi, num=51)\n>>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) \n>>> plt.plot(x, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-vonmises-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.vonmises.htmlnumpy.random.RandomState.wald\n=============================\n\n method\n\n random.RandomState.wald(*mean*, *scale*, *size=None*)\n \nDraw samples from a Wald, or inverse Gaussian, distribution.\n\n As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an inverse Gaussian with mean equal to 1, but this is by no means universal.\n\n The inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 <NAME> used the name inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time.\n\n Note\n\n New code should use the `wald` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**float or array_like of floats\n\nDistribution mean, must be > 0.\n\n \n**scale**float or array_like of floats\n\nScale parameter, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `scale` are both scalars. Otherwise, `np.broadcast(mean, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Wald distribution.\n\n See also\n\n [`random.Generator.wald`](numpy.random.generator.wald#numpy.random.Generator.wald \"numpy.random.Generator.wald\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the Wald distribution is\n\n \\[P(x;mean,scale) = \\sqrt{\\frac{scale}{2\\pi x^3}}e^ \\frac{-scale(x-mean)^2}{2\\cdotp mean^2x}\\] As noted above the inverse Gaussian distribution first arise from attempts to model Brownian motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes.\n\n #### References\n\n 1 \nBrighton Webs Ltd., Wald Distribution, <https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp 2 \nChhikara, <NAME>., and <NAME>, “The Inverse Gaussian Distribution: Theory : Methodology, and Applications”, CRC Press, 1988.\n\n 3 \nWikipedia, “Inverse Gaussian distribution” <https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-wald-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.wald.htmlnumpy.random.RandomState.weibull\n================================\n\n method\n\n random.RandomState.weibull(*a*, *size=None*)\n \nDraw samples from a Weibull distribution.\n\n Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`.\n\n \\[X = (-ln(U))^{1/a}\\] Here, U is drawn from the uniform distribution over (0,1].\n\n The more common 2-parameter Weibull, including a scale parameter \\(\\lambda\\) is just \\(X = \\lambda(-ln(U))^{1/a}\\).\n\n Note\n\n New code should use the `weibull` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nShape parameter of the distribution. Must be nonnegative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Weibull distribution.\n\n See also\n\n [`scipy.stats.weibull_max`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_max.html#scipy.stats.weibull_max \"(in SciPy v1.8.1)\")\n[`scipy.stats.weibull_min`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`gumbel`](numpy.random.randomstate.gumbel#numpy.random.RandomState.gumbel \"numpy.random.RandomState.gumbel\")\n[`random.Generator.weibull`](numpy.random.generator.weibull#numpy.random.Generator.weibull \"numpy.random.Generator.weibull\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions.\n\n The probability density for the Weibull distribution is\n\n \\[p(x) = \\frac{a} {\\lambda}(\\frac{x}{\\lambda})^{a-1}e^{-(x/\\lambda)^a},\\] where \\(a\\) is the shape and \\(\\lambda\\) the scale.\n\n The function has its peak (the mode) at \\(\\lambda(\\frac{a-1}{a})^{1/a}\\).\n\n When `a = 1`, the Weibull distribution reduces to the exponential distribution.\n\n #### References\n\n 1 \n<NAME>, Royal Technical University, Stockholm, 1939 “A Statistical Theory Of The Strength Of Materials”, Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm.\n\n 2 \n<NAME>, “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper 1951.\n\n 3 \nWikipedia, “Weibull distribution”, <https://en.wikipedia.org/wiki/Weibull_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 5. # shape\n>>> s = np.random.weibull(a, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x = np.arange(1,100.)/50.\n>>> def weib(x,n,a):\n... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)\n\n```\n \n```\n>>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))\n>>> x = np.arange(1,100.)/50.\n>>> scale = count.max()/weib(x, 1., 5.).max()\n>>> plt.plot(x, weib(x, 1., 5.)*scale)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-weibull-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.weibull.htmlnumpy.random.RandomState.zipf\n=============================\n\n method\n\n random.RandomState.zipf(*a*, *size=None*)\n \nDraw samples from a Zipf distribution.\n\n Samples are drawn from a Zipf distribution with specified parameter `a` > 1.\n\n The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf’s law: the frequency of an item is inversely proportional to its rank in a frequency table.\n\n Note\n\n New code should use the `zipf` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nDistribution parameter. Must be greater than 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Zipf distribution.\n\n See also\n\n [`scipy.stats.zipf`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zipf.html#scipy.stats.zipf \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n [`random.Generator.zipf`](numpy.random.generator.zipf#numpy.random.Generator.zipf \"numpy.random.Generator.zipf\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Zipf distribution is\n\n \\[p(k) = \\frac{k^{-a}}{\\zeta(a)},\\] for integers \\(k \\geq 1\\), where \\(\\zeta\\) is the Riemann Zeta function.\n\n It is named for the American linguist <NAME>, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table.\n\n #### References\n\n 1 \n<NAME>., “Selected Studies of the Principle of Relative Frequency in Language,” Cambridge, MA: Harvard Univ. Press, 1932.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 4.0\n>>> n = 20000\n>>> s = np.random.zipf(a, n)\n\n```\n Display the histogram of the samples, along with the expected histogram based on the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import zeta \n\n```\n [`bincount`](../../generated/numpy.bincount#numpy.bincount \"numpy.bincount\") provides a fast histogram for small integers.\n\n \n```\n>>> count = np.bincount(s)\n>>> k = np.arange(1, s.max() + 1)\n\n```\n \n```\n>>> plt.bar(k, count[1:], alpha=0.5, label='sample count')\n>>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5,\n... label='expected count') \n>>> plt.semilogy()\n>>> plt.grid(alpha=0.4)\n>>> plt.legend()\n>>> plt.title(f'Zipf sample, a={a}, size={n}')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-RandomState-zipf-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.RandomState.zipf.htmlnumpy.random.beta\n=================\n\n random.beta(*a*, *b*, *size=None*)\n \nDraw samples from a Beta distribution.\n\n The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function\n\n \\[f(x; a,b) = \\frac{1}{B(\\alpha, \\beta)} x^{\\alpha - 1} (1 - x)^{\\beta - 1},\\] where the normalization, B, is the beta function,\n\n \\[B(\\alpha, \\beta) = \\int_0^1 t^{\\alpha - 1} (1 - t)^{\\beta - 1} dt.\\] It is often seen in Bayesian inference and order statistics.\n\n Note\n\n New code should use the `beta` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nAlpha, positive (>0).\n\n \n**b**float or array_like of floats\n\nBeta, positive (>0).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` and `b` are both scalars. Otherwise, `np.broadcast(a, b).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized beta distribution.\n\n See also\n\n [`random.Generator.beta`](numpy.random.generator.beta#numpy.random.Generator.beta \"numpy.random.Generator.beta\")\n\nwhich should be used for new code.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.beta.htmlnumpy.random.binomial\n=====================\n\n random.binomial(*n*, *p*, *size=None*)\n \nDraw samples from a binomial distribution.\n\n Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use)\n\n Note\n\n New code should use the `binomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**int or array_like of ints\n\nParameter of the distribution, >= 0. Floats are also accepted, but they will be truncated to integers.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution, >= 0 and <=1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized binomial distribution, where each sample is equal to the number of successes over the n trials.\n\n See also\n\n [`scipy.stats.binom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html#scipy.stats.binom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.binomial`](numpy.random.generator.binomial#numpy.random.Generator.binomial \"numpy.random.Generator.binomial\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the binomial distribution is\n\n \\[P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\\] where \\(n\\) is the number of trials, \\(p\\) is the probability of success, and \\(N\\) is the number of successes.\n\n When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case.\n\n #### References\n\n 1 \n<NAME>, “Introductory Statistics with R”, Springer-Verlag, 2002.\n\n 2 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 3 \n<NAME>, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 4 \nWeisstein, <NAME>. “Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/BinomialDistribution.html 5 \nWikipedia, “Binomial distribution”, <https://en.wikipedia.org/wiki/Binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> n, p = 10, .5 # number of trials, probability of each trial\n>>> s = np.random.binomial(n, p, 1000)\n# result of flipping a coin 10 times, tested 1000 times.\n\n```\n A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening?\n\n Let’s do 20,000 trials of the model, and count the number that generate zero positive results.\n\n \n```\n>>> sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.\n# answer = 0.38885, or 38%.\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.binomial.htmlnumpy.random.bytes\n==================\n\n random.bytes(*length*)\n \nReturn random bytes.\n\n Note\n\n New code should use the `bytes` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**length**int\n\nNumber of random bytes.\n\n Returns \n \n**out**bytes\n\nString of length `length`.\n\n See also\n\n [`random.Generator.bytes`](numpy.random.generator.bytes#numpy.random.Generator.bytes \"numpy.random.Generator.bytes\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.bytes(10)\nb' eh\\x85\\x022SZ\\xbf\\xa4' #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.bytes.htmlnumpy.random.chisquare\n======================\n\n random.chisquare(*df*, *size=None*)\n \nDraw samples from a chi-square distribution.\n\n When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing.\n\n Note\n\n New code should use the `chisquare` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nNumber of degrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized chi-square distribution.\n\n Raises \n ValueError\n\nWhen `df` <= 0 or when an inappropriate `size` (e.g. `size=-1`) is given.\n\n See also\n\n [`random.Generator.chisquare`](numpy.random.generator.chisquare#numpy.random.Generator.chisquare \"numpy.random.Generator.chisquare\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The variable obtained by summing the squares of `df` independent, standard normally distributed random variables:\n\n \\[Q = \\sum_{i=0}^{\\mathtt{df}} X^2_i\\] is chi-square distributed, denoted\n\n \\[Q \\sim \\chi^2_k.\\] The probability density function of the chi-squared distribution is\n\n \\[p(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)} x^{k/2 - 1} e^{-x/2},\\] where \\(\\Gamma\\) is the gamma function,\n\n \\[\\Gamma(x) = \\int_0^{-\\infty} t^{x - 1} e^{-t} dt.\\] #### References\n\n 1 \nNIST “Engineering Statistics Handbook” <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm #### Examples\n\n \n```\n>>> np.random.chisquare(2,4)\narray([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.chisquare.htmlnumpy.random.choice\n===================\n\n random.choice(*a*, *size=None*, *replace=True*, *p=None*)\n \nGenerates a random sample from a given 1-D array\n\n New in version 1.7.0.\n\n Note\n\n New code should use the `choice` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**1-D array-like or int\n\nIf an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if it were `np.arange(a)`\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**replace**boolean, optional\n\nWhether the sample is with or without replacement. Default is True, meaning that a value of `a` can be selected multiple times.\n\n \n**p**1-D array-like, optional\n\nThe probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in `a`.\n\n Returns \n \n**samples**single item or ndarray\n\nThe generated random samples\n\n Raises \n ValueError\n\nIf a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size\n\n See also\n\n \n[`randint`](numpy.random.randint#numpy.random.randint \"numpy.random.randint\"), [`shuffle`](numpy.random.shuffle#numpy.random.shuffle \"numpy.random.shuffle\"), [`permutation`](numpy.random.permutation#numpy.random.permutation \"numpy.random.permutation\")\n\n[`random.Generator.choice`](numpy.random.generator.choice#numpy.random.Generator.choice \"numpy.random.Generator.choice\")\n\nwhich should be used in new code\n\n #### Notes\n\n Setting user-specified probabilities through `p` uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of `p` is 1 / len(a).\n\n Sampling random rows from a 2-D array is not possible with this function, but is possible with [`Generator.choice`](numpy.random.generator.choice#numpy.random.Generator.choice \"numpy.random.Generator.choice\") through its `axis` keyword.\n\n #### Examples\n\n Generate a uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> np.random.choice(5, 3)\narray([0, 3, 4]) # random\n>>> #This is equivalent to np.random.randint(0,5,3)\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3:\n\n \n```\n>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])\narray([3, 3, 0]) # random\n\n```\n Generate a uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> np.random.choice(5, 3, replace=False)\narray([3,1,0]) # random\n>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]\n\n```\n Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:\n\n \n```\n>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])\narray([2, 3, 0]) # random\n\n```\n Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:\n\n \n```\n>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']\n>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])\narray(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random\n dtype='<U11')\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.choice.htmlnumpy.random.dirichlet\n======================\n\n random.dirichlet(*alpha*, *size=None*)\n \nDraw samples from the Dirichlet distribution.\n\n Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference.\n\n Note\n\n New code should use the `dirichlet` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**alpha**sequence of floats, length k\n\nParameter of the distribution (length `k` for sample of length `k`).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n)`, then `m * n * k` samples are drawn. Default is None, in which case a vector of length `k` is returned.\n\n Returns \n \n**samples**ndarray,\n\nThe drawn samples, of shape `(size, k)`.\n\n Raises \n ValueError\n\nIf any value in `alpha` is less than or equal to zero\n\n See also\n\n [`random.Generator.dirichlet`](numpy.random.generator.dirichlet#numpy.random.Generator.dirichlet \"numpy.random.Generator.dirichlet\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Dirichlet distribution is a distribution over vectors \\(x\\) that fulfil the conditions \\(x_i>0\\) and \\(\\sum_{i=1}^k x_i = 1\\).\n\n The probability density function \\(p\\) of a Dirichlet-distributed random vector \\(X\\) is proportional to\n\n \\[p(x) \\propto \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i},\\] where \\(\\alpha\\) is a vector containing the positive concentration parameters.\n\n The method uses the following property for computation: let \\(Y\\) be a random vector which has components that follow a standard gamma distribution, then \\(X = \\frac{1}{\\sum_{i=1}^k{Y_i}} Y\\) is Dirichlet-distributed\n\n #### References\n\n 1 \n<NAME>, “Information Theory, Inference and Learning Algorithms,” chapter 23, <http://www.inference.org.uk/mackay/itila/ 2 \nWikipedia, “Dirichlet distribution”, <https://en.wikipedia.org/wiki/Dirichlet_distribution #### Examples\n\n Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.\n\n \n```\n>>> s = np.random.dirichlet((10, 5, 3), 20).transpose()\n\n```\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.barh(range(20), s[0])\n>>> plt.barh(range(20), s[1], left=s[0], color='g')\n>>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')\n>>> plt.title(\"Lengths of Strings\")\n\n```\n ![../../../_images/numpy-random-dirichlet-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.dirichlet.htmlnumpy.random.exponential\n========================\n\n random.exponential(*scale=1.0*, *size=None*)\n \nDraw samples from an exponential distribution.\n\n Its probability density function is\n\n \\[f(x; \\frac{1}{\\beta}) = \\frac{1}{\\beta} \\exp(-\\frac{x}{\\beta}),\\] for `x > 0` and 0 elsewhere. \\(\\beta\\) is the scale parameter, which is the inverse of the rate parameter \\(\\lambda = 1/\\beta\\). The rate parameter is an alternative, widely used parameterization of the exponential distribution [[3]](#r3cbd6af2d0d3-3).\n\n The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [[1]](#r3cbd6af2d0d3-1), or the time between page requests to Wikipedia [[2]](#r3cbd6af2d0d3-2).\n\n Note\n\n New code should use the `exponential` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**scale**float or array_like of floats\n\nThe scale parameter, \\(\\beta = 1/\\lambda\\). Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized exponential distribution.\n\n See also\n\n [`random.Generator.exponential`](numpy.random.generator.exponential#numpy.random.Generator.exponential \"numpy.random.Generator.exponential\")\n\nwhich should be used for new code.\n\n #### References\n\n [1](#id2) \n<NAME>r., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.\n\n [2](#id3) \nWikipedia, “Poisson process”, <https://en.wikipedia.org/wiki/Poisson_process [3](#id1) \nWikipedia, “Exponential distribution”, <https://en.wikipedia.org/wiki/Exponential_distribution © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.exponential.htmlnumpy.random.f\n==============\n\n random.f(*dfnum*, *dfden*, *size=None*)\n \nDraw samples from an F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters must be greater than zero.\n\n The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates.\n\n Note\n\n New code should use the `f` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nDegrees of freedom in numerator, must be > 0.\n\n \n**dfden**float or array_like of float\n\nDegrees of freedom in denominator, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum` and `dfden` are both scalars. Otherwise, `np.broadcast(dfnum, dfden).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Fisher distribution.\n\n See also\n\n [`scipy.stats.f`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f.html#scipy.stats.f \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.f`](numpy.random.generator.f#numpy.random.Generator.f \"numpy.random.Generator.f\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups.\n\n #### References\n\n 1 \nGlantz, <NAME>. “Primer of Biostatistics.”, McGraw-Hill, Fifth Edition, 2002.\n\n 2 \nWikipedia, “F-distribution”, <https://en.wikipedia.org/wiki/F-distribution #### Examples\n\n An example from Glantz[1], pp 47-40:\n\n Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children’s blood glucose levels? Calculating the F statistic from the data gives a value of 36.01.\n\n Draw samples from the distribution:\n\n \n```\n>>> dfnum = 1. # between group degrees of freedom\n>>> dfden = 48. # within groups degrees of freedom\n>>> s = np.random.f(dfnum, dfden, 1000)\n\n```\n The lower bound for the top 1% of the samples is :\n\n \n```\n>>> np.sort(s)[-10]\n7.61988120985 # random\n\n```\n So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.f.htmlnumpy.random.gamma\n==================\n\n random.gamma(*shape*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, [`shape`](../../generated/numpy.shape#numpy.shape \"numpy.shape\") (sometimes designated “k”) and `scale` (sometimes designated “theta”), where both parameters are > 0.\n\n Note\n\n New code should use the `gamma` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**shape**float or array_like of floats\n\nThe shape of the gamma distribution. Must be non-negative.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale of the gamma distribution. Must be non-negative. Default is equal to 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` and `scale` are both scalars. Otherwise, `np.broadcast(shape, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.gamma`](numpy.random.generator.gamma#numpy.random.Generator.gamma \"numpy.random.Generator.gamma\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2)\n>>> s = np.random.gamma(shape, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1)*(np.exp(-bins/scale) / \n... (sps.gamma(shape)*scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.gamma.htmlnumpy.random.geometric\n======================\n\n random.geometric(*p*, *size=None*)\n \nDraw samples from the geometric distribution.\n\n Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, `k = 1, 2, ...`.\n\n The probability mass function of the geometric distribution is\n\n \\[f(k) = (1 - p)^{k - 1} p\\] where `p` is the probability of success of an individual trial.\n\n Note\n\n New code should use the `geometric` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**p**float or array_like of floats\n\nThe probability of success of an individual trial.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized geometric distribution.\n\n See also\n\n [`random.Generator.geometric`](numpy.random.generator.geometric#numpy.random.Generator.geometric \"numpy.random.Generator.geometric\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35:\n\n \n```\n>>> z = np.random.geometric(p=0.35, size=10000)\n\n```\n How many trials succeeded after a single run?\n\n \n```\n>>> (z == 1).sum() / 10000.\n0.34889999999999999 #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.geometric.htmlnumpy.random.get_state\n=======================\n\n random.get_state()\n \nReturn a tuple representing the internal state of the generator.\n\n For more details, see [`set_state`](numpy.random.set_state#numpy.random.set_state \"numpy.random.set_state\").\n\n Parameters \n \n**legacy**bool, optional\n\nFlag indicating to return a legacy tuple state when the BitGenerator is MT19937, instead of a dict.\n\n Returns \n \n**out**{tuple(str, ndarray of 624 uints, int, int, float), dict}\n\nThe returned tuple has the following items:\n\n 1. the string ‘MT19937’.\n2. a 1-D array of 624 unsigned integer keys.\n3. an integer `pos`.\n4. an integer `has_gauss`.\n5. a float `cached_gaussian`.\n\n If `legacy` is False, or the BitGenerator is not MT19937, then state is returned as a dictionary.\n\n See also\n\n [`set_state`](numpy.random.set_state#numpy.random.set_state \"numpy.random.set_state\")\n #### Notes\n\n [`set_state`](numpy.random.set_state#numpy.random.set_state \"numpy.random.set_state\") and [`get_state`](#numpy.random.get_state \"numpy.random.get_state\") are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.get_state.htmlnumpy.random.gumbel\n===================\n\n random.gumbel(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a Gumbel distribution.\n\n Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below.\n\n Note\n\n New code should use the `gumbel` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe location of the mode of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nThe scale parameter of the distribution. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Gumbel distribution.\n\n See also\n\n [`scipy.stats.gumbel_l`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_l.html#scipy.stats.gumbel_l \"(in SciPy v1.8.1)\")\n[`scipy.stats.gumbel_r`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`weibull`](numpy.random.weibull#numpy.random.weibull \"numpy.random.weibull\")\n[`random.Generator.gumbel`](numpy.random.generator.gumbel#numpy.random.Generator.gumbel \"numpy.random.Generator.gumbel\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with “exponential-like” tails.\n\n The probability density for the Gumbel distribution is\n\n \\[p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/ \\beta}},\\] where \\(\\mu\\) is the mode, a location parameter, and \\(\\beta\\) is the scale parameter.\n\n The Gumbel (named for German mathematician <NAME>) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a “fat-tailed” distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events.\n\n It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet.\n\n The function has a mean of \\(\\mu + 0.57721\\beta\\) and a variance of \\(\\frac{\\pi^2}{6}\\beta^2\\).\n\n #### References\n\n 1 \n<NAME>., “Statistics of Extremes,” New York: Columbia University Press, 1958.\n\n 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields,” Basel: Birkhauser Verlag, 2001.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, beta = 0, 0.1 # location and scale\n>>> s = np.random.gumbel(mu, beta, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp( -np.exp( -(bins - mu) /beta) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-gumbel-1_00_00.png] Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian:\n\n \n```\n>>> means = []\n>>> maxima = []\n>>> for i in range(0,1000) :\n... a = np.random.normal(mu, beta, 1000)\n... means.append(a.mean())\n... maxima.append(a.max())\n>>> count, bins, ignored = plt.hist(maxima, 30, density=True)\n>>> beta = np.std(maxima) * np.sqrt(6) / np.pi\n>>> mu = np.mean(maxima) - 0.57721*beta\n>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)\n... * np.exp(-np.exp(-(bins - mu)/beta)),\n... linewidth=2, color='r')\n>>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))\n... * np.exp(-(bins - mu)**2 / (2 * beta**2)),\n... linewidth=2, color='g')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-gumbel-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.gumbel.htmlnumpy.random.hypergeometric\n===========================\n\n random.hypergeometric(*ngood*, *nbad*, *nsample*, *size=None*)\n \nDraw samples from a Hypergeometric distribution.\n\n Samples are drawn from a hypergeometric distribution with specified parameters, `ngood` (ways to make a good selection), `nbad` (ways to make a bad selection), and `nsample` (number of items sampled, which is less than or equal to the sum `ngood + nbad`).\n\n Note\n\n New code should use the `hypergeometric` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**ngood**int or array_like of ints\n\nNumber of ways to make a good selection. Must be nonnegative.\n\n \n**nbad**int or array_like of ints\n\nNumber of ways to make a bad selection. Must be nonnegative.\n\n \n**nsample**int or array_like of ints\n\nNumber of items sampled. Must be at least 1 and at most `ngood + nbad`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `ngood`, `nbad`, and `nsample` are all scalars. Otherwise, `np.broadcast(ngood, nbad, nsample).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized hypergeometric distribution. Each sample is the number of good items within a randomly selected subset of size `nsample` taken from a set of `ngood` good items and `nbad` bad items.\n\n See also\n\n [`scipy.stats.hypergeom`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hypergeom.html#scipy.stats.hypergeom \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.hypergeometric`](numpy.random.generator.hypergeometric#numpy.random.Generator.hypergeometric \"numpy.random.Generator.hypergeometric\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Hypergeometric distribution is\n\n \\[P(x) = \\frac{\\binom{g}{x}\\binom{b}{n-x}}{\\binom{g+b}{n}},\\] where \\(0 \\le x \\le n\\) and \\(n-b \\le x \\le g\\)\n\n for P(x) the probability of `x` good results in the drawn sample, g = `ngood`, b = `nbad`, and n = `nsample`.\n\n Consider an urn with black and white marbles in it, `ngood` of them are black and `nbad` are white. If you draw `nsample` balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample.\n\n Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial.\n\n #### References\n\n 1 \nLentner, Marvin, “Elementary Applied Statistics”, Bogden and Quigley, 1972.\n\n 2 \nWeisstein, <NAME>. “Hypergeometric Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/HypergeometricDistribution.html 3 \nWikipedia, “Hypergeometric distribution”, <https://en.wikipedia.org/wiki/Hypergeometric_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> ngood, nbad, nsamp = 100, 2, 10\n# number of good, number of bad, and number of samples\n>>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)\n>>> from matplotlib.pyplot import hist\n>>> hist(s)\n# note that it is very unlikely to grab both bad items\n\n```\n Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color?\n\n \n```\n>>> s = np.random.hypergeometric(15, 15, 15, 100000)\n>>> sum(s>=12)/100000. + sum(s<=3)/100000.\n# answer = 0.003 ... pretty unlikely!\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.hypergeometric.htmlnumpy.random.laplace\n====================\n\n random.laplace(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).\n\n The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables.\n\n Note\n\n New code should use the `laplace` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nThe position, \\(\\mu\\), of the distribution peak. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\n\\(\\lambda\\), the exponential decay. Default is 1. Must be non- negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Laplace distribution.\n\n See also\n\n [`random.Generator.laplace`](numpy.random.generator.laplace#numpy.random.Generator.laplace \"numpy.random.Generator.laplace\")\n\nwhich should be used for new code.\n\n #### Notes\n\n It has the probability density function\n\n \\[f(x; \\mu, \\lambda) = \\frac{1}{2\\lambda} \\exp\\left(-\\frac{|x - \\mu|}{\\lambda}\\right).\\] The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution.\n\n #### References\n\n 1 \n<NAME> <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \n<NAME>, et. al. “The Laplace Distribution and Generalizations, ” Birkhauser, 2001.\n\n 3 \nWeisstein, <NAME>. “Laplace Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LaplaceDistribution.html 4 \nWikipedia, “Laplace distribution”, <https://en.wikipedia.org/wiki/Laplace_distribution #### Examples\n\n Draw samples from the distribution\n\n \n```\n>>> loc, scale = 0., 1.\n>>> s = np.random.laplace(loc, scale, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> x = np.arange(-8., 8., .01)\n>>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)\n>>> plt.plot(x, pdf)\n\n```\n Plot Gaussian for comparison:\n\n \n```\n>>> g = (1/(scale * np.sqrt(2 * np.pi)) *\n... np.exp(-(x - loc)**2 / (2 * scale**2)))\n>>> plt.plot(x,g)\n\n```\n ![../../../_images/numpy-random-laplace-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.laplace.htmlnumpy.random.logistic\n=====================\n\n random.logistic(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw samples from a logistic distribution.\n\n Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).\n\n Note\n\n New code should use the `logistic` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats, optional\n\nParameter of the distribution. Default is 0.\n\n \n**scale**float or array_like of floats, optional\n\nParameter of the distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logistic distribution.\n\n See also\n\n [`scipy.stats.logistic`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logistic.html#scipy.stats.logistic \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.logistic`](numpy.random.generator.logistic#numpy.random.Generator.logistic \"numpy.random.Generator.logistic\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Logistic distribution is\n\n \\[P(x) = P(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2},\\] where \\(\\mu\\) = location and \\(s\\) = scale.\n\n The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (2001), “Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,” Birkhauser Verlag, Basel, pp 132-133.\n\n 2 \nWeisstein, <NAME>. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/LogisticDistribution.html 3 \nWikipedia, “Logistic-distribution”, <https://en.wikipedia.org/wiki/Logistic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> loc, scale = 10, 1\n>>> s = np.random.logistic(loc, scale, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=50)\n\n```\n # plot against distribution\n\n \n```\n>>> def logist(x, loc, scale):\n... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)\n>>> lgst_val = logist(bins, loc, scale)\n>>> plt.plot(bins, lgst_val * count.max() / lgst_val.max())\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-logistic-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.logistic.htmlnumpy.random.lognormal\n======================\n\n random.lognormal(*mean=0.0*, *sigma=1.0*, *size=None*)\n \nDraw samples from a log-normal distribution.\n\n Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.\n\n Note\n\n New code should use the `lognormal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**float or array_like of floats, optional\n\nMean value of the underlying normal distribution. Default is 0.\n\n \n**sigma**float or array_like of floats, optional\n\nStandard deviation of the underlying normal distribution. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `sigma` are both scalars. Otherwise, `np.broadcast(mean, sigma).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized log-normal distribution.\n\n See also\n\n [`scipy.stats.lognorm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, cumulative density function, etc.\n\n [`random.Generator.lognormal`](numpy.random.generator.lognormal#numpy.random.Generator.lognormal \"numpy.random.Generator.lognormal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is:\n\n \\[p(x) = \\frac{1}{\\sigma x \\sqrt{2\\pi}} e^{(-\\frac{(ln(x)-\\mu)^2}{2\\sigma^2})}\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables.\n\n #### References\n\n 1 \n<NAME>., <NAME>., and <NAME>., “Log-normal Distributions across the Sciences: Keys and Clues,” BioScience, Vol. 51, No. 5, May, 2001. <https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf 2 \n<NAME>. and <NAME>., “Statistical Analysis of Extreme Values,” Basel: Birkhauser Verlag, 2001, pp. 31-32.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, sigma = 3., 1. # mean and standard deviation\n>>> s = np.random.lognormal(mu, sigma, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 100, density=True, align='mid')\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, linewidth=2, color='r')\n>>> plt.axis('tight')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-lognormal-1_00_00.png] Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function.\n\n \n```\n>>> # Generate a thousand samples: each is the product of 100 random\n>>> # values, drawn from a normal distribution.\n>>> b = []\n>>> for i in range(1000):\n... a = 10. + np.random.standard_normal(100)\n... b.append(np.product(a))\n\n```\n \n```\n>>> b = np.array(b) / np.min(b) # scale values to be positive\n>>> count, bins, ignored = plt.hist(b, 100, density=True, align='mid')\n>>> sigma = np.std(np.log(b))\n>>> mu = np.mean(np.log(b))\n\n```\n \n```\n>>> x = np.linspace(min(bins), max(bins), 10000)\n>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))\n... / (x * sigma * np.sqrt(2 * np.pi)))\n\n```\n \n```\n>>> plt.plot(x, pdf, color='r', linewidth=2)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-lognormal-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.lognormal.htmlnumpy.random.logseries\n======================\n\n random.logseries(*p*, *size=None*)\n \nDraw samples from a logarithmic series distribution.\n\n Samples are drawn from a log series distribution with specified shape parameter, 0 < `p` < 1.\n\n Note\n\n New code should use the `logseries` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**p**float or array_like of floats\n\nShape parameter for the distribution. Must be in the range (0, 1).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `p` is a scalar. Otherwise, `np.array(p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized logarithmic series distribution.\n\n See also\n\n [`scipy.stats.logser`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logser.html#scipy.stats.logser \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.logseries`](numpy.random.generator.logseries#numpy.random.Generator.logseries \"numpy.random.Generator.logseries\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Log Series distribution is\n\n \\[P(k) = \\frac{-p^k}{k \\ln(1-p)},\\] where p = probability.\n\n The log series distribution is frequently used to represent species richness and occurrence, first proposed by <NAME>, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3].\n\n #### References\n\n 1 \n<NAME>.; <NAME>., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9).\n\n 2 \n<NAME>,, <NAME>, and <NAME>. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58.\n\n 3 \n<NAME>, <NAME>, <NAME>, <NAME>, A Handbook of Small Data Sets, CRC Press, 1994.\n\n 4 \nWikipedia, “Logarithmic distribution”, <https://en.wikipedia.org/wiki/Logarithmic_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = .6\n>>> s = np.random.logseries(a, 10000)\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s)\n\n```\n # plot against distribution\n\n \n```\n>>> def logseries(k, p):\n... return -p**k/(k*np.log(1-p))\n>>> plt.plot(bins, logseries(bins, a)*count.max()/\n... logseries(bins, a).max(), 'r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-logseries-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.logseries.htmlnumpy.random.multinomial\n========================\n\n random.multinomial(*n*, *pvals*, *size=None*)\n \nDraw samples from a multinomial distribution.\n\n The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of `p` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, `X_i = [X_0, X_1, ..., X_p]`, represent the number of times the outcome was `i`.\n\n Note\n\n New code should use the `multinomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**int\n\nNumber of experiments.\n\n \n**pvals**sequence of floats, length p\n\nProbabilities of each of the `p` different outcomes. These must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as `sum(pvals[:-1]) <= 1)`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape *size*, if that was provided. If not, the shape is `(N,)`.\n\n In other words, each entry `out[i,j,...,:]` is an N-dimensional value drawn from the distribution.\n\n See also\n\n [`random.Generator.multinomial`](numpy.random.generator.multinomial#numpy.random.Generator.multinomial \"numpy.random.Generator.multinomial\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Throw a dice 20 times:\n\n \n```\n>>> np.random.multinomial(20, [1/6.]*6, size=1)\narray([[4, 1, 7, 5, 2, 1]]) # random\n\n```\n It landed 4 times on 1, once on 2, etc.\n\n Now, throw the dice 20 times, and 20 times again:\n\n \n```\n>>> np.random.multinomial(20, [1/6.]*6, size=2)\narray([[3, 4, 3, 3, 4, 3], # random\n [2, 4, 3, 4, 0, 7]])\n\n```\n For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc.\n\n A loaded die is more likely to land on number 6:\n\n \n```\n>>> np.random.multinomial(100, [1/7.]*5 + [2/7.])\narray([11, 16, 14, 17, 16, 26]) # random\n\n```\n The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so:\n\n \n```\n>>> np.random.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT\narray([38, 62]) # random\n\n```\n not like:\n\n \n```\n>>> np.random.multinomial(100, [1.0, 2.0]) # WRONG\nTraceback (most recent call last):\nValueError: pvals < 0, pvals > 1 or pvals contains NaNs\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.multinomial.htmlnumpy.random.multivariate_normal\n=================================\n\n random.multivariate_normal(*mean*, *cov*, *size=None*, *check_valid='warn'*, *tol=1e-8*)\n \nDraw random samples from a multivariate normal distribution.\n\n The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or “center”) and variance (standard deviation, or “width,” squared) of the one-dimensional normal distribution.\n\n Note\n\n New code should use the `multivariate_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**1-D array_like, of length N\n\nMean of the N-dimensional distribution.\n\n \n**cov**2-D array_like, of shape (N, N)\n\nCovariance matrix of the distribution. It must be symmetric and positive-semidefinite for proper sampling.\n\n \n**size**int or tuple of ints, optional\n\nGiven a shape of, for example, `(m,n,k)`, `m*n*k` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is `(m,n,k,N)`. If no shape is specified, a single (`N`-D) sample is returned.\n\n \n**check_valid**{ ‘warn’, ‘raise’, ‘ignore’ }, optional\n\nBehavior when the covariance matrix is not positive semidefinite.\n\n \n**tol**float, optional\n\nTolerance when checking the singular values in covariance matrix. cov is cast to double before the check.\n\n Returns \n \n**out**ndarray\n\nThe drawn samples, of shape *size*, if that was provided. If not, the shape is `(N,)`.\n\n In other words, each entry `out[i,j,...,:]` is an N-dimensional value drawn from the distribution.\n\n See also\n\n [`random.Generator.multivariate_normal`](numpy.random.generator.multivariate_normal#numpy.random.Generator.multivariate_normal \"numpy.random.Generator.multivariate_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution.\n\n Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, \\(X = [x_1, x_2, ... x_N]\\). The covariance matrix element \\(C_{ij}\\) is the covariance of \\(x_i\\) and \\(x_j\\). The element \\(C_{ii}\\) is the variance of \\(x_i\\) (i.e. its “spread”).\n\n Instead of specifying the full covariance matrix, popular approximations include:\n\n * Spherical covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") is a multiple of the identity matrix)\n* Diagonal covariance ([`cov`](../../generated/numpy.cov#numpy.cov \"numpy.cov\") has non-negative elements, and only on the diagonal)\n\n This geometrical property can be seen in two dimensions by plotting generated data-points:\n\n \n```\n>>> mean = [0, 0]\n>>> cov = [[1, 0], [0, 100]] # diagonal covariance\n\n```\n Diagonal covariance means that points are oriented along x or y-axis:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x, y = np.random.multivariate_normal(mean, cov, 5000).T\n>>> plt.plot(x, y, 'x')\n>>> plt.axis('equal')\n>>> plt.show()\n\n```\n Note that the covariance matrix must be positive semidefinite (a.k.a. nonnegative-definite). Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed.\n\n #### References\n\n 1 \n<NAME>., “Probability, Random Variables, and Stochastic Processes,” 3rd ed., New York: McGraw-Hill, 1991.\n\n 2 \n<NAME>., <NAME>., and <NAME>., “Pattern Classification,” 2nd ed., New York: Wiley, 2001.\n\n #### Examples\n\n \n```\n>>> mean = (1, 2)\n>>> cov = [[1, 0], [0, 1]]\n>>> x = np.random.multivariate_normal(mean, cov, (3, 3))\n>>> x.shape\n(3, 3, 2)\n\n```\n Here we generate 800 samples from the bivariate normal distribution with mean [0, 0] and covariance matrix [[6, -3], [-3, 3.5]]. The expected variances of the first and second components of the sample are 6 and 3.5, respectively, and the expected correlation coefficient is -3/sqrt(6*3.5) ≈ -0.65465.\n\n \n```\n>>> cov = np.array([[6, -3], [-3, 3.5]])\n>>> pts = np.random.multivariate_normal([0, 0], cov, size=800)\n\n```\n Check that the mean, covariance, and correlation coefficient of the sample are close to the expected values:\n\n \n```\n>>> pts.mean(axis=0)\narray([ 0.0326911 , -0.01280782]) # may vary\n>>> np.cov(pts.T)\narray([[ 5.96202397, -2.85602287],\n [-2.85602287, 3.47613949]]) # may vary\n>>> np.corrcoef(pts.T)[0, 1]\n-0.6273591314603949 # may vary\n\n```\n We can visualize this data with a scatter plot. The orientation of the point cloud illustrates the negative correlation of the components of this sample.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(pts[:, 0], pts[:, 1], '.', alpha=0.5)\n>>> plt.axis('equal')\n>>> plt.grid()\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-multivariate_normal-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.multivariate_normal.htmlnumpy.random.negative_binomial\n===============================\n\n random.negative_binomial(*n*, *p*, *size=None*)\n \nDraw samples from a negative binomial distribution.\n\n Samples are drawn from a negative binomial distribution with specified parameters, `n` successes and `p` probability of success where `n` is > 0 and `p` is in the interval [0, 1].\n\n Note\n\n New code should use the `negative_binomial` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**n**float or array_like of floats\n\nParameter of the distribution, > 0.\n\n \n**p**float or array_like of floats\n\nParameter of the distribution, >= 0 and <=1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `n` and `p` are both scalars. Otherwise, `np.broadcast(n, p).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached.\n\n See also\n\n [`random.Generator.negative_binomial`](numpy.random.generator.negative_binomial#numpy.random.Generator.negative_binomial \"numpy.random.Generator.negative_binomial\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability mass function of the negative binomial distribution is\n\n \\[P(N;n,p) = \\frac{\\Gamma(N+n)}{N!\\Gamma(n)}p^{n}(1-p)^{N},\\] where \\(n\\) is the number of successes, \\(p\\) is the probability of success, \\(N+n\\) is the number of trials, and \\(\\Gamma\\) is the gamma function. When \\(n\\) is an integer, \\(\\frac{\\Gamma(N+n)}{N!\\Gamma(n)} = \\binom{N+n-1}{N}\\), which is the more common form of this term in the the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial.\n\n If one throws a die repeatedly until the third time a “1” appears, then the probability distribution of the number of non-“1”s that appear before the third “1” is a negative binomial distribution.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Negative Binomial Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NegativeBinomialDistribution.html 2 \nWikipedia, “Negative binomial distribution”, <https://en.wikipedia.org/wiki/Negative_binomial_distribution #### Examples\n\n Draw samples from the distribution:\n\n A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.?\n\n \n```\n>>> s = np.random.negative_binomial(1, 0.1, 100000)\n>>> for i in range(1, 11): \n... probability = sum(s<i) / 100000.\n... print(i, \"wells drilled, probability of one success =\", probability)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.negative_binomial.htmlnumpy.random.noncentral_chisquare\n==================================\n\n random.noncentral_chisquare(*df*, *nonc*, *size=None*)\n \nDraw samples from a noncentral chi-square distribution.\n\n The noncentral \\(\\chi^2\\) distribution is a generalization of the \\(\\chi^2\\) distribution.\n\n Note\n\n New code should use the `noncentral_chisquare` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n Changed in version 1.10.0: Earlier NumPy versions required dfnum > 1.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` and `nonc` are both scalars. Otherwise, `np.broadcast(df, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral chi-square distribution.\n\n See also\n\n [`random.Generator.noncentral_chisquare`](numpy.random.generator.noncentral_chisquare#numpy.random.Generator.noncentral_chisquare \"numpy.random.Generator.noncentral_chisquare\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the noncentral Chi-square distribution is\n\n \\[P(x;df,nonc) = \\sum^{\\infty}_{i=0} \\frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x),\\] where \\(Y_{q}\\) is the Chi-square with q degrees of freedom.\n\n #### References\n\n 1 \nWikipedia, “Noncentral chi-squared distribution” <https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-noncentral_chisquare-1_00_00.png] Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> values2 = plt.hist(np.random.chisquare(3, 100000),\n... bins=np.arange(0., 25, .1), density=True)\n>>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-noncentral_chisquare-1_01_00.png] Demonstrate how large values of non-centrality lead to a more symmetric distribution.\n\n \n```\n>>> plt.figure()\n>>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),\n... bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-noncentral_chisquare-1_02_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.noncentral_chisquare.htmlnumpy.random.noncentral_f\n==========================\n\n random.noncentral_f(*dfnum*, *dfden*, *nonc*, *size=None*)\n \nDraw samples from the noncentral F distribution.\n\n Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter.\n\n Note\n\n New code should use the `noncentral_f` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**dfnum**float or array_like of floats\n\nNumerator degrees of freedom, must be > 0.\n\n Changed in version 1.14.0: Earlier NumPy versions required dfnum > 1.\n\n \n**dfden**float or array_like of floats\n\nDenominator degrees of freedom, must be > 0.\n\n \n**nonc**float or array_like of floats\n\nNon-centrality parameter, the sum of the squares of the numerator means, must be >= 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `dfnum`, `dfden`, and `nonc` are all scalars. Otherwise, `np.broadcast(dfnum, dfden, nonc).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized noncentral Fisher distribution.\n\n See also\n\n [`random.Generator.noncentral_f`](numpy.random.generator.noncentral_f#numpy.random.Generator.noncentral_f \"numpy.random.Generator.noncentral_f\")\n\nwhich should be used for new code.\n\n #### Notes\n\n When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/NoncentralF-Distribution.html 2 \nWikipedia, “Noncentral F-distribution”, <https://en.wikipedia.org/wiki/Noncentral_F-distribution #### Examples\n\n In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We’ll plot the two probability distributions for comparison.\n\n \n```\n>>> dfnum = 3 # between group deg of freedom\n>>> dfden = 20 # within groups degrees of freedom\n>>> nonc = 3.0\n>>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)\n>>> NF = np.histogram(nc_vals, bins=50, density=True)\n>>> c_vals = np.random.f(dfnum, dfden, 1000000)\n>>> F = np.histogram(c_vals, bins=50, density=True)\n>>> import matplotlib.pyplot as plt\n>>> plt.plot(F[1][1:], F[0])\n>>> plt.plot(NF[1][1:], NF[0])\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-noncentral_f-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.noncentral_f.htmlnumpy.random.normal\n===================\n\n random.normal(*loc=0.0*, *scale=1.0*, *size=None*)\n \nDraw random samples from a normal (Gaussian) distribution.\n\n The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [[2]](#rf578abb8fba2-2), is often called the bell curve because of its characteristic shape (see the example below).\n\n The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [[2]](#rf578abb8fba2-2).\n\n Note\n\n New code should use the `normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**loc**float or array_like of floats\n\nMean (“centre”) of the distribution.\n\n \n**scale**float or array_like of floats\n\nStandard deviation (spread or “width”) of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `loc` and `scale` are both scalars. Otherwise, `np.broadcast(loc, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized normal distribution.\n\n See also\n\n [`scipy.stats.norm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.normal`](numpy.random.generator.normal#numpy.random.Generator.normal \"numpy.random.Generator.normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gaussian distribution is\n\n \\[p(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }} e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\\] where \\(\\mu\\) is the mean and \\(\\sigma\\) the standard deviation. The square of the standard deviation, \\(\\sigma^2\\), is called the variance.\n\n The function has its peak at the mean, and its “spread” increases with the standard deviation (the function reaches 0.607 times its maximum at \\(x + \\sigma\\) and \\(x - \\sigma\\) [[2]](#rf578abb8fba2-2)). This implies that normal is more likely to return samples lying close to the mean, rather than those far away.\n\n #### References\n\n 1 \nWikipedia, “Normal distribution”, <https://en.wikipedia.org/wiki/Normal_distribution2([1](#id1),[2](#id2),[3](#id3))\n \n<NAME> Jr., “Central Limit Theorem” in “Probability, Random Variables and Random Signal Principles”, 4th ed., 2001, pp. 51, 51, 125.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, sigma = 0, 0.1 # mean and standard deviation\n>>> s = np.random.normal(mu, sigma, 1000)\n\n```\n Verify the mean and the variance:\n\n \n```\n>>> abs(mu - np.mean(s))\n0.0 # may vary\n\n```\n \n```\n>>> abs(sigma - np.std(s, ddof=1))\n0.1 # may vary\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 30, density=True)\n>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n... linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-normal-1_00_00.png]:\n\n \n```\n>>> np.random.normal(3, 2.5, size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.normal.htmlnumpy.random.pareto\n===================\n\n random.pareto(*a*, *size=None*)\n \nDraw samples from a Pareto II or Lomax distribution with specified shape.\n\n The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding 1 and multiplying by the scale parameter `m` (see Notes). The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is `mu`, where the standard Pareto distribution has location `mu = 1`. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero.\n\n The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the “80-20 rule”. In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range.\n\n Note\n\n New code should use the `pareto` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nShape of the distribution. Must be positive.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Pareto distribution.\n\n See also\n\n [`scipy.stats.lomax`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lomax.html#scipy.stats.lomax \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`scipy.stats.genpareto`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.pareto`](numpy.random.generator.pareto#numpy.random.Generator.pareto \"numpy.random.Generator.pareto\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Pareto distribution is\n\n \\[p(x) = \\frac{am^a}{x^{a+1}}\\] where \\(a\\) is the shape and \\(m\\) the scale.\n\n The Pareto distribution, named after the Italian economist <NAME>, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [[1]](#r3973533a530a-1). It is one of the so-called “fat-tailed” distributions.\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, On the Pareto Distribution of Sourceforge projects.\n\n 2 \n<NAME>. (1896). Course of Political Economy. Lausanne.\n\n 3 \n<NAME>., <NAME>.(2001), Statistical Analysis of Extreme Values, <NAME>l, pp 23-30.\n\n 4 \nWikipedia, “Pareto distribution”, <https://en.wikipedia.org/wiki/Pareto_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a, m = 3., 2. # shape and mode\n>>> s = (np.random.pareto(a, 1000) + 1) * m\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, _ = plt.hist(s, 100, density=True)\n>>> fit = a*m**a / bins**(a+1)\n>>> plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-pareto-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.pareto.htmlnumpy.random.permutation\n========================\n\n random.permutation(*x*)\n \nRandomly permute a sequence, or return a permuted range.\n\n If `x` is a multi-dimensional array, it is only shuffled along its first index.\n\n Note\n\n New code should use the `permutation` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**x**int or array_like\n\nIf `x` is an integer, randomly permute `np.arange(x)`. If `x` is an array, make a copy and shuffle the elements randomly.\n\n Returns \n \n**out**ndarray\n\nPermuted sequence or array range.\n\n See also\n\n [`random.Generator.permutation`](numpy.random.generator.permutation#numpy.random.Generator.permutation \"numpy.random.Generator.permutation\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.permutation(10)\narray([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) # random\n\n```\n \n```\n>>> np.random.permutation([1, 4, 9, 12, 15])\narray([15, 1, 9, 4, 12]) # random\n\n```\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> np.random.permutation(arr)\narray([[6, 7, 8], # random\n [0, 1, 2],\n [3, 4, 5]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.permutation.htmlnumpy.random.poisson\n====================\n\n random.poisson(*lam=1.0*, *size=None*)\n \nDraw samples from a Poisson distribution.\n\n The Poisson distribution is the limit of the binomial distribution for large N.\n\n Note\n\n New code should use the `poisson` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**lam**float or array_like of floats\n\nExpected number of events occurring in a fixed-time interval, must be >= 0. A sequence must be broadcastable over the requested size.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `lam` is a scalar. Otherwise, `np.array(lam).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Poisson distribution.\n\n See also\n\n [`random.Generator.poisson`](numpy.random.generator.poisson#numpy.random.Generator.poisson \"numpy.random.Generator.poisson\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Poisson distribution\n\n \\[f(k; \\lambda)=\\frac{\\lambda^k e^{-\\lambda}}{k!}\\] For events with an expected separation \\(\\lambda\\) the Poisson distribution \\(f(k; \\lambda)\\) describes the probability of \\(k\\) events occurring within the observed interval \\(\\lambda\\).\n\n Because the output is limited to the range of the C int64 type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/PoissonDistribution.html 2 \nWikipedia, “Poisson distribution”, <https://en.wikipedia.org/wiki/Poisson_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> import numpy as np\n>>> s = np.random.poisson(5, 10000)\n\n```\n Display histogram of the sample:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 14, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-poisson-1_00_00.png] Draw each 100 values for lambda 100 and 500:\n\n \n```\n>>> s = np.random.poisson(lam=(100., 500.), size=(100, 2))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.poisson.htmlnumpy.random.power\n==================\n\n random.power(*a*, *size=None*)\n \nDraws samples in [0, 1] from a power distribution with positive exponent a - 1.\n\n Also known as the power function distribution.\n\n Note\n\n New code should use the `power` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nParameter of the distribution. Must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized power distribution.\n\n Raises \n ValueError\n\nIf a <= 0.\n\n See also\n\n [`random.Generator.power`](numpy.random.generator.power#numpy.random.Generator.power \"numpy.random.Generator.power\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function is\n\n \\[P(x; a) = ax^{a-1}, 0 \\le x \\le 1, a>0.\\] The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution.\n\n It is used, for example, in modeling the over-reporting of insurance claims.\n\n #### References\n\n 1 \n<NAME>, <NAME>, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.\n\n 2 \n<NAME>. and <NAME>. “NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions”, National Institute of Standards and Technology Handbook Series, June 2003. <https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 5. # shape\n>>> samples = 1000\n>>> s = np.random.power(a, samples)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, bins=30)\n>>> x = np.linspace(0, 1, 100)\n>>> y = a*x**(a-1.)\n>>> normed_y = samples*np.diff(bins)[0]*y\n>>> plt.plot(x, normed_y)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-power-1_00_00.png] Compare the power function distribution to the inverse of the Pareto.\n\n \n```\n>>> from scipy import stats \n>>> rvs = np.random.power(5, 1000000)\n>>> rvsp = np.random.pareto(5, 1000000)\n>>> xx = np.linspace(0,1,100)\n>>> powpdf = stats.powerlaw.pdf(xx,5) \n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(rvs, bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('np.random.power(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of 1 + np.random.pareto(5)')\n\n```\n \n```\n>>> plt.figure()\n>>> plt.hist(1./(1.+rvsp), bins=50, density=True)\n>>> plt.plot(xx,powpdf,'r-') \n>>> plt.title('inverse of stats.pareto(5)')\n\n```\n ![../../../_images/numpy-random-power-1_01_00.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.power.htmlnumpy.random.rand\n=================\n\n random.rand(*d0*, *d1*, *...*, *dn*)\n \nRandom values in a given shape.\n\n Note\n\n This is a convenience function for users porting code from Matlab, and wraps [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\"). That function takes a tuple to specify the size of the output, which is consistent with other NumPy functions like [`numpy.zeros`](../../generated/numpy.zeros#numpy.zeros \"numpy.zeros\") and [`numpy.ones`](../../generated/numpy.ones#numpy.ones \"numpy.ones\").\n\n Create an array of the given shape and populate it with random samples from a uniform distribution over `[0, 1)`.\n\n Parameters \n \n**d0, d1, …, dn**int, optional\n\nThe dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.\n\n Returns \n \n**out**ndarray, shape `(d0, d1, ..., dn)`\n\nRandom values.\n\n See also\n\n [`random`](../index#module-numpy.random \"numpy.random\")\n #### Examples\n\n \n```\n>>> np.random.rand(3,2)\narray([[ 0.14022471, 0.96360618], #random\n [ 0.37601032, 0.25528411], #random\n [ 0.49313049, 0.94909878]]) #random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.rand.htmlnumpy.random.randint\n====================\n\n random.randint(*low*, *high=None*, *size=None*, *dtype=int*)\n \nReturn random integers from `low` (inclusive) to `high` (exclusive).\n\n Return random integers from the “discrete uniform” distribution of the specified dtype in the “half-open” interval [`low`, `high`). If `high` is None (the default), then results are from [0, `low`).\n\n Note\n\n New code should use the `integers` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**low**int or array-like of ints\n\nLowest (signed) integers to be drawn from the distribution (unless `high=None`, in which case this parameter is one above the *highest* such integer).\n\n \n**high**int or array-like of ints, optional\n\nIf provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if `high=None`). If array-like, must contain integer values\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**dtype**dtype, optional\n\nDesired dtype of the result. Byteorder must be native. The default value is int.\n\n New in version 1.11.0.\n\n Returns \n \n**out**int or ndarray of ints\n\n`size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided.\n\n See also\n\n [`random_integers`](numpy.random.random_integers#numpy.random.random_integers \"numpy.random.random_integers\")\n\nsimilar to [`randint`](#numpy.random.randint \"numpy.random.randint\"), only for the closed interval [`low`, `high`], and 1 is the lowest value if `high` is omitted.\n\n [`random.Generator.integers`](numpy.random.generator.integers#numpy.random.Generator.integers \"numpy.random.Generator.integers\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.randint(2, size=10)\narray([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random\n>>> np.random.randint(1, size=10)\narray([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n\n```\n Generate a 2 x 4 array of ints between 0 and 4, inclusive:\n\n \n```\n>>> np.random.randint(5, size=(2, 4))\narray([[4, 0, 2, 1], # random\n [3, 2, 2, 0]])\n\n```\n Generate a 1 x 3 array with 3 different upper bounds\n\n \n```\n>>> np.random.randint(1, [3, 5, 10])\narray([2, 2, 9]) # random\n\n```\n Generate a 1 by 3 array with 3 different lower bounds\n\n \n```\n>>> np.random.randint([1, 5, 7], 10)\narray([9, 8, 7]) # random\n\n```\n Generate a 2 by 4 array using broadcasting with dtype of uint8\n\n \n```\n>>> np.random.randint([1, 3, 5, 7], [[10], [20]], dtype=np.uint8)\narray([[ 8, 6, 9, 7], # random\n [ 1, 16, 9, 12]], dtype=uint8)\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.randint.htmlnumpy.random.randn\n==================\n\n random.randn(*d0*, *d1*, *...*, *dn*)\n \nReturn a sample (or samples) from the “standard normal” distribution.\n\n Note\n\n This is a convenience function for users porting code from Matlab, and wraps [`standard_normal`](numpy.random.standard_normal#numpy.random.standard_normal \"numpy.random.standard_normal\"). That function takes a tuple to specify the size of the output, which is consistent with other NumPy functions like [`numpy.zeros`](../../generated/numpy.zeros#numpy.zeros \"numpy.zeros\") and [`numpy.ones`](../../generated/numpy.ones#numpy.ones \"numpy.ones\").\n\n Note\n\n New code should use the `standard_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n If positive int_like arguments are provided, [`randn`](#numpy.random.randn \"numpy.random.randn\") generates an array of shape `(d0, d1, ..., dn)`, filled with random floats sampled from a univariate “normal” (Gaussian) distribution of mean 0 and variance 1. A single float randomly sampled from the distribution is returned if no argument is provided.\n\n Parameters \n \n**d0, d1, …, dn**int, optional\n\nThe dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.\n\n Returns \n \n**Z**ndarray or float\n\nA `(d0, d1, ..., dn)`-shaped array of floating-point samples from the standard normal distribution, or a single such float if no parameters were supplied.\n\n See also\n\n [`standard_normal`](numpy.random.standard_normal#numpy.random.standard_normal \"numpy.random.standard_normal\")\n\nSimilar, but takes a tuple as its argument.\n\n [`normal`](numpy.random.normal#numpy.random.normal \"numpy.random.normal\")\n\nAlso accepts mu and sigma arguments.\n\n [`random.Generator.standard_normal`](numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n For random samples from \\(N(\\mu, \\sigma^2)\\), use:\n\n `sigma * np.random.randn(...) + mu`\n\n #### Examples\n\n \n```\n>>> np.random.randn()\n2.1923875335537315 # random\n\n```\n Two-by-four array of samples from N(3, 6.25):\n\n \n```\n>>> 3 + 2.5 * np.random.randn(2, 4)\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.randn.htmlnumpy.random.random_integers\n=============================\n\n random.random_integers(*low*, *high=None*, *size=None*)\n \nRandom integers of type `np.int_` between `low` and `high`, inclusive.\n\n Return random integers of type `np.int_` from the “discrete uniform” distribution in the closed interval [`low`, `high`]. If `high` is None (the default), then results are from [1, `low`]. The `np.int_` type translates to the C long integer type and its precision is platform dependent.\n\n This function has been deprecated. Use randint instead.\n\n Deprecated since version 1.11.0.\n\n Parameters \n \n**low**int\n\nLowest (signed) integer to be drawn from the distribution (unless `high=None`, in which case this parameter is the *highest* such integer).\n\n \n**high**int, optional\n\nIf provided, the largest (signed) integer to be drawn from the distribution (see above for behavior if `high=None`).\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**int or ndarray of ints\n\n`size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided.\n\n See also\n\n [`randint`](numpy.random.randint#numpy.random.randint \"numpy.random.randint\")\n\nSimilar to [`random_integers`](#numpy.random.random_integers \"numpy.random.random_integers\"), only for the half-open interval [`low`, `high`), and 0 is the lowest value if `high` is omitted.\n\n #### Notes\n\n To sample from N evenly spaced floating-point numbers between a and b, use:\n\n \n```\na + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)\n\n```\n #### Examples\n\n \n```\n>>> np.random.random_integers(5)\n4 # random\n>>> type(np.random.random_integers(5))\n<class 'numpy.int64'>\n>>> np.random.random_integers(5, size=(3,2))\narray([[5, 4], # random\n [3, 3],\n [4, 5]])\n\n```\n Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (*i.e.*, from the set \\({0, 5/8, 10/8, 15/8, 20/8}\\)):\n\n \n```\n>>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4.\narray([ 0.625, 1.25 , 0.625, 0.625, 2.5 ]) # random\n\n```\n Roll two six sided dice 1000 times and sum the results:\n\n \n```\n>>> d1 = np.random.random_integers(1, 6, 1000)\n>>> d2 = np.random.random_integers(1, 6, 1000)\n>>> dsums = d1 + d2\n\n```\n Display results as a histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(dsums, 11, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-random_integers-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.random_integers.htmlnumpy.random.random_sample\n===========================\n\n random.random_sample(*size=None*)\n \nReturn random floats in the half-open interval [0.0, 1.0).\n\n Results are from the “continuous uniform” distribution over the stated interval. To sample \\(Unif[a, b), b > a\\) multiply the output of [`random_sample`](#numpy.random.random_sample \"numpy.random.random_sample\") by `(b-a)` and add `a`:\n\n \n```\n(b - a) * random_sample() + a\n\n```\n Note\n\n New code should use the `random` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray of floats\n\nArray of random floats of shape `size` (unless `size=None`, in which case a single float is returned).\n\n See also\n\n [`random.Generator.random`](numpy.random.generator.random#numpy.random.Generator.random \"numpy.random.Generator.random\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> np.random.random_sample()\n0.47108547995356098 # random\n>>> type(np.random.random_sample())\n<class 'float'>\n>>> np.random.random_sample((5,))\narray([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) # random\n\n```\n Three-by-two array of random numbers from [-5, 0):\n\n \n```\n>>> 5 * np.random.random_sample((3, 2)) - 5\narray([[-3.99149989, -0.52338984], # random\n [-2.99091858, -0.79479508],\n [-1.23204345, -1.75224494]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.random_sample.htmlnumpy.random.ranf\n=================\n\n random.ranf()\n \nThis is an alias of [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\"). See [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\") for the complete documentation.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.ranf.htmlnumpy.random.rayleigh\n=====================\n\n random.rayleigh(*scale=1.0*, *size=None*)\n \nDraw samples from a Rayleigh distribution.\n\n The \\(\\chi\\) and Weibull distributions are generalizations of the Rayleigh.\n\n Note\n\n New code should use the `rayleigh` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**scale**float or array_like of floats, optional\n\nScale, also equals the mode. Must be non-negative. Default is 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Rayleigh distribution.\n\n See also\n\n [`random.Generator.rayleigh`](numpy.random.generator.rayleigh#numpy.random.Generator.rayleigh \"numpy.random.Generator.rayleigh\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the Rayleigh distribution is\n\n \\[P(x;scale) = \\frac{x}{scale^2}e^{\\frac{-x^2}{2 \\cdotp scale^2}}\\] The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.\n\n #### References\n\n 1 \nBrighton Webs Ltd., “Rayleigh Distribution,” <https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp 2 \nWikipedia, “Rayleigh distribution” <https://en.wikipedia.org/wiki/Rayleigh_distribution #### Examples\n\n Draw values from the distribution and plot the histogram\n\n \n```\n>>> from matplotlib.pyplot import hist\n>>> values = hist(np.random.rayleigh(3, 100000), bins=200, density=True)\n\n```\n Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters?\n\n \n```\n>>> meanvalue = 1\n>>> modevalue = np.sqrt(2 / np.pi) * meanvalue\n>>> s = np.random.rayleigh(modevalue, 1000000)\n\n```\n The percentage of waves larger than 3 meters is:\n\n \n```\n>>> 100.*sum(s>3)/1000000.\n0.087300000000000003 # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.rayleigh.htmlnumpy.random.sample\n===================\n\n random.sample()\n \nThis is an alias of [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\"). See [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\") for the complete documentation.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.sample.htmlnumpy.random.seed\n=================\n\n random.seed(*self*, *seed=None*)\n \nReseed a legacy MT19937 BitGenerator\n\n #### Notes\n\n This is a convenience, legacy function.\n\n The best practice is to **not** reseed a BitGenerator, rather to recreate a new one. This method is here for legacy reasons. This example demonstrates best practice.\n\n \n```\n>>> from numpy.random import MT19937\n>>> from numpy.random import RandomState, SeedSequence\n>>> rs = RandomState(MT19937(SeedSequence(123456789)))\n# Later, you want to restart the stream\n>>> rs = RandomState(MT19937(SeedSequence(987654321)))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.seed.htmlnumpy.random.set_state\n=======================\n\n random.set_state(*state*)\n \nSet the internal state of the generator from a tuple.\n\n For use if one has reason to manually (re-)set the internal state of the bit generator used by the RandomState instance. By default, RandomState uses the “Mersenne Twister”[[1]](#rf0f3f75f485b-1) pseudo-random number generating algorithm.\n\n Parameters \n \n**state**{tuple(str, ndarray of 624 uints, int, int, float), dict}\n\nThe `state` tuple has the following items:\n\n 1. the string ‘MT19937’, specifying the Mersenne Twister algorithm.\n2. a 1-D array of 624 unsigned integers `keys`.\n3. an integer `pos`.\n4. an integer `has_gauss`.\n5. a float `cached_gaussian`.\n\n If state is a dictionary, it is directly set using the BitGenerators `state` property.\n\n Returns \n \n**out**None\n\nReturns ‘None’ on success.\n\n See also\n\n [`get_state`](numpy.random.get_state#numpy.random.get_state \"numpy.random.get_state\")\n #### Notes\n\n [`set_state`](#numpy.random.set_state \"numpy.random.set_state\") and [`get_state`](numpy.random.get_state#numpy.random.get_state \"numpy.random.get_state\") are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing.\n\n For backwards compatibility, the form (str, array of 624 uints, int) is also accepted although it is missing some information about the cached Gaussian value: `state = ('MT19937', keys, pos)`.\n\n #### References\n\n [1](#id1) \n<NAME> and <NAME>, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” *ACM Trans. on Modeling and Computer Simulation*, Vol. 8, No. 1, pp. 3-30, Jan. 1998.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.set_state.htmlnumpy.random.shuffle\n====================\n\n random.shuffle(*x*)\n \nModify a sequence in-place by shuffling its contents.\n\n This function only shuffles the array along the first axis of a multi-dimensional array. The order of sub-arrays is changed but their contents remains the same.\n\n Note\n\n New code should use the `shuffle` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**x**ndarray or MutableSequence\n\nThe array, list or mutable sequence to be shuffled.\n\n Returns \n None\n See also\n\n [`random.Generator.shuffle`](numpy.random.generator.shuffle#numpy.random.Generator.shuffle \"numpy.random.Generator.shuffle\")\n\nwhich should be used for new code.\n\n #### Examples\n\n \n```\n>>> arr = np.arange(10)\n>>> np.random.shuffle(arr)\n>>> arr\n[1 7 5 2 9 4 3 6 0 8] # random\n\n```\n Multi-dimensional arrays are only shuffled along the first axis:\n\n \n```\n>>> arr = np.arange(9).reshape((3, 3))\n>>> np.random.shuffle(arr)\n>>> arr\narray([[3, 4, 5], # random\n [6, 7, 8],\n [0, 1, 2]])\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.shuffle.htmlnumpy.random.standard_cauchy\n=============================\n\n random.standard_cauchy(*size=None*)\n \nDraw samples from a standard Cauchy distribution with mode = 0.\n\n Also known as the Lorentz distribution.\n\n Note\n\n New code should use the `standard_cauchy` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**samples**ndarray or scalar\n\nThe drawn samples.\n\n See also\n\n [`random.Generator.standard_cauchy`](numpy.random.generator.standard_cauchy#numpy.random.Generator.standard_cauchy \"numpy.random.Generator.standard_cauchy\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the full Cauchy distribution is\n\n \\[P(x; x_0, \\gamma) = \\frac{1}{\\pi \\gamma \\bigl[ 1+ (\\frac{x-x_0}{\\gamma})^2 \\bigr] }\\] and the Standard Cauchy distribution just sets \\(x_0=0\\) and \\(\\gamma=1\\)\n\n The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis.\n\n When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails.\n\n #### References\n\n 1 \nNIST/SEMATECH e-Handbook of Statistical Methods, “Cauchy Distribution”, <https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm 2 \nWeisstein, <NAME>. “Cauchy Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/CauchyDistribution.html 3 \nWikipedia, “Cauchy distribution” <https://en.wikipedia.org/wiki/Cauchy_distribution #### Examples\n\n Draw samples and plot the distribution:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.standard_cauchy(1000000)\n>>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well\n>>> plt.hist(s, bins=100)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-standard_cauchy-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.standard_cauchy.htmlnumpy.random.standard_exponential\n==================================\n\n random.standard_exponential(*size=None*)\n \nDraw samples from the standard exponential distribution.\n\n [`standard_exponential`](#numpy.random.standard_exponential \"numpy.random.standard_exponential\") is identical to the exponential distribution with a scale parameter of 1.\n\n Note\n\n New code should use the `standard_exponential` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray\n\nDrawn samples.\n\n See also\n\n [`random.Generator.standard_exponential`](numpy.random.generator.standard_exponential#numpy.random.Generator.standard_exponential \"numpy.random.Generator.standard_exponential\")\n\nwhich should be used for new code.\n\n #### Examples\n\n Output a 3x8000 array:\n\n \n```\n>>> n = np.random.standard_exponential((3, 8000))\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.standard_exponential.htmlnumpy.random.standard_gamma\n============================\n\n random.standard_gamma(*shape*, *size=None*)\n \nDraw samples from a standard Gamma distribution.\n\n Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.\n\n Note\n\n New code should use the `standard_gamma` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**shape**float or array_like of floats\n\nParameter, must be non-negative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `shape` is a scalar. Otherwise, `np.array(shape).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard gamma distribution.\n\n See also\n\n [`scipy.stats.gamma`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution or cumulative density function, etc.\n\n [`random.Generator.standard_gamma`](numpy.random.generator.standard_gamma#numpy.random.Generator.standard_gamma \"numpy.random.Generator.standard_gamma\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Gamma distribution is\n\n \\[p(x) = x^{k-1}\\frac{e^{-x/\\theta}}{\\theta^k\\Gamma(k)},\\] where \\(k\\) is the shape and \\(\\theta\\) the scale, and \\(\\Gamma\\) is the Gamma function.\n\n The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.\n\n #### References\n\n 1 \nWeisstein, <NAME>. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. <http://mathworld.wolfram.com/GammaDistribution.html 2 \nWikipedia, “Gamma distribution”, <https://en.wikipedia.org/wiki/Gamma_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> shape, scale = 2., 1. # mean and width\n>>> s = np.random.standard_gamma(shape, 1000000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> import scipy.special as sps \n>>> count, bins, ignored = plt.hist(s, 50, density=True)\n>>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \n... (sps.gamma(shape) * scale**shape))\n>>> plt.plot(bins, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-standard_gamma-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.standard_gamma.htmlnumpy.random.standard_normal\n=============================\n\n random.standard_normal(*size=None*)\n \nDraw samples from a standard Normal distribution (mean=0, stdev=1).\n\n Note\n\n New code should use the `standard_normal` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n Returns \n \n**out**float or ndarray\n\nA floating-point array of shape `size` of drawn samples, or a single sample if `size` was not specified.\n\n See also\n\n [`normal`](numpy.random.normal#numpy.random.normal \"numpy.random.normal\")\n\nEquivalent function with additional `loc` and `scale` arguments for setting the mean and standard deviation.\n\n [`random.Generator.standard_normal`](numpy.random.generator.standard_normal#numpy.random.Generator.standard_normal \"numpy.random.Generator.standard_normal\")\n\nwhich should be used for new code.\n\n #### Notes\n\n For random samples from \\(N(\\mu, \\sigma^2)\\), use one of:\n\n \n```\nmu + sigma * np.random.standard_normal(size=...)\nnp.random.normal(mu, sigma, size=...)\n\n```\n #### Examples\n\n \n```\n>>> np.random.standard_normal()\n2.1923875335537315 #random\n\n```\n \n```\n>>> s = np.random.standard_normal(8000)\n>>> s\narray([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, # random\n -0.38672696, -0.4685006 ]) # random\n>>> s.shape\n(8000,)\n>>> s = np.random.standard_normal(size=(3, 4, 2))\n>>> s.shape\n(3, 4, 2)\n\n```\n Two-by-four array of samples from \\(N(3, 6.25)\\):\n\n \n```\n>>> 3 + 2.5 * np.random.standard_normal(size=(2, 4))\narray([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random\n [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.standard_normal.htmlnumpy.random.standard_t\n========================\n\n random.standard_t(*df*, *size=None*)\n \nDraw samples from a standard Student’s t distribution with `df` degrees of freedom.\n\n A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution ([`standard_normal`](numpy.random.standard_normal#numpy.random.standard_normal \"numpy.random.standard_normal\")).\n\n Note\n\n New code should use the `standard_t` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**df**float or array_like of floats\n\nDegrees of freedom, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `df` is a scalar. Otherwise, `np.array(df).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized standard Student’s t distribution.\n\n See also\n\n [`random.Generator.standard_t`](numpy.random.generator.standard_t#numpy.random.Generator.standard_t \"numpy.random.Generator.standard_t\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the t distribution is\n\n \\[P(x, df) = \\frac{\\Gamma(\\frac{df+1}{2})}{\\sqrt{\\pi df} \\Gamma(\\frac{df}{2})}\\Bigl( 1+\\frac{x^2}{df} \\Bigr)^{-(df+1)/2}\\] The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean.\n\n The derivation of the t-distribution was first published in 1908 by <NAME> while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student.\n\n #### References\n\n [1](#id3) \nDalgaard, Peter, “Introductory Statistics With R”, Springer, 2002.\n\n 2 \nWikipedia, “Student’s t-distribution” [https://en.wikipedia.org/wiki/Student’s_t-distribution](https://en.wikipedia.org/wiki/Student's_t-distribution)\n\n #### Examples\n\n From Dalgaard page 83 [[1]](#r755c9bae090e-1), suppose the daily energy intake for 11 women in kilojoules (kJ) is:\n\n \n```\n>>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \\\n... 7515, 8230, 8770])\n\n```\n Does their energy intake deviate systematically from the recommended value of 7725 kJ? Our null hypothesis will be the absence of deviation, and the alternate hypothesis will be the presence of an effect that could be either positive or negative, hence making our test 2-tailed.\n\n Because we are estimating the mean and we have N=11 values in our sample, we have N-1=10 degrees of freedom. We set our significance level to 95% and compute the t statistic using the empirical mean and empirical standard deviation of our intake. We use a ddof of 1 to base the computation of our empirical standard deviation on an unbiased estimate of the variance (note: the final estimate is not unbiased due to the concave nature of the square root).\n\n \n```\n>>> np.mean(intake)\n6753.636363636364\n>>> intake.std(ddof=1)\n1142.1232221373727\n>>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake)))\n>>> t\n-2.8207540608310198\n\n```\n We draw 1000000 samples from Student’s t distribution with the adequate degrees of freedom.\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> s = np.random.standard_t(10, size=1000000)\n>>> h = plt.hist(s, bins=100, density=True)\n\n```\n Does our t statistic land in one of the two critical regions found at both tails of the distribution?\n\n \n```\n>>> np.sum(np.abs(t) < np.abs(s)) / float(len(s))\n0.018318 #random < 0.05, statistic is in critical region\n\n```\n The probability value for this 2-tailed test is about 1.83%, which is lower than the 5% pre-determined significance threshold.\n\n Therefore, the probability of observing values as extreme as our intake conditionally on the null hypothesis being true is too low, and we reject the null hypothesis of no deviation.\n\n ![../../../_images/numpy-random-standard_t-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.standard_t.htmlnumpy.random.triangular\n=======================\n\n random.triangular(*left*, *mode*, *right*, *size=None*)\n \nDraw samples from the triangular distribution over the interval `[left, right]`.\n\n The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf.\n\n Note\n\n New code should use the `triangular` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**left**float or array_like of floats\n\nLower limit.\n\n \n**mode**float or array_like of floats\n\nThe value where the peak of the distribution occurs. The value must fulfill the condition `left <= mode <= right`.\n\n \n**right**float or array_like of floats\n\nUpper limit, must be larger than `left`.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `left`, `mode`, and `right` are all scalars. Otherwise, `np.broadcast(left, mode, right).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized triangular distribution.\n\n See also\n\n [`random.Generator.triangular`](numpy.random.generator.triangular#numpy.random.Generator.triangular \"numpy.random.Generator.triangular\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the triangular distribution is\n\n \\[\\begin{split}P(x;l, m, r) = \\begin{cases} \\frac{2(x-l)}{(r-l)(m-l)}& \\text{for $l \\leq x \\leq m$},\\\\ \\frac{2(r-x)}{(r-l)(r-m)}& \\text{for $m \\leq x \\leq r$},\\\\ 0& \\text{otherwise}. \\end{cases}\\end{split}\\] The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations.\n\n #### References\n\n 1 \nWikipedia, “Triangular distribution” <https://en.wikipedia.org/wiki/Triangular_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200,\n... density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-triangular-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.triangular.htmlnumpy.random.uniform\n====================\n\n random.uniform(*low=0.0*, *high=1.0*, *size=None*)\n \nDraw samples from a uniform distribution.\n\n Samples are uniformly distributed over the half-open interval `[low, high)` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by [`uniform`](#numpy.random.uniform \"numpy.random.uniform\").\n\n Note\n\n New code should use the `uniform` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**low**float or array_like of floats, optional\n\nLower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0.\n\n \n**high**float or array_like of floats\n\nUpper boundary of the output interval. All values generated will be less than or equal to high. The high limit may be included in the returned array of floats due to floating-point rounding in the equation `low + (high-low) * random_sample()`. The default value is 1.0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `low` and `high` are both scalars. Otherwise, `np.broadcast(low, high).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized uniform distribution.\n\n See also\n\n [`randint`](numpy.random.randint#numpy.random.randint \"numpy.random.randint\")\n\nDiscrete uniform distribution, yielding integers.\n\n [`random_integers`](numpy.random.random_integers#numpy.random.random_integers \"numpy.random.random_integers\")\n\nDiscrete uniform distribution over the closed interval `[low, high]`.\n\n [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\")\n\nFloats uniformly distributed over `[0, 1)`.\n\n [`random`](../index#module-numpy.random \"numpy.random\")\n\nAlias for [`random_sample`](numpy.random.random_sample#numpy.random.random_sample \"numpy.random.random_sample\").\n\n [`rand`](numpy.random.rand#numpy.random.rand \"numpy.random.rand\")\n\nConvenience function that accepts dimensions as input, e.g., `rand(2,2)` would generate a 2-by-2 array of floats, uniformly distributed over `[0, 1)`.\n\n [`random.Generator.uniform`](numpy.random.generator.uniform#numpy.random.Generator.uniform \"numpy.random.Generator.uniform\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function of the uniform distribution is\n\n \\[p(x) = \\frac{1}{b - a}\\] anywhere within the interval `[a, b)`, and zero elsewhere.\n\n When `high` == `low`, values of `low` will be returned. If `high` < `low`, the results are officially undefined and may eventually raise an error, i.e. do not rely on this function to behave when passed arguments satisfying that inequality condition. The `high` limit may be included in the returned array of floats due to floating-point rounding in the equation `low + (high-low) * random_sample()`. For example:\n\n \n```\n>>> x = np.float32(5*0.99999999)\n>>> x\n5.0\n\n```\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> s = np.random.uniform(-1,0,1000)\n\n```\n All values are within the given interval:\n\n \n```\n>>> np.all(s >= -1)\nTrue\n>>> np.all(s < 0)\nTrue\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> count, bins, ignored = plt.hist(s, 15, density=True)\n>>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-uniform-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.uniform.htmlnumpy.random.vonmises\n=====================\n\n random.vonmises(*mu*, *kappa*, *size=None*)\n \nDraw samples from a von Mises distribution.\n\n Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi].\n\n The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution.\n\n Note\n\n New code should use the `vonmises` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mu**float or array_like of floats\n\nMode (“center”) of the distribution.\n\n \n**kappa**float or array_like of floats\n\nDispersion of the distribution, has to be >=0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mu` and `kappa` are both scalars. Otherwise, `np.broadcast(mu, kappa).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized von Mises distribution.\n\n See also\n\n [`scipy.stats.vonmises`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html#scipy.stats.vonmises \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n [`random.Generator.vonmises`](numpy.random.generator.vonmises#numpy.random.Generator.vonmises \"numpy.random.Generator.vonmises\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the von Mises distribution is\n\n \\[p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},\\] where \\(\\mu\\) is the mode and \\(\\kappa\\) the dispersion, and \\(I_0(\\kappa)\\) is the modified Bessel function of order 0.\n\n The von Mises is named for <NAME>, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science.\n\n #### References\n\n 1 \n<NAME>. and <NAME>. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.\n\n 2 \n<NAME>., “Mathematical Theory of Probability and Statistics”, New York: Academic Press, 1964.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> mu, kappa = 0.0, 4.0 # mean and dispersion\n>>> s = np.random.vonmises(mu, kappa, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import i0 \n>>> plt.hist(s, 50, density=True)\n>>> x = np.linspace(-np.pi, np.pi, num=51)\n>>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) \n>>> plt.plot(x, y, linewidth=2, color='r') \n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-vonmises-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.vonmises.htmlnumpy.random.wald\n=================\n\n random.wald(*mean*, *scale*, *size=None*)\n \nDraw samples from a Wald, or inverse Gaussian, distribution.\n\n As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an inverse Gaussian with mean equal to 1, but this is by no means universal.\n\n The inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 <NAME> used the name inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time.\n\n Note\n\n New code should use the `wald` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**mean**float or array_like of floats\n\nDistribution mean, must be > 0.\n\n \n**scale**float or array_like of floats\n\nScale parameter, must be > 0.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `mean` and `scale` are both scalars. Otherwise, `np.broadcast(mean, scale).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Wald distribution.\n\n See also\n\n [`random.Generator.wald`](numpy.random.generator.wald#numpy.random.Generator.wald \"numpy.random.Generator.wald\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density function for the Wald distribution is\n\n \\[P(x;mean,scale) = \\sqrt{\\frac{scale}{2\\pi x^3}}e^ \\frac{-scale(x-mean)^2}{2\\cdotp mean^2x}\\] As noted above the inverse Gaussian distribution first arise from attempts to model Brownian motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes.\n\n #### References\n\n 1 \nBrighton Webs Ltd., Wald Distribution, <https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp 2 \n<NAME>., and <NAME>, “The Inverse Gaussian Distribution: Theory : Methodology, and Applications”, CRC Press, 1988.\n\n 3 \nWikipedia, “Inverse Gaussian distribution” <https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution #### Examples\n\n Draw values from the distribution and plot the histogram:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, density=True)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-wald-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.wald.htmlnumpy.random.weibull\n====================\n\n random.weibull(*a*, *size=None*)\n \nDraw samples from a Weibull distribution.\n\n Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`.\n\n \\[X = (-ln(U))^{1/a}\\] Here, U is drawn from the uniform distribution over (0,1].\n\n The more common 2-parameter Weibull, including a scale parameter \\(\\lambda\\) is just \\(X = \\lambda(-ln(U))^{1/a}\\).\n\n Note\n\n New code should use the `weibull` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nShape parameter of the distribution. Must be nonnegative.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Weibull distribution.\n\n See also\n\n [`scipy.stats.weibull_max`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_max.html#scipy.stats.weibull_max \"(in SciPy v1.8.1)\")\n[`scipy.stats.weibull_min`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min \"(in SciPy v1.8.1)\")\n[`scipy.stats.genextreme`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme \"(in SciPy v1.8.1)\")\n[`gumbel`](numpy.random.gumbel#numpy.random.gumbel \"numpy.random.gumbel\")\n[`random.Generator.weibull`](numpy.random.generator.weibull#numpy.random.Generator.weibull \"numpy.random.Generator.weibull\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions.\n\n The probability density for the Weibull distribution is\n\n \\[p(x) = \\frac{a} {\\lambda}(\\frac{x}{\\lambda})^{a-1}e^{-(x/\\lambda)^a},\\] where \\(a\\) is the shape and \\(\\lambda\\) the scale.\n\n The function has its peak (the mode) at \\(\\lambda(\\frac{a-1}{a})^{1/a}\\).\n\n When `a = 1`, the Weibull distribution reduces to the exponential distribution.\n\n #### References\n\n 1 \n<NAME>, Royal Technical University, Stockholm, 1939 “A Statistical Theory Of The Strength Of Materials”, Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm.\n\n 2 \n<NAME>, “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper 1951.\n\n 3 \nWikipedia, “Weibull distribution”, <https://en.wikipedia.org/wiki/Weibull_distribution #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 5. # shape\n>>> s = np.random.weibull(a, 1000)\n\n```\n Display the histogram of the samples, along with the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> x = np.arange(1,100.)/50.\n>>> def weib(x,n,a):\n... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)\n\n```\n \n```\n>>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))\n>>> x = np.arange(1,100.)/50.\n>>> scale = count.max()/weib(x, 1., 5.).max()\n>>> plt.plot(x, weib(x, 1., 5.)*scale)\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-weibull-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.weibull.htmlnumpy.random.zipf\n=================\n\n random.zipf(*a*, *size=None*)\n \nDraw samples from a Zipf distribution.\n\n Samples are drawn from a Zipf distribution with specified parameter `a` > 1.\n\n The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf’s law: the frequency of an item is inversely proportional to its rank in a frequency table.\n\n Note\n\n New code should use the `zipf` method of a `default_rng()` instance instead; please see the [Quick Start](../index#random-quick-start).\n\n Parameters \n \n**a**float or array_like of floats\n\nDistribution parameter. Must be greater than 1.\n\n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. If size is `None` (default), a single value is returned if `a` is a scalar. Otherwise, `np.array(a).size` samples are drawn.\n\n Returns \n \n**out**ndarray or scalar\n\nDrawn samples from the parameterized Zipf distribution.\n\n See also\n\n [`scipy.stats.zipf`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zipf.html#scipy.stats.zipf \"(in SciPy v1.8.1)\")\n\nprobability density function, distribution, or cumulative density function, etc.\n\n [`random.Generator.zipf`](numpy.random.generator.zipf#numpy.random.Generator.zipf \"numpy.random.Generator.zipf\")\n\nwhich should be used for new code.\n\n #### Notes\n\n The probability density for the Zipf distribution is\n\n \\[p(k) = \\frac{k^{-a}}{\\zeta(a)},\\] for integers \\(k \\geq 1\\), where \\(\\zeta\\) is the Riemann Zeta function.\n\n It is named for the American linguist <NAME>, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table.\n\n #### References\n\n 1 \n<NAME>., “Selected Studies of the Principle of Relative Frequency in Language,” Cambridge, MA: Harvard Univ. Press, 1932.\n\n #### Examples\n\n Draw samples from the distribution:\n\n \n```\n>>> a = 4.0\n>>> n = 20000\n>>> s = np.random.zipf(a, n)\n\n```\n Display the histogram of the samples, along with the expected histogram based on the probability density function:\n\n \n```\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import zeta \n\n```\n [`bincount`](../../generated/numpy.bincount#numpy.bincount \"numpy.bincount\") provides a fast histogram for small integers.\n\n \n```\n>>> count = np.bincount(s)\n>>> k = np.arange(1, s.max() + 1)\n\n```\n \n```\n>>> plt.bar(k, count[1:], alpha=0.5, label='sample count')\n>>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5,\n... label='expected count') \n>>> plt.semilogy()\n>>> plt.grid(alpha=0.4)\n>>> plt.legend()\n>>> plt.title(f'Zipf sample, a={a}, size={n}')\n>>> plt.show()\n\n```\n ![../../../_images/numpy-random-zipf-1.png] \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/generated/numpy.random.zipf.htmlPermuted Congruential Generator (64-bit, PCG64 DXSM)\n====================================================\n\n *class*numpy.random.PCG64DXSM(*seed=None*)\n \nBitGenerator for the PCG-64 DXSM pseudo-random number generator.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n #### Notes\n\n PCG-64 DXSM is a 128-bit implementation of O’Neill’s permutation congruential generator ([[1]](#rad26d0f7d970-1), [[2]](#rad26d0f7d970-2)). PCG-64 DXSM has a period of \\(2^{128}\\) and supports advancing an arbitrary number of steps as well as \\(2^{127}\\) streams. The specific member of the PCG family that we use is PCG CM DXSM 128/64. It differs from `PCG64` in that it uses the stronger DXSM output function, a 64-bit “cheap multiplier” in the LCG, and outputs from the state before advancing it rather than advance-then-output.\n\n `PCG64DXSM` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a `Generator` or similar object that supports low-level access.\n\n Supports the method [`advance`](generated/numpy.random.pcg64dxsm.advance#numpy.random.PCG64DXSM.advance \"numpy.random.PCG64DXSM.advance\") to advance the RNG an arbitrary number of steps. The state of the PCG-64 DXSM RNG is represented by 2 128-bit unsigned integers.\n\n **State and Seeding**\n\n The `PCG64DXSM` state vector consists of 2 unsigned 128-bit values, which are represented externally as Python ints. One is the state of the PRNG, which is advanced by a linear congruential generator (LCG). The second is a fixed odd increment used in the LCG.\n\n The input seed is processed by [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to generate both values. The increment is not independently settable.\n\n **Parallel Features**\n\n The preferred way to use a BitGenerator in parallel applications is to use the [`SeedSequence.spawn`](generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\") method to obtain entropy values, and to use these to generate new BitGenerators:\n\n \n```\n>>> from numpy.random import Generator, PCG64DXSM, SeedSequence\n>>> sg = SeedSequence(1234)\n>>> rg = [Generator(PCG64DXSM(s)) for s in sg.spawn(10)]\n\n```\n **Compatibility Guarantee**\n\n `PCG64DXSM` makes a guarantee that a fixed seed will always produce the same random integer stream.\n\n #### References\n\n [1](#id1) \n[“PCG, A Family of Better Random Number Generators”](http://www.pcg-random.org/)\n\n [2](#id2) \nO’Neill, <NAME>. [“PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation”](https://www.cs.hmc.edu/tr/hmc-cs-2014-0905.pdf)\n\n \n State\n-----\n\n \n\n| | |\n| --- | --- |\n| [`state`](generated/numpy.random.pcg64dxsm.state#numpy.random.PCG64DXSM.state \"numpy.random.PCG64DXSM.state\") | Get or set the PRNG state |\n\n Parallel generation\n-------------------\n\n \n\n| | |\n| --- | --- |\n| [`advance`](generated/numpy.random.pcg64dxsm.advance#numpy.random.PCG64DXSM.advance \"numpy.random.PCG64DXSM.advance\")(delta) | Advance the underlying RNG as-if delta draws have occurred. |\n| [`jumped`](generated/numpy.random.pcg64dxsm.jumped#numpy.random.PCG64DXSM.jumped \"numpy.random.PCG64DXSM.jumped\")([jumps]) | Returns a new bit generator with the state jumped. |\n\n Extending\n---------\n\n \n\n| | |\n| --- | --- |\n| [`cffi`](generated/numpy.random.pcg64dxsm.cffi#numpy.random.PCG64DXSM.cffi \"numpy.random.PCG64DXSM.cffi\") | CFFI interface |\n| [`ctypes`](generated/numpy.random.pcg64dxsm.ctypes#numpy.random.PCG64DXSM.ctypes \"numpy.random.PCG64DXSM.ctypes\") | ctypes interface |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/pcg64dxsm.htmlPhilox Counter-based RNG\n========================\n\n *class*numpy.random.Philox(*seed=None*, *counter=None*, *key=None*)\n \nContainer for the Philox (4x64) pseudo-random number generator.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n \n**counter**{None, int, array_like}, optional\n\nCounter to use in the Philox state. Can be either a Python int (long in 2.x) in [0, 2**256) or a 4-element uint64 array. If not provided, the RNG is initialized at 0.\n\n \n**key**{None, int, array_like}, optional\n\nKey to use in the Philox state. Unlike `seed`, the value in key is directly set. Can be either a Python int in [0, 2**128) or a 2-element uint64 array. `key` and `seed` cannot both be used.\n\n #### Notes\n\n Philox is a 64-bit PRNG that uses a counter-based design based on weaker (and faster) versions of cryptographic functions [[1]](#r40f8e2ad755a-1). Instances using different values of the key produce independent sequences. Philox has a period of \\(2^{256} - 1\\) and supports arbitrary advancing and jumping the sequence in increments of \\(2^{128}\\). These features allow multiple non-overlapping sequences to be generated.\n\n `Philox` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a `Generator` or similar object that supports low-level access.\n\n **State and Seeding**\n\n The `Philox` state vector consists of a 256-bit value encoded as a 4-element uint64 array and a 128-bit value encoded as a 2-element uint64 array. The former is a counter which is incremented by 1 for every 4 64-bit randoms produced. The second is a key which determined the sequence produced. Using different keys produces independent sequences.\n\n The input `seed` is processed by [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to generate the key. The counter is set to 0.\n\n Alternately, one can omit the `seed` parameter and set the `key` and `counter` directly.\n\n **Parallel Features**\n\n The preferred way to use a BitGenerator in parallel applications is to use the [`SeedSequence.spawn`](generated/numpy.random.seedsequence.spawn#numpy.random.SeedSequence.spawn \"numpy.random.SeedSequence.spawn\") method to obtain entropy values, and to use these to generate new BitGenerators:\n\n \n```\n>>> from numpy.random import Generator, Philox, SeedSequence\n>>> sg = SeedSequence(1234)\n>>> rg = [Generator(Philox(s)) for s in sg.spawn(10)]\n\n```\n `Philox` can be used in parallel applications by calling the `jumped` method to advances the state as-if \\(2^{128}\\) random numbers have been generated. Alternatively, `advance` can be used to advance the counter for any positive step in [0, 2**256). When using `jumped`, all generators should be chained to ensure that the segments come from the same sequence.\n\n \n```\n>>> from numpy.random import Generator, Philox\n>>> bit_generator = Philox(1234)\n>>> rg = []\n>>> for _ in range(10):\n... rg.append(Generator(bit_generator))\n... bit_generator = bit_generator.jumped()\n\n```\n Alternatively, `Philox` can be used in parallel applications by using a sequence of distinct keys where each instance uses different key.\n\n \n```\n>>> key = 2**96 + 2**33 + 2**17 + 2**9\n>>> rg = [Generator(Philox(key=key+i)) for i in range(10)]\n\n```\n **Compatibility Guarantee**\n\n `Philox` makes a guarantee that a fixed `seed` will always produce the same random integer stream.\n\n #### References\n\n [1](#id1) \n<NAME>, <NAME>, <NAME>, and <NAME>, “Parallel Random Numbers: As Easy as 1, 2, 3,” Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC11), New York, NY: ACM, 2011.\n\n #### Examples\n\n \n```\n>>> from numpy.random import Generator, Philox\n>>> rg = Generator(Philox(1234))\n>>> rg.standard_normal()\n0.123 # random\n\n```\n Attributes \n **lock: threading.Lock**\n\nLock instance that is shared so that the same bit git generator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.\n\n \n State\n-----\n\n \n\n| | |\n| --- | --- |\n| [`state`](generated/numpy.random.philox.state#numpy.random.Philox.state \"numpy.random.Philox.state\") | Get or set the PRNG state |\n\n Parallel generation\n-------------------\n\n \n\n| | |\n| --- | --- |\n| [`advance`](generated/numpy.random.philox.advance#numpy.random.Philox.advance \"numpy.random.Philox.advance\")(delta) | Advance the underlying RNG as-if delta draws have occurred. |\n| [`jumped`](generated/numpy.random.philox.jumped#numpy.random.Philox.jumped \"numpy.random.Philox.jumped\")([jumps]) | Returns a new bit generator with the state jumped |\n\n Extending\n---------\n\n \n\n| | |\n| --- | --- |\n| [`cffi`](generated/numpy.random.philox.cffi#numpy.random.Philox.cffi \"numpy.random.Philox.cffi\") | CFFI interface |\n| [`ctypes`](generated/numpy.random.philox.ctypes#numpy.random.Philox.ctypes \"numpy.random.Philox.ctypes\") | ctypes interface |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/philox.htmlSFC64 Small Fast Chaotic PRNG\n=============================\n\n *class*numpy.random.SFC64(*seed=None*)\n \nBitGenerator for <NAME>’s Small Fast Chaotic PRNG.\n\n Parameters \n \n**seed**{None, int, array_like[ints], SeedSequence}, optional\n\nA seed to initialize the [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\"). If None, then fresh, unpredictable entropy will be pulled from the OS. If an `int` or `array_like[ints]` is passed, then it will be passed to [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to derive the initial [`BitGenerator`](generated/numpy.random.bitgenerator#numpy.random.BitGenerator \"numpy.random.BitGenerator\") state. One may also pass in a [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") instance.\n\n #### Notes\n\n `SFC64` is a 256-bit implementation of <NAME>’s Small Fast Chaotic PRNG ([[1]](#r50352647a6aa-1)). `SFC64` has a few different cycles that one might be on, depending on the seed; the expected period will be about \\(2^{255}\\) ([[2]](#r50352647a6aa-2)). `SFC64` incorporates a 64-bit counter which means that the absolute minimum cycle length is \\(2^{64}\\) and that distinct seeds will not run into each other for at least \\(2^{64}\\) iterations.\n\n `SFC64` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a `Generator` or similar object that supports low-level access.\n\n **State and Seeding**\n\n The `SFC64` state vector consists of 4 unsigned 64-bit values. The last is a 64-bit counter that increments by 1 each iteration.\n\n The input seed is processed by [`SeedSequence`](generated/numpy.random.seedsequence#numpy.random.SeedSequence \"numpy.random.SeedSequence\") to generate the first 3 values, then the `SFC64` algorithm is iterated a small number of times to mix.\n\n **Compatibility Guarantee**\n\n `SFC64` makes a guarantee that a fixed seed will always produce the same random integer stream.\n\n #### References\n\n [1](#id1) \n[“PractRand”](http://pracrand.sourceforge.net/RNG_engines.txt)\n\n [2](#id2) \n[“Random Invertible Mapping Statistics”](http://www.pcg-random.org/posts/random-invertible-mapping-statistics.html)\n\n \n State\n-----\n\n \n\n| | |\n| --- | --- |\n| [`state`](generated/numpy.random.sfc64.state#numpy.random.SFC64.state \"numpy.random.SFC64.state\") | Get or set the PRNG state |\n\n Extending\n---------\n\n \n\n| | |\n| --- | --- |\n| [`cffi`](generated/numpy.random.sfc64.cffi#numpy.random.SFC64.cffi \"numpy.random.SFC64.cffi\") | CFFI interface |\n| [`ctypes`](generated/numpy.random.sfc64.ctypes#numpy.random.SFC64.ctypes \"numpy.random.SFC64.ctypes\") | ctypes interface |\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/sfc64.htmlnumpy.random.PCG64.advance\n==========================\n\n method\n\n random.PCG64.advance(*delta*)\n \nAdvance the underlying RNG as-if delta draws have occurred.\n\n Parameters \n \n**delta**integer, positive\n\nNumber of draws to advance the RNG. Must be less than the size state variable in the underlying RNG.\n\n Returns \n \n**self**PCG64\n\nRNG advanced delta steps\n\n #### Notes\n\n Advancing a RNG updates the underlying RNG state as-if a given number of calls to the underlying RNG have been made. In general there is not a one-to-one relationship between the number output random values from a particular distribution and the number of draws from the core RNG. This occurs for two reasons:\n\n * The random values are simulated using a rejection-based method and so, on average, more than one value from the underlying RNG is required to generate an single draw.\n* The number of bits required to generate a simulated value differs from the number of bits generated by the underlying RNG. For example, two 16-bit integer values can be simulated from a single draw of a 32-bit RNG.\n\n Advancing the RNG state resets any pre-computed random numbers. This is required to ensure exact reproducibility.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64.advance.htmlnumpy.random.MT19937.jumped\n===========================\n\n method\n\n random.MT19937.jumped(*jumps=1*)\n \nReturns a new bit generator with the state jumped\n\n The state of the returned bit generator is jumped as-if 2**(128 * jumps) random numbers have been generated.\n\n Parameters \n \n**jumps**integer, positive\n\nNumber of times to jump the state of the bit generator returned\n\n Returns \n \n**bit_generator**MT19937\n\nNew instance of generator jumped iter times\n\n #### Notes\n\n The jump step is computed using a modified version of Matsumoto’s implementation of Horner’s method. The step polynomial is precomputed to perform 2**128 steps. The jumped state has been verified to match the state produced using Matsumoto’s original code.\n\n #### References\n\n 1 \nMatsumoto, M, Generating multiple disjoint streams of pseudorandom number sequences. Accessed on: May 6, 2020. <http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/JUMP/ 2 \n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>, “Efficient Jump Ahead for F2-Linear Random Number Generators”, INFORMS JOURNAL ON COMPUTING, Vol. 20, No. 3, Summer 2008, pp. 385-390.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.MT19937.jumped.htmlnumpy.random.PCG64.jumped\n=========================\n\n method\n\n random.PCG64.jumped(*jumps=1*)\n \nReturns a new bit generator with the state jumped.\n\n Jumps the state as-if jumps * 210306068529402873165736369884012333109 random numbers have been generated.\n\n Parameters \n \n**jumps**integer, positive\n\nNumber of times to jump the state of the bit generator returned\n\n Returns \n \n**bit_generator**PCG64\n\nNew instance of generator jumped iter times\n\n #### Notes\n\n The step size is phi-1 when multiplied by 2**128 where phi is the golden ratio.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64.jumped.htmlExtending via Numba\n===================\n\n \n```\nimport numpy as np\nimport numba as nb\n\nfrom numpy.random import PCG64\nfrom timeit import timeit\n\nbit_gen = PCG64()\nnext_d = bit_gen.cffi.next_double\nstate_addr = bit_gen.cffi.state_address\n\ndef normals(n, state):\n out = np.empty(n)\n for i in range((n + 1) // 2):\n x1 = 2.0 * next_d(state) - 1.0\n x2 = 2.0 * next_d(state) - 1.0\n r2 = x1 * x1 + x2 * x2\n while r2 >= 1.0 or r2 == 0.0:\n x1 = 2.0 * next_d(state) - 1.0\n x2 = 2.0 * next_d(state) - 1.0\n r2 = x1 * x1 + x2 * x2\n f = np.sqrt(-2.0 * np.log(r2) / r2)\n out[2 * i] = f * x1\n if 2 * i + 1 < n:\n out[2 * i + 1] = f * x2\n return out\n\n# Compile using Numba\nnormalsj = nb.jit(normals, nopython=True)\n# Must use state address not state with numba\nn = 10000\n\ndef numbacall():\n return normalsj(n, state_addr)\n\nrg = np.random.Generator(PCG64())\n\ndef numpycall():\n return rg.normal(size=n)\n\n# Check that the functions work\nr1 = numbacall()\nr2 = numpycall()\nassert r1.shape == (n,)\nassert r1.shape == r2.shape\n\nt1 = timeit(numbacall, number=1000)\nprint(f'{t1:.2f} secs for {n} PCG64 (Numba/PCG64) gaussian randoms')\nt2 = timeit(numpycall, number=1000)\nprint(f'{t2:.2f} secs for {n} PCG64 (NumPy/PCG64) gaussian randoms')\n\n# example 2\n\nnext_u32 = bit_gen.ctypes.next_uint32\nctypes_state = bit_gen.ctypes.state\n\n@nb.jit(nopython=True)\ndef bounded_uint(lb, ub, state):\n mask = delta = ub - lb\n mask |= mask >> 1\n mask |= mask >> 2\n mask |= mask >> 4\n mask |= mask >> 8\n mask |= mask >> 16\n\n val = next_u32(state) & mask\n while val > delta:\n val = next_u32(state) & mask\n\n return lb + val\n\nprint(bounded_uint(323, 2394691, ctypes_state.value))\n\n@nb.jit(nopython=True)\ndef bounded_uints(lb, ub, n, state):\n out = np.empty(n, dtype=np.uint32)\n for i in range(n):\n out[i] = bounded_uint(lb, ub, state)\n\nbounded_uints(323, 2394691, 10000000, ctypes_state.value)\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/numba.htmlExtending via Numba and CFFI\n============================\n\n \n```\nr\"\"\"\nBuilding the required library in this example requires a source distribution\nof NumPy or clone of the NumPy git repository since distributions.c is not\nincluded in binary distributions.\n\nOn *nix, execute in numpy/random/src/distributions\n\nexport ${PYTHON_VERSION}=3.8 # Python version\nexport PYTHON_INCLUDE=#path to Python's include folder, usually \\\n ${PYTHON_HOME}/include/python${PYTHON_VERSION}m\nexport NUMPY_INCLUDE=#path to numpy's include folder, usually \\\n ${PYTHON_HOME}/lib/python${PYTHON_VERSION}/site-packages/numpy/core/include\ngcc -shared -o libdistributions.so -fPIC distributions.c \\\n -I${NUMPY_INCLUDE} -I${PYTHON_INCLUDE}\nmv libdistributions.so ../../_examples/numba/\n\nOn Windows\n\nrem PYTHON_HOME and PYTHON_VERSION are setup dependent, this is an example\nset PYTHON_HOME=c:\\Anaconda\nset PYTHON_VERSION=38\ncl.exe /LD .\\distributions.c -DDLL_EXPORT \\\n -I%PYTHON_HOME%\\lib\\site-packages\\numpy\\core\\include \\\n -I%PYTHON_HOME%\\include %PYTHON_HOME%\\libs\\python%PYTHON_VERSION%.lib\nmove distributions.dll ../../_examples/numba/\n\"\"\"\nimport os\n\nimport numba as nb\nimport numpy as np\nfrom cffi import FFI\n\nfrom numpy.random import PCG64\n\nffi = FFI()\nif os.path.exists('./distributions.dll'):\n lib = ffi.dlopen('./distributions.dll')\nelif os.path.exists('./libdistributions.so'):\n lib = ffi.dlopen('./libdistributions.so')\nelse:\n raise RuntimeError('Required DLL/so file was not found.')\n\nffi.cdef(\"\"\"\ndouble random_standard_normal(void *bitgen_state);\n\"\"\")\nx = PCG64()\nxffi = x.cffi\nbit_generator = xffi.bit_generator\n\nrandom_standard_normal = lib.random_standard_normal\n\ndef normals(n, bit_generator):\n out = np.empty(n)\n for i in range(n):\n out[i] = random_standard_normal(bit_generator)\n return out\n\nnormalsj = nb.jit(normals, nopython=True)\n\n# Numba requires a memory address for void *\n# Can also get address from x.ctypes.bit_generator.value\nbit_generator_address = int(ffi.cast('uintptr_t', bit_generator))\n\nnorm = normalsj(1000, bit_generator_address)\nprint(norm[:12])\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/numba_cffi.htmlExtending numpy.random via Cython\n=================================\n\n * <setup.py>\n* <extending.pyx>\n* <extending_distributions.pyx © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/cython/index.htmlnumpy.random.BitGenerator.cffi\n==============================\n\n attribute\n\n random.BitGenerator.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.BitGenerator.cffi.htmlsetup.py\n========\n\n \n```\n#!/usr/bin/env python3\n\"\"\"\nBuild the Cython demonstrations of low-level access to NumPy random\n\nUsage: python setup.py build_ext -i\n\"\"\"\nimport setuptools # triggers monkeypatching distutils\nfrom distutils.core import setup\nfrom os.path import dirname, join, abspath\n\nimport numpy as np\nfrom Cython.Build import cythonize\nfrom numpy.distutils.misc_util import get_info\nfrom setuptools.extension import Extension\n\npath = dirname(__file__)\nsrc_dir = join(dirname(path), '..', 'src')\ndefs = [('NPY_NO_DEPRECATED_API', 0)]\ninc_path = np.get_include()\nlib_path = [abspath(join(np.get_include(), '..', '..', 'random', 'lib'))]\nlib_path += get_info('npymath')['library_dirs']\n\nextending = Extension(\"extending\",\n sources=[join('.', 'extending.pyx')],\n include_dirs=[\n np.get_include(),\n join(path, '..', '..')\n ],\n define_macros=defs,\n )\ndistributions = Extension(\"extending_distributions\",\n sources=[join('.', 'extending_distributions.pyx')],\n include_dirs=[inc_path],\n library_dirs=lib_path,\n libraries=['npyrandom', 'npymath'],\n define_macros=defs,\n )\n\nextensions = [extending, distributions]\n\nsetup(\n ext_modules=cythonize(extensions)\n)\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/cython/setup.py.htmlextending.pyx\n=============\n\n \n```\n#!/usr/bin/env python3\n#cython: language_level=3\n\nfrom libc.stdint cimport uint32_t\nfrom cpython.pycapsule cimport PyCapsule_IsValid, PyCapsule_GetPointer\n\nimport numpy as np\ncimport numpy as np\ncimport cython\n\nfrom numpy.random cimport bitgen_t\nfrom numpy.random import PCG64\n\nnp.import_array()\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef uniform_mean(Py_ssize_t n):\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef double[::1] random_values\n cdef np.ndarray randoms\n\n x = PCG64()\n capsule = x.capsule\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n random_values = np.empty(n)\n # Best practice is to acquire the lock whenever generating random values.\n # This prevents other threads from modifying the state. Acquiring the lock\n # is only necessary if the GIL is also released, as in this example.\n with x.lock, nogil:\n for i in range(n):\n random_values[i] = rng.next_double(rng.state)\n randoms = np.asarray(random_values)\n return randoms.mean()\n\n# This function is declared nogil so it can be used without the GIL below\ncdef uint32_t bounded_uint(uint32_t lb, uint32_t ub, bitgen_t *rng) nogil:\n cdef uint32_t mask, delta, val\n mask = delta = ub - lb\n mask |= mask >> 1\n mask |= mask >> 2\n mask |= mask >> 4\n mask |= mask >> 8\n mask |= mask >> 16\n\n val = rng.next_uint32(rng.state) & mask\n while val > delta:\n val = rng.next_uint32(rng.state) & mask\n\n return lb + val\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef bounded_uints(uint32_t lb, uint32_t ub, Py_ssize_t n):\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef uint32_t[::1] out\n cdef const char *capsule_name = \"BitGenerator\"\n\n x = PCG64()\n out = np.empty(n, dtype=np.uint32)\n capsule = x.capsule\n\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n rng = <bitgen_t *>PyCapsule_GetPointer(capsule, capsule_name)\n\n with x.lock, nogil:\n for i in range(n):\n out[i] = bounded_uint(lb, ub, rng)\n return np.asarray(out)\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/cython/extending.pyx.htmlextending_distributions.pyx\n============================\n\n \n```\n#!/usr/bin/env python3\n#cython: language_level=3\n\"\"\"\nThis file shows how the to use a BitGenerator to create a distribution.\n\"\"\"\nimport numpy as np\ncimport numpy as np\ncimport cython\nfrom cpython.pycapsule cimport PyCapsule_IsValid, PyCapsule_GetPointer\nfrom libc.stdint cimport uint16_t, uint64_t\nfrom numpy.random cimport bitgen_t\nfrom numpy.random import PCG64\nfrom numpy.random.c_distributions cimport (\n random_standard_uniform_fill, random_standard_uniform_fill_f)\n\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef uniforms(Py_ssize_t n):\n \"\"\"\n Create an array of `n` uniformly distributed doubles.\n A 'real' distribution would want to process the values into\n some non-uniform distribution\n \"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef double[::1] random_values\n\n x = PCG64()\n capsule = x.capsule\n # Optional check that the capsule if from a BitGenerator\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n # Cast the pointer\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n random_values = np.empty(n, dtype='float64')\n with x.lock, nogil:\n for i in range(n):\n # Call the function\n random_values[i] = rng.next_double(rng.state)\n randoms = np.asarray(random_values)\n\n return randoms\n\n# cython example 2\n@cython.boundscheck(False)\n@cython.wraparound(False)\ndef uint10_uniforms(Py_ssize_t n):\n \"\"\"Uniform 10 bit integers stored as 16-bit unsigned integers\"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef uint16_t[::1] random_values\n cdef int bits_remaining\n cdef int width = 10\n cdef uint64_t buff, mask = 0x3FF\n\n x = PCG64()\n capsule = x.capsule\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n random_values = np.empty(n, dtype='uint16')\n # Best practice is to release GIL and acquire the lock\n bits_remaining = 0\n with x.lock, nogil:\n for i in range(n):\n if bits_remaining < width:\n buff = rng.next_uint64(rng.state)\n random_values[i] = buff & mask\n buff >>= width\n\n randoms = np.asarray(random_values)\n return randoms\n\n# cython example 3\ndef uniforms_ex(bit_generator, Py_ssize_t n, dtype=np.float64):\n \"\"\"\n Create an array of `n` uniformly distributed doubles via a \"fill\" function.\n\n A 'real' distribution would want to process the values into\n some non-uniform distribution\n\n Parameters\n ----------\n bit_generator: BitGenerator instance\n n: int\n Output vector length\n dtype: {str, dtype}, optional\n Desired dtype, either 'd' (or 'float64') or 'f' (or 'float32'). The\n default dtype value is 'd'\n \"\"\"\n cdef Py_ssize_t i\n cdef bitgen_t *rng\n cdef const char *capsule_name = \"BitGenerator\"\n cdef np.ndarray randoms\n\n capsule = bit_generator.capsule\n # Optional check that the capsule if from a BitGenerator\n if not PyCapsule_IsValid(capsule, capsule_name):\n raise ValueError(\"Invalid pointer to anon_func_state\")\n # Cast the pointer\n rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)\n\n _dtype = np.dtype(dtype)\n randoms = np.empty(n, dtype=_dtype)\n if _dtype == np.float32:\n with bit_generator.lock:\n random_standard_uniform_fill_f(rng, n, <float*>np.PyArray_DATA(randoms))\n elif _dtype == np.float64:\n with bit_generator.lock:\n random_standard_uniform_fill(rng, n, <double*>np.PyArray_DATA(randoms))\n else:\n raise TypeError('Unsupported dtype %r for random' % _dtype)\n return randoms\n\n```\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/examples/cython/extending_distributions.pyx.htmlnumpy.random.BitGenerator.random_raw\n=====================================\n\n method\n\n random.BitGenerator.random_raw(*self*, *size=None*)\n \nReturn randoms as generated by the underlying BitGenerator\n\n Parameters \n \n**size**int or tuple of ints, optional\n\nOutput shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn. Default is None, in which case a single value is returned.\n\n \n**output**bool, optional\n\nOutput values. Used for performance testing since the generated values are not returned.\n\n Returns \n \n**out**uint or ndarray\n\nDrawn samples.\n\n #### Notes\n\n This method directly exposes the raw underlying pseudo-random number generator. All values are returned as unsigned 64-bit values irrespective of the number of bits produced by the PRNG.\n\n See the class docstring for the number of bits returned.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.BitGenerator.random_raw.htmlnumpy.random.PCG64.state\n========================\n\n attribute\n\n random.PCG64.state\n \nGet or set the PRNG state\n\n Returns \n \n**state**dict\n\nDictionary containing the information required to describe the state of the PRNG\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64.state.htmlnumpy.random.MT19937.ctypes\n===========================\n\n attribute\n\n random.MT19937.ctypes\n \nctypes interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing ctypes wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.MT19937.ctypes.htmlnumpy.random.MT19937.state\n==========================\n\n attribute\n\n random.MT19937.state\n \nGet or set the PRNG state\n\n Returns \n \n**state**dict\n\nDictionary containing the information required to describe the state of the PRNG\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.MT19937.state.htmlnumpy.random.MT19937.cffi\n=========================\n\n attribute\n\n random.MT19937.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.MT19937.cffi.htmlnumpy.random.SeedSequence.spawn_key\n====================================\n\n attribute\n\n random.SeedSequence.spawn_key\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SeedSequence.spawn_key.htmlnumpy.random.SeedSequence.generate_state\n=========================================\n\n method\n\n random.SeedSequence.generate_state(*n_words*, *dtype=np.uint32*)\n \nReturn the requested number of words for PRNG seeding.\n\n A BitGenerator should call this method in its constructor with an appropriate `n_words` parameter to properly seed itself.\n\n Parameters \n \n**n_words**int\n\n**dtype**np.uint32 or np.uint64, optional\n\nThe size of each word. This should only be either [`uint32`](../../../arrays.scalars#numpy.uint32 \"numpy.uint32\") or [`uint64`](../../../arrays.scalars#numpy.uint64 \"numpy.uint64\"). Strings (`‘uint32’`, `‘uint64’`) are fine. Note that requesting [`uint64`](../../../arrays.scalars#numpy.uint64 \"numpy.uint64\") will draw twice as many bits as [`uint32`](../../../arrays.scalars#numpy.uint32 \"numpy.uint32\") for the same `n_words`. This is a convenience for `BitGenerator`s that express their states as `uint64` arrays.\n\n Returns \n \n**state**uint32 or uint64 array, shape=(n_words,)\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SeedSequence.generate_state.htmlnumpy.random.SeedSequence.entropy\n=================================\n\n attribute\n\n random.SeedSequence.entropy\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SeedSequence.entropy.htmlnumpy.random.SFC64.ctypes\n=========================\n\n attribute\n\n random.SFC64.ctypes\n \nctypes interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing ctypes wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SFC64.ctypes.htmlnumpy.testing.suppress_warnings.__call__\n=============================================\n\n method\n\n testing.suppress_warnings.__call__(*func*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L2292-L2302)\n \nFunction decorator to apply certain suppressions to a whole function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.suppress_warnings.__call__.htmlnumpy.testing.suppress_warnings.filter\n=======================================\n\n method\n\n testing.suppress_warnings.filter(*category=<class 'Warning'>*, *message=''*, *module=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L2148-L2169)\n \nAdd a new suppressing filter or apply it if the state is entered.\n\n Parameters \n \n**category**class, optional\n\nWarning class to filter\n\n \n**message**string, optional\n\nRegular expression matching the warning message.\n\n \n**module**module, optional\n\nModule to filter for. Note that the module (and its file) must match exactly and cannot be a submodule. This may make it unreliable for external modules.\n\n #### Notes\n\n When added within a context, filters are only added inside the context and will be forgotten when the context is exited.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.suppress_warnings.filter.htmlnumpy.testing.suppress_warnings.record\n=======================================\n\n method\n\n testing.suppress_warnings.record(*category=<class 'Warning'>*, *message=''*, *module=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/testing/_private/utils.py#L2171-L2199)\n \nAppend a new recording filter or apply it if the state is entered.\n\n All warnings matching will be appended to the `log` attribute.\n\n Parameters \n \n**category**class, optional\n\nWarning class to filter\n\n \n**message**string, optional\n\nRegular expression matching the warning message.\n\n \n**module**module, optional\n\nModule to filter for. Note that the module (and its file) must match exactly and cannot be a submodule. This may make it unreliable for external modules.\n\n Returns \n \n**log**list\n\nA list which will be filled with all matched warnings.\n\n #### Notes\n\n When added within a context, filters are only added inside the context and will be forgotten when the context is exited.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.testing.suppress_warnings.record.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.cache_flush\n========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.cache_flush()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L850-L876)\n \nForce update the cache.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.cache_flush.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.cc_normalize_flags\n================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.cc_normalize_flags(*flags*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1099-L1128)\n \nRemove the conflicts that caused due gathering implied features flags.\n\n Parameters \n **‘flags’ list, compiler flags**\n\nflags should be sorted from the lowest to the highest interest.\n\n Returns \n list, filtered from any conflicts.\n #### Examples\n\n \n```\n>>> self.cc_normalize_flags(['-march=armv8.2-a+fp16', '-march=armv8.2-a+dotprod'])\n['armv8.2-a+fp16+dotprod']\n\n```\n \n```\n>>> self.cc_normalize_flags(\n ['-msse', '-msse2', '-msse3', '-mssse3', '-msse4.1', '-msse4.2', '-mavx', '-march=core-avx2']\n)\n['-march=core-avx2']\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.cc_normalize_flags.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.conf_features_partial\n===================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.conf_features_partial()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L329-L562)\n \nReturn a dictionary of supported CPU features by the platform, and accumulate the rest of undefined options in [`conf_features`](numpy.distutils.ccompiler_opt.ccompileropt.conf_features#numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features \"numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features\"), the returned dict has same rules and notes in class attribute [`conf_features`](numpy.distutils.ccompiler_opt.ccompileropt.conf_features#numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features \"numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features\"), also its override any options that been set in ‘conf_features’.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features_partial.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_flags\n================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_flags()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2238-L2242)\n \nReturns a list of final CPU baseline compiler flags\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_flags.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_names\n================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_names()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2244-L2248)\n \nreturn a list of final CPU baseline feature names\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_baseline_names.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.cpu_dispatch_names\n================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.cpu_dispatch_names()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2250-L2254)\n \nreturn a list of final CPU dispatch feature names\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.cpu_dispatch_names.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_compile\n=========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.dist_compile(*sources*, *flags*, *ccompiler=None*, ***kwargs*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L599-L607)\n \nWrap CCompiler.compile()\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_compile.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_error\n=======================================================\n\n method\n\n *static*distutils.ccompiler_opt.CCompilerOpt.dist_error(**args*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L672-L676)\n \nRaise a compiler error\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_error.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_fatal\n=======================================================\n\n method\n\n *static*distutils.ccompiler_opt.CCompilerOpt.dist_fatal(**args*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L678-L682)\n \nRaise a distutils error\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_fatal.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_info\n======================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.dist_info()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L635-L670)\n \nReturn a tuple containing info about (platform, compiler, extra_args), required by the abstract class ‘_CCompiler’ for discovering the platform environment. This is also used as a cache factor in order to detect any changes happening from outside.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_info.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_load_module\n==============================================================\n\n method\n\n *static*distutils.ccompiler_opt.CCompilerOpt.dist_load_module(*name*, *path*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L694-L702)\n \nLoad a module from file, required by the abstract class ‘_Cache’.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_load_module.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_log\n=====================================================\n\n method\n\n *static*distutils.ccompiler_opt.CCompilerOpt.dist_log(**args*, *stderr=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L684-L692)\n \nPrint a console message\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_log.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.dist_test\n======================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.dist_test(*source*, *flags*, *macros=[]*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L609-L633)\n \nReturn True if ‘CCompiler.compile()’ able to compile a source file with certain flags.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.dist_test.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_ahead\n==========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_ahead(*names*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1392-L1428)\n \nReturn list of features in ‘names’ after remove any implied features and keep the origins.\n\n Parameters \n **‘names’: sequence**\n\nsequence of CPU feature names in uppercase.\n\n Returns \n list of CPU features sorted as-is ‘names’\n #### Examples\n\n \n```\n>>> self.feature_ahead([\"SSE2\", \"SSE3\", \"SSE41\"])\n[\"SSE41\"]\n# assume AVX2 and FMA3 implies each other and AVX2\n# is the highest interest\n>>> self.feature_ahead([\"SSE2\", \"SSE3\", \"SSE41\", \"AVX2\", \"FMA3\"])\n[\"AVX2\"]\n# assume AVX2 and FMA3 don't implies each other\n>>> self.feature_ahead([\"SSE2\", \"SSE3\", \"SSE41\", \"AVX2\", \"FMA3\"])\n[\"AVX2\", \"FMA3\"]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_ahead.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_c_preprocessor\n====================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_c_preprocessor(*feature_name*, *tabs=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1649-L1696)\n \nGenerate C preprocessor definitions and include headers of a CPU feature.\n\n Parameters \n **‘feature_name’: str**\n\nCPU feature name in uppercase.\n\n **‘tabs’: int**\n\nif > 0, align the generated strings to the right depend on number of tabs.\n\n Returns \n str, generated C preprocessor\n #### Examples\n\n \n```\n>>> self.feature_c_preprocessor(\"SSE3\")\n/** SSE3 **/\n#define NPY_HAVE_SSE3 1\n#include <pmmintrin.h```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_c_preprocessor.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_detect\n===========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_detect(*names*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1498-L1508)\n \nReturn a list of CPU features that required to be detected sorted from the lowest to highest interest.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_detect.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_get_til\n=============================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_get_til(*names*, *keyisfalse*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1471-L1496)\n \nsame as `feature_implies_c()` but stop collecting implied features when feature’s option that provided through parameter ‘keyisfalse’ is False, also sorting the returned features.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_get_til.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies\n============================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_implies(*names*, *keep_origins=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1335-L1382)\n \nReturn a set of CPU features that implied by ‘names’\n\n Parameters \n \n**names**str or sequence of str\n\nCPU feature name(s) in uppercase.\n\n \n**keep_origins**bool\n\nif False(default) then the returned set will not contain any features from ‘names’. This case happens only when two features imply each other.\n\n #### Examples\n\n \n```\n>>> self.feature_implies(\"SSE3\")\n{'SSE', 'SSE2'}\n>>> self.feature_implies(\"SSE2\")\n{'SSE'}\n>>> self.feature_implies(\"SSE2\", keep_origins=True)\n# 'SSE2' found here since 'SSE' and 'SSE2' imply each other\n{'SSE', 'SSE2'}\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies_c\n===============================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_implies_c(*names*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1384-L1390)\n \nsame as feature_implies() but combining ‘names’\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_implies_c.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_is_exist\n==============================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_is_exist(*name*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1296-L1307)\n \nReturns True if a certain feature is exist and covered within `_Config.conf_features`.\n\n Parameters \n **‘name’: str**\n\nfeature name in uppercase.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_is_exist.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_names\n==========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_names(*names=None*, *force_flags=None*, *macros=[]*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1261-L1294)\n \nReturns a set of CPU feature names that supported by platform and the **C** compiler.\n\n Parameters \n \n**names**sequence or None, optional\n\nSpecify certain CPU features to test it against the **C** compiler. if None(default), it will test all current supported features. **Note**: feature names must be in upper-case.\n\n \n**force_flags**list or None, optional\n\nIf None(default), default compiler flags for every CPU feature will be used during the test.\n\n \n**macros**list of tuples, optional\n\nA list of C macro definitions.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_names.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_sorted\n===========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_sorted(*names*, *reverse=False*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1309-L1333)\n \nSort a list of CPU features ordered by the lowest interest.\n\n Parameters \n **‘names’: sequence**\n\nsequence of supported feature names in uppercase.\n\n **‘reverse’: bool, optional**\n\nIf true, the sorted features is reversed. (highest interest)\n\n Returns \n list, sorted CPU features\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_sorted.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.feature_untied\n===========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.feature_untied(*names*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1430-L1469)\n \nsame as ‘feature_ahead()’ but if both features implied each other and keep the highest interest.\n\n Parameters \n **‘names’: sequence**\n\nsequence of CPU feature names in uppercase.\n\n Returns \n list of CPU features sorted as-is ‘names’\n #### Examples\n\n \n```\n>>> self.feature_untied([\"SSE2\", \"SSE3\", \"SSE41\"])\n[\"SSE2\", \"SSE3\", \"SSE41\"]\n# assume AVX2 and FMA3 implies each other\n>>> self.feature_untied([\"SSE2\", \"SSE3\", \"SSE41\", \"FMA3\", \"AVX2\"])\n[\"SSE2\", \"SSE3\", \"SSE41\", \"AVX2\"]\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.feature_untied.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.generate_dispatch_header\n======================================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.generate_dispatch_header(*header_path*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2343-L2424)\n \nGenerate the dispatch header which contains the #definitions and headers for platform-specific instruction-sets for the enabled CPU baseline and dispatch-able features.\n\n Its highly recommended to take a look at the generated header also the generated source files via `try_dispatch()` in order to get the full picture.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.generate_dispatch_header.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.is_cached\n======================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.is_cached()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L2232-L2236)\n \nReturns True if the class loaded from the cache file\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.is_cached.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.me\n==============================================\n\n method\n\n *static*distutils.ccompiler_opt.CCompilerOpt.me(*cb*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L888-L904)\n \nA static method that can be treated as a decorator to dynamically cache certain methods.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.me.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets\n==========================================================\n\n method\n\n distutils.ccompiler_opt.CCompilerOpt.parse_targets(*source*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/distutils/ccompiler_opt.py#L1827-L1879)\n \nFetch and parse configuration statements that required for defining the targeted CPU features, statements should be declared in the top of source in between **C** comment and start with a special mark **@targets**.\n\n Configuration statements are sort of keywords representing CPU features names, group of statements and policies, combined together to determine the required optimization.\n\n Parameters \n \n**source**str\n\nthe path of **C** source file.\n\n Returns \n* bool, True if group has the ‘baseline’ option\n* list, list of CPU features\n* list, list of extra compiler flags\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.parse_targets.htmlnumpy.distutils.ccompiler_opt.CCompilerOpt.conf_features\n==========================================================\n\n attribute\n\n distutils.ccompiler_opt.CCompilerOpt.conf_features*={'ASIMD': {'implies': 'NEON_FP16 NEON_VFPV4', 'implies_detect': False, 'interest': 4}, 'ASIMDDP': {'implies': 'ASIMD', 'interest': 6}, 'ASIMDFHM': {'implies': 'ASIMDHP', 'interest': 7}, 'ASIMDHP': {'implies': 'ASIMD', 'interest': 5}, 'AVX': {'headers': 'immintrin.h', 'implies': 'SSE42', 'implies_detect': False, 'interest': 8}, 'AVX2': {'implies': 'F16C', 'interest': 13}, 'AVX512CD': {'implies': 'AVX512F', 'interest': 21}, 'AVX512F': {'extra_checks': 'AVX512F_REDUCE', 'implies': 'FMA3 AVX2', 'implies_detect': False, 'interest': 20}, 'AVX512_CLX': {'detect': 'AVX512_CLX', 'group': 'AVX512VNNI', 'implies': 'AVX512_SKX', 'interest': 43}, 'AVX512_CNL': {'detect': 'AVX512_CNL', 'group': 'AVX512IFMA AVX512VBMI', 'implies': 'AVX512_SKX', 'implies_detect': False, 'interest': 44}, 'AVX512_ICL': {'detect': 'AVX512_ICL', 'group': 'AVX512VBMI2 AVX512BITALG AVX512VPOPCNTDQ', 'implies': 'AVX512_CLX AVX512_CNL', 'implies_detect': False, 'interest': 45}, 'AVX512_KNL': {'detect': 'AVX512_KNL', 'group': 'AVX512ER AVX512PF', 'implies': 'AVX512CD', 'implies_detect': False, 'interest': 40}, 'AVX512_KNM': {'detect': 'AVX512_KNM', 'group': 'AVX5124FMAPS AVX5124VNNIW AVX512VPOPCNTDQ', 'implies': 'AVX512_KNL', 'implies_detect': False, 'interest': 41}, 'AVX512_SKX': {'detect': 'AVX512_SKX', 'extra_checks': 'AVX512BW_MASK AVX512DQ_MASK', 'group': 'AVX512VL AVX512BW AVX512DQ', 'implies': 'AVX512CD', 'implies_detect': False, 'interest': 42}, 'F16C': {'implies': 'AVX', 'interest': 11}, 'FMA3': {'implies': 'F16C', 'interest': 12}, 'FMA4': {'headers': 'x86intrin.h', 'implies': 'AVX', 'interest': 10}, 'NEON': {'headers': 'arm_neon.h', 'interest': 1}, 'NEON_FP16': {'implies': 'NEON', 'interest': 2}, 'NEON_VFPV4': {'implies': 'NEON_FP16', 'interest': 3}, 'POPCNT': {'headers': 'popcntintrin.h', 'implies': 'SSE41', 'interest': 6}, 'SSE': {'headers': 'xmmintrin.h', 'implies': 'SSE2', 'interest': 1}, 'SSE2': {'headers': 'emmintrin.h', 'implies': 'SSE', 'interest': 2}, 'SSE3': {'headers': 'pmmintrin.h', 'implies': 'SSE2', 'interest': 3}, 'SSE41': {'headers': 'smmintrin.h', 'implies': 'SSSE3', 'interest': 5}, 'SSE42': {'implies': 'POPCNT', 'interest': 7}, 'SSSE3': {'headers': 'tmmintrin.h', 'implies': 'SSE3', 'interest': 4}, 'VSX': {'extra_checks': 'VSX_ASM', 'headers': 'altivec.h', 'interest': 1}, 'VSX2': {'implies': 'VSX', 'implies_detect': False, 'interest': 2}, 'VSX3': {'implies': 'VSX2', 'implies_detect': False, 'interest': 3}, 'VSX4': {'extra_checks': 'VSX4_MMA', 'implies': 'VSX3', 'implies_detect': False, 'interest': 4}, 'VX': {'headers': 'vecintrin.h', 'interest': 1}, 'VXE': {'implies': 'VX', 'implies_detect': False, 'interest': 2}, 'VXE2': {'implies': 'VXE', 'implies_detect': False, 'interest': 3}, 'XOP': {'headers': 'x86intrin.h', 'implies': 'AVX', 'interest': 9}}*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.distutils.ccompiler_opt.CCompilerOpt.conf_features.htmlnumpy.polynomial.chebyshev.Chebyshev.domain\n===========================================\n\n attribute\n\n polynomial.chebyshev.Chebyshev.domain*=array([-1, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.domain.htmlnumpy.polynomial.chebyshev.Chebyshev.__call__\n=================================================\n\n method\n\n polynomial.chebyshev.Chebyshev.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.__call__.htmlnumpy.polynomial.chebyshev.Chebyshev.basis\n==========================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.basis.htmlnumpy.polynomial.chebyshev.Chebyshev.cast\n=========================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.chebyshev.chebyshev.convert#numpy.polynomial.chebyshev.Chebyshev.convert \"numpy.polynomial.chebyshev.Chebyshev.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.cast.htmlnumpy.polynomial.chebyshev.Chebyshev.convert\n============================================\n\n method\n\n polynomial.chebyshev.Chebyshev.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.convert.htmlnumpy.polynomial.chebyshev.Chebyshev.copy\n=========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.copy.htmlnumpy.polynomial.chebyshev.Chebyshev.cutdeg\n===========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.cutdeg.htmlnumpy.polynomial.chebyshev.Chebyshev.degree\n===========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.degree.htmlnumpy.polynomial.chebyshev.Chebyshev.deriv\n==========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.deriv.htmlnumpy.polynomial.chebyshev.Chebyshev.fromroots\n==============================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.fromroots.htmlnumpy.polynomial.chebyshev.Chebyshev.has_samecoef\n==================================================\n\n method\n\n polynomial.chebyshev.Chebyshev.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.has_samecoef.htmlnumpy.polynomial.chebyshev.Chebyshev.has_samedomain\n====================================================\n\n method\n\n polynomial.chebyshev.Chebyshev.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.has_samedomain.htmlnumpy.polynomial.chebyshev.Chebyshev.has_sametype\n==================================================\n\n method\n\n polynomial.chebyshev.Chebyshev.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.has_sametype.htmlnumpy.polynomial.chebyshev.Chebyshev.has_samewindow\n====================================================\n\n method\n\n polynomial.chebyshev.Chebyshev.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.has_samewindow.htmlnumpy.polynomial.chebyshev.Chebyshev.identity\n=============================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.identity.htmlnumpy.polynomial.chebyshev.Chebyshev.integ\n==========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.integ.htmlnumpy.polynomial.chebyshev.Chebyshev.interpolate\n================================================\n\n method\n\n *classmethod*polynomial.chebyshev.Chebyshev.interpolate(*func*, *deg*, *domain=None*, *args=()*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/chebyshev.py#L2030-L2070)\n \nInterpolate a function at the Chebyshev points of the first kind.\n\n Returns the series that interpolates `func` at the Chebyshev points of the first kind scaled and shifted to the [`domain`](numpy.polynomial.chebyshev.chebyshev.domain#numpy.polynomial.chebyshev.Chebyshev.domain \"numpy.polynomial.chebyshev.Chebyshev.domain\"). The resulting series tends to a minmax approximation of `func` when the function is continuous in the domain.\n\n New in version 1.14.0.\n\n Parameters \n \n**func**function\n\nThe function to be interpolated. It must be a function of a single variable of the form `f(x, a, b, c...)`, where `a, b, c...` are extra arguments passed in the `args` parameter.\n\n \n**deg**int\n\nDegree of the interpolating polynomial.\n\n \n**domain**{None, [beg, end]}, optional\n\nDomain over which `func` is interpolated. The default is None, in which case the domain is [-1, 1].\n\n \n**args**tuple, optional\n\nExtra arguments to be used in the function call. Default is no extra arguments.\n\n Returns \n \n**polynomial**Chebyshev instance\n\nInterpolating Chebyshev instance.\n\n #### Notes\n\n See `numpy.polynomial.chebfromfunction` for more details.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.interpolate.htmlnumpy.polynomial.chebyshev.Chebyshev.linspace\n=============================================\n\n method\n\n polynomial.chebyshev.Chebyshev.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.linspace.htmlnumpy.polynomial.chebyshev.Chebyshev.mapparms\n=============================================\n\n method\n\n polynomial.chebyshev.Chebyshev.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.mapparms.htmlnumpy.polynomial.chebyshev.Chebyshev.roots\n==========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.roots.htmlnumpy.polynomial.chebyshev.Chebyshev.trim\n=========================================\n\n method\n\n polynomial.chebyshev.Chebyshev.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.trim.htmlnumpy.polynomial.chebyshev.Chebyshev.truncate\n=============================================\n\n method\n\n polynomial.chebyshev.Chebyshev.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.chebyshev.Chebyshev.truncate.htmlnumpy.polynomial.hermite.Hermite.domain\n=======================================\n\n attribute\n\n polynomial.hermite.Hermite.domain*=array([-1, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.domain.htmlnumpy.polynomial.hermite.Hermite.__call__\n=============================================\n\n method\n\n polynomial.hermite.Hermite.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.__call__.htmlnumpy.polynomial.hermite.Hermite.basis\n======================================\n\n method\n\n *classmethod*polynomial.hermite.Hermite.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.basis.htmlnumpy.polynomial.hermite.Hermite.cast\n=====================================\n\n method\n\n *classmethod*polynomial.hermite.Hermite.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.hermite.hermite.convert#numpy.polynomial.hermite.Hermite.convert \"numpy.polynomial.hermite.Hermite.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.cast.htmlnumpy.polynomial.hermite.Hermite.convert\n========================================\n\n method\n\n polynomial.hermite.Hermite.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.convert.htmlnumpy.polynomial.hermite.Hermite.copy\n=====================================\n\n method\n\n polynomial.hermite.Hermite.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.copy.htmlnumpy.polynomial.hermite.Hermite.cutdeg\n=======================================\n\n method\n\n polynomial.hermite.Hermite.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.cutdeg.htmlnumpy.polynomial.hermite.Hermite.degree\n=======================================\n\n method\n\n polynomial.hermite.Hermite.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.degree.htmlnumpy.polynomial.hermite.Hermite.deriv\n======================================\n\n method\n\n polynomial.hermite.Hermite.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.deriv.htmlnumpy.polynomial.hermite.Hermite.fit\n====================================\n\n method\n\n *classmethod*polynomial.hermite.Hermite.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.fit.htmlnumpy.polynomial.hermite.Hermite.fromroots\n==========================================\n\n method\n\n *classmethod*polynomial.hermite.Hermite.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.fromroots.htmlnumpy.polynomial.hermite.Hermite.has_samecoef\n==============================================\n\n method\n\n polynomial.hermite.Hermite.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.has_samecoef.htmlnumpy.polynomial.hermite.Hermite.has_samedomain\n================================================\n\n method\n\n polynomial.hermite.Hermite.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.has_samedomain.htmlnumpy.polynomial.hermite.Hermite.has_sametype\n==============================================\n\n method\n\n polynomial.hermite.Hermite.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.has_sametype.htmlnumpy.polynomial.hermite.Hermite.has_samewindow\n================================================\n\n method\n\n polynomial.hermite.Hermite.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.has_samewindow.htmlnumpy.polynomial.hermite.Hermite.identity\n=========================================\n\n method\n\n *classmethod*polynomial.hermite.Hermite.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.identity.htmlnumpy.polynomial.hermite.Hermite.integ\n======================================\n\n method\n\n polynomial.hermite.Hermite.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.integ.htmlnumpy.polynomial.hermite.Hermite.linspace\n=========================================\n\n method\n\n polynomial.hermite.Hermite.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.linspace.htmlnumpy.polynomial.hermite.Hermite.mapparms\n=========================================\n\n method\n\n polynomial.hermite.Hermite.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.mapparms.htmlnumpy.polynomial.hermite.Hermite.roots\n======================================\n\n method\n\n polynomial.hermite.Hermite.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.roots.htmlnumpy.polynomial.hermite.Hermite.trim\n=====================================\n\n method\n\n polynomial.hermite.Hermite.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.trim.htmlnumpy.polynomial.hermite.Hermite.truncate\n=========================================\n\n method\n\n polynomial.hermite.Hermite.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite.Hermite.truncate.htmlnumpy.polynomial.hermite_e.HermiteE.domain\n===========================================\n\n attribute\n\n polynomial.hermite_e.HermiteE.domain*=array([-1, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.domain.htmlnumpy.polynomial.hermite_e.HermiteE.__call__\n=================================================\n\n method\n\n polynomial.hermite_e.HermiteE.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.__call__.htmlnumpy.polynomial.hermite_e.HermiteE.basis\n==========================================\n\n method\n\n *classmethod*polynomial.hermite_e.HermiteE.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.basis.htmlnumpy.polynomial.hermite_e.HermiteE.cast\n=========================================\n\n method\n\n *classmethod*polynomial.hermite_e.HermiteE.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.hermite_e.hermitee.convert#numpy.polynomial.hermite_e.HermiteE.convert \"numpy.polynomial.hermite_e.HermiteE.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.cast.htmlnumpy.polynomial.hermite_e.HermiteE.convert\n============================================\n\n method\n\n polynomial.hermite_e.HermiteE.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.convert.htmlnumpy.polynomial.hermite_e.HermiteE.copy\n=========================================\n\n method\n\n polynomial.hermite_e.HermiteE.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.copy.htmlnumpy.polynomial.hermite_e.HermiteE.cutdeg\n===========================================\n\n method\n\n polynomial.hermite_e.HermiteE.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.cutdeg.htmlnumpy.polynomial.hermite_e.HermiteE.degree\n===========================================\n\n method\n\n polynomial.hermite_e.HermiteE.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.degree.htmlnumpy.polynomial.hermite_e.HermiteE.deriv\n==========================================\n\n method\n\n polynomial.hermite_e.HermiteE.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.deriv.htmlnumpy.polynomial.hermite_e.HermiteE.fit\n========================================\n\n method\n\n *classmethod*polynomial.hermite_e.HermiteE.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.fit.htmlnumpy.polynomial.hermite_e.HermiteE.fromroots\n==============================================\n\n method\n\n *classmethod*polynomial.hermite_e.HermiteE.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.fromroots.htmlnumpy.polynomial.hermite_e.HermiteE.has_samecoef\n==================================================\n\n method\n\n polynomial.hermite_e.HermiteE.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.has_samecoef.htmlnumpy.polynomial.hermite_e.HermiteE.has_samedomain\n====================================================\n\n method\n\n polynomial.hermite_e.HermiteE.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.has_samedomain.htmlnumpy.polynomial.hermite_e.HermiteE.has_sametype\n==================================================\n\n method\n\n polynomial.hermite_e.HermiteE.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.has_sametype.htmlnumpy.polynomial.hermite_e.HermiteE.has_samewindow\n====================================================\n\n method\n\n polynomial.hermite_e.HermiteE.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.has_samewindow.htmlnumpy.polynomial.hermite_e.HermiteE.identity\n=============================================\n\n method\n\n *classmethod*polynomial.hermite_e.HermiteE.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.identity.htmlnumpy.polynomial.hermite_e.HermiteE.integ\n==========================================\n\n method\n\n polynomial.hermite_e.HermiteE.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.integ.htmlnumpy.polynomial.hermite_e.HermiteE.linspace\n=============================================\n\n method\n\n polynomial.hermite_e.HermiteE.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.linspace.htmlnumpy.polynomial.hermite_e.HermiteE.mapparms\n=============================================\n\n method\n\n polynomial.hermite_e.HermiteE.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.mapparms.htmlnumpy.polynomial.hermite_e.HermiteE.roots\n==========================================\n\n method\n\n polynomial.hermite_e.HermiteE.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.roots.htmlnumpy.polynomial.hermite_e.HermiteE.trim\n=========================================\n\n method\n\n polynomial.hermite_e.HermiteE.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.trim.htmlnumpy.polynomial.hermite_e.HermiteE.truncate\n=============================================\n\n method\n\n polynomial.hermite_e.HermiteE.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.hermite_e.HermiteE.truncate.htmlnumpy.polynomial.laguerre.Laguerre.domain\n=========================================\n\n attribute\n\n polynomial.laguerre.Laguerre.domain*=array([0, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.domain.htmlnumpy.polynomial.laguerre.Laguerre.__call__\n===============================================\n\n method\n\n polynomial.laguerre.Laguerre.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.__call__.htmlnumpy.polynomial.laguerre.Laguerre.basis\n========================================\n\n method\n\n *classmethod*polynomial.laguerre.Laguerre.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.basis.htmlnumpy.polynomial.laguerre.Laguerre.cast\n=======================================\n\n method\n\n *classmethod*polynomial.laguerre.Laguerre.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.laguerre.laguerre.convert#numpy.polynomial.laguerre.Laguerre.convert \"numpy.polynomial.laguerre.Laguerre.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.cast.htmlnumpy.polynomial.laguerre.Laguerre.convert\n==========================================\n\n method\n\n polynomial.laguerre.Laguerre.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.convert.htmlnumpy.polynomial.laguerre.Laguerre.copy\n=======================================\n\n method\n\n polynomial.laguerre.Laguerre.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.copy.htmlnumpy.polynomial.laguerre.Laguerre.cutdeg\n=========================================\n\n method\n\n polynomial.laguerre.Laguerre.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.cutdeg.htmlnumpy.polynomial.laguerre.Laguerre.degree\n=========================================\n\n method\n\n polynomial.laguerre.Laguerre.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.degree.htmlnumpy.polynomial.laguerre.Laguerre.deriv\n========================================\n\n method\n\n polynomial.laguerre.Laguerre.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.deriv.htmlnumpy.polynomial.laguerre.Laguerre.fit\n======================================\n\n method\n\n *classmethod*polynomial.laguerre.Laguerre.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.fit.htmlnumpy.polynomial.laguerre.Laguerre.fromroots\n============================================\n\n method\n\n *classmethod*polynomial.laguerre.Laguerre.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.fromroots.htmlnumpy.polynomial.laguerre.Laguerre.has_samecoef\n================================================\n\n method\n\n polynomial.laguerre.Laguerre.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.has_samecoef.htmlnumpy.polynomial.laguerre.Laguerre.has_samedomain\n==================================================\n\n method\n\n polynomial.laguerre.Laguerre.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.has_samedomain.htmlnumpy.polynomial.laguerre.Laguerre.has_sametype\n================================================\n\n method\n\n polynomial.laguerre.Laguerre.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.has_sametype.htmlnumpy.polynomial.laguerre.Laguerre.has_samewindow\n==================================================\n\n method\n\n polynomial.laguerre.Laguerre.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.has_samewindow.htmlnumpy.polynomial.laguerre.Laguerre.identity\n===========================================\n\n method\n\n *classmethod*polynomial.laguerre.Laguerre.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.identity.htmlnumpy.polynomial.laguerre.Laguerre.integ\n========================================\n\n method\n\n polynomial.laguerre.Laguerre.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.integ.htmlnumpy.polynomial.laguerre.Laguerre.linspace\n===========================================\n\n method\n\n polynomial.laguerre.Laguerre.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.linspace.htmlnumpy.polynomial.laguerre.Laguerre.mapparms\n===========================================\n\n method\n\n polynomial.laguerre.Laguerre.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.mapparms.htmlnumpy.polynomial.laguerre.Laguerre.roots\n========================================\n\n method\n\n polynomial.laguerre.Laguerre.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.roots.htmlnumpy.polynomial.laguerre.Laguerre.trim\n=======================================\n\n method\n\n polynomial.laguerre.Laguerre.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.trim.htmlnumpy.polynomial.laguerre.Laguerre.truncate\n===========================================\n\n method\n\n polynomial.laguerre.Laguerre.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.laguerre.Laguerre.truncate.htmlnumpy.polynomial.legendre.Legendre.domain\n=========================================\n\n attribute\n\n polynomial.legendre.Legendre.domain*=array([-1, 1])*\n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.domain.htmlnumpy.polynomial.legendre.Legendre.__call__\n===============================================\n\n method\n\n polynomial.legendre.Legendre.__call__(*arg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L480-L483)\n \nCall self as a function.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.__call__.htmlnumpy.polynomial.legendre.Legendre.basis\n========================================\n\n method\n\n *classmethod*polynomial.legendre.Legendre.basis(*deg*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1062-L1099)\n \nSeries basis polynomial of degree `deg`.\n\n Returns the series representing the basis polynomial of degree `deg`.\n\n New in version 1.7.0.\n\n Parameters \n \n**deg**int\n\nDegree of the basis polynomial for the series. Must be >= 0.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series with the coefficient of the `deg` term set to one and all others zero.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.basis.htmlnumpy.polynomial.legendre.Legendre.cast\n=======================================\n\n method\n\n *classmethod*polynomial.legendre.Legendre.cast(*series*, *domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1101-L1141)\n \nConvert series to series of this class.\n\n The `series` is expected to be an instance of some polynomial series of one of the types supported by by the numpy.polynomial module, but could be some other class that supports the convert method.\n\n New in version 1.7.0.\n\n Parameters \n \n**series**series\n\nThe series instance to be converted.\n\n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nA series of the same kind as the calling class and equal to `series` when evaluated.\n\n See also\n\n [`convert`](numpy.polynomial.legendre.legendre.convert#numpy.polynomial.legendre.Legendre.convert \"numpy.polynomial.legendre.Legendre.convert\")\n\nsimilar instance method\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.cast.htmlnumpy.polynomial.legendre.Legendre.convert\n==========================================\n\n method\n\n polynomial.legendre.Legendre.convert(*domain=None*, *kind=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L732-L767)\n \nConvert series to a different kind and/or domain and/or window.\n\n Parameters \n \n**domain**array_like, optional\n\nThe domain of the converted series. If the value is None, the default domain of `kind` is used.\n\n \n**kind**class, optional\n\nThe polynomial series type class to which the current instance should be converted. If kind is None, then the class of the current instance is used.\n\n \n**window**array_like, optional\n\nThe window of the converted series. If the value is None, the default window of `kind` is used.\n\n Returns \n \n**new_series**series\n\nThe returned class can be of different type than the current instance and/or have a different domain and/or different window.\n\n #### Notes\n\n Conversion between domains and class types can result in numerically ill defined series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.convert.htmlnumpy.polynomial.legendre.Legendre.copy\n=======================================\n\n method\n\n polynomial.legendre.Legendre.copy()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L631-L640)\n \nReturn a copy.\n\n Returns \n \n**new_series**series\n\nCopy of self.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.copy.htmlnumpy.polynomial.legendre.Legendre.cutdeg\n=========================================\n\n method\n\n polynomial.legendre.Legendre.cutdeg(*deg*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L655-L678)\n \nTruncate series to the given degree.\n\n Reduce the degree of the series to `deg` by discarding the high order terms. If `deg` is greater than the current degree a copy of the current series is returned. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n New in version 1.5.0.\n\n Parameters \n \n**deg**non-negative int\n\nThe series is reduced to degree `deg` by discarding the high order terms. The value of `deg` must be a non-negative integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with reduced degree.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.cutdeg.htmlnumpy.polynomial.legendre.Legendre.degree\n=========================================\n\n method\n\n polynomial.legendre.Legendre.degree()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L642-L653)\n \nThe degree of the series.\n\n New in version 1.5.0.\n\n Returns \n \n**degree**int\n\nDegree of the series, one less than the number of coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.degree.htmlnumpy.polynomial.legendre.Legendre.deriv\n========================================\n\n method\n\n polynomial.legendre.Legendre.deriv(*m=1*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L831-L851)\n \nDifferentiate.\n\n Return a series instance of that is the derivative of the current series.\n\n Parameters \n \n**m**non-negative int\n\nFind the derivative of order `m`.\n\n Returns \n \n**new_series**series\n\nA new series representing the derivative. The domain is the same as the domain of the differentiated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.deriv.htmlnumpy.polynomial.legendre.Legendre.fit\n======================================\n\n method\n\n *classmethod*polynomial.legendre.Legendre.fit(*x*, *y*, *deg*, *domain=None*, *rcond=None*, *full=False*, *w=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L900-L986)\n \nLeast squares fit to data.\n\n Return a series instance that is the least squares fit to the data `y` sampled at `x`. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.\n\n Parameters \n \n**x**array_like, shape (M,)\n\nx-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**y**array_like, shape (M,)\n\ny-coordinates of the M sample points `(x[i], y[i])`.\n\n \n**deg**int or 1-D array_like\n\nDegree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`’th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.\n\n \n**domain**{None, [beg, end], []}, optional\n\nDomain to use for the returned series. If `None`, then a minimal domain that covers the points `x` is chosen. If `[]` the class domain is used. The default value was the class domain in NumPy 1.4 and `None` in later versions. The `[]` option was added in numpy 1.5.0.\n\n \n**rcond**float, optional\n\nRelative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.\n\n \n**full**bool, optional\n\nSwitch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.\n\n \n**w**array_like, shape (M,), optional\n\nWeights. If not None, the weight `w[i]` applies to the unsquared residual `y[i] - y_hat[i]` at `x[i]`. Ideally the weights are chosen so that the errors of the products `w[i]*y[i]` all have the same variance. When using inverse-variance weighting, use `w[i] = 1/sigma(y[i])`. The default value is None.\n\n New in version 1.5.0.\n\n \n**window**{[beg, end]}, optional\n\nWindow to use for the returned series. The default value is the default class domain\n\n New in version 1.6.0.\n\n Returns \n \n**new_series**series\n\nA series that represents the least squares fit to the data and has the domain and window specified in the call. If the coefficients for the unscaled and unshifted basis polynomials are of interest, do `new_series.convert().coef`.\n\n \n**[resid, rank, sv, rcond]**list\n\nThese values are only returned if `full == True`\n\n * resid – sum of squared residuals of the least squares fit\n* rank – the numerical rank of the scaled Vandermonde matrix\n* sv – singular values of the scaled Vandermonde matrix\n* rcond – value of `rcond`.\n\n For more details, see [`linalg.lstsq`](numpy.linalg.lstsq#numpy.linalg.lstsq \"numpy.linalg.lstsq\").\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.fit.htmlnumpy.polynomial.legendre.Legendre.fromroots\n============================================\n\n method\n\n *classmethod*polynomial.legendre.Legendre.fromroots(*roots*, *domain=[]*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L988-L1027)\n \nReturn series instance that has the specified roots.\n\n Returns a series representing the product `(x - r[0])*(x - r[1])*...*(x - r[n-1])`, where `r` is a list of roots.\n\n Parameters \n \n**roots**array_like\n\nList of roots.\n\n \n**domain**{[], None, array_like}, optional\n\nDomain for the resulting series. If None the domain is the interval from the smallest root to the largest. If [] the domain is the class domain. The default is [].\n\n \n**window**{None, array_like}, optional\n\nWindow for the returned series. If None the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries with the specified roots.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.fromroots.htmlnumpy.polynomial.legendre.Legendre.has_samecoef\n================================================\n\n method\n\n polynomial.legendre.Legendre.has_samecoef(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L177-L198)\n \nCheck if coefficients match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `coef` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the coefficients are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.has_samecoef.htmlnumpy.polynomial.legendre.Legendre.has_samedomain\n==================================================\n\n method\n\n polynomial.legendre.Legendre.has_samedomain(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L200-L216)\n \nCheck if domains match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `domain` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the domains are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.has_samedomain.htmlnumpy.polynomial.legendre.Legendre.has_sametype\n================================================\n\n method\n\n polynomial.legendre.Legendre.has_sametype(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L236-L252)\n \nCheck if types match.\n\n New in version 1.7.0.\n\n Parameters \n \n**other**object\n\nClass instance.\n\n Returns \n \n**bool**boolean\n\nTrue if other is same class as self\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.has_sametype.htmlnumpy.polynomial.legendre.Legendre.has_samewindow\n==================================================\n\n method\n\n polynomial.legendre.Legendre.has_samewindow(*other*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L218-L234)\n \nCheck if windows match.\n\n New in version 1.6.0.\n\n Parameters \n \n**other**class instance\n\nThe other class must have the `window` attribute.\n\n Returns \n \n**bool**boolean\n\nTrue if the windows are the same, False otherwise.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.has_samewindow.htmlnumpy.polynomial.legendre.Legendre.identity\n===========================================\n\n method\n\n *classmethod*polynomial.legendre.Legendre.identity(*domain=None*, *window=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L1029-L1060)\n \nIdentity function.\n\n If `p` is the returned series, then `p(x) == x` for all values of x.\n\n Parameters \n \n**domain**{None, array_like}, optional\n\nIf given, the array must be of the form `[beg, end]`, where `beg` and `end` are the endpoints of the domain. If None is given then the class domain is used. The default is None.\n\n \n**window**{None, array_like}, optional\n\nIf given, the resulting array must be if the form `[beg, end]`, where `beg` and `end` are the endpoints of the window. If None is given then the class window is used. The default is None.\n\n Returns \n \n**new_series**series\n\nSeries of representing the identity.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.identity.htmlnumpy.polynomial.legendre.Legendre.integ\n========================================\n\n method\n\n polynomial.legendre.Legendre.integ(*m=1*, *k=[]*, *lbnd=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L798-L829)\n \nIntegrate.\n\n Return a series instance that is the definite integral of the current series.\n\n Parameters \n \n**m**non-negative int\n\nThe number of integrations to perform.\n\n \n**k**array_like\n\nIntegration constants. The first constant is applied to the first integration, the second to the second, and so on. The list of values must less than or equal to `m` in length and any missing values are set to zero.\n\n \n**lbnd**Scalar\n\nThe lower bound of the definite integral.\n\n Returns \n \n**new_series**series\n\nA new series representing the integral. The domain is the same as the domain of the integrated series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.integ.htmlnumpy.polynomial.legendre.Legendre.linspace\n===========================================\n\n method\n\n polynomial.legendre.Legendre.linspace(*n=100*, *domain=None*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L868-L898)\n \nReturn x, y values at equally spaced points in domain.\n\n Returns the x, y values at `n` linearly spaced points across the domain. Here y is the value of the polynomial at the points x. By default the domain is the same as that of the series instance. This method is intended mostly as a plotting aid.\n\n New in version 1.5.0.\n\n Parameters \n \n**n**int, optional\n\nNumber of point pairs to return. The default value is 100.\n\n \n**domain**{None, array_like}, optional\n\nIf not None, the specified domain is used instead of that of the calling instance. It should be of the form `[beg,end]`. The default is None which case the class domain is used.\n\n Returns \n \n**x, y**ndarray\n\nx is equal to linspace(self.domain[0], self.domain[1], n) and y is the series evaluated at element of x.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.linspace.htmlnumpy.polynomial.legendre.Legendre.mapparms\n===========================================\n\n method\n\n polynomial.legendre.Legendre.mapparms()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L769-L796)\n \nReturn the mapping parameters.\n\n The returned values define a linear map `off + scl*x` that is applied to the input arguments before the series is evaluated. The map depends on the `domain` and `window`; if the current `domain` is equal to the `window` the resulting map is the identity. If the coefficients of the series instance are to be used by themselves outside this class, then the linear function must be substituted for the `x` in the standard representation of the base polynomials.\n\n Returns \n \n**off, scl**float or complex\n\nThe mapping function is defined by `off + scl*x`.\n\n #### Notes\n\n If the current domain is the interval `[l1, r1]` and the window is `[l2, r2]`, then the linear mapping function `L` is defined by the equations:\n\n \n```\nL(l1) = l2\nL(r1) = r2\n\n```\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.mapparms.htmlnumpy.polynomial.legendre.Legendre.roots\n========================================\n\n method\n\n polynomial.legendre.Legendre.roots()[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L853-L866)\n \nReturn the roots of the series polynomial.\n\n Compute the roots for the series. Note that the accuracy of the roots decrease the further outside the domain they lie.\n\n Returns \n \n**roots**ndarray\n\nArray containing the roots of the series.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.roots.htmlnumpy.polynomial.legendre.Legendre.trim\n=======================================\n\n method\n\n polynomial.legendre.Legendre.trim(*tol=0*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L680-L701)\n \nRemove trailing coefficients\n\n Remove trailing coefficients until a coefficient is reached whose absolute value greater than `tol` or the beginning of the series is reached. If all the coefficients would be removed the series is set to `[0]`. A new series instance is returned with the new coefficients. The current instance remains unchanged.\n\n Parameters \n \n**tol**non-negative number.\n\nAll trailing coefficients less than `tol` will be removed.\n\n Returns \n \n**new_series**series\n\nNew instance of series with trimmed coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.trim.htmlnumpy.polynomial.legendre.Legendre.truncate\n===========================================\n\n method\n\n polynomial.legendre.Legendre.truncate(*size*)[[source]](https://github.com/numpy/numpy/blob/v1.23.0/numpy/polynomial/_polybase.py#L703-L730)\n \nTruncate series to length `size`.\n\n Reduce the series to length `size` by discarding the high degree terms. The value of `size` must be a positive integer. This can be useful in least squares where the coefficients of the high degree terms may be very small.\n\n Parameters \n \n**size**positive int\n\nThe series is reduced to length `size` by discarding the high degree terms. The value of `size` must be a positive integer.\n\n Returns \n \n**new_series**series\n\nNew instance of series with truncated coefficients.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/generated/numpy.polynomial.legendre.Legendre.truncate.htmlnumpy.random.PCG64DXSM.advance\n==============================\n\n method\n\n random.PCG64DXSM.advance(*delta*)\n \nAdvance the underlying RNG as-if delta draws have occurred.\n\n Parameters \n \n**delta**integer, positive\n\nNumber of draws to advance the RNG. Must be less than the size state variable in the underlying RNG.\n\n Returns \n \n**self**PCG64\n\nRNG advanced delta steps\n\n #### Notes\n\n Advancing a RNG updates the underlying RNG state as-if a given number of calls to the underlying RNG have been made. In general there is not a one-to-one relationship between the number output random values from a particular distribution and the number of draws from the core RNG. This occurs for two reasons:\n\n * The random values are simulated using a rejection-based method and so, on average, more than one value from the underlying RNG is required to generate an single draw.\n* The number of bits required to generate a simulated value differs from the number of bits generated by the underlying RNG. For example, two 16-bit integer values can be simulated from a single draw of a 32-bit RNG.\n\n Advancing the RNG state resets any pre-computed random numbers. This is required to ensure exact reproducibility.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64DXSM.advance.htmlnumpy.random.PCG64DXSM.state\n============================\n\n attribute\n\n random.PCG64DXSM.state\n \nGet or set the PRNG state\n\n Returns \n \n**state**dict\n\nDictionary containing the information required to describe the state of the PRNG\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64DXSM.state.htmlnumpy.random.PCG64DXSM.jumped\n=============================\n\n method\n\n random.PCG64DXSM.jumped(*jumps=1*)\n \nReturns a new bit generator with the state jumped.\n\n Jumps the state as-if jumps * 210306068529402873165736369884012333109 random numbers have been generated.\n\n Parameters \n \n**jumps**integer, positive\n\nNumber of times to jump the state of the bit generator returned\n\n Returns \n \n**bit_generator**PCG64DXSM\n\nNew instance of generator jumped iter times\n\n #### Notes\n\n The step size is phi-1 when multiplied by 2**128 where phi is the golden ratio.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64DXSM.jumped.htmlnumpy.random.PCG64DXSM.cffi\n===========================\n\n attribute\n\n random.PCG64DXSM.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64DXSM.cffi.htmlnumpy.random.PCG64DXSM.ctypes\n=============================\n\n attribute\n\n random.PCG64DXSM.ctypes\n \nctypes interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing ctypes wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.PCG64DXSM.ctypes.htmlnumpy.random.Philox.state\n=========================\n\n attribute\n\n random.Philox.state\n \nGet or set the PRNG state\n\n Returns \n \n**state**dict\n\nDictionary containing the information required to describe the state of the PRNG\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.Philox.state.htmlnumpy.random.Philox.advance\n===========================\n\n method\n\n random.Philox.advance(*delta*)\n \nAdvance the underlying RNG as-if delta draws have occurred.\n\n Parameters \n \n**delta**integer, positive\n\nNumber of draws to advance the RNG. Must be less than the size state variable in the underlying RNG.\n\n Returns \n \n**self**Philox\n\nRNG advanced delta steps\n\n #### Notes\n\n Advancing a RNG updates the underlying RNG state as-if a given number of calls to the underlying RNG have been made. In general there is not a one-to-one relationship between the number output random values from a particular distribution and the number of draws from the core RNG. This occurs for two reasons:\n\n * The random values are simulated using a rejection-based method and so, on average, more than one value from the underlying RNG is required to generate an single draw.\n* The number of bits required to generate a simulated value differs from the number of bits generated by the underlying RNG. For example, two 16-bit integer values can be simulated from a single draw of a 32-bit RNG.\n\n Advancing the RNG state resets any pre-computed random numbers. This is required to ensure exact reproducibility.\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.Philox.advance.htmlnumpy.random.Philox.jumped\n==========================\n\n method\n\n random.Philox.jumped(*jumps=1*)\n \nReturns a new bit generator with the state jumped\n\n The state of the returned bit generator is jumped as-if (2**128) * jumps random numbers have been generated.\n\n Parameters \n \n**jumps**integer, positive\n\nNumber of times to jump the state of the bit generator returned\n\n Returns \n \n**bit_generator**Philox\n\nNew instance of generator jumped iter times\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.Philox.jumped.htmlnumpy.random.Philox.cffi\n========================\n\n attribute\n\n random.Philox.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.Philox.cffi.htmlnumpy.random.Philox.ctypes\n==========================\n\n attribute\n\n random.Philox.ctypes\n \nctypes interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing ctypes wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.Philox.ctypes.htmlnumpy.random.SFC64.state\n========================\n\n attribute\n\n random.SFC64.state\n \nGet or set the PRNG state\n\n Returns \n \n**state**dict\n\nDictionary containing the information required to describe the state of the PRNG\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SFC64.state.htmlnumpy.random.SFC64.cffi\n=======================\n\n attribute\n\n random.SFC64.cffi\n \nCFFI interface\n\n Returns \n \n**interface**namedtuple\n\nNamed tuple containing CFFI wrapper\n\n * state_address - Memory address of the state struct\n* state - pointer to the state struct\n* next_uint64 - function pointer to produce 64 bit integers\n* next_uint32 - function pointer to produce 32 bit integers\n* next_double - function pointer to produce doubles\n* bitgen - pointer to the bit generator struct\n\n \n\n © 2005–2022 NumPy Developers \nLicensed under the 3-clause BSD License. \n\n<https://numpy.org/doc/1.23/reference/random/bit_generators/generated/numpy.random.SFC64.cffi.htmlnumpy~1.23"}}},{"rowIdx":59463,"cells":{"project":{"kind":"string","value":"roxyglobals"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘roxyglobals’\n August 21, 2023\nTitle 'Roxygen2' Global Variable Declarations\nVersion 1.0.0\nDescription Generate utils::globalVariables() from 'roxygen2' @global and @autoglobal tags.\nLicense MIT + file LICENSE\nURL https://github.com/anthonynorth/roxyglobals\nBugReports https://github.com/anthonynorth/roxyglobals/issues\nImports brio, codetools, desc, roxygen2\nSuggests covr, testthat (>= 3.0.0), withr\nConfig/testthat/edition 3\nEncoding UTF-8\nRoxygenNote 7.2.3\nNeedsCompilation no\nAuthor <NAME> [aut, cre, cph],\n <NAME> [ctb] (<https://orcid.org/0000-0003-2865-2548>)\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-08-21 14:20:08 UTC\nR topics documented:\nglobal_rocle... 2\nuse_roxyglobal... 2\n global_roclet Roclet: global\nDescription\n This roclet automates utils::globalVariables() declaration from @global and @autoglobal\n roxygen tags.\n Package authors will not typically need to invoke global_roclet() directly. Global roclet in-\n stances are created by roxygen2 during roxygen2::roxygenise() (or devtools::document()).\nUsage\n global_roclet()\nValue\n A roxygen2::roclet() instance for declaring utils::globalVariables() during roxygen2::roxygenise()\nExamples\n #' @autoglobal\n foo <- function(x) {\n # bar isn't declared -> add to utils::globalVariables()\n subset(x, bar == 4)\n }\n #' @global bar\n foo <- function(x) {\n # bar is explicitly defined as a global -> add to utils::globalVariables()\n subset(x, bar == 4)\n }\n use_roxyglobals Use roxyglobals\nDescription\n Configures roxygen to use global_roclet(), adds roxyglobals to Suggests\nUsage\n use_roxyglobals()\nValue\n nothing\nuse_roxyglobals 3\nExamples\n ## Not run:\n use_roxyglobals()\n ## End(Not run)"}}},{"rowIdx":59464,"cells":{"project":{"kind":"string","value":"SafeVote"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘SafeVote’\n January 18, 2023\nType Package\nTitle Election Vote Counting with Safety Features\nVersion 1.0.0\nDate 2023-01-18\nDescription Fork of 'vote_2.3-2', Raftery et al. (2021)\n <DOI:10.32614/RJ-2021-086>, with additional support\n for stochastic experimentation.\nDepends R (>= 3.5.0)\nImports formattable, knitr, fields, grDevices, graphics, utils,\n ggplot2, data.table, stringr, forcats, dplyr\nEncoding UTF-8\nLicense GPL (>= 2)\nLanguage EN-GB\nNeedsCompilation no\nRoxygenNote 7.2.3\nLazyData true\nURL https://cthombor.github.io/SafeVote/\nSuggests testthat (>= 3.0.0), vote, STV\nConfig/testthat/edition 3\nAuthor <NAME> [cre, aut] (<https://orcid.org/0000-0002-4147-7898>)\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-01-18 11:50:06 UTC\nR topics documented:\n.print.summary.SafeVot... 3\n.summary.SafeVot... 4\na3_hi... 4\na4_hi... 5\na53_hi... 5\napprova... 6\nas.SafeRankExp... 7\nassemble.args.for.check.scor... 7\nassemble.args.for.check.st... 8\nbackwards.tiebrea... 8\ncheck.nseat... 9\ncheck.rankin... 9\ncheck.vote... 10\ncheck.votes.approva... 10\ncheck.votes.condorce... 11\ncheck.votes.pluralit... 11\ncheck.votes.scor... 12\ncheck.votes.st... 12\ncheck.votes.tworound.runof... 13\ncombineRanking... 13\ncompleteRankingTabl... 14\ncondorce... 14\ncorrect.rankin... 16\ndublin_wes... 16\nelection.inf... 17\nextractMargin... 17\nextractRan... 18\nfood_electio... 18\nforwards.tiebrea... 19\nimage.SafeVote.condorce... 19\nimage.SafeVote.st... 20\nims_approva... 20\nims_electio... 21\nims_pluralit... 21\nims_scor... 22\nims_st... 22\ninvalid.vote... 23\nis.SafeRankExp... 23\nis.valid.vot... 24\nloserMargi... 24\nnew_SafeRankExp... 25\nordered.preference... 26\nordered.tiebrea... 26\nplot.SafeRankExp... 26\nplot.SafeVote.st... 28\npluralit... 29\nprepare.vote... 29\nprint.summary.SafeRankExp... 30\nprint.summary.SafeVote.approva... 30\nprint.summary.SafeVote.condorce... 31\nprint.summary.SafeVote.pluralit... 31\nprint.summary.SafeVote.scor... 32\nprint.summary.SafeVote.st... 32\nrbind.SafeRankExp... 33\nreadHi... 33\nremove.candidat... 34\nscor... 34\nsolveTiebrea... 35\nst... 36\nsummary.SafeRankExp... 38\nsummary.SafeVote.approva... 39\nsummary.SafeVote.condorce... 39\nsummary.SafeVote.pluralit... 40\nsummary.SafeVote.scor... 40\nsummary.SafeVote.st... 41\nsumOfVote... 41\ntestAddition... 42\ntestDeletion... 43\ntestFractio... 44\ntranslate.tie... 45\nuk_labour_201... 46\nvie... 46\nview.SafeVote.approva... 47\nview.SafeVote.condorce... 47\nview.SafeVote.pluralit... 48\nview.SafeVote.scor... 48\nview.SafeVote.st... 49\nwinnerMargi... 49\nyale_ballot... 50\n .print.summary.SafeVote\n .print method for summary object\nDescription\n .print method for summary object\nUsage\n .print.summary.SafeVote(x, ...)\nArguments\n x, ... undocumented\nValue\n undocumented\n .summary.SafeVote summarises vote-totals for subsequent printing\nDescription\n summarises vote-totals for subsequent printing\nUsage\n .summary.SafeVote(object, larger.wins = TRUE, reorder = TRUE)\nArguments\n object vector of total votes per candidate\n larger.wins TRUE if candidates are \"voted in\" rather than voted-out\n reorder TRUE if output data.frame columns should be in rank-order\nValue\n a data.frame with three columns and nc+1 rows, where nc is the number of candidates. The first\n column contains candidate names and a final entry named \"Sum\". The second column contains vote\n totals. The third column is a vector of chars which indicate whether the candidate has been elected.\n The data.frame has four named attributes carrying election parameters.\n TODO: refactor into a modern dialect of R, perhaps by defining a constructor for an election_info\n S3 object with a summary method and a print method\n a3_hil Tideman a3_hil\nDescription\n This data is one of 87 sets of ballots from the Tideman data collection, as curated by The Center for\n Range Voting.\n This set of ballots was collected in 1987 by <NAME>, with support from NSF grant SES86-\n 18328. \"The data are records of ballots from elections of British organizations (mostly trade unions\n using PR-STV or IRV voting) in which the voters ranked the candidates. The data were gathered\n under a stipulation that the organizations involved would remain anonymous.\"\n The ballots were encoded in David Hill’s format, and have been converted to the preference-vector\n format of this package. The archival file A4.HIL at rangevoting.org contains eight blank ballot\n papers (1, 616, 619, 620, 685, 686, 687, 688) which we have retained. This set may be counted by\n stv(a3_hil,nseats=attr(a3_hil,\"nseats\")).\nUsage\n data(a3_hil)\nFormat\n A data frame with attribute \"nseats\" = 7, consisting of 989 observations and 15 candidates.\n a4_hil Tideman a4_hil\nDescription\n This data is one of 87 sets of ballots from the Tideman data collection, as curated by The Center\n for Range Voting. The ballots were archived in David Hill’s format, and have been converted to the\n preference-vector format of this package.\n This set of ballots was collected in 1987 by <NAME>, with support from NSF grant SES86-\n 18328. \"The data are records of ballots from elections of British organizations (mostly trade unions\n using PR-STV or IRV voting) in which the voters ranked the candidates. The data were gathered\n under a stipulation that the organizations involved would remain anonymous.\"\nUsage\n data(a4_hil)\nFormat\n A data frame with attribute \"nseats\" = 2, consisting of 43 observations and 14 candidates.\n a53_hil Tideman a53_hil\nDescription\n This data is one of 87 sets of ballots from the Tideman data collection, as curated by The Center for\n Range Voting.\n This set of ballots was collected in 1988 by <NAME>, with support from NSF grant SES86-\n 18328. \"The data are records of ballots from elections of British organizations (mostly trade unions\n using PR-STV or IRV voting) in which the voters ranked the candidates. The data were gathered\n under a stipulation that the organizations involved would remain anonymous.\"\n The ballots were encoded in David Hill’s format, and have been converted to the preference-vector\n format of this package. Candidates have been renamed to letters of the alphabet, for ease of compar-\n ison with Table 3 of Tideman (2000). Note: the DOI for this article is 10.1023/A:1005082925477,\n with an embedded colon which isn’t handled by the usual DOI-to-URL conversions.\n As noted in this table, it is a very close race between candidates D, F, and B in the final rounds of a\n Meek count of a53_hil.\n Tideman’s implementation of Meek’s method excludes B (on 59.02 votes), then elects D in the final\n round (on 88.33 votes) with a margin of 0.95 votes ahead of F (on 87.38 votes).\n In v1.0, stv(a53.hil,quota.hare=TRUE) excludes F (on 56.418 votes), then elects D in the final\n round (on 79.705 votes) with a winning margin of 0.747 votes ahead of B (on 78.958 votes). The\n result of the election is the same but the vote counts and winning margins differ significantly; so\n we conclude that stv(quota.hare=TRUE) in SafeVote v1.0 is not a reliable proxy for Tideman’s\n implementation of Meek’s algorithm.\n Future researchers may wish to adjust the quota calculation of vote.stv() so that it is no longer\n biased upward by a \"fuzz\" of 0.001, to see if this change significantly reduces the discrepancies\n with Tideman’s implementation of Meek.\n It would be unreasonable to expect an exact replication of results from two different implementa-\n tions of an STV method. We leave it to future researchers to develop a formal specification, so\n that it would be possible to verify the correctness of an implementation. We also leave it to fu-\n ture researchers to develop a set of test cases with appropriate levels of tolerance for the vagaries\n of floating-point roundoff in optimised (or even unoptimised!) compilations of the same code on\n different computing systems. We suggest that a53_hil be included in any such test set.\n We note in passing that <NAME>, in \"Checking two STV programs\", Voting Matters 11,\n 2000, discussed the cross-validation exercise he conducted between the ERBS implementation of\n its voting rules and the Church of England’s implementation of its voting rules. In both cases, he\n discovered ambiguities in the specification as well as defects in the implementation.\nUsage\n data(a53_hil)\nFormat\n A data frame with attribute \"nseats\" = 4, consisting of 460 observations and 10 candidates.\n approval Count votes using the approval method\nDescription\n See https://arxiv.org/abs/2102.05801\nUsage\n approval(votes, nseats = 1, fsep = \"\\t\", quiet = FALSE, ...)\nArguments\n votes, nseats, fsep, quiet, ...\n undocumented\nValue\n undocumented\n as.SafeRankExpt as.SafeRankExpt()\nDescription\n as.SafeRankExpt()\nUsage\n as.SafeRankExpt(df)\nArguments\n df data.frame object\nValue\n a SafeRankExpt object, or stop() if df fails some sanity checks\n assemble.args.for.check.score\n undocumented internal method\nDescription\n undocumented internal method\nUsage\n assemble.args.for.check.score(x, max.score = NULL, ...)\nArguments\n x, max.score, ...\n undocumented\nValue\n undocumented\n assemble.args.for.check.stv\n undocumented internal method\nDescription\n undocumented internal method\nUsage\n assemble.args.for.check.stv(x, equal.ranking = FALSE, ...)\nArguments\n x, equal.ranking, ...\n undocumented\nValue\n undocumented\n backwards.tiebreak Undocumented internal method\nDescription\n Undocumented internal method\nUsage\n backwards.tiebreak(prefs, icans, elim = TRUE)\nArguments\n prefs undocumented\n icans undocumented\n elim undocumented\n check.nseats parameter-checking method for nseats (internal)\nDescription\n parameter-checking method for nseats (internal)\nUsage\n check.nseats(\n nseats = NULL,\n ncandidates,\n default = 1,\n mcan = NULL,\n complete.ranking = FALSE\n )\nArguments\n nseats initially-specified number of seats to be filled in an election\n ncandidates the number of candidates standing for election\n default the return value of this function when nseats=NULL\n mcan a deprecated name for nseats\n complete.ranking\n when TRUE, the return value is in 1..ncandidates When FALSE, the return value\n is in 1..ncandidates-1 (for backwards compatibility)\nValue\n a valid non-NULL value for the number of seats to be filled\n check.ranking check the validity of a partial ranking\nDescription\n check the validity of a partial ranking\nUsage\n check.ranking(r)\nArguments\n r a numeric vector\nValue\n a partial ranking of the elements of r, using ties.method=\"min\"\n check.votes undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes(x, ..., quiet = FALSE)\nArguments\n x, quiet, ... undocumented\nValue\n undocumented\n check.votes.approval undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.approval(record, ...)\nArguments\n record, ... undocumented\nValue\n undocumented\ncheck.votes.condorcet 11\n check.votes.condorcet undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.condorcet(record, ...)\nArguments\n record, ... undocumented\nValue\n undocumented\n check.votes.plurality undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.plurality(record, ...)\nArguments\n record, ... undocumented\nValue\n undocumented\n check.votes.score undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.score(record, max.score, ...)\nArguments\n record, max.score, ...\n undocumented\nValue\n undocumented\n check.votes.stv undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.stv(record, equal.ranking = FALSE, ...)\nArguments\n record, equal.ranking, ...\n undocumented\nValue\n undocumented\n check.votes.tworound.runoff\n undocumented internal method\nDescription\n undocumented internal method\nUsage\n check.votes.tworound.runoff(record, ...)\nArguments\n record, ... undocumented\nValue\n undocumented\n combineRankings the least upper bound on a pair of rankings\nDescription\n the least upper bound on a pair of rankings\nUsage\n combineRankings(r1, r2)\nArguments\n r1, r2 numeric vectors\nValue\n the most complete (but possibly partial) ranking which is consistent with both r1 and r2. Uses\n ties.method=\"min\"\nExamples\n combineRankings( c(3,1,2), c(2,1,3) )\n completeRankingTable internal method to analyse the partial results of an stv() ballot count,\n to discover a complete ranking of all candidates. The ranking may de-\n pend on the value of nseats, because this affects how votes are trans-\n ferred.\nDescription\n internal method to analyse the partial results of an stv() ballot count, to discover a complete ranking\n of all candidates. The ranking may depend on the value of nseats, because this affects how votes\n are transferred.\nUsage\n completeRankingTable(object, quiet, verbose)\nArguments\n object partial results\n quiet TRUE to suppress console output\n verbose TRUE to produce diagnostic output\nValue\n data.frame with columns TotalRank, Margin, Candidate, Elected, SafeRank\n condorcet Count votes using the Condorcet voting method.\nDescription\n The Condorcet method elects the candidate who wins a majority of the ranked vote in every head to\n head election against each of the other candidates. A Condorcet winner is a candidate who beats all\n other candidates in pairwise comparisons. Analogously, a Condorcet loser is a candidate who loses\n against all other candidates. Neither Condorcet winner nor loser might exist.\nUsage\n condorcet(\n votes,\n runoff = FALSE,\n nseats = 1,\n safety = 1,\n fsep = \"\\t\",\n quiet = FALSE,\n ...\n )\nArguments\n votes A matrix or data.frame containing the votes. Rows correspond to the votes,\n columns correspond to the candidates. If votes is a character string, it is inter-\n preted as a file name from which the votes are to be read. See below.\n runoff Logical. If TRUE and no Condorcet winner exists, the election goes into a run-\n off, see below.\n nseats the number of seats to be filled in this election\n safety Parameter for a clustering heuristic on a total ranking of the candidates. Conjec-\n ture: the default of 1.0 ensures a separation of one s.d. between clusters, when\n votes are i.u.d. permutations on the candidates.\n fsep If votes is a file name, this argument gives the column separator in the file.\n quiet If TRUE no output is printed.\n ... Undocumented intent (preserved from legacy code)\nDetails\n If the runoff argument is set to TRUE and no Condorcet winner exists, two or more candidates\n with the most pairwise wins are selected and the method is applied to such subset. If more than two\n candidates are in such run-off, the selection is performed repeatedly, until either a winner is selected\n or no more selection is possible.\n The input data votes is structured the same way as for the stv method: Row i contains the prefer-\n ences of voter i numbered 1; 2; : : : ; r; 0; 0; 0; 0, in some order, while equal preferences\n are allowed. The columns correspond to the candidates. The dimnames of the columns are the\n names of the candidates; if these are not supplied then the candidates are lettered A, B, C, .... If\n the dataset contains missing values (NA), they are replaced by zeros.\n If a ballot has equally-ranked candidates, its rankings are tested for validity: for each preference i\n which does not have any duplicate, there are exactly i−1 preferences j with 0 < j < i. If any ballot\n x fails this validity test, it is automatically corrected (aka \"converted\") into a valid ballot using x <-\n rank(x, ties.method = \"min\"), and a warning is issued.\n This method also computes a Borda ranking of all candidates, using tournament-style scoring. This\n ranking is \"fuzzed\" into a safeRank, with approximately 1 s.d. of fuzz when safety=1.0 and\n voter preferences are i.u.d. A warning is thrown if a safeRank violates the (extended) Condorcet\n principle: that Candidate i is more highly ranked than Candidate j only if a majority of voters agree\n with this.\nValue\n Object of class SafeVote.condorcet\nExamples\n {\n data(food_election)\n condorcet(food_election)\n }\n correct.ranking Amend ballots with equal or incomplete preferences\nDescription\n The correct.ranking function returns a modified set of ballots. Its argument partial deter-\n mines if ballots are partially set to 0 (TRUE), or if it is a complete re-ranking, as allowed when\n equal.ranking = TRUE. It can be used by calling it explicitly. It is called by stv if equal.ranking\n = TRUE or invalid.partial = TRUE. It is also called from within the condorcet function with the\n default value (FALSE) for partial, i.e. interpreting any 0 as a last= preference.\nUsage\n correct.ranking(votes, partial = FALSE, quiet = FALSE)\nArguments\n votes original contents of ballot box\n partial if FALSE (default), each ballot is interpreted, if possible, as a complete (but not\n necessarily total) ranking of the candidates. If TRUE, a ballot will contain a 0 on\n unranked candidates.\n quiet suppress diagnostics\nValue\n corrected ballots\n dublin_west Dublin West\nDescription\n Dataset containing ranked votes for the Dublin West constituency in 2002, Ireland.\nUsage\n data(dublin_west)\nFormat\n A data frame with 29988 observations and 9 candidates. Each record corresponds to one ballot with\n candidates being ranked between 1 and 9 with zeros allowed.\nSee Also\n Wikipedia\n election.info prints the basic results of an election\nDescription\n prints the basic results of an election\nUsage\n election.info(x)\nArguments\n x basic election results, as named attributes of an R structure or object\nValue\n data.frame : an invisible copy of the printed results\n TODO: refactor into a modern dialect of R, e.g. defining a constructor for an election_info S3 object\n with a print method\n extractMargins extract margins from the results of a ballot count\nDescription\n extract margins from the results of a ballot count\nUsage\n extractMargins(marginNames, crRanks, cr)\nArguments\n marginNames list of colnames of the margins in our SafeRank result\n crRanks ranks of candidates, not necessarily total\n cr structure returned by a ballot-counting method\n Margins are adjusted for tied candidates, such that candidates within a tie group\n have margins indicative of their relative strengths. Extremely small margins are\n indicative of floating-point roundoff errors.\nValue\n named list of margins\n extractRank Extract a ranking vector by name from the results of a ballot count\nDescription\n Extract a ranking vector by name from the results of a ballot count\nUsage\n extractRank(rankMethod, cr)\nArguments\n rankMethod \"safeRank\", \"elected\", or \"rank\"\n cr structure returned by a ballot-counting method\nValue\n a numeric ranking vector, in order of colnames(cr$data)\n food_election Food Election\nDescription\n Sample data for testing SafeVote\nUsage\n data(food_election)\nFormat\n A data frame with 20 observations and 5 candidates (Oranges, Pears, Chocolate, Strawberries,\n Sweets). Each record corresponds to one ballot with ranking for each of the candidates.\n forwards.tiebreak Undocumented internal method\nDescription\n Undocumented internal method\nUsage\n forwards.tiebreak(prefs, icans, elim = TRUE)\nArguments\n prefs undocumented\n icans undocumented\n elim undocumented\n image.SafeVote.condorcet\n The image function visualizes the joint distribution of two preferences\n (if all.pref=FALSE) given xpref and ypref, as well as the marginal\n distribution of all preferences (if all.pref=TRUE). The joint distribu-\n tion can be shown as proportions (if proportion=TRUE) or raw vote\n counts (if proportion=FALSE).\nDescription\n The image function visualizes the joint distribution of two preferences (if all.pref=FALSE) given\n xpref and ypref, as well as the marginal distribution of all preferences (if all.pref=TRUE).\n The joint distribution can be shown as proportions (if proportion=TRUE) or raw vote counts (if\n proportion=FALSE).\nUsage\n ## S3 method for class 'SafeVote.condorcet'\n image(x, ...)\nArguments\n x object of type SafeVote.condorcet\n ... See arguments for image.SafeVote.stv, especially xpref, ypref, all.pref and\n proportion.\nValue\n image object, with side-effect in RStudio Plots pane\n image.SafeVote.stv visualisation of joint and marginal distributions in STV preferences\nDescription\n visualisation of joint and marginal distributions in STV preferences\nUsage\n ## S3 method for class 'SafeVote.stv'\n image(x, xpref = 2, ypref = 1, all.pref = FALSE, proportion = TRUE, ...)\nArguments\n x STV results to be visualised\n xpref, ypref candidates shown in a joint distribution plot\n all.pref plot the joint distribution of two preferences (if all.pref=FALSE) or the marginal\n distribution of all preferences (if all.pref=TRUE).\n proportion The joint distribution can be shown either as proportions (if proportion=TRUE)\n or raw vote counts (if proportion=FALSE).\n ... args passed to fields::image.plot()\nValue\n image object, with side-effect in RStudio Plots pane\n ims_approval IMS Approval\nDescription\n Modified version of ims_election, for use in approval voting.\nUsage\n data(ims_approval)\nFormat\n A data frame with 620 observations and 10 candidates (names were made up). Each record corre-\n sponds to one ballot, with 0 indicating disapproval of a candidate and 1 indicating approval.\n ims_election IMS Election\nDescription\n Datasets containing anonymized votes for a past Council election of the Institute of Mathematical\n Statistics (IMS). The dataset ims_election is the original dataset used with single transferable vote,\n where candidate names have been changed.\nUsage\n data(ims_election)\nFormat\n A data frame with 620 observations and 10 candidates (names were made up). Each record cor-\n responds to one ballot. The IMS Council voting is done using the STV method, and thus the\n ims_election dataset contains ballots with candidates being ranked between 1 and 10 with zeros\n allowed.\n ims_plurality IMS Plurality\nDescription\n Modified version of ims_election, for use in plurality voting.\nUsage\n data(ims_plurality)\nFormat\n A data frame with 620 observations and 10 candidates (names were made up). Each record cor-\n responds to one ballot, with 1 against the voter’s most-preferred candidate and 0 against all other\n candidates.\n ims_score IMS Score\nDescription\n Modified version of ims_election, for use in score voting.\nUsage\n data(ims_score)\nFormat\n A data frame with 620 observations and 10 candidates (names were made up). Each record corre-\n sponds to one ballot, with higher values indicating the more-preferred candidates.\n ims_stv IMS STV\nDescription\n Copy of ims_election, included for backwards compatibility.\nUsage\n data(ims_election)\nFormat\n A data frame with 620 observations and 10 candidates (names were made up). Each record cor-\n responds to one ballot. The IMS Council voting is done using the STV method, and thus the\n ims_election dataset contains ballots with candidates being ranked between 1 and 10 with zeros\n allowed.\n invalid.votes Extracts the invalid.votes member (if any) from the result of a count\nDescription\n This method was added Jan 2022 – it was named in a warning message but had apparently either\n never been implemented, or had been \"lost\" through versioning.\nUsage\n invalid.votes(x)\nArguments\n x value returned by stv, condorcet, approval, plurality, or score\nValue\n matrix with one column per candidate and one row per invalid ballot\n is.SafeRankExpt is.SafeRankExpt()\nDescription\n is.SafeRankExpt()\nUsage\n is.SafeRankExpt(x)\nArguments\n x object of unknown class\nValue\n TRUE if x is a valid SafeRankExpt object\n is.valid.vote undocumented internal method\nDescription\n undocumented internal method\nUsage\n is.valid.vote(x, method, ...)\nArguments\n x, method, ... undocumented\nValue\n undocumented\n loserMargin Find a loser and their margin of victory\nDescription\n Find a loser and their margin of victory\nUsage\n loserMargin(votes)\nArguments\n votes cleaned ballots\nValue\n length-2 vector: the index of a losing candidate, and their margin of loss (0 if a tie, NA if no winners)\n new_SafeRankExpt Constructor for the results of a SafeRank experiment\nDescription\n Constructor for the results of a SafeRank experiment\nUsage\n new_SafeRankExpt(\n rankNames = list(),\n marginNames = list(),\n countMethod = character(0),\n rankMethod = character(0),\n datasetName = character(0),\n experimentalMethod = character(0),\n countArgs = list(),\n nseats = integer(0),\n otherFactors = list(),\n unitFactors = list()\n )\nArguments\n rankNames colnames for per-candidate ranks\n marginNames colnames for per-candidate margins\n countMethod secondary factor: counting method e.g. \"stv\"\n rankMethod secondary factor: ranking method e.g. \"elected\"\n datasetName secondary factor: name of the dataset of ballots\n experimentalMethod\n secondary factor: name of the method which simulated these elections e.g. \"test-\n Fraction\"\n countArgs secondary factor: args passed to countMethod\n nseats secondary factor: number of seats to be filled\n otherFactors other secondary factors, e.g. parameters to experimentalMethod\n unitFactors per-unit factors derived from PRNG of the experimental harness, e.g describing\n the ballots randomly deleted during testDeletions\nValue\n object of class SafeRankExpt\n ordered.preferences Undocumented internal method\nDescription\n Undocumented internal method\nUsage\n ordered.preferences(vmat)\nArguments\n vmat undocumented\n ordered.tiebreak Undocumented internal method\nDescription\n Undocumented internal method\nUsage\n ordered.tiebreak(vmat, seed = NULL)\nArguments\n vmat undocumented\n seed undocumented\n plot.SafeRankExpt plot() method for the result of an experiment with varying numbers of\n ballots\nDescription\n The \"adjusted rank\"\n √ of a candidate is their ranking r plus their scaled \"winning margin\". The scaled\n margin is e−cx/ n , where x is the adjusted margin (i.e. the number of votes by which this candidate\n is ahead of the next-weaker candidate, adjusted for the number of ballots n and the number of seats\n s), and c > 0 is the margin-scaling parameter cMargin.\nUsage\n ## S3 method for class 'SafeRankExpt'\n plot(\n x,\n facetWrap = FALSE,\n nResults = NA,\n anBallots = 0,\n cMargin = 1,\n xlab = \"Ballots\",\n ylab = \"Adjusted Rank\",\n title = NULL,\n subtitle = \"(default)\",\n line = TRUE,\n boxPlot = FALSE,\n boxPlotCutInterval = 10,\n pointSize = 1,\n ...\n )\nArguments\n x object containing experimental results\n facetWrap TRUE provides per-candidate scatterplots\n nResults number of candidates whose results are plotted (omitting the least-favoured can-\n didates first)\n anBallots, cMargin\n parameters in the rank-adjustment formula\n xlab, ylab axis labels\n title overall title for the plot. Default: NULL\n subtitle subtitle for the plot. Default: value of nSeats and any non-zero rank-adjustment\n parameters\n line TRUE will connect points with lines, and will disable jitter\n boxPlot TRUE for a boxplot, rather than the default xy-scatter\n boxPlotCutInterval\n parameter of boxplot, default 10\n pointSize diameter of points\n ... params for generic plot()\nDetails\n The default value of cMargin=1.0 draws visual attention to candidates with a very small winning\n margin, as their adjusted rank is very near to r + 1. Candidates with anything more than a small\n winning margin have only a small rank adjustment, due to the exponential scaling.\n A scaling linear in s/n is applied to margins when anBallots>0. Such a linear scaling may be a\n helpful way to visualise the winning margins in STV elections because the margin of victory for an\n elected candidate is typically not much larger than the quota of n/(s + 1) (Droop) or n/s (Hare).\n The linear scaling factor is as/n, where a is the value of anBallots, s is the number of seats, and\n n is the number of ballots. For plotting on the (inverted) adjusted rank scale, the linearly-scaled\n margin is added to the candidate’s rank. Note that the linearly-scaled margins are zero when a = 0,\n and thus have no effect on the adjusted rank. You might want to increase the value of anBallots,\n starting from 1.0, until the winning candidate’s adjusted rank is 1.0 when all ballots are counted,\n then confirm that the adjusted ranks of other candidates are still congruent with their ranking (i.e.\n that the rank-adjustment is less than 1 in all cases except perhaps on an initial transient with small\n numbers of ballots).\n When both anBallots and cMargins are non-zero, the ranks are adjusted with both exponentially-\n scaled margins and linearly-scaled margins. The resulting plot would be difficult to interpret in a\n valid way.\n Todo: Accept a list of SafeVoteExpt objects.\n Todo: Multiple counts with the same number of ballots could be summarised with a box-and-\n whisker graphic, rather than a set of jittered points.\n Todo: Consider developing a linear scaling that is appropriate for plotting stochastic experimental\n data derived from Condorcet elections.\nValue\n graphics object, with side-effect in RStudio Plots pane\n plot.SafeVote.stv plot() method for the result of an stv() ballot-count\nDescription\n The plot function shows the evolution of the total score for each candidate as well as the quota.\nUsage\n ## S3 method for class 'SafeVote.stv'\n plot(x, xlab = \"Count\", ylab = \"Preferences\", point.size = 2, ...)\nArguments\n x stv results\n xlab, ylab axis labels\n point.size diameter of elected/eliminated points\n ... params for generic plot()\nValue\n graphics object, with side-effect in RStudio’s Plots pane\n plurality Count votes using the plurality method\nDescription\n See https://arxiv.org/abs/2102.05801\nUsage\n plurality(votes, nseats = 1, fsep = \"\\t\", quiet = FALSE, ...)\nArguments\n votes, nseats, fsep, quiet, ...\n undocumented\nValue\n undocumented\n prepare.votes Coerce input ’data’ into a matrix\nDescription\n Coerce input ’data’ into a matrix\nUsage\n prepare.votes(data, fsep = \"\\n\")\nArguments\n data possibly a .csv file, possibly an R object\n fsep separation character for .csv e.g. tab or comma\nValue\n a matrix with one row per ballot, one column per candidate, with named rows and columns\n print.summary.SafeRankExpt\n Print method for summary.SafeRankExpt\nDescription\n Print method for summary.SafeRankExpt\nUsage\n ## S3 method for class 'summary.SafeRankExpt'\n print(x, ...)\nArguments\n x experimental results\n ... args for generic print()\nValue\n invisible(x), with side-effects to console\n print.summary.SafeVote.approval\n print method for summary object\nDescription\n print method for summary object\nUsage\n ## S3 method for class 'summary.SafeVote.approval'\n print(x, ...)\nArguments\n x, ... undocumented\nValue\n undocumented\nprint.summary.SafeVote.condorcet 31\n print.summary.SafeVote.condorcet\n print method for summary.SafeVote.condorcet\nDescription\n print method for summary.SafeVote.condorcet\nUsage\n ## S3 method for class 'summary.SafeVote.condorcet'\n print(x, ...)\nArguments\n x object of type summary.SafeVote.condorcet\n ... parameters passed to generic print\nValue\n textual description of x\n print.summary.SafeVote.plurality\n print method for summary of plurality object\nDescription\n print method for summary of plurality object\nUsage\n ## S3 method for class 'summary.SafeVote.plurality'\n print(x, ...)\nArguments\n x, ... undocumented\nValue\n undocumented\n print.summary.SafeVote.score\n print method for summary.score object\nDescription\n print method for summary.score object\nUsage\n ## S3 method for class 'summary.SafeVote.score'\n print(x, ...)\nArguments\n x, ... undocumented\nValue\n undocumented\n print.summary.SafeVote.stv\n print() method for a summary() of a SafeVote result\nDescription\n print() method for a summary() of a SafeVote result\nUsage\n ## S3 method for class 'summary.SafeVote.stv'\n print(x, ...)\nArguments\n x election results\n ... args to be passed to kable()\nValue\n no return value, called for side-effect of printing to console\n rbind.SafeRankExpt add a row to a SafeRankExpt object\nDescription\n add a row to a SafeRankExpt object\nUsage\n ## S3 method for class 'SafeRankExpt'\n rbind(object, row)\nArguments\n object prior results of experimentation\n row new observations\nValue\n SafeRankExpt object with an additional row\n readHil read a set of ballots in .HIL format\nDescription\n rangevoting.org/TidemanData.html: The data are in a format developed by <NAME>. The first\n line contains the number of candidates and the number to be elected. (Many but not all elections\n were multi-winner.) In subsequent lines that represent ballot papers, the first number is always\n 1. (The format was designed for a counting program that treats the first number as the number of\n instances of the ordering of the candidates on the line.) Next on these lines is a sequence of numbers\n representing a voter’s reported ranking: The number of the candidate ranked first, the number of\n the candidate ranked second, and so on. The end of the reported ranking is signaled by a zero. A\n zero at the beginning of the ranking is a signal that the list of ballot papers has ended. Next come\n the names of the candidates, each in parentheses, as required by the counting program, and finally\n the name of the election.\nUsage\n readHil(filnm, quiet = FALSE)\nArguments\n filnm name of a file in .HIL format\n quiet suppress diagnostic output\nValue\n a matrix with one row per ballot, one column per candidate, with named rows and columns, and\n with attributes \"nseats\" and \"ename\"\n remove.candidate Remove a candidate, amending ballot papers as required\nDescription\n Remove a candidate, amending ballot papers as required\nUsage\n remove.candidate(votes, can, quiet = TRUE)\nArguments\n votes ballot box\n can candidate to be removed\n quiet suppress diagnostics\nValue\n amended ballot box\n score Count votes using the score (or range) method.\nDescription\n See https://arxiv.org/abs/2102.05801\nUsage\n score(\n votes,\n nseats = 1,\n max.score = NULL,\n larger.wins = TRUE,\n fsep = \"\\t\",\n quiet = FALSE,\n ...\n )\nArguments\n votes, nseats, max.score, larger.wins, fsep, quiet, ...\n undocumented\nValue\n undocumented\n solveTiebreak Undocumented internal method, renamed from ’solve.tiebreak’ to\n avoid confusion with generic solve()\nDescription\n Undocumented internal method, renamed from ’solve.tiebreak’ to avoid confusion with generic\n solve()\nUsage\n solveTiebreak(method, prefs, icans, ordered.ranking = NULL, elim = TRUE)\nArguments\n method undocumented\n prefs undocumented\n icans undocumented\n ordered.ranking\n undocumented\n elim undocumented\nValue\n undocumented\n stv Count preferential ballots using an STV method\nDescription\n The votes parameter is as described in condorcet() with the following additional semantics.\nUsage\n stv(\n votes,\n nseats = NULL,\n eps = 0.001,\n equal.ranking = FALSE,\n fsep = \"\\t\",\n ties = c(\"f\", \"b\"),\n quota.hare = FALSE,\n constant.quota = FALSE,\n win.by.elim = TRUE,\n group.nseats = NULL,\n group.members = NULL,\n complete.ranking = FALSE,\n invalid.partial = FALSE,\n verbose = FALSE,\n seed = NULL,\n quiet = FALSE,\n digits = 3,\n backwards.compatible = FALSE,\n safety = 1,\n ...\n )\nArguments\n votes an array with one column per candidate and one row per ballot, as described in\n condorcet()\n nseats the number of seats to be filled in this election\n eps fuzz-factor when comparing fractional votes. The default of 0.001 is preserved\n from the legacy code, injecting substantial validity hazards into the codebase.\n We have not attempted to mitigate any of these hazards in SafeVote v1.0.0.\n We prefer instead to retain backwards-compatibility with the legacy code in\n vote_2.3-2 in the knowledge that, even if these hazards were adequately ad-\n dressed, the resulting code is unlikely to be reliable at replicating the results\n of any other implementation of any of the many variants of \"STV\" counting\n methods. Please see the description of the a53_hil dataset in this package for\n some preliminary findings on the magnitude of the vote-count-variances which\n may be injected by differing implementations of broadly-similar \"STV\" count-\n ing methods.\n equal.ranking if TRUE, equal preferences are allowed.\n fsep column-separator for output\n ties vector of tie-breaking methods: 'f' for forward, 'b' for backward\n quota.hare TRUE if Hare quota, FALSE if Droop quota (default)\n constant.quota TRUE if quota is held constant. Over-rides quota.hare. Default is FALSE\n win.by.elim TRUE (default) if the quota is waived when there are no more candidates than va-\n cant seats. Note: there is no lower limit when the quota is waived, so a candidate\n may be elected on zero votes.\n group.nseats number of seats reserved to members of a group\n group.members vector of members of the group with reserved seats\n complete.ranking\n is TRUE by default. This parameter is retained solely for backwards compatibility\n with vote::stv(). It has no effect on elections in which nseats is explicitly\n specified in the call to stv().\n invalid.partial\n TRUE if ballots which do not specify a complete ranking of candidates are infor-\n mal (aka \"invalid\") i.e. ignored (with a warning). Default is FALSE.\n verbose TRUE for diagnostic output\n seed integer seed for tie-breaking. Warning: if non-NULL, the PRNG for R is reseeded\n prior to every random tie-break among the possibly-elected candidates. We have\n preserved this functionality in this branch to allow regression against the legacy\n codebase of vote::stv(). In stv() the default value for seed is NULL rather\n than the legacy value of 1234, to mitigate the validity hazard of PRNG reseed-\n ings during a stochastic experiment.\n quiet TRUE to suppress console output\n digits number of significant digits in the output table\n backwards.compatible\n TRUE to regress against vote2_3.2 by disabling $margins, $fuzz, $rankingTable,\n $safeRank\n safety number of standard deviations on vote-counts, when producing a safeRank by\n clustering near-ties in a complete ranking\n ... undocumented intent (preserved from legacy code)\nDetails\n By default the preferences are not allowed to contain duplicates per ballot. However, if the argument\n equal.ranking is set to TRUE, ballots are allowed to have the same ranking for multiple candidates.\n The desired format is such that for each preference $i$ that does not have any duplicate, there must\n be exactly $i – 1$ preferences $j$ with $0 < j < i$. For example, valid ordered preferences are\n 1; 1; 3; 4; . . . , or 1; 2; 3; 3; 3; 6; . . . , but NOT 1; 1; 2; 3; . . . , or NOT\n 1; 2; 3; 3; 3; 5; 6; . . . . If the data contain such invalid votes, they are automatically\n corrected and a warning is issued by calling the correct.ranking function.\n If equal ranking is not allowed (equal.ranking = FALSE), the argument invalid.partial can be\n used to make ballots containing duplicates or gaps partially valid. If it is TRUE, a ballot is considered\n valid up to a preference that is in normal case not allowed. For example, ballots 1; 2; 3; 4; 4; 6\n or 1; 2; 3; 5; 6; 7 would be both converted into 1; 2; 3; 0; 0; 0, because the ballots contain\n valid ranking only up to the third preference.\n By default, ties in the STV algorithm are resolved using the forwards tie-breaking method, see\n Newland and Briton (Section 5.2.5). Argument ties can be set to ”b” in order to use the back-\n wards tie-breaking method, see O’Neill (2004). In addition, both methods are complemented by\n the following “ordered” method: Prior to the STV election candidates are ordered by the number\n of first preferences. Equal ranks are resolved by moving to the number of second preferences, then\n third and so on. Remaining ties are broken by random draws. Such complete ordering is used to\n break any tie that cannot be resolved by the forwards or backwards method. If there is at least one\n tie during the processing, the output contains a row indicating in which count a tie-break happened\n (see the ties element in the Value section for an explanation of the symbols).\n The ordered tiebreaking described above can be analysed from outside of the stv function by using\n the ordered.tiebreak function for viewing the a-priori ordering (the highest number is the best\n and lowest is the worst). Such ranking is produced by comparing candidates along the columns of\n the matrix returned by ordered.preferences.\nValue\n object of class vote.stv. Note: the winning margins in this object are valid for the elected candi-\n dates and their (total) ranking, but must be adjusted within tiegroups to be valid for the candidates’\n (possibly partial) safeRank.\nExamples\n data(food_election)\n stv(food_election, safety = 0.0)\n stv(food_election, nseats = 2)\n summary.SafeRankExpt summary method for SafeRankExpt\nDescription\n summary method for SafeRankExpt\nUsage\n ## S3 method for class 'SafeRankExpt'\n summary(object, ...)\nArguments\n object experimental results to be summarised\n ... args for generic summary()\nsummary.SafeVote.approval 39\nValue\n summary.SafeRankExpt object\n summary.SafeVote.approval\n summary method for approval results\nDescription\n summary method for approval results\nUsage\n ## S3 method for class 'SafeVote.approval'\n summary(object, ...)\nArguments\n object, ... undocumented\nValue\n undocumented\n summary.SafeVote.condorcet\n Summary method for condorcet() results\nDescription\n Summary method for condorcet() results\nUsage\n ## S3 method for class 'SafeVote.condorcet'\n summary(object, ...)\nArguments\n object of type SafeVote.condorcet\n ... undocumented, currently unused\nValue\n data.frame object\n summary.SafeVote.plurality\n summary method for plurality object\nDescription\n summary method for plurality object\nUsage\n ## S3 method for class 'SafeVote.plurality'\n summary(object, ...)\nArguments\n object, ... undocumented\nValue\n descriptive dataframe\n summary.SafeVote.score\n summary method for score object\nDescription\n summary method for score object\nUsage\n ## S3 method for class 'SafeVote.score'\n summary(object, ...)\nArguments\n object, ... undocumented\nValue\n undocumented\n summary.SafeVote.stv summary() method for a SafeVote result\nDescription\n summary() method for a SafeVote result\nUsage\n ## S3 method for class 'SafeVote.stv'\n summary(object, ..., digits = 3)\nArguments\n object undocumented, legacy code\n ... undocumented\n digits undocumented\nValue\n data.frame summarising object, for use by print method\n sumOfVotes internal method, computes column-sums\nDescription\n Renamed from ’sum.votes’ to avoid confusion with the generic sum()\nUsage\n sumOfVotes(votes)\nArguments\n votes ballots are rows, candidates are columns\nValue\n vector of votes for each candidate\n testAdditions Test the sensitivity of a result to tactical voting.\nDescription\n Ballots are added until a specified number of simulated elections (arep) have been held. If a\n favoured candidate is specified, then the ballot-box is stuffed with ballots awarding first-preference\n to this candidate. Alternatively, a tacticalBallot may be specified. If both favoured and\n tacticalBallot are NULL, then a random candidate is selected as the favoured one.\nUsage\n testAdditions(\n votes,\n ainc = 1,\n arep = NULL,\n favoured = NULL,\n tacticalBallot = NULL,\n rankMethod = \"safeRank\",\n countMethod = \"stv\",\n countArgs = list(),\n exptName = NULL,\n equiet = FALSE,\n everbose = FALSE\n )\nArguments\n votes A set of ballots, as in vote_2.3.2\n ainc Number of ballots to be added in each step\n arep Maximum number of ballot-stuffed elections to run\n favoured Name of the candidate being \"plumped\". If NULL, a random candidate is se-\n lected from among the candidates not initially top-ranked. All other candidates\n are fully-ranked at random, with an identical ballot paper being stuffed multi-\n ple times. An integer value for favoured is interpreted as an index into the\n candidate names.\n tacticalBallot A ballot paper i.e. a vector of length ncol(ballots). If this argument is non-\n NULL, it takes precedence over favoured when the ballot box is being stuffed.\n rankMethod \"safeRank\" (default), \"elected\", or \"rank\". \"rank\" is a total ranking of the can-\n didates, with ties broken at random. \"elected\" assigns rank=1 to elected candi-\n dates, rank=2 for eliminated candidates.\n countMethod countMethod \"stv\" (default) or \"condorcet\"\n countArgs List of args to be passed to countMethod (in addition to votes)\n exptName stem-name of experimental units e.g. \"E\". If NULL, then a 3-character string of\n capital letters is chosen at random.\n equiet TRUE to suppress all experimental output\n everbose TRUE to produce diagnostic output from the experiment\nValue\n A matrix of experimental results, of dimension n by 2m + 1, where n is the number of elections\n and m is the number of candidates. The first column is named \"nBallots\". Other columns indicate\n the ranking of the eponymous candidate, and their margin over the next-lower-ranked candidate.\nExamples\n data(food_election)\n testAdditions(food_election, arep = 2, favoured = \"Strawberries\",\n countArgs = list(safety = 0))\n testDeletions Assess the safety of a preliminary result for an election\nDescription\n Ballots are deleted at random from the ballot-box, with election results computed once per dinc\n ballot-deletions. The experiment terminates after a specified number of ballots have been deleted,\n or a specified number of ballot-counts have occurred. Note: these ballot-counts are correlated. Use\n testFraction() to experiment with independently-drawn samples from the ballot-box.\nUsage\n testDeletions(\n votes,\n countMethod = \"stv\",\n countArgs = list(),\n dstart = NULL,\n dinc = NULL,\n dlimit = NULL,\n drep = NULL,\n rankMethod = \"safeRank\",\n exptName = NULL,\n equiet = FALSE,\n everbose = FALSE\n )\nArguments\n votes A set of ballots, as in vote_2.3.2\n countMethod \"stv\" (default) or \"condorcet\"\n countArgs List of args to be passed to countMethod (in addition to votes)\n dstart Number of ballots in the first ballot-count (selected at random from votes, with-\n out replacement)\n dinc Number of ballots to be deleted in subsequent steps\n dlimit Maximum number of ballots to delete (in addition to dstart)\n drep Maximum number of elections (required if dinc=0)\n rankMethod \"safeRank\" (default), \"elected\", or \"rank\". \"rank\" is a total ranking of the can-\n didates, with ties broken at random. \"elected\" assigns rank=1 to elected candi-\n dates, rank=2 for eliminated candidates.\n exptName stem-name of experimental units e.g. \"E\". If NULL, then a 3-character string of\n capital letters is chosen at random.\n equiet TRUE to suppress all experimental output\n everbose TRUE to produce diagnostic output from the experiment\nValue\n SafeRankExpt object, describing this experiment and its results\nExamples\n data(food_election)\n testDeletions(food_election)\n testDeletions(food_election, countMethod=\"stv\",\n countArgs=list(complete.ranking=TRUE))\n testFraction Bootstrapping experiment, with fractional counts of a ballot box.\nDescription\n Starting from some number (astart) of randomly-selected ballots, an increasingly-large collection\n of randomly-selected ballots are counted. The ballots are chosen independently without replace-\n ment for each experimental unit; if you want to count decreasingly-sized portions of a single sample\n of ballots, use testDeletions().\nUsage\n testFraction(\n votes = NULL,\n astart = NULL,\n ainc = NULL,\n arep = NULL,\n trep = NULL,\n rankMethod = \"safeRank\",\n countMethod = \"stv\",\n countArgs = list(),\n exptName = NULL,\n equiet = FALSE,\n everbose = FALSE\n )\nArguments\n votes A numeric matrix: one row per ballot, one column per candidate\n astart Starting number of ballots (min 2)\n ainc Number of ballots to be added in each step. Must be non-negative.\n arep Number of repetitions of the test on each step. Required to be non-NULL if\n ainc=0 && is.null(trep)‘.\n trep Limit on the total number of simulated elections. Required to be non-NULL if\n ainc=0 && is.null(arep).\n rankMethod \"safeRank\" (default), \"elected\", or \"rank\". \"rank\" is a total ranking of the can-\n didates, with ties broken at random. \"elected\" assigns rank=1 to elected candi-\n dates, rank=2 for eliminated candidates.\n countMethod countMethod \"stv\" (default) or \"condorcet\"\n countArgs List of args to be passed to countMethod (in addition to votes)\n exptName stem-name of experimental units e.g. \"E\". If NULL, then a 3-character string of\n capital letters is chosen at random.\n equiet TRUE to suppress all experimental output\n everbose TRUE to produce diagnostic output from the experiment\nValue\n a SafeRankExpt object of experimental results.\nExamples\n data(food_election)\n testFraction(food_election, countMethod=\"condorcet\",\n countArgs=list(safety=0.5,complete.ranking=TRUE))\n testFraction(dublin_west, astart=20, ainc=10, arep=2, trep=3,\n countMethod=\"stv\", rankMethod=\"elected\", equiet=FALSE)\n translate.ties Undocumented internal method from original code\nDescription\n Undocumented internal method from original code\nUsage\n translate.ties(ties, method)\nArguments\n ties undocumented\n method ’f’ for forward, ’b’ for backward\nValue\n undocumented\n uk_labour_2010 UK Labour Party Leader 2010\nDescription\n These are the ballots cast by Labour MPs and MEPs in an election of their party’s leader in 2010,\n as published by the Manchester Guardian. The names of the electors have been suppressed in this\n file, but are available at rangevoting.org, along with extensive commentary on the election.\nUsage\n data(uk_labour_2010)\nFormat\n A data frame with 266 observations and 5 candidates.\n view generic view() for classes defined in this package\nDescription\n generic view() for classes defined in this package\nUsage\n view(object, ...)\nArguments\n object election object to be viewed\n ... additional parameters, passed to formattable::formattable()\nValue\n html-formatted object, with side-effect in RStudio’s Viewer pane\nview.SafeVote.approval 47\n view.SafeVote.approval\n view method for approval object\nDescription\n view method for approval object\nUsage\n ## S3 method for class 'SafeVote.approval'\n view(object, ...)\nArguments\n object, ... undocumented\nValue\n undocumented\n view.SafeVote.condorcet\n view method for SafeVote.condorcet\nDescription\n view method for SafeVote.condorcet\nUsage\n ## S3 method for class 'SafeVote.condorcet'\n view(object, ...)\nArguments\n object of type SafeVote.condorcet\n ... see view.SafeVote.approval\nValue\n view object\n view.SafeVote.plurality\n view method for plurality object\nDescription\n view method for plurality object\nUsage\n ## S3 method for class 'SafeVote.plurality'\n view(object, ...)\nArguments\n object, ... undocumented\nValue\n undocumented\n view.SafeVote.score view method for score object\nDescription\n view method for score object\nUsage\n ## S3 method for class 'SafeVote.score'\n view(object, ...)\nArguments\n object, ... undocumented\nValue\n undocumented\n view.SafeVote.stv view method for the result of an stv() ballot-count\nDescription\n view method for the result of an stv() ballot-count\nUsage\n ## S3 method for class 'SafeVote.stv'\n view(object, ...)\nArguments\n object object to be viewed\n ... additional parameters, passed to formattable::formattable()\nValue\n html-formatted object\n winnerMargin Find a winner and their margin of victory\nDescription\n Find a winner and their margin of victory\nUsage\n winnerMargin(votes)\nArguments\n votes cleaned ballots\nValue\n length-2 vector: the index of a winning candidate, and their margin of victory (0 if a tie, NA if no\n losers)\n yale_ballots Yale Faculty Senate 2016\nDescription\n This data follows the structure of a 2016 Yale Faculty Senate election, with candidate names\n anonymised and permuted. Imported to SafeVote from STV v1.0.2, after applying the STV::cleanBallots\n method to remove the ten empty rows.\nUsage\n data(yale_ballots)\nFormat\n A data frame with 479 observations and 44 candidates."}}},{"rowIdx":59465,"cells":{"project":{"kind":"string","value":"github.com/ribice/glice"},"source":{"kind":"string","value":"go"},"language":{"kind":"string","value":"Go"},"content":{"kind":"string","value":"README\n [¶](#section-readme)\n---\n\n### glice\n\n[](https://travis-ci.org/ribice/glice)\n[](https://coveralls.io/github/ribice/glice?branch=master)\n[](https://goreportcard.com/report/github.com/ribice/glice)\n\nGolang license and dependency checker. Prints list of all dependencies (both from std and 3rd party), number of times used, their license and saves all the license files in /licenses.\n\n#### Introduction\n\nglice analyzes the source code of your project and gets the list of all dependencies (by default only third-party ones, standard library can be enabled with flag) and prints in a tabular format their name, URL (for third-party ones, currently only GitHub is supported) and license short-name (MIT, GPL..).\n\n#### Installation\n\nDownload and install glice by executing:\n```\n go get github.com/ribice/glice\n go install github.com/ribice/glice\n```\nTo update:\n```\n go get -u github.com/ribice/glice\n```\n#### Usage\n\nTo run glice, navigate to a folder in gopath and execute:\n```\n glice\n```\nAlternatively, you can provide path which you want to be scanned with -p flag:\n```\n glice -p\"github.com/ribice/glice/\"\n```\nBy default glice:\n\n* Prints only to stdout\n* Gets dependencies and licenses from current directory\n* Shows only third-party dependencies, grouped under project name (e.g. github.com/author/repo/http and github.com/author/repo/http/middleware are counted as 2 github.com/author/repo, and that's being displayed)\n* Shows only dependencies of project where you're currently located (does not go recursively through dependencies)\n* Is limited to 60 API calls on GitHub (up to 60 dependencies from github.com)\n* Ignores files in vendor folder\n\nAll flags are optional. Glice supports the following flags:\n```\n- s [boolean - include standard library]// return standard library dependencies as well as third-party ones\n- v [boolean - verbose] // by default, github.com/author/repo/http and github.com/author/repo/http/middleware are counted as 2 times github.com/author/repo, and that's being displayed. With verbose, they are counted and shown separately.\n- r [boolean - recursive] // returns dependencies of dependencies (single level only)\n- f [boolean - fileWrite] // writes all license files inside /licenses folder\n- i [string - ignoreFolders] // list of comma-separated folders that should be ignored\n- p [string - path] // path to be scanned in form of github.com/author/repo/\n- gh [string - githubAPIKey] // used to increase GitHub API's rate limit from 60req/h to 5000req/h\n- t [boolean - thanks] // if GitHub API key is provided, setting this flag will star all GitHub repos from dependency. __In order to do this, API key must have access to public_repo__\n- c [boolean - count] // print usage count of dependencies in packages (max one count per package)\n```\nDon't forget `-help` flag for detailed usage information.\n\n#### Sample output\n\nExecuting glice -c on github.com/qiangxue/golang-restful-starter-kit prints (with additional colors for links and licenses):\n```\n+---+---+---+---+\n| DEPENDENCY | COUNT | REPOURL | LICENSE |\n+---+---+---+---+\n| fmt | 5 | | |\n| github.com/Sirupsen/logrus | 2 | https://github.com/Sirupsen/logrus | MIT |\n| github.com/go-ozzo/ozzo-dbx | 3 | https://github.com/go-ozzo/ozzo-dbx | MIT |\n| github.com/go-ozzo/ozzo-routing | 9 | https://github.com/go-ozzo/ozzo-routing | MIT |\n| github.com/lib/pq | 2 | https://github.com/lib/pq | MIT |\n| net/http | 3 | | |\n| github.com/dgrijalva/jwt-go | 1 | https://github.com/dgrijalva/jwt-go | MIT |\n| strconv | 1 | | |\n| time | 2 | | |\n| database/sql | 1 | | |\n| github.com/go-ozzo/ozzo-validation | 3 | https://github.com/go-ozzo/ozzo-validation | MIT |\n| github.com/spf13/viper | 1 | https://github.com/spf13/viper | MIT |\n| gopkg.in/yaml.v2 | 1 | | |\n| io/ioutil | 2 | | |\n| sort | 1 | | |\n| strings | 3 | | |\n| os | 1 | | |\n+---+---+---+---+\n```\n#### To-Do\n\n* Improve tests and code coverage\n* Add flag to disable dependencies from test files\n* Implement license checking for projects hosted on GitLab.com\n* Implement license checking for projects hosted on Bitbucket.org\n* Implement license checking for projects hosted on other third party sites (e.g. gitea.io, gogs.io)\n* Add ability to send path of project via flag\n* Remove dependency on go-github\n* Implement concurrency\n* Add naming option when saving licenses to files (currently author-repo-license.MD)\n\n#### License\n\nglice is licensed under the MIT license. Check the [LICENSE](https://github.com/ribice/glice/blob/v1.0.0/LICENSE.md) file for details.\n\n#### Author\n\n[<NAME>](https://ribice.ba)\n\nDocumentation\n [¶](#section-documentation)\n---\n\n\nThere is no documentation for this package."}}},{"rowIdx":59466,"cells":{"project":{"kind":"string","value":"pypi_bcolz.jsonl"},"source":{"kind":"string","value":"personal_doc"},"language":{"kind":"string","value":"Dart"},"content":{"kind":"string","value":"* Optimized Hyper-slicing in PyTables with Blosc2 NDim\n * Dynamic plugins in C-Blosc2\n * Bytedelta: Enhance Your Compression Toolset\n * Introducing Blosc2 NDim\n * 100 Trillion Rows Baby\n * 20 years of PyTables\n * Blosc2 Meets PyTables: Making HDF5 I/O Performance Awesome\n * User Defined Pipeline for Python-Blosc2\n * New features in Python-Blosc2\n * Announcing Support for Lossy ZFP Codec as a Plugin for C-Blosc2\n * Caterva Slicing Performance: A Study\n * Registering plugins in C-Blosc2\n * Wrapping C-Blosc2 in Python (a beginner's view)\n * C-Blosc2 Ready for General Review\n * Blosc metalayers, where the user metainformation is stored\n * Introducing Sparse Frames\n * Announcing Blosc Wheels\n * Mid 2020 Progress Report\n * C-Blosc Beast Release\n * Blosc Received a $50,000 USD donation\n * Blosc2-Meets-Rome\n * C-Blosc2 Enters Beta Stage\n * Is ARM Hungry Enough to Eat Intel's Favorite Pie?\n * Breaking Down Memory Walls\n * New Forward Compatibility Policy\n * Blosc Has Won Google's Open Source Peer Bonus Program\n * The Lizard Codec\n * Testing PGO with LZ4 and Zstd codecs\n * Fine Tuning the BloscLZ codec\n * Zstd has just landed in Blosc\n * ARM is becoming a first-class citizen for Blosc\n * Hairy situation of Microsoft Windows compilers\n * New 'bitshuffle' filter\n * Seeking Sponsorship for Bcolz/Blosc\n * Compress Me, Stupid!\n\n# Why it works?\n\nBlosc is a high-performance compressor that has been optimized for binary data. Its design allows for faster transmission of data to the processor cache than the traditional, non-compressed, direct memory fetch approach through an memcpy() OS call. This can be useful not only in reducing the size of large datasets, but also in accelerating I/O, be either on-disk or in-memory (both are supported).\n\nWatch this introductory video to learn more about the main features of Blosc:\n\nBlosc2 is the new iteration of the Blosc 1.x series, which adds more features and better documentation. You can also check out the slides that explain the highlights of Blosc2.\n\nBlosc2 also includes NDim, a container with multi-dimensional capabilities. In particular, Blosc2 NDim excels at reading multi-dimensional slices, thanks to its innovative pineapple-style partitioning. To learn more, watch the video Why slicing in a pineapple-style is useful.\n\nYou can also check out the slides that explain the highlights of Blosc2 NDim, specially when dealing with highly sparse, multidimensional datasets that appear when exploring the Milky Way. There it is also discussed Btune, a tool that helps you finding the best Blosc2 configuration for your data.\n\nWhen Blosc2 is used in combination with other libraries, magic can happen. For example, when used with HDF5/PyTables, Blosc2 can help to query tables with 100 trillion rows in human time frames. Read more on this in these slides on the latest developments of Blosc2.\n\n## Why it works?\n\nBlosc uses the blocking technique (as described here) to reduce activity on the memory bus as much as possible. The blocking technique divides datasets into blocks small enough to fit in the caches of modern processors and performs compression/decompression there. It also leverages SIMD (SSE2) and multi-threading capabilities present in modern multi-core processors to accelerate the compression/decompression process to the maximum.\n\nBlosc2 also applies more advanced techniques to improve the compression ratio on sparse datasets, and a larger diversity of filters such as bytedelta. This makes Blosc2 a very versatile compressor that can be used in a wide range of situations.\n\n## Performance\n\nBlosc2 is also designed to be efficient when retrieving blocks and chunks in multidimensional datasets. For comparison purposes, see below the speed that BloscLZ, one of the fastest codecs available in Blosc, can achieve when combined with different libraries supporting Blosc(1)/Blosc2 when accessing a 7.3 TB dataset:\n\nNote how BloscLZ does not need a lot of threads to reach its performance. Such a low requirement on CPU core count makes it ideal for running on small laptops while guaranteeing reasonable performance.\n\nAnd below is the compression ratio that BloscLZ, and also Zstd (the codec that can typically achieve better compression ratios in Blosc), can achieve when combined with different libraries supporting Blosc(1)/Blosc2:\n\nSee how Blosc2 can make better use of the space required to store the compressed data and internal indices, specially when dealing with sparse datasets (as is the case above). More info in these slides.\n\nYou can find more benchmarks on our blog. Additionally, you may be interested in reading this article on Breaking Down Memory Walls. Finally, make sure to check out Blosc2, the next generation of Blosc, with support for n-dimensional data as well as more efficient handling of sparse data.\n\n## Blosc as a Meta-Compressor\n\nBlosc is not like other compressors; it should rather be called a meta-compressor. This is because it can use different codecs (libraries that reduce the size of inputs) and filters (libraries that improve compression ratio) under the hood. Nonetheless, it can still be referred to as a compressor because it includes several codecs conveniently packaged and made accessible for you.\n\nCurrently, Blosc uses BloscLZ by default, a codec heavily based on FastLZ. Blosc also includes support for LZ4 and LZ4HC, Zlib and Zstd right out-of-the-box. Also, it comes with highly optimized shuffle, bitshuffle, bytedelta and precision truncation filters. These can use SSE2, AVX2 (Intel), NEON (ARM) or VMX/AltiVec/VSX (PowerPC) instructions (if available).\n\nBlosc is responsible for coordinating codecs and filters to leverage the blocking technique (described above) and multi-threaded execution (when several cores are available), while making minimal use of temporary buffers. This ensures that every codec and filter can operate at high speeds, even if it was not initially designed for blocking or multi-threading. For instance, Blosc allows the use of the LZ4 codec in a multi-threaded manner by default.\n\n## Other Advantages over Existing Compressors\n\nMeant for binary data: Can take advantage of the type size meta-information to improve the compression ratio by using the integrated shuffle and bitshuffle filters.\n * \n\nSmall overhead on non-compressible data: Only a maximum of 32 for Blosc2 (16 for Blosc1) of additional bytes per data chunk are needed on non-compressible data.\n * \n\n63-bit containers: In Blosc2, we have introduced super-chunks as a way to overcome the limitations of chunks, which can only be up to 2^31 bytes in size. Super-chunks, on the other hand, can host data up to 2^63 bytes in size.\n * \n\nFrames: Blosc2 also has introduced a way to serialize data either in-memory or on-disk. Frames provide an efficient way to persist or transmit the data in a compressed format.\n\nHowever, there is much more to Blosc. For an updated list of features, please refer to our ROADMAP. When combined, these features distinguish Blosc from other similar solutions.\n\n## Where Can Blosc Be Used?\n\nProvided that data is compressible enough, applications that use Blosc are expected to surpass expected physical limits for I/O performance, either for network, disk, or in-memory storage, simply because applications needs to transmit less (compressed) data, and compression/decompression is very fast and usually happens entirely in CPU caches. For instance, see how Blosc can break down memory walls.\n\nBlosc2 also adds support for sparse and multi-dimensional datasets, which are common in scientific applications. See an example on how Blosc can make an efficient access to much larger datasets than the available memory.\n\nCurrently, there is support for using Blosc in Zarr, h5py (via hdf5plugin) or PyTables; all of these projects have binary packages, so it is easy to start using it.\n\n## Adapt Blosc to your needs\n\nWe understand that every user has unique needs, so we have made it possible to register your own codecs and filters to better adapt Blosc to different scenarios. Additionally, you can request that they be included in the main C-Blosc2 library, which not only allows for easier deployment, but also contributes to creating a richer and more useful ecosystem.\n\nAdditionally, we have created Btune, an innovative AI tool that can automatically determine the best compression parameters for your specific use case. The Blosc Development Team is continuously working on improving it to meet your needs.\n\n## Is Blosc Ready for Production Use?\n\nYes, it is!\n\nBlosc is currently being used in various libraries and is able to compress data at a rate that exceeds several petabytes per month worldwide. Fortunately, there haven't been many reports of failures caused by Blosc itself, but we strive to respond as quickly as possible when such issues do arise.\n\nAfter a long period of testing, C-Blosc2 has entered the production stage in version 2.0.0. Additionally, all new releases are guaranteed to read from persistent storage generated from previous releases (as of 2.0.0).\n\n## Git repository, downloads and ticketing\n\nThe home of the git repository for all Blosc-related libraries is located at:\n\nYou can download the sources and file tickets there too.\n\n## Twitter feed\n\nKeep informed about the latest developments by following the @Blosc2 twitter account:\n\n## Mailing list\n\nThere is an official Blosc blosc mailing list at:\n\n## Python wrappers\n\nThe official Python wrappers can be found at:\n\nhttp://github.com/Blosc/python-blosc http://github.com/Blosc/python-blosc2\n\n## Want To Contribute?\n\nYour contribution is crucial to making Blosc as solid as possible. If you detect a bug or wish to propose an enhancement, feel free to open a new ticket or make yourself heard on the mailing list. Also, please note that we have a Code of Conduct that you should read before contributing in any way.\n\n## Blosc License\n\nBlosc is a free software released under the permissive BSD license. This means that you can use it in almost any way you want!\n\n-- The Blosc Development Team\n\nDate: 2009-01-01\nCategories: \nTags: \n\n## A fast, compressed and persistent data store library for C#\n\nThe Blosc Development Team\n * Contact\n * URL\n * Gitter\n * Actions\n * NumFOCUS\n * Code of Conduct\n\n## What is it?#\n\nBlosc is a high performance compressor optimized for binary data (i.e. floating point numbers, integers and booleans, although it can handle string data too). It has been designed to transmit data to the processor cache faster than the traditional, non-compressed, direct memory fetch approach via a memcpy() OS call. Blosc main goal is not just to reduce the size of large datasets on-disk or in-memory, but also to accelerate memory-bound computations.\n\nC-Blosc2 is the new major version of C-Blosc, and is backward compatible with both the C-Blosc1 API and its in-memory format. However, the reverse thing is generally not true for the format; buffers generated with C-Blosc2 are not format-compatible with C-Blosc1 (i.e. forward compatibility is not supported). In case you want to ensure full API compatibility with C-Blosc1 API, define the BLOSC1_COMPAT symbol.\n\nSee a 3 minutes introductory video to Blosc2.\n\n## Blosc2 NDim: an N-Dimensional store#\n\nOne of the latest and more exciting additions in C-Blosc2 is the Blosc2 NDim layer (or b2nd for short), allowing to create and read n-dimensional datasets in an extremely efficient way thanks to a n-dim 2-level partitioning, that allows to slice and dice arbitrary large and compressed data in a more fine-grained way:\n\nTo wet you appetite, here it is how the NDArray object in the Python wrapper performs on getting slices orthogonal to the different axis of a 4-dim dataset:\n\nWe have blogged about this: https://www.blosc.org/posts/blosc2-ndim-intro\n\n## New features in C-Blosc2#\n\n64-bit containers: the first-class container in C-Blosc2 is the super-chunk or, for brevity, schunk, that is made by smaller chunks which are essentially C-Blosc1 32-bit containers. The super-chunk can be backed or not by another container which is called a frame (see later).\n * \n\nNDim containers (b2nd): allow to store n-dimensional data that can efficiently read datasets in slices that can be n-dimensional too. To achieve this, a n-dimensional 2-level partitioning has been implemented. This capabilities were formerly part of Caterva, and now it is included in C-Blosc2 for convenience. Caterva is now deprecated.\n * \n\nMore filters: besides shuffle and bitshuffle already present in C-Blosc1, C-Blosc2 already implements:\n\nbytedelta: calculates the difference between bytes in a block that has been shuffled already. We have blogged about bytedelta.\n * \n\ndelta: the stored blocks inside a chunk are diff’ed with respect to first block in the chunk. The idea is that, in some situations, the diff will have more zeros than the original data, leading to better compression.\n * \n\ntrunc_prec: it zeroes the least significant bits of the mantissa of float32 and float64 types. When combined with the shuffle or bitshuffle filter, this leads to more contiguous zeros, which are compressed better.\n * \n\nA filter pipeline: the different filters can be pipelined so that the output of one can the input for the other. A possible example is a delta followed by shuffle, or as described above, trunc_prec followed by bitshuffle.\n * \n\nPrefilters: allow to apply user-defined C callbacks prior the filter pipeline during compression. See test_prefilter.c for an example of use.\n * \n\nPostfilters: allow to apply user-defined C callbacks after the filter pipeline during decompression. The combination of prefilters and postfilters could be interesting for supporting e.g. encryption (via prefilters) and decryption (via postfilters). Also, a postfilter alone can be used to produce on-the-flight computation based on existing data (or other metadata, like e.g. coordinates). See test_postfilter.c for an example of use.\n * \n\nSIMD support for ARM (NEON): this allows for faster operation on ARM architectures. Only shuffle is supported right now, but the idea is to implement bitshuffle for NEON too. Thanks to <NAME>.\n * \n\nSIMD support for PowerPC (ALTIVEC): this allows for faster operation on PowerPC architectures. Both shuffle and bitshuffle are supported; however, this has been done via a transparent mapping from SSE2 into ALTIVEC emulation in GCC 8, so performance could be better (but still, it is already a nice improvement over native C code; see PR Blosc/c-blosc2#59 for details). Thanks to <NAME> and ESRF for sponsoring the Blosc team in helping him in this task.\n * \n\nDictionaries: when a block is going to be compressed, C-Blosc2 can use a previously made dictionary (stored in the header of the super-chunk) for compressing all the blocks that are part of the chunks. This usually improves the compression ratio, as well as the decompression speed, at the expense of a (small) overhead in compression speed. Currently, it is only supported in the zstd codec, but would be nice to extend it to lz4 and blosclz at least.\n * \n\nContiguous frames: allow to store super-chunks contiguously, either on-disk or in-memory. When a super-chunk is backed by a frame, instead of storing all the chunks sparsely in-memory, they are serialized inside the frame container. The frame can be stored on-disk too, meaning that persistence of super-chunks is supported.\n * \n\nSparse frames: each chunk in a super-chunk is stored in a separate file or different memory area, as well as the metadata. This is allows for more efficient updates/deletes than in contiguous frames (i.e. avoiding ‘holes’ in monolithic files). The drawback is that it consumes more inodes when on-disk. Thanks to <NAME> for this contribution.\n * \n\nPartial chunk reads: there is support for reading just part of chunks, so avoiding to read the whole thing and then discard the unnecessary data.\n * \n\nParallel chunk reads: when several blocks of a chunk are to be read, this is done in parallel by the decompressing machinery. That means that every thread is responsible to read, post-filter and decompress a block by itself, leading to an efficient overlap of I/O and CPU usage that optimizes reads to a maximum.\n * \n\nMeta-layers: optionally, the user can add meta-data for different uses and in different layers. For example, one may think on providing a meta-layer for NumPy so that most of the meta-data for it is stored in a meta-layer; then, one can place another meta-layer on top of the latter for adding more high-level info if desired (e.g. geo-spatial, meteorological…).\n * \n\nVariable length meta-layers: the user may want to add variable-length meta information that can be potentially very large (up to 2 GB). The regular meta-layer described above is very quick to read, but meant to store fixed-length and relatively small meta information. Variable length metalayers are stored in the trailer of a frame, whereas regular meta-layers are in the header.\n * \n\nEfficient support for special values: large sequences of repeated values can be represented with an efficient, simple and fast run-length representation, without the need to use regular codecs. With that, chunks or super-chunks with values that are the same (zeros, NaNs or any value in general) can be built in constant time, regardless of the size. This can be useful in situations where a lot of zeros (or NaNs) need to be stored (e.g. sparse matrices).\n * \n\nNice markup for documentation: we are currently using a combination of Sphinx + Doxygen + Breathe for documenting the C-API. See https://www.blosc.org/c-blosc2/c-blosc2.html. Thanks to <NAME> and <NAME> for contributing the support for this.\n * \n\nPlugin capabilities for filters and codecs: we have a plugin register capability inplace so that the info about the new filters and codecs can be persisted and transmitted to different machines. See Blosc/c-blosc2 for a self-contained example. Thanks to the NumFOCUS foundation for providing a grant for doing this, and <NAME> and <NAME> for the implementation.\n * \n\nPluggable tuning capabilities: this will allow users with different needs to define an interface so as to better tune different parameters like the codec, the compression level, the filters to use, the blocksize or the shuffle size. Thanks to ironArray for sponsoring us in doing this.\n * \n\nSupport for I/O plugins: so that users can extend the I/O capabilities beyond the current filesystem support. Things like the use of databases or S3 interfaces should be possible by implementing these interfaces. Thanks to ironArray for sponsoring us in doing this.\n * \n\nPython wrapper: we have a preliminary wrapper in the works. You can have a look at our ongoing efforts in the python-blosc2 repo. Thanks to the Python Software Foundation for providing a grant for doing this.\n * \n\nSecurity: we are actively using using the OSS-Fuzz and ClusterFuzz for uncovering programming errors in C-Blosc2. Thanks to Google for sponsoring us in doing this, and to <NAME> for most of the work here.\n\nMore info about the improved capabilities of C-Blosc2 can be found in this talk.\n\nC-Blosc2 API and format have been frozen, and that means that there is guarantee that your programs will continue to work with future versions of the library, and that next releases will be able to read from persistent storage generated from previous releases (as of 2.0.0).\n\n## Python wrapper#\n\nWe are officially supporting (thanks to the Python Software Foundation) a Python wrapper for Blosc2. It supports all the features of the predecessor python-blosc package plus most of the bells and whistles of C-Blosc2, like 64-bit and multidimensional containers. As a bonus, the python-blosc2 package comes with wheels and binary versions of the C-Blosc2 libraries, so anyone, even non-Python users can install C-Blosc2 binaries easily with:\n `pip install blosc2` \n\n## Compiling the C-Blosc2 library with CMake#\n\nBlosc can be built, tested and installed using CMake. The following procedure describes a typical CMake build.\n\nCreate the build directory inside the sources and move into it:\n\n```\ngit clone https://github.com/Blosc/c-blosc2\ncd c-blosc2\nmkdir build\ncd build\n```\n\nNow run CMake configuration and optionally specify the installation directory (e.g. ‘/usr’ or ‘/usr/local’):\n\n```\ncmake -DCMAKE_INSTALL_PREFIX=your_install_prefix_directory ..\n```\n\nCMake allows to configure Blosc in many different ways, like preferring internal or external sources for compressors or enabling/disabling them. Please note that configuration can also be performed using UI tools provided by CMake (ccmake or cmake-gui):\n\n```\nccmake .. # run a curses-based interface\ncmake-gui .. # run a graphical interface\n```\n\nBuild, test and install Blosc:\n\n```\ncmake --build .\nctest\ncmake --build . --target install\n```\n\nThe static and dynamic version of the Blosc library, together with header files, will be installed into the specified CMAKE_INSTALL_PREFIX.\n\nOnce you have compiled your Blosc library, you can easily link your apps with it as shown in the examples/ directory.\n\n### Handling support for codecs (LZ4, LZ4HC, Zstd, Zlib)#\n\nC-Blosc2 comes with full sources for LZ4, LZ4HC, Zstd, and Zlib and in general, you should not worry about not having (or CMake not finding) the libraries in your system because by default the included sources will be automatically compiled and included in the C-Blosc2 library. This means that you can be confident in having a complete support for all these codecs in all the official Blosc deployments. Of course, if you consider this is too bloated, you can exclude support for some of them.\n\nFor example, let’s suppose that you want to disable support for Zstd:\n\n```\ncmake -DDEACTIVATE_ZSTD=ON ..\n```\n\nOr, you may want to use a codec in an external library already in the system:\n\n```\ncmake -DPREFER_EXTERNAL_LZ4=ON ..\n```\n\n### Supported platforms#\n\nC-Blosc2 is meant to support all platforms where a C99 compliant C compiler can be found. The ones that are mostly tested are Intel (Linux, Mac OSX and Windows), ARM (Linux, Mac), and PowerPC (Linux). More on ARM support in README_ARM.rst.\n\nFor Windows, you will need at least VS2015 or higher on x86 and x64 targets (i.e. ARM is not supported on Windows).\n\nFor Mac OSX, make sure that you have the command line developer tools available. You can always install them with:\n\n```\nxcode-select --install\n```\n\nFor Mac OSX on arm64 architecture, you may want to compile it like this:\n\n```\nCC=\"clang -arch arm64\" cmake ..\n```\n\n### Display error messages#\n\n By default error messages are disabled. To display them, you just need to activate the Blosc tracing machinery by setting the `BLOSC_TRACE` environment variable. \n\n## Contributing#\n\nIf you want to collaborate in this development you are welcome. We need help in the different areas listed at the ROADMAP; also, be sure to read our DEVELOPING-GUIDE and our Code of Conduct. Blosc is distributed using the BSD license.\n\n## Tweeter feed#\n\nFollow @Blosc2 so as to get informed about the latest developments.\n\n## Citing Blosc#\n\nYou can cite our work on the different libraries under the Blosc umbrella as:\n\n```\n@ONLINE{blosc,\n author = {{Blosc Development Team}},\n title = \"{A fast, compressed and persistent data store library}\",\n year = {2009-2023},\n note = {https://blosc.org}\n}\n```\n\n## Acknowledgments#\n\nSee THANKS document.\n\nDate: 2017-01-27\nCategories: \nTags: \n\n## A Python wrapper for the extremely fast Blosc compression library#\n\nThe Blosc development team\n * Contact\n * Github\n * URL\n * PyPi\n * Anaconda\n * Gitter\n * Code of Conduct\n\n## What it is#\n\nBlosc (https://blosc.org) is a high performance compressor optimized for binary data. It has been designed to transmit data to the processor cache faster than the traditional, non-compressed, direct memory fetch approach via a memcpy() OS call.\n\nBlosc works well for compressing numerical arrays that contains data with relatively low entropy, like sparse data, time series, grids with regular-spaced values, etc.\n\npython-blosc a Python package that wraps Blosc. python-blosc supports Python 3.8 or higher versions.\n\n## Installing#\n\n Blosc is now offering Python wheels for the main OS (Win, Mac and Linux) and platforms. You can install binary packages from PyPi using `pip` : `$ pip install blosc` \n\n## Documentation#\n\nThe Sphinx based documentation is here:\n\nhttps://blosc.org/python-blosc/python-blosc.html\n\nAlso, some examples are available on python-blosc wiki page:\n\nLastly, here is the recording and the slides from the talk “Compress me stupid” at the EuroPython 2014.\n\n## Building#\n\nIf you need more control, there are different ways to compile python-blosc, depending if you want to link with an already installed Blosc library or not.\n\n### Installing via setuptools#\n\npython-blosc comes with the Blosc sources with it and can be built with:\n\n```\n$ python -m pip install -r requirements-dev.txt\n$ python setup.py build_ext --inplace\n```\n\nAny codec can be enabled (=1) or disabled (=0) on this build-path with the appropriate OS environment variables INCLUDE_LZ4, INCLUDE_SNAPPY, INCLUDE_ZLIB, and INCLUDE_ZSTD. By default all the codecs in Blosc are enabled except Snappy (due to some issues with C++ with the gcc toolchain).\n\nCompiler specific optimisations are automatically enabled by inspecting the CPU flags building Blosc. They can be manually disabled by setting the following environmental variables: DISABLE_BLOSC_SSE2 and DISABLE_BLOSC_AVX2.\n\nsetuptools is limited to using the compiler specified in the environment variable CC which on posix systems is usually gcc. This often causes trouble with the Snappy codec, which is written in C++, and as a result Snappy is no longer compiled by default. This problem is not known to affect MSVC or clang. Snappy is considered optional in Blosc as its compression performance is below that of the other codecs.\n\nThat’s all. You can proceed with testing section now.\n\n### Compiling with an installed Blosc library#\n\nThis approach uses pre-built, fully optimized versions of Blosc built via CMake.\n\nGo to Blosc/c-blosc and download and install the C-Blosc library. Then, you can tell python-blosc where is the C-Blosc library in a couple of ways:\n\nUsing an environment variable:\n\n```\n$ export USE_SYSTEM_BLOSC=1 # or \"set USE_SYSTEM_BLOSC=1\" on Windows\n$ export Blosc_ROOT=/usr/local/customprefix # If you installed Blosc into a custom location\n$ python setup.py build_ext --inplace\n```\n\nUsing flags:\n\n```\n$ python setup.py build_ext --inplace -DUSE_SYSTEM_BLOSC:BOOL=YES -DBlosc_ROOT:PATH=/usr/local/customprefix\n```\n\n## Testing#\n\n After compiling, you can quickly check that the package is sane by running the doctests in `blosc/test.py` : \n\n```\n$ python -m blosc.test (add -v for verbose mode)\n```\n\nOnce installed, you can re-run the tests at any time with:\n\n```\n$ python -c \"import blosc; blosc.test()\"\n```\n\n## Benchmarking#\n\nIf curious, you may want to run a small benchmark that compares a plain NumPy array copy against compression through different compressors in your Blosc build:\n\n```\n$ PYTHONPATH=. python bench/compress_ptr.py\n```\n\nJust to whet your appetite, here are the results for an Intel Xeon E5-2695 v3 @ 2.30GHz, running Python 3.5, CentOS 7, but YMMV (and will vary!):\n\n```\n-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=\npython-blosc version: 1.5.1.dev0\nBlosc version: 1.11.2 ($Date:: 2017-01-27 #$)\nCompressors available: ['blosclz', 'lz4', 'lz4hc', 'snappy', 'zlib', 'zstd']\nCompressor library versions:\n BloscLZ: 1.0.5\n LZ4: 1.7.5\n Snappy: 1.1.1\n Zlib: 1.2.7\n Zstd: 1.1.2\nPython version: 3.5.2 |Continuum Analytics, Inc.| (default, Jul 2 2016, 17:53:06)\n[GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\nPlatform: Linux-3.10.0-327.18.2.el7.x86_64-x86_64 (#1 SMP Thu May 12 11:03:55 UTC 2016)\nLinux dist: CentOS Linux 7.2.1511\nProcessor: x86_64\nByte-ordering: little\nDetected cores: 56\nNumber of threads to use by default: 4\n -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=\nCreating NumPy arrays with 10**8 int64/float64 elements:\n *** ctypes.memmove() *** Time for memcpy(): 0.276 s (2.70 GB/s)\n\nTimes for compressing/decompressing with clevel=5 and 24 threads\n\n*** the arange linear distribution ***\n *** blosclz , noshuffle *** 0.382 s (1.95 GB/s) / 0.300 s (2.48 GB/s) Compr. ratio: 1.0x\n *** blosclz , shuffle *** 0.042 s (17.77 GB/s) / 0.027 s (27.18 GB/s) Compr. ratio: 57.1x\n *** blosclz , bitshuffle *** 0.094 s (7.94 GB/s) / 0.041 s (18.28 GB/s) Compr. ratio: 74.0x\n *** lz4 , noshuffle *** 0.156 s (4.79 GB/s) / 0.052 s (14.30 GB/s) Compr. ratio: 2.0x\n *** lz4 , shuffle *** 0.033 s (22.58 GB/s) / 0.034 s (22.03 GB/s) Compr. ratio: 68.6x\n *** lz4 , bitshuffle *** 0.059 s (12.63 GB/s) / 0.053 s (14.18 GB/s) Compr. ratio: 33.1x\n *** lz4hc , noshuffle *** 0.443 s (1.68 GB/s) / 0.070 s (10.62 GB/s) Compr. ratio: 2.0x\n *** lz4hc , shuffle *** 0.102 s (7.31 GB/s) / 0.029 s (25.42 GB/s) Compr. ratio: 97.5x\n *** lz4hc , bitshuffle *** 0.206 s (3.62 GB/s) / 0.038 s (19.85 GB/s) Compr. ratio: 180.5x\n *** snappy , noshuffle *** 0.154 s (4.84 GB/s) / 0.056 s (13.28 GB/s) Compr. ratio: 2.0x\n *** snappy , shuffle *** 0.044 s (16.89 GB/s) / 0.047 s (15.95 GB/s) Compr. ratio: 17.4x\n *** snappy , bitshuffle *** 0.064 s (11.58 GB/s) / 0.061 s (12.26 GB/s) Compr. ratio: 18.2x\n *** zlib , noshuffle *** 1.172 s (0.64 GB/s) / 0.135 s (5.50 GB/s) Compr. ratio: 5.3x\n *** zlib , shuffle *** 0.260 s (2.86 GB/s) / 0.086 s (8.67 GB/s) Compr. ratio: 120.8x\n *** zlib , bitshuffle *** 0.262 s (2.84 GB/s) / 0.094 s (7.96 GB/s) Compr. ratio: 260.1x\n *** zstd , noshuffle *** 0.973 s (0.77 GB/s) / 0.093 s (8.00 GB/s) Compr. ratio: 7.8x\n *** zstd , shuffle *** 0.093 s (7.97 GB/s) / 0.023 s (32.71 GB/s) Compr. ratio: 156.7x\n *** zstd , bitshuffle *** 0.115 s (6.46 GB/s) / 0.029 s (25.60 GB/s) Compr. ratio: 320.6x\n\n*** the linspace linear distribution ***\n *** blosclz , noshuffle *** 0.341 s (2.19 GB/s) / 0.291 s (2.56 GB/s) Compr. ratio: 1.0x\n *** blosclz , shuffle *** 0.132 s (5.65 GB/s) / 0.023 s (33.10 GB/s) Compr. ratio: 2.0x\n *** blosclz , bitshuffle *** 0.166 s (4.50 GB/s) / 0.036 s (20.89 GB/s) Compr. ratio: 2.8x\n *** lz4 , noshuffle *** 0.142 s (5.26 GB/s) / 0.028 s (27.07 GB/s) Compr. ratio: 1.0x\n *** lz4 , shuffle *** 0.093 s (8.01 GB/s) / 0.030 s (24.87 GB/s) Compr. ratio: 3.4x\n *** lz4 , bitshuffle *** 0.102 s (7.31 GB/s) / 0.039 s (19.13 GB/s) Compr. ratio: 5.3x\n *** lz4hc , noshuffle *** 0.700 s (1.06 GB/s) / 0.044 s (16.77 GB/s) Compr. ratio: 1.1x\n *** lz4hc , shuffle *** 0.203 s (3.67 GB/s) / 0.021 s (36.22 GB/s) Compr. ratio: 8.6x\n *** lz4hc , bitshuffle *** 0.342 s (2.18 GB/s) / 0.028 s (26.50 GB/s) Compr. ratio: 14.2x\n *** snappy , noshuffle *** 0.271 s (2.75 GB/s) / 0.274 s (2.72 GB/s) Compr. ratio: 1.0x\n *** snappy , shuffle *** 0.099 s (7.54 GB/s) / 0.042 s (17.55 GB/s) Compr. ratio: 4.2x\n *** snappy , bitshuffle *** 0.127 s (5.86 GB/s) / 0.043 s (17.20 GB/s) Compr. ratio: 6.1x\n *** zlib , noshuffle *** 1.525 s (0.49 GB/s) / 0.158 s (4.70 GB/s) Compr. ratio: 1.6x\n *** zlib , shuffle *** 0.346 s (2.15 GB/s) / 0.098 s (7.59 GB/s) Compr. ratio: 10.7x\n *** zlib , bitshuffle *** 0.420 s (1.78 GB/s) / 0.104 s (7.20 GB/s) Compr. ratio: 18.0x\n *** zstd , noshuffle *** 1.061 s (0.70 GB/s) / 0.096 s (7.79 GB/s) Compr. ratio: 1.9x\n *** zstd , shuffle *** 0.203 s (3.68 GB/s) / 0.052 s (14.21 GB/s) Compr. ratio: 14.2x\n *** zstd , bitshuffle *** 0.251 s (2.97 GB/s) / 0.047 s (15.84 GB/s) Compr. ratio: 22.2x\n\n*** the random distribution ***\n *** blosclz , noshuffle *** 0.340 s (2.19 GB/s) / 0.285 s (2.61 GB/s) Compr. ratio: 1.0x\n *** blosclz , shuffle *** 0.091 s (8.21 GB/s) / 0.017 s (44.29 GB/s) Compr. ratio: 3.9x\n *** blosclz , bitshuffle *** 0.080 s (9.27 GB/s) / 0.029 s (26.12 GB/s) Compr. ratio: 6.1x\n *** lz4 , noshuffle *** 0.150 s (4.95 GB/s) / 0.027 s (28.05 GB/s) Compr. ratio: 2.4x\n *** lz4 , shuffle *** 0.068 s (11.02 GB/s) / 0.029 s (26.03 GB/s) Compr. ratio: 4.5x\n *** lz4 , bitshuffle *** 0.063 s (11.87 GB/s) / 0.054 s (13.70 GB/s) Compr. ratio: 6.2x\n *** lz4hc , noshuffle *** 0.645 s (1.15 GB/s) / 0.019 s (39.22 GB/s) Compr. ratio: 3.5x\n *** lz4hc , shuffle *** 0.257 s (2.90 GB/s) / 0.022 s (34.62 GB/s) Compr. ratio: 5.1x\n *** lz4hc , bitshuffle *** 0.128 s (5.80 GB/s) / 0.029 s (25.52 GB/s) Compr. ratio: 6.2x\n *** snappy , noshuffle *** 0.164 s (4.54 GB/s) / 0.048 s (15.46 GB/s) Compr. ratio: 2.2x\n *** snappy , shuffle *** 0.082 s (9.09 GB/s) / 0.043 s (17.39 GB/s) Compr. ratio: 4.3x\n *** snappy , bitshuffle *** 0.071 s (10.48 GB/s) / 0.046 s (16.08 GB/s) Compr. ratio: 5.0x\n *** zlib , noshuffle *** 1.223 s (0.61 GB/s) / 0.093 s (7.97 GB/s) Compr. ratio: 4.0x\n *** zlib , shuffle *** 0.636 s (1.17 GB/s) / 0.126 s (5.89 GB/s) Compr. ratio: 5.5x\n *** zlib , bitshuffle *** 0.327 s (2.28 GB/s) / 0.109 s (6.81 GB/s) Compr. ratio: 6.2x\n *** zstd , noshuffle *** 1.432 s (0.52 GB/s) / 0.103 s (7.27 GB/s) Compr. ratio: 4.2x\n *** zstd , shuffle *** 0.388 s (1.92 GB/s) / 0.031 s (23.71 GB/s) Compr. ratio: 5.9x\n *** zstd , bitshuffle *** 0.127 s (5.86 GB/s) / 0.033 s (22.77 GB/s) Compr. ratio: 6.4x\n```\n\nAlso, Blosc works quite well on ARM processors (even without NEON support yet):\n\n```\n-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=\npython-blosc version: 1.4.4\nBlosc version: 1.11.2 ($Date:: 2017-01-27 #$)\nCompressors available: ['blosclz', 'lz4', 'lz4hc', 'snappy', 'zlib', 'zstd']\nCompressor library versions:\n BloscLZ: 1.0.5\n LZ4: 1.7.5\n Snappy: 1.1.1\n Zlib: 1.2.8\n Zstd: 1.1.2\nPython version: 3.6.0 (default, Dec 31 2016, 21:20:16)\n[GCC 4.9.2]\nPlatform: Linux-3.4.113-sun8i-armv7l (#50 SMP PREEMPT Mon Nov 14 08:41:55 CET 2016)\nLinux dist: debian 9.0\nProcessor: not recognized\nByte-ordering: little\nDetected cores: 4\nNumber of threads to use by default: 4\n-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=\n *** ctypes.memmove() *** Time for memcpy(): 0.015 s (93.57 MB/s)\n\nTimes for compressing/decompressing with clevel=5 and 4 threads\n\n*** user input ***\n *** blosclz , noshuffle *** 0.015 s (89.93 MB/s) / 0.010 s (138.32 MB/s) Compr. ratio: 2.7x\n *** blosclz , shuffle *** 0.023 s (60.25 MB/s) / 0.012 s (112.71 MB/s) Compr. ratio: 2.3x\n *** blosclz , bitshuffle *** 0.018 s (77.63 MB/s) / 0.021 s (66.76 MB/s) Compr. ratio: 7.3x\n *** lz4 , noshuffle *** 0.008 s (177.14 MB/s) / 0.009 s (159.00 MB/s) Compr. ratio: 3.6x\n *** lz4 , shuffle *** 0.010 s (131.29 MB/s) / 0.012 s (117.69 MB/s) Compr. ratio: 3.5x\n *** lz4 , bitshuffle *** 0.015 s (89.97 MB/s) / 0.022 s (63.62 MB/s) Compr. ratio: 8.4x\n *** lz4hc , noshuffle *** 0.071 s (19.30 MB/s) / 0.007 s (186.64 MB/s) Compr. ratio: 8.6x\n *** lz4hc , shuffle *** 0.079 s (17.30 MB/s) / 0.014 s (95.99 MB/s) Compr. ratio: 6.2x\n *** lz4hc , bitshuffle *** 0.062 s (22.23 MB/s) / 0.027 s (51.53 MB/s) Compr. ratio: 9.7x\n *** snappy , noshuffle *** 0.008 s (173.87 MB/s) / 0.009 s (148.77 MB/s) Compr. ratio: 4.4x\n *** snappy , shuffle *** 0.011 s (123.22 MB/s) / 0.016 s (85.16 MB/s) Compr. ratio: 4.4x\n *** snappy , bitshuffle *** 0.015 s (89.02 MB/s) / 0.021 s (64.87 MB/s) Compr. ratio: 6.2x\n *** zlib , noshuffle *** 0.047 s (29.26 MB/s) / 0.011 s (121.83 MB/s) Compr. ratio: 14.7x\n *** zlib , shuffle *** 0.080 s (17.20 MB/s) / 0.022 s (63.61 MB/s) Compr. ratio: 9.4x\n *** zlib , bitshuffle *** 0.059 s (23.50 MB/s) / 0.033 s (41.10 MB/s) Compr. ratio: 10.5x\n *** zstd , noshuffle *** 0.113 s (12.21 MB/s) / 0.011 s (124.64 MB/s) Compr. ratio: 15.6x\n *** zstd , shuffle *** 0.154 s (8.92 MB/s) / 0.026 s (52.56 MB/s) Compr. ratio: 9.9x\n *** zstd , bitshuffle *** 0.116 s (11.86 MB/s) / 0.036 s (38.40 MB/s) Compr. ratio: 11.4x\n```\n\nFor details on the ARM benchmark see: Blosc/python-blosc#105\n\nIn case you find your own results interesting, please report them back to the authors!\n\n## License#\n\nThe software is licensed under a 3-Clause BSD license. A copy of the python-blosc license can be found in LICENSE.txt.\n\n## Mailing list#\n\nDiscussion about this module is welcome in the Blosc list:\n\nhttps://groups.google.com/g/blosc\n ## Contents#\n\n* Introduction\n * Installation\n * Tutorials\n * Library Reference\n\nPython-Blosc2 is a Python package that wraps C-Blosc2, the newest version of the Blosc compressor.\n\nGetting Started\n\nNew to Python-Blosc2? Check out the getting started guides. They contain an introduction to Python-Blosc2 main concepts and different tutorials.\n\nAPI Reference\n\nThe reference guide contains a detailed description of the Python-Blosc2 API. The reference describes how the functions work and which parameters can be used.\n\nDevelopment\n\nSaw a typo in the documentation? Want to improve existing functionalities? The contributing guidelines will guide you through the process of improving Python-Blosc2.\n\nRelease Notes\n\nWant to see what’s new in the latest release? Check out the release notes to find out!\n\n### What is Btune?\n\nBtune is a dynamic plugin for Blosc2 that can help you find the optimal combination of compression parameters for your datasets. Depending on your needs, Btune has three different tiers of support for tuning datasets:\n\nGenetic (Btune Free): This genetic algorithm tests different combinations of compression parameters to meet the user's requirements for both compression ratio and speed for each chunk in the dataset. It assigns a score to each combination and, after a number of iterations, the software stops and uses the best score (minimal value) found for the rest of the dataset. For a graphical visualization, click on the image, select an example, and click on the 'play' button (it may require clicking twice). This is best suited for personal use.\n * \n\nTrained (Btune Models): With this approach, the user sends a representative sample of datasets to the Blosc development team and receives back trained neural network models that enable Btune to predict the best compression parameters for similar or related datasets. This approach is best for workgroups that need to optimize for a limited variety of datasets.\n * \n\nFully managed (Btune Studio): The user receives a license to use our training software, which enables on-site training for an unlimited number of datasets. The license also includes a specified number of training/consultancy hours to help the user get the most out of the training process. Refer to the details below for more information. This approach is best suited for organizations that need to optimize for a wide range of datasets.\n\n### Why Btune?\n\nEssentially, because compression is not a one-codec-fits-all problem. Compressing data involves a trade-off between compression ratio and speed. A higher compression ratio results in a slower compression process. Depending on your needs, you may want to prioritize one over the other.\n\nFor instance, if you are storing data from high-speed data acquisition systems, you may want to prioritize compression speed over compression ratio. This is because you will be writing data at speeds near the capacity of your systems. On the other hand, if the goal is to access the data repeatedly from a file system, you may want to prioritize decompression speed over compression ratio for optimal performance.\n\nFinally, if you are storing data in the cloud, you may want to prioritize compression ratio over speed. This is because you pay for the storage (and potentially upload/download costs) of data.\n\nFinding the optimal compression parameters in Blosc2 can be a slow process due to the large number of combinations of compression parameters (codec, compression level, filter, split mode, number of threads, etc.), and it may require a significant amount of manual trial and error to find the best combinations. However, you can significantly speed up this process by using Btune while compressing your datasets.\n\n### What's in a Model?\n\nA neural network is a simplified model of the way the human brain processes information. It simulates a large number of interconnected processing units that resemble abstract versions of neurons. These processing units are arranged in layers, which are connected by weights that are adjusted during the training process. To train the network, a large number of examples are fed into it, and the weights are adjusted to minimize the difference between the expected output and the actual output. Once training is complete, the network can be used to predict the output for new inputs.\n\nIn our context, the \"model\" refers to the serialization of the layers and weights of the trained neural network. It is delivered to you as a set of small files (in JSON and TensorFlow format) that can be placed anywhere in your filesystem for Btune to access. By using this model, Btune can predict the optimal combination of compression parameters for a given chunk of data. The inference process is very fast, making it suitable for selecting the appropriate compression parameters on a chunk-by-chunk basis while consolidating large amounts of data.\n\n### How To Use Btune?\n\nBtune is a plugin for Blosc2 that can be obtained from the PyPI repository. You can learn how to use it in the Btune README. The plugin is currently only available for Linux and macOS, and only for Intel architecture. However, we plan to add support for other architectures in the future.\n\nThe Btune plugin above can be used for both Btune Free and Btune Models. For Btune Studio, you will need to contact us to get the additional software for training the models.\n\n### Licensing Model\n\nThere are different licenses available for Btune.\n\nBtune Free allows you to explore compression parameters that are better suited to your datasets. However, this process can be slow and may require a large number of iterations before finding the best combination. Additionally, certain chunks in the same dataset may benefit more from a particular combination, while others may benefit more from a different one.\n\nBtune Models addresses the limitations of Btune Free by automatically finding the best combination for chunks in a dataset, without requiring any manual operation. This is made possible by using pre-trained neural network models, which allow the best combination to be found on a chunk-by-chunk basis, thereby increasing the effectiveness of the compression process.\n\nFinally, for those who need to train a wide range of datasets, Btune Studio provides access to the software necessary for training the datasets yourself. In this way, you have control over all the necessary components to find optimal compression parameters and avoid external dependencies.\n\n### Pricing\n\n# Btune Free\n\nIt is free to use. Please note that it is licensed under an Affero GPLv3 license. This license comes with limited support, as it is mostly a community-supported project.\n\n# Btune Models\n\nRequires a fee of $1500 USD (or 1500 EUR) for up to 3 trained models per year, including 3 hours of support. You can ask to re-train models for the same or a different set of datasets on a yearly basis. If you need more than 3 models, you can ask for a quote.\n\nRenewal is $1200 USD (or 1200 EUR) per year. If you don't renew, you keep the right to use the models you already have forever, but you will not be able to ask for training new models.\n\n# Btune Studio\n\nRequires a fee of $7500 USD (or 7500 EUR) per year, or $750 USD (or 750 EUR) per month for at least 1 year, whichever fits best for you. This includes 25 hours of support per year, or up to 3 hours of support per month when using the monthly fee.\n\nRenewal is $6000 USD (or 6000 EUR) per year, or $600 USD (or 600 EUR) monthly after the 1st year. If you don't renew, you keep the right to use Btune Studio for producing models internally in your organization forever, but you will not have access to newer versions.\n\nNote: Btune Studio is not open source software, but we deliver sources with it, so that you can build/fix it yourself. However, you cannot include it in your own software and distribute it without permission.\n\n# Priority Support\n\nFor all licenses we offer an optional priority support pack that includes up to 3 hours of support per month for a monthly fee of $250 (or 250 EUR). For more support hours, please contact us. The contracted support can be used for training in the use of the software, or for consultation on compression for big data in general.\n\n# How To Pay?\n\nYou can do the payments via the donations form for the Blosc project where, at the end of the form, you can specify the kind of license and support you are interested in. If for some reason, you cannot (or you don't want to) donate via NumFOCUS, please contact us; we can invoice you directly as well.\n\n# Why donations via NumFOCUS?\n\nNumFOCUS is a non-profit organization with a mission to promote open practices in research, data, and scientific computing. They serve as a fiscal sponsor for open-source projects and organize community-driven educational programs.\n\nThe Blosc project has benefited significantly from NumFOCUS Small Development Grant Program, and they have been instrumental in helping us to channel donations. When you pay Btune fees by donating to the Blosc project via NumFOCUS, 15% of the amount goes to them as a fee. We believe this fee is fair and helps repay NumFOCUS for the services, support, and love they have shown us over the years. Your donation will not only strengthen the Blosc project, but also many other open-source projects.\n\nIf you or your organization encounter issues donating via NumFOCUS, the Blosc development team can also produce invoices directly.\n\n### Practical Example\n\nIn the figure below, you can see the most predicted combinations of codecs and filters when optimizing for decompression performance on a subset of the Gaia dataset. The subset contains stars that are less than 10,000 light years away from our Sun (around 500 millions). The data is stored in an array of shape (20,000, 20,000, 20,000), with the number of stars in every cubic light year cell, resulting in a total uncompressed size of 7.3 TB.\n\nThe following figure displays the speed that can be achieved by obtaining multiple multidimensional slices of the dataset along different axes, using the most efficient codecs and filters for various tradeoffs. The speed is measured in GB/s, so a higher value is better.\n\nThe results indicate that the fastest compression combination is BloscLZ (compression level 5), closely followed by Zstd (compression level 9). Also, note how the fastest codecs, BloscLZ and also Zstd, are not affected very much by the number of threads used, which means that they are not CPU-bound, so small computers or laptops with low core counts will be able to reach good speeds.\n\nFinally, it is important to compare the compression ratios achieved by different codecs and filters. In the following figure, we can see the file sizes created when using the most commonly predicted codecs and filters for various trade-offs. The file sizes are measured in GB, so the lower, the better.\n\nIn this case, the trained model recommends using Zstd (compression level 9) for a good balance between compression ratio and decompression speed, and that can be confirmed by seeing the large difference in size. However, note that BitShuffle + Zstd (compression level 9) is not a good option in general, unless you are looking for the absolute best compression ratio.\n\nYou can read more context about this example in our forthcoming article for SciPy 2023.\n\n### Testimonials\n\n Blosc2 and Btune are fantastic tools that allow us to efficiently compress and load large volumes of data for the development of AI algorithms for clinical applications. In particular, the new NDarray structure became immensely useful when dealing with large spectral video sequences.\n\n-- <NAME>, Div. Intelligent Medical Systems, German Cancer Research Center (DKFZ)\n Btune is a simple and highly effective tool. We tried this out with @LEAPSinitiative data and found some super useful spots in the parameter space of Blosc2 compression arguments! Awesome work, @Blosc2 team!\n\n-- <NAME>, Helmholtz AI Consultants Team Lead for Matter Research @HZDR_Dresden\n\n### Contact\n\nIf you are interested in Btune and have any further questions, please contact us at <EMAIL>.\n\n# Thank you for supporting Blosc!\n\nPlease review before submitting your payment.\n\n Questions?(512) 831-2870 | <EMAIL> \nPlease review before submitting your payment.\n\n Questions?(512) 831-2870 | <EMAIL>\n\nSkip to main content 2023-10-11 11:00 Optimized Hyper-slicing in PyTables with Blosc2 NDim\n\n# Cárabos Coop. V.\n\nDate: 2003-01-01\nCategories: \nTags: \n\nBack in October 2002 the first version of PyTables was released. It was an attempt to store a large amount of tabular data while being able to provide a hierarchical structure around it. Here it is the first public announcement by me:\n > Hi!, PyTables is a Python package which allows dealing with HDF5 tables. Such a table is defined as a collection of records whose values are stored in fixed-length fields. PyTables is intended to be easy-to-use, and tried to be a high-performance interface to HDF5. To achieve this, the newest improvements in Python 2.2 (like generators or slots and metaclasses in brand-new classes) has been used. Python creation extension tool has been chosen to access the HDF5 library. This package should be platform independent, but until now I’ve tested it only with Linux. It’s the first public release (v 0.1), and it is in alpha state.\n\nAs noted, PyTables was an early adopter of generators and metaclasses that were introduced in the new (by that time) Python 2.2. It turned out that generators demonstrated to be an excellent tool in many libraries related with data science. Also, Pyrex adoption (which was released just a few months ago) greatly simplified the wrapping of native C libraries like HDF5.\n\nBy that time there were not that much Python libraries for persisting tabular data with a format that allowed on-the-flight compression, and that gave PyTables a chance to be considered as a good option. Some months later, PyCon 2003 accepted our first talk about PyTables. Since then, we (mainly me, with the support from S<NAME> on the documentation part) gave several presentations in different international conferences, like SciPy or EuroSciPy and its popularity skyrocketed somehow.\n\n## Cárabos Coop. V.\n\nIn 2005, and after receiving some good inputs on PyTables by some customers (including The HDF Group), we decided to try to make a life out of PyTables development and together with <NAME> and <NAME>, we set out to create a cooperative called Cárabos Coop V. Unfortunately, and after 3 years of enthusiastic (and hard) work, we did not succeed in making the project profitable, and we had to close by 2008.\n\nDuring this period we managed to make a professional version of PyTables that was using out-of core indexes (aka OPSI) as well as a GUI called ViTables. After closing Cárabos we open sourced both technologies, and we are happy to say that they are still in good use, most specially OPSI indexes, that are meant to perform fast queries in very large datasets; OPSI can still be used straight from pandas.\n\n## Crew renewal\n\nAfter Cárabos closure, I (<NAME>) continued to maintain PyTables for a while, but in 2010 I expressed my desire to handover the project, and shortly after, a new gang of people, including <NAME> and <NAME>, with <NAME> joining shortly after, stepped ahead and took the challenge. This is where open source is strong: whenever a project faces difficulties, there are always people eager to jump up to the wagon and continue providing traction for it.\n\n## Attempt to merge with h5py\n\nMeanwhile, the h5py package was receiving a great adoption, specially from the community that valued more the multidimensional arrays than the tabular side of the things. There was a feeling that we were duplicating efforts and by 2016, <NAME>, with the help of <NAME>, organized a HackFest in Perth, Australia where developers of the h5py and PyTables gathered to attempt a merge of the two projects. After the initial work there, we continued this effort with a grant from NumFOCUS.\n\nUnfortunately, the effort demonstrated to be rather complex, and we could not finish it properly (for the sake of curiosity, the attempt is still available). At any rate, we are actively encouraging people using both packages depending on the need; see for example, the tutorial on h5py/PyTables that Tom Kooij taught at SciPy 2017.\n\n## Satellite Projects: Blosc and numexpr\n\nAs many other open sources libraries, PyTables stands in the shoulders of giants, and makes use of amazing libraries like HDF5 or NumPy for doing its magic. In addition to that, and in order to allow PyTables push against the hardware I/O and computational limits, it leverages two high-performance packages: Blosc and numexpr. Blosc is in charge of compressing data efficiently and at very high speeds to overcome the limits imposed by the I/O subsystem, while numexpr allows to get maximum performance from computations in CPU when querying large tables. Both projects have been substantially improved by the PyTables crew, and actually, they are quite popular by themselves.\n\nSpecifically, the Blosc compressor, although born out of the needs of PyTables, it spun off as a standalone compressor (or meta-compressor, as it can use several codecs internally) meant to accelerate not just disk I/O, but also memory access in general. In an unexpected twist, Blosc2, has developed its own multi-level data partitioning system, which goes beyond the single-level partitions in HDF5, and is currently helping PyTables to reach new performance heights. By teaming with the HDF5 library (and hence PyTables), Blosc2 is allowing PyTables to query 100 trillion rows in human timeframes.\n\n## Thank you!\n\nIt has been a long way since PyTables started 20 years ago. We are happy to have helped in providing a useful framework for data storage and querying needs for many people during the journey.\n\nMany thanks to all maintainers and contributors (either with code or donations) to the project; they are too numerous to mention them all here, but if you are reading this and are among them, you should be proud to have contributed to PyTables. In hindsight, the road may have been certainly bumpy, but it somehow worked and many difficulties have been surpassed; such is the magic and grace of Open Source!\n\n# How second partition allows for Big Chunking\n\nPyTables lets users to easily handle data tables and array objects in a hierarchical structure. It also supports a variety of different data compression libraries through HDF5 filters. With the release of PyTables 3.8.0, the Blosc Development Team is pleased to announce the availability of Blosc2, acting not only as another HDF5 filter, but also as an additional partition tool (aka 'second partition') that complements the existing HDF5 chunking schema.\n\nBy providing support for a second partition in HDF5, the chunks (aka the 'first partition') can be made larger, ideally fitting in cache level 3 in modern CPUs (see below for advantages of this). Meanwhile, Blosc2 will use its internal blocks (aka the second partition) as the minimum amount of data that should be read and decompressed during data retrieval, no matter how small the hyperslice to be read is.\n\nWhen Blosc2 is used to implement a second partition for data (referred ahead as 'optimized Blosc2' too), it can bypass the HDF5 pipeline for writing and for reading. This brings another degree of freedom when choosing the different internal I/O buffers, which can be of extraordinary importance in terms of performance and/or resource saving.\n\n## How second partition allows for Big Chunking\n\nBlosc2 in PyTables is meant for compressing data in big chunks (typically in the range of level 3 caches in modern CPUs, that is, 10 ~ 1000 MB). This has some interesting advantages:\n\nIt allows to reduce the number of entries in the HDF5 hash table. This means less resource consumption in the HDF5 side, so PyTables can handle larger tables using less resources.\n * \n\nIt speeds-up compression and decompression because multithreading works better with more blocks. Remember that you can specify the number of threads to use by using the MAX_BLOSC_THREADS parameter, or by using the BLOSC_NTHREADS environment variable.\n\nHowever, the traditional drawback of having large chunks is that getting small slices would take long time because the whole chunk has to be read completely and decompressed. Blosc2 surmounts that difficulty like this: it asks HDF5 where chunks start on-disk (via H5Dget_chunk_info()), and then it access to the internal blocks (aka the second partition) independently instead of having to decompress the entire chunk. This effectively avoids penalizing access to small data slices.\n\nIn the graphic below you can see the second partition in action where, in order to retrieve the green slice, only blocks 2 and 3 needs to be addressed and decompressed, instead of the (potentially much) larger chunk 0 and 1, which would be the case for the traditional 1 single partition in HDF5:\n\nIn the benchmarks below we are comparing the performance of existing filters inside PyTables (like Zlib or Blosc(1)) against Blosc2, both working as a filter or in optimized mode, that is, bypassing the HDF5 filter pipeline completely.\n\n## Benchmarks\n\nThe data used in this section have been fetched from ERA5 database (see downloading script), which provides hourly estimates of a large number of atmospheric, land and oceanic climate variables. To build the tables used for reading and writing operations, we have used five different ERA5 datasets with the same shape (100 x 720 x 1440) and the same variables (latitude, longitude and time). Then, we have built a table with a column for each variable and each dataset and added the latitude, longitude and time as columns (for a total of 8 cols). Finally, there have been written 100 x 720 x 1440 rows (more than 100 million) to this table, which makes for a total data size of 3.1 GB.\n\nWe present different scenarios when comparing resource usage for writing and reading between the Blosc and Blosc2 filters, including the Blosc2 optimized versions. First one is when PyTables is choosing the chunkshape automatically (the default); as Blosc2 is meant towards large chunks, PyTables has been tuned to produce far larger chunks for Blosc2 in this case (Blosc and other filters will remain using the same chunk sizes as usual). Second, we will visit the case where the chunkshape is equal for both Blosc and Blosc2. Spoiler alert: we will see how Blosc2 behaves well (and sometimes much beter) in both scenarios.\n\n### Automatic chunkshape\n\n# Inkernel searches\n\nWe start by performing inkernel queries where the chunkshape for the table is chosen automatically by the PyTables machinery (see query script here). This size is the same for Blosc, Zlib and uncompressed cases which are all using 16384 rows (about 512 KB), whereas for Blosc2 the computed chunkshape is quite larger: 1179648 rows (about 36 MB; this actually depends on the size of the L3 cache, which is automatically queried in real-time by PyTables and it turns out to be exactly 36 MB for our CPU, an Intel i9-13900K).\n\nNow, we are going to analyze the memory and time usage of performing six inkernel searches, which means scanning the full table six times, in different cases:\n\nWith no compression; size is 3,1 GB.\n * \n\nUsing HDF5 with ZLIB + Shuffle; size is 407 MB.\n * \n\nUsing Blosc2 filter with Zstd codec + Bitshuffle; size is 341 MB.\n\nAs we can see, the queries with no compression enable do not take much time or memory consumption, but it requires storing the full 3.1 GB of data. When using ZLIB, which is the HDF5 default, it does not require much memory either, but it takes a much more time (about 10x more), although the stored data is more than 6x smaller. When using Blosc, the time spent in (de-)compression is much less, but the queries still takes more time (1.7x more) than the no compression case; in addition, the compression ratio is quite close to the ZLIB case.\n\nHowever, the big jump comes when using Blosc2 with BloscLZ and BitShuffle, since although it uses just a little bit more memory than Blosc (a consequence of using larger chunks), in exchange it is quite faster than the previous methods while achieving a noticeably better compression ratio. Actually, this combination is 1.3x faster than using no compression; this is one of the main features of Blosc (and even more with Blosc2): it can accelerate operation by using compression.\n\nFinally, in case we want to improve compression further, Blosc2 can be used with the ZSTD codec, which achieves the best compression ratio here, in exchange for a slightly slower time (but still 1.15x faster than not using compression).\n\n# PyTables inkernel vs pandas queries\n\nNow that we have seen how Blosc2 can help PyTables in getting great query performance, we are going to compare it against pandas queries; to make things more interesting, we will be using the same NumExpr engine in both PyTables (where it is used in inkernel queries) and pandas.\n\nFor this benchmark, we have been exploring the best configuration for speed, so we will be using 16 threads (for both Blosc2 and NumExpr) and the Shuffle filter instead of Bitshuffle; this leads to slightly less compression ratios (see below), but now the goal is getting full speed, not reducing storage (keep in mind that Pandas stores data in-memory without compression).\n\nHere it is how PyTables and pandas behave when doing the same 6 queries than in the previous section.\n\nAnd here it is another plot for the same queries, but comparing raw I/O performance for a variety of codecs and filters:\n\nAs we can see, the queries using Blosc2 are generally faster (up to 2x faster) than not using compression. Furthermore, Blosc2 + LZ4 get nearly as good times as pandas, while the memory consumption is much smaller with Blosc2 (as much as 20x less in this case; more for larger tables indeed). This is remarkable, as this means that Blosc2 compression results in acceleration that almost compensates for all the additional layers in PyTables (the disk subsystem and the HDF5 library itself).\n\nAnd in case you wonder how much compression ratio we have lost by switching from Bitshuffle to Shuffle, not much actually:\n\nThe take away message here is that, when used correctly, compression can make out-of-core queries go as fast as pure in-memory ones (even when using a high performance tool-set like pandas + NumExpr).\n\n# Writing and reading speed with automatic chunkshape\n\nNow, let's have a look at the raw write and read performance. In this case we are going to compare Blosc, Blosc2 as an HDF5 filter, and the optimized Blosc2 (acting as a de facto second partition). Remember that in this section the chunkshape determination is still automatic and different for Blosc (16384 rows, about 512 KB) and Blosc2 (1179648 rows, about 36 MB).\n\nFor writing, optimized Blosc2 is able to do the job faster and get better compression ratios than others, mainly because it uses the HDF5 direct chunking mechanism, bypassing the overhead of the HDF5 pipeline.\n\nNote: the standard Blosc2 filter cannot make of use HDF5 direct chunking, but it still has an advantage when using bigger chunks because it allows for more threads working in parallel and hence, allowing improved parallel (de-)compression.\n\nThe plot below shows how optimized Blosc2 is able to read the table faster and how the performance advantage grows as we use more threads.\n\nAnd now, let's compare the mean times of Blosc and Blosc2 optimized to read a small slice. In this case, Blosc chunkshape is much smaller, but optimized Blosc2 still can reach similar speed since it uses blocks that are similar in size to Blosc chunks.\n\n### Writing and reading speed when using the same chunkshape\n\nIn this scenario, we are choosing the same chunkshape (720 x 1440 rows, about 32 MB) for both Blosc and Blosc2. Let's see how this affects performance:\n\nThe plot above shows how optimized Blosc2 manages to write the table faster (mainly because it can bypass the HDF5 pipeline); with the advantage being larger as more threads are used.\n\nRegarding reading, the optimized Blosc2 is able to perform faster too, and we continue to see the same trend of getting more speed when more threads are thrown at the task, with optimized Blosc2 scaling better.\n\nFinally, let's compare the mean times of Blosc and Blosc2 when reading a small slice in this same chunkshape scenario. In this case, since chunkshapes are equal and large, optimized Blosc2 is much faster than the others because it has the ability to decompresses just the necessary internal blocks, instead of the whole chunks. However, the Blosc and the Blosc2 filter still need to decompress the whole chunk, so getting much worse times. See this effect below:\n\nBy allowing a second partition on top of the HDF5 layer, Blosc2 provides a great boost in PyTables I/O speed, specially when using big chunks (mainly when they fit in L3 CPU cache). That means that you can read, write and query large compressed datasets in less time. Interestingly, Blosc2 compression can make these operations faster than when using no compression at all, and even being competitive against a pure in-memory solution like pandas (but consuming vastly less memory).\n\nOn the other hand, there are situations where using big chunks would not be acceptable. For example, when using other HDF5 apps that do not support the optimized paths for Blosc2 second partition, and one is forced to use the plain Blosc2 filter. In this case having large chunks would penalize the retrieval of small data slices too much. By the way, you can find a nice assortment of generic filters (including Blosc2) for HDF5 in the hdf5plugin library.\n\nAlso note that, in the current implementation we have just provided optimized Blosc2 paths for the Table object in PyTables. That makes sense because Table is probably the most used entity in PyTables. Other chunked objects in PyTables (like EArray or CArray) could be optimized with Blosc2 in the future too (although that would require providing a *multidimensional* second partition for Blosc2).\n\nLast but not least, we would like to thank NumFOCUS and other PyTables donors for providing the funds required to implement Blosc2 support in PyTables. If you like what we are doing, and would like our effort to continue developing well, you can support our work by donating to PyTables project or Blosc project teams. Thank you!\n\n# Going multidimensional in the first and the second partition\n\nDate: 2023-02-24\nCategories: \nTags: \n\nOne of the latest and more exciting additions in recently released C-Blosc2 2.7.0 is the Blosc2 NDim layer (or b2nd for short). It allows to create and read n-dimensional datasets in an extremely efficient way thanks to a completely general n-dim 2-level partitioning, allowing to slice and dice arbitrary large (and compressed!) data in a more fine-grained way.\n\nRemember that having a second partition means that we have better flexibility to fit the different partitions at the different CPU cache levels; typically the first partition (aka chunks) should be made to fit in L3 cache, whereas the second partition (aka blocks) should rather fit in L2/L1 caches (depending on whether compression ratio or speed is desired).\n\nThis capability was formerly part of Caterva, and now we are including it in C-Blosc2 for convenience. As a consequence, the Caterva and Python-Caterva projects are now officially deprecated and all the action will happen in the C-Blosc2 / Python-Blosc2 side of the things.\n\nLast but not least, Blosc NDim is gaining support for a full-fledged data type system like NumPy. Keep reading.\n\n## Going multidimensional in the first and the second partition\n\nBlosc (both Blosc1 and Blosc2) has always had a two-level partition schema to leverage the different cache levels in modern CPUs and make compression happen as quickly as possible. This allows, among other things, to create and query tables with 100 trillion of rows when properly cooperating with existing libraries like HDF5.\n\nWith Blosc2 NDim we are taking this feature a step further and both partitions, known as chunks and blocks, are gaining multidimensional capabilities meaning that one can split some dataset (super-chunk in Blosc2 parlance) in such a n-dim cubes and sub-cubes:\n\nWith these more fine-grained cubes (aka partitions), it is possible to retrieve arbitrary n-dim slices more rapidly because you don't have to decompress all the data that is necessary for the more coarse-grained partitions typical in other libraries.\n\nFor example, for a 4-d array with a shape of (50, 100, 300, 250) with float64 items, we can choose a chunk with shape (10, 25, 50, 50) and a block with shape (3, 5, 10, 20) which makes for about 5 MB and 23 KB respectively. This way, a chunk fits comfortably on a L3 cache in most of modern CPUs, and a block in a L1 cache (we are tuning for speed here). With that configuration, the NDArray object in the Python-Blosc2 package can slice the array as fast as it is shown below:\n\nOf course, the double partition comes with some overhead during the creation of the partitions: more data moves and computations are required in order to place the data in the correct positions. However, we have done our best in order to minimize the data movement as much as possible. Below we can see how the speed of creation (write) of an array from anew is still quite competitive:\n\nOn the other hand, we can also see that, when reading the complete array, the double partitioning overhead is not really a big issue, and actually, it benefits Blosc2 NDArray somewhat.\n\nAll the plots above have been generated using the compare_getslice.py script, where we have been using the Zstd codec with compression level 1 (the fastest inside Blosc2) + the Shuffle filter for all the packages. The box used was an Intel 13900K CPU with 32 GB of RAM and using an up-to-date Clear Linux distro.\n\n## Data types are in!\n\nAnother important thing that we are adding to Blosc2 NDim is the support for data types. This was not previously supported in either C-Blosc2 or Caterva, where only a typesize was available to characterize the type. Now, the data type becomes a first class citizen for the b2nd metalayer. Metalayers in Blosc2 are stored in msgpack format, so it is pretty easy to introspect into them by using external msgpack tools. For example, the b2nd file created in the section above contains this meta info:\n > $ dd bs=1 skip=112 count=1000 < compare_getslice.b2nd | msgpack2json -b <snip> [0,4,[50,100,300,250],[10,25,50,50],[3,5,10,20],0,\"<f8\"]\n\nHere we can see the version of the metalayer (0), the number of dimensions of the array (4), followed by the shape, chunk shape and block shape. Then it comes the version of the dtype representation (it support up to 127; the default is 0, meaning NumPy). Finally, we can spot the \"<f8\" string, so a little-endian double precision data type. Note that the all data types in NumPy are supported by the Python wrapper of Blosc2; that means that with the NDArray object you can store e.g. datetimes (including units), or arbitrarily nested heterogeneous types, which allows to create multidimensional tables.\n\nWe have seen how, when sensibly chosen, the double partition provides a formidable boost in retrieving arbitrary slices in potentially large multidimensional arrays. In addition, the new support for arbitrary data types represents a powerful addition as well. Combine that with the excellent compression capabilities of Blosc2, and you will get a first class data container for many types of (numerical, but also textual) data.\n\nFinally, we will be releasing the new NDArray object in the forthcoming release of Python-Blosc2 very soon. This will enable full access to these shiny new features of Blosc2 from the convenience of Python. Stay tuned!\n\n## Update (2023-02-24)\n\nWe have released Python-Blosc2 2.1.1 with the new NDArray object: https://github.com/Blosc/python-blosc2/releases/\n * \n\nEnjoy the meal!\n\n# Creating a dynamically loaded filter\n\nDate: 2023-08-03\nCategories: \nTags: \n\nUpdated: 2023-08-03 Added a new example of a dynamic filter for Python. Also, we have improved the content so that it can work more as a tutorial on how to make dynamic plugins for Blosc2. Finally, there is support now for dynamic plugins on Windows and MacOS/ARM64. Enjoy!\n\nThe Blosc Development Team is excited to announce that the latest version of C-Blosc2 and Python-Blosc2 include a great new feature: the ability to dynamically load plugins, such as codecs and filters. This means that these codecs or filters will only be loaded at runtime when they are needed. These C libraries will be easily distributed inside Python wheels and be used from both C and Python code without problems. Keep reading for a gentle introduction to this new feature.\n\n## Creating a dynamically loaded filter\n\nTo learn how to create dynamic plugins, we'll use an already created example. Suppose you have a filter that you want Blosc2 to load dynamically only when it is used. In this case, you need to create a Python package to build a wheel and install it as a separate library. You can follow the structure used in blosc2_plugin_example to do this:\n > ├── CMakeLists.txt ├── README.md ├── blosc2_plugin_name │ └── __init__.py ├── examples │ ├── array_roundtrip.py │ ├── schunk_roundtrip.py │ └── test_plugin.c ├── pyproject.toml ├── requirements-build.txt ├── setup.py └── src ├── CMakeLists.txt ├── urfilters.c └── urfilters.h\n\nNote that the project name has to be blosc2_ followed by the plugin name (plugin_example in this case). The corresponding functions will be defined in the src folder, in our case in urfilters.c, following the same format as functions for user-defined filters (see https://github.com/Blosc/c-blosc2/blob/main/plugins/README.md for more information). Here it is the sample code:\n > int blosc2_plugin_example_forward(const uint8_t* src, uint8_t* dest, int32_t size, uint8_t meta, blosc2_cparams *cparams, uint8_t id) { blosc2_schunk *schunk = cparams->schunk; for (int i = 0; i < size / schunk->typesize; ++i) { switch (schunk->typesize) { case 8: ((int64_t *) dest)[i] = ((int64_t *) src)[i] + 1; break; default: BLOSC_TRACE_ERROR(\"Item size %d not supported\", schunk->typesize); return BLOSC2_ERROR_FAILURE; } } return BLOSC2_ERROR_SUCCESS; } int blosc2_plugin_example_backward(const uint8_t* src, uint8_t* dest, int32_t size, uint8_t meta, blosc2_dparams *dparams, uint8_t id) { blosc2_schunk *schunk = dparams->schunk; for (int i = 0; i < size / schunk->typesize; ++i) { switch (schunk->typesize) { case 8: ((int64_t *) dest)[i] = ((int64_t *) src)[i] - 1; break; default: BLOSC_TRACE_ERROR(\"Item size %d not supported\", schunk->typesize); return BLOSC2_ERROR_FAILURE; } } return BLOSC2_ERROR_SUCCESS; }\n\nIn addition to these functions, we need to create a filter_info (or codec_info or tune_info in each case) named info. This variable will contain the names of the forward and backward functions. In our case, we will have:\n > filter_info info = {\"blosc2_plugin_example_forward\", \"blosc2_plugin_example_backward\"};\n\nTo find the functions, the variable must always be named info. Furthermore, the symbols info and the functions forward and backward must be exported in order for Windows to find them. You can see all the details for doing that in the blosc2_plugin_example repository.\n\n## Creating and installing the wheel\n\nOnce the project is done, you can create a wheel and install it locally:\n > python setup.py bdist_wheel pip install dist/*.whl\n\nThis wheel can be uploaded to PyPI so that anybody can use it. Once tested and stable enough, you can request the Blosc Team to register it globally. This way, an ID for the filter or codec will be booked so that the data will always be able to be encoded/decoded by the same code, ensuring portability.\n\n## Registering the plugin in C-Blosc2\n\nAfter installation, and prior to use it, you must register it in C-Blosc2. This step is necessary only if the filter is not already registered globally by C-Blosc2, which is likely if you are testing it or you are not ready to share it with other users. To register it, follow the same process as registering a user-defined plugin, but leave the function pointers as NULL:\n > blosc2_filter plugin_example; plugin_example.id = 250; plugin_example.name = \"plugin_example\"; plugin_example.version = 1; plugin_example.forward = NULL; plugin_example.backward = NULL; blosc2_register_filter(&plugin_example);\n\nWhen the filter is used for the first time, C-Blosc2 will automatically fill in the function pointers.\n\n## Registering the plugin in Python-Blosc2\n\nThe same applies for Python-Blosc2. You can register the filter as follows:\n > import blosc2 blosc2.register_filter(250, None, None, \"plugin_example\")\n\n## Using the plugin in C-Blosc2\n\nTo use the plugin, simply set the filter ID in the filters pipeline, as you would do with user-defined filters:\n > blosc2_cparams cparams = BLOSC2_CPARAMS_DEFAULTS; cparams.filters[4] = 250; cparams.filters_meta[4] = 0; blosc2_dparams dparams = BLOSC2_DPARAMS_DEFAULTS; blosc2_schunk* schunk; /* Create a super-chunk container */ cparams.typesize = sizeof(int32_t); blosc2_storage storage = {.cparams=&cparams, .dparams=&dparams}; schunk = blosc2_schunk_new(&storage);\n\nTo see a full usage example, refer to https://github.com/Blosc/blosc2_plugin_example/blob/main/examples/test_plugin.c. Keep in mind that the executable using the plugin must be launched from the same virtual environment where the plugin wheel was installed. When compressing or decompressing, C-Blosc2 will dynamically load the library and call its functions automatically (as depicted below).\n\nOnce you are satisfied with your plugin, you may choose to request the Blosc Development Team to register it as a global plugin. The only difference (aside from its ID number) is that users won't need to register it locally anymore. Also, a dynamic plugin will not be loaded until it is explicitly requested by any compression or decompression function, saving resources.\n\n## Using the plugin in Python-Blosc2\n\nAs in C-Blosc2, just set the filter ID in the filters pipeline, as you would do with user-defined filters:\n > shape = [100, 100] size = int(np.prod(shape)) nparray = np.arange(size, dtype=np.int32).reshape(shape) blosc2_array = blosc2.asarray(nparray, cparams={\"filters\": [250]})\n\nTo see a full usage example, refer to https://github.com/Blosc/blosc2_plugin_example/blob/main/examples/array_roundtrip.py.\n\nC-Blosc2's ability to support dynamically loaded plugins allows the library to grow in features without increasing the size and complexity of the library itself. For more information about user-defined plugins, refer to this blog entry.\n\nWe appreciate your interest in our project! If you find our work useful and valuable, we would be grateful if you could support us by making a donation. Your contribution will help us continue to develop and improve Blosc packages, making them more accessible and useful for everyone. Our team is committed to creating high-quality and efficient software, and your support will help us to achieve this goal.\n\nDate: 2023-05-10\nCategories: \nTags: \n\nSkip to main content 2023-05-10 08:32 Dynamic plugins in C-Blosc2 2022-10-06 10:32 New features in Python-Blosc2\n\n# Register for user plugins\n\nBlosc has traditionally supported different filters and codecs for compressing data, and it was up to the user to choose one or another depending on her needs. However, there will always be scenarios where a more richer variety of them could be useful.\n\nBlosc2 has now a new plugin register capability in place so that the info about the new filters and codecs can be persisted and transmitted to different machines. In this way Blosc can figure out the info of persistent plugins, and use them so as to decompress the data without problems.\n\nBesides, the Blosc Development Team has implemented a centralized repository so that people can propose new plugins; and if these plugins fulfill a series of requirements, they will be officially accepted, and distributed within the C-Blosc2 library. This provides an easy path for extending C-Blosc2 and hence, better adapt to user needs.\n\nThe plugins that can be registered in the repository can be either codecs or filters.\n\nA codec is a program able to compress and decompress a data stream with the objective of reducing its size and to enable a faster transmission of data.\n * \n\nA filter is a program that reorders the data without changing its size, so that the initial and final size are equal. A filter consists of encoder and decoder. The filter encoder is applied before the codec compressor (or codec encoder) in order to make data easier to compress and the filter decoder is used after codec decompressor (or codec decoder) to restore the original data arrangement.\n\nHere it is an example on how the compression process goes:\n > -------------------- filter encoder ------------------- codec encoder ------- | src | -----------> | tmp | ----------> | c_src | -------------------- ------------------- -------\n\nAnd the decompression process:\n > -------- codec decoder ------------------- filter decoder ------------------- | c_src | -----------> | tmp | ----------> | src | -------- ------------------- -------------------\n\n## Register for user plugins\n\nUser registered plugins are plugins that users register locally so that they can be used in the same way as Blosc official codecs and filters. This option is perfect for users that want to try new filters or codecs on their own.\n The register process is quite simple. You just use the\n\nfunction and then the Blosc2 machinery\nwill store its info with the rest of plugins. After that you will be able to access your plugin through its ID by setting Blosc2 compression or decompression\nparams. > filters pipeline ---------------------- | BLOSC_SHUFFLE 1 | ---------------------- | BLOSC_BITSHUFFLE 2 | ---------------------- | BLOSC_DELTA 3 | ---------------------- | BLOSC_TRUNC 4 | ---------------------- | ... | ---------------------- | BLOSC_NDCELL 32 | ---------------------- | BLOSC_NDMEAN 33 | ---------------------- | ... | ---------------------- | urfilter1 160 | ---------------------- blosc2_register_filter(urfilter2) ---> | urfilter2 161 | ---> cparams.filters[4] = 161; // can be used now ---------------------- | ... | ----------------------\n\n## Global register for Blosc plugins\n\nBlosc global registered plugins are Blosc plugins that have passed through a selection process and a review by the Blosc Development Team. These plugins will be available for everybody using the C-Blosc2 library.\n\nYou should consider this option if you think that your codec or filter could be useful for the community, or you just want being able to use them with upstream C-Blosc2 library. The steps for registering an official Blosc plugin can be seen at: https://github.com/Blosc/c-blosc2/blob/main/plugins/README.md\n Some well documented examples of these kind of plugins are the codec `ndlz` and the filters `ndcell` and `ndmean` on the C-Blosc2 GitHub repository:\nhttps://github.com/Blosc/c-blosc2/tree/main/plugins \n\n## Compiling plugins examples using Blosc2 wheels\n\nSo as to easy the use of the registered filters, full-fledged C-Blosc2 binary libraries including plugins functionality can be installed from python-blosc2 (>= 0.1.8) wheels:\n > $ pip install blosc2 Collecting blosc2 Downloading blosc2-0.1.8-cp37-cp37m-manylinux2010_x86_64.whl (3.3 MB) |████████████████████████████████| 3.3 MB 4.7 MB/s Installing collected packages: blosc2 Successfully installed blosc2-0.1.8\n\nOnce you have installed the C-Blosc2 libraries you can not only use the official Blosc filters and codecs, but you can also register and use them. You can find directions on how to compile C files using the Blosc2 libraries inside these wheels at: https://github.com/Blosc/c-blosc2/blob/main/COMPILING_WITH_WHEELS.rst\n\n### Using user plugins\n\n To use your own plugins with the Blosc machinery you first have to register them through the function\n\nwith an ID between \n\n```\nBLOSC2_USER_DEFINED_FILTERS_START\n```\n\nand \n\n```\nBLOSC2_USER_DEFINED_FILTERS_STOP\n```\n\n. Then you can use this ID in the compression parameters (cparams.compcode, cparams.filters) and decompression parameters (dparams.compcode, dparams.filters).\nFor any doubts you can see the whole process in the examples urcodecs.c and urfilters.c. \n\n### Using Blosc official plugins\n\nTo use the Blosc official plugins it is mandatory to add the next lines in order to activate the plugins mechanism:\n\n```\n#include \"blosc2/codecs-registery.h\"\n```\n\n```\n#include \"blosc2/filters-registery.h\"\n```\n\ndepending on the plugin type at the beginning of the file * \n\n```\n#include \"blosc2/blosc2.h\"\n```\n\nat the beginning of the file * \n\nCall\n `blosc_init()` at the beginning of main() function * \n\nCall\n `blosc_destroy()` at the end of main() function Then you just have to use the ID of the plugin that you want to use in the compression parameters ( `cparams.compcode` ). > #include \"blosc2.h\" #include \"../codecs-registry.h\" int main(void) { blosc_init(); ... blosc2_cparams cparams = BLOSC2_CPARAMS_DEFAULTS; cparams.compcode = BLOSC_CODEC_NDLZ; cparams.compcode_meta = 4; ... blosc_destroy(); }\n\nIn case of doubts, you can see how the whole process works in working tests like: test_ndlz.c, test_ndcell.c, test_ndmean_mean.c and test_ndmean_repart.c.\n\n## Final remarks\n\nThe plugin register functionality let use new codecs and filters within Blosc in an easy and quick way. To enhance the plugin experience, we have implemented a centralized plugin repository, so that users can propose their own plugins to be in the standard C-Blosc2 library for the benefit of all the Blosc community.\n\nThe Blosc Development Team kindly invites you to test the different plugins we already offer, but also to try with your own one. Besides, if you are willing to contribute it to the community, then apply to register it. This way everyone will be able to enjoy a variety of different and unique plugins. Hope you will enjoy this new and exciting feature!\n\nLast but not least, a big thank you to the NumFOCUS foundation for providing a grant for implementing the register functionality.\n\n# Compressing ERA5 datasets\n\nBytedelta is a new filter that calculates the difference between bytes in a data stream. Combined with the shuffle filter, it can improve compression for some datasets. Bytedelta is based on initial work by <NAME>.\n\nTL;DR: We have a brief introduction to bytedelta in the 3rd section of this presentation.\n\nThe basic concept is simple: after applying the shuffle filter,\n\nthen compute the difference for each byte in the byte streams (also called splits in Blosc terminology):\n\nThe key insight enabling the bytedelta algorithm lies in its implementation, especially the use of SIMD on Intel/AMD and ARM NEON CPUs, making the filter overhead minimal.\n\nAlthough Aras's original code implemented shuffle and bytedelta together, it was limited to a specific item size (4 bytes). Making it more general would require significant effort. Instead, for Blosc2 we built on the existing shuffle filter and created a new one that just does bytedelta. When we insert both in the Blosc2 filter pipeline (it supports up to 6 chained filters), it leads to a completely general filter that works for any type size supported by existing shuffle filter.\n\nWith that said, the implementation of the bytedelta filter has been a breeze thanks to the plugin support in C-Blosc2. You can also implement your own filters and codecs on your own, or if you are too busy, we will be happy to assist you.\n\n## Compressing ERA5 datasets\n\nThe best approach to evaluate a new filter is to apply it to real data. For this, we will use some of the ERA5 datasets, representing different measurements and labeled as \"wind\", \"snow\", \"flux\", \"pressure\" and \"precip\". They all contain floating point data (float32) and we will use a full month of each one, accounting for 2.8 GB for each dataset.\n\nThe diverse datasets exhibit rather dissimilar complexity, which proves advantageous for testing diverse compression scenarios. For instance, the wind dataset appears as follows:\n\nThe image shows the intricate network of winds across the globe on October 1, 1987. The South American continent is visible on the right side of the map.\n\nAnother example is the snow dataset:\n\nThis time the image is quite flat. Here one can spot Antarctica, Greenland, North America and of course, Siberia, which was pretty full of snow by 1987-10-01 23:00:00 already.\n\nLet's see how the new bytedelta filter performs when compressing these datasets. All the plots below have been made using a box with an Intel i13900k processor, 32 GB of RAM and using Clear Linux.\n\nIn the box plot above, we summarized the compression ratios for all datasets using different codecs (BLOSCLZ, LZ4, LZ4HC and ZSTD). The main takeaway is that using bytedelta yields the best median compression ratio: bytedelta achieves a median of 5.86x, compared to 5.62x for bitshuffle, 5.1x for shuffle, and 3.86x for codecs without filters. Overall, bytedelta seems to improve compression ratios here, which is good news.\n\nWhile the compression ratio is a useful metric for evaluating the new bytedelta filter, there is more to consider. For instance, does the filter work better on some data sets than others? How does it impact the performance of different codecs? If you're interested in learning more, read on.\n\n## Effects on various datasets\n\nLet's see how different filters behave on various datasets:\n\nHere we see that, for datasets that compress easily (precip, snow), the behavior is quite different from those that are less compressible. For precip, bytedelta actually worsens results, whereas for snow, it slightly improves them. For less compressible datasets, the trend is more apparent, as can be seen in this zoomed in image:\n\nIn these cases, bytedelta clearly provides a better compression ratio, most specifically with the pressure dataset, where compression ratio by using bytedelta has increased by 25% compared to the second best, bitshuffle (5.0x vs 4.0x, using ZSTD clevel 9). Overall, only one dataset (precip) shows an actual decrease. This is good news for bytedelta indeed.\n\nFurthermore, Blosc2 supports another compression parameter for splitting the compressed streams into bytes with the same significance. Normally, this leads to better speed but less compression ratio, so this is automatically activated for faster codecs, whereas it is disabled for slower ones. However, it turns out that, when we activate splitting for all the codecs, we find a welcome surprise: bytedelta enables ZSTD to find significantly better compression paths, resulting in higher compression ratios.\n\nAs can be seen, in general ZSTD + bytedelta can compress these datasets better. For the pressure dataset in particular, it goes up to 5.7x, 37% more than the second best, bitshuffle (5.7x vs 4.1x, using ZSTD clevel 9). Note also that this new highest is 14% more than without splitting (the default).\n\nThis shows that when compressing, you cannot just trust your intuition for setting compression parameters - there is no substitute for experimentation.\n\n## Effects on different codecs\n\nNow, let's see how bytedelta affects performance for different codecs and compression levels.\n\nInterestingly, on average bytedelta proves most useful for ZSTD and higher compression levels of ZLIB (Blosc2 comes with ZLIB-NG). On the other hand, the fastest codecs (LZ4, BLOSCLZ) seem to benefit more from bitshuffle instead.\n\nRegarding compression speed, in general we can see that bytedelta has little effect on performance:\n\nAs we can see, compression algorithms like BLOSCLZ, LZ4 and ZSTD can achieve extremely high speeds. LZ4 reaches and surpasses speeds of 30 GB/s, even when using bytedelta. BLOSCLZ and ZSTD can also exceed 20 GB/s, which is quite impressive.\n\nHere one can see that, to achieve the highest compression rates when combined with shuffle and bytedelta, the codecs require significant CPU resources; this is especially noticeable in the zoomed-in view:\n\nwhere capable compressors like ZSTD do require up to 2x more time to compress when using bytedelta, especially for high compression levels (6 and 9).\n\nNow, let us examine decompression speeds:\n\nIn general, decompression is faster than compression. BLOSCLZ, LZ4 and LZ4HC can achieve over 100 GB/s. BLOSCLZ reaches nearly 180 GB/s using no filters on the snow dataset (lowest complexity).\n\nThe bytedelta filter noticeably reduces speed for most codecs, up to 20% or more. ZSTD performance is less impacted.\n\n## Achieving a balance between compression ratio and speed\n\nOften, you want to achieve a good balance of compression and speed, rather than extreme values of either. We will conclude by showing plots depicting a combination of both metrics and how bytedelta influences them.\n\nLet's first represent the compression ratio versus compression speed:\n\nAs we can see, the shuffle filter is typically found on the Pareto frontier (in this case, the point furthest to the right and top). Bytedelta comes next. In contrast, not using a filter at all is on the opposite side. This is typically the case for most real-world numerical datasets.\n\nLet's now group filters and datasets and calculate the mean values of combining (in this case, multiplying) the compression ratio and compression speed for all codecs.\n\nAs can be seen, bytedelta works best with the wind dataset (which is quite complex), while bitshuffle does a good job in general for the others. The shuffle filter wins on the snow dataset (low complexity).\n\nIf we group by compression level:\n\nWe see that bytedelta works well with LZ4 here, and also with ZSTD at the lowest compression level (1).\n\nLet's revise the compression ratio versus decompression speed comparison:\n\nLet's group together the datasets and calculate the mean for all codecs:\n\nIn this case, shuffle generally prevails, with bitshuffle also doing reasonably well, winning on precip and pressure datasets.\n\nAlso, let’s group the data by compression level:\n\nWe find that bytedelta compression does not outperform shuffle compression in any scenario. This is unsurprising since decompression is typically fast, and bytedelta's extra processing can decrease performance more easily. We also see that LZ4HC (clevel 6 and 9) + shuffle strikes the best balance in this scenario.\n\nFinally, let's consider the balance between compression ratio, compression speed, and decompression speed:\n\nHere the winners are shuffle and bitshuffle, depending on the data set, but bytedelta never wins.\n\nIf we group by compression levels:\n\nOverall, we see LZ4 as the clear winner at any level, especially when combined with shuffle. On the other hand, bytedelta did not win in any scenario here.\n\n## Benchmarks for other computers\n\nWe have run the benchmarks presented here in an assortment of different boxes:\n\nAlso, find here a couple of runs using the i9-13900K box above, but with the always split and never split settings:\n\nReproducing the benchmarks is straightforward. First, download the data; the downloaded files will be in the new era5_pds/ directory. Then perform the series of benchmarks; this is takes time, so grab coffee and wait 30 min (fast workstations) to 6 hours (slow laptops). Finally, run the plotting Jupyter notebook to explore your results. If you wish to share your results with the Blosc development team, we will appreciate hearing from you!\n\nBytedelta can achieve higher compression ratios in most datasets, specially in combination with capable codecs like ZSTD, with a maximum gain of 37% (pressure) over other codecs; only in one case (precip) compression ratio decreases. By compressing data more efficiently, bytedelta can reduce file sizes even more, accelerating transfer and storage.\n\nOn the other hand, while bytedelta excels at achieving high compression ratios, this requires more computing power. We have found that for striking a good balance between high compression and fast compression/decompression, other filters, particularly shuffle, are superior overall.\n\nWe've learned that no single codec/filter combination is best for all datasets:\n\nZSTD (clevel 9) + bytedelta can get better absolute compression ratio for most of the datasets.\n * \n\nLZ4 + shuffle is well-balanced for all metrics (compression ratio, speed, decompression speed).\n * \n\nLZ4 (clevel 6) and ZSTD (clevel 1) + shuffle strike a good balance of compression ratio and speed.\n * \n\nLZ4HC (clevel 6 and 9) + shuffle balances well compression ratio and decompression speed.\n * \n\nBLOSCLZ without filters achieves best decompression speed (at least in one instance).\n\nIn summary, the optimal choice depends on your priorities.\n\nAs a final note, the Blosc development team is working on BTune, a new deep learning tuner for Blosc2. BTune can be trained to automatically recognize different kinds of datasets and choose the optimal codec and filters to achieve the best balance, based on the user's needs. This would create a much more intelligent compressor that can adapt itself to your data faster, without requiring time-consuming manual tuning. If interested, contact us; we are looking for beta testers!\n\nDate: 2023-03-24\nCategories: \nTags: \n\n* Bytedelta: Enhance Your Compression Toolset\n * 100 Trillion Rows Baby\n * 20 years of PyTables\n * C-Blosc2 Ready for General Review\n * Mid 2020 Progress Report\n * C-Blosc Beast Release\n * Blosc Received a $50,000 USD donation\n * Blosc2-Meets-Rome\n * C-Blosc2 Enters Beta Stage\n * Is ARM Hungry Enough to Eat Intel's Favorite Pie?\n * Breaking Down Memory Walls\n * New Forward Compatibility Policy\n * Blosc Has Won Google's Open Source Peer Bonus Program\n * The Lizard Codec\n * Testing PGO with LZ4 and Zstd codecs\n * Fine Tuning the BloscLZ codec\n * Zstd has just landed in Blosc\n * ARM is becoming a first-class citizen for Blosc\n * Hairy situation of Microsoft Windows compilers\n * New 'bitshuffle' filter\n * Compress Me, Stupid!\n\nfilter | clevel | codec | cspeed | dspeed | cratio | cratio * cspeed | cratio * dspeed | cratio * cspeed * dspeed |\n | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n0 | bitshuffle | 1 | BLOSCLZ | 8.521135 | 37.163098 | 12.394004 | 148.448453 | 501.408152 | 6253.902051 |\n1 | bitshuffle | 1 | LZ4 | 9.909460 | 44.217161 | 12.307460 | 166.358353 | 576.647578 | 7988.992414 |\n2 | bitshuffle | 1 | LZ4HC | 4.159958 | 43.733051 | 13.208067 | 70.761302 | 605.809677 | 3295.282965 |\n3 | bitshuffle | 1 | ZLIB | 5.168855 | 13.940715 | 11.603630 | 77.505811 | 186.900015 | 1311.426899 |\n4 | bitshuffle | 1 | ZSTD | 8.797193 | 26.460997 | 16.284555 | 204.352339 | 486.648768 | 6403.270085 |\n... | ... | ... | ... | ... | ... | ... | ... | ... | ... |\n75 | shuffle | 9 | BLOSCLZ | 7.090165 | 44.120614 | 11.680731 | 148.535757 | 703.817960 | 10643.652492 |\n76 | shuffle | 9 | LZ4 | 10.490418 | 58.993959 | 11.310522 | 198.642207 | 867.525260 | 17219.304417 |\n77 | shuffle | 9 | LZ4HC | 1.491062 | 67.126168 | 13.315973 | 32.524722 | 1046.584163 | 2841.998079 |\n78 | shuffle | 9 | ZLIB | 0.601809 | 6.119631 | 16.804231 | 14.217234 | 107.050088 | 87.078144 |\n79 | shuffle | 9 | ZSTD | 0.064413 | 26.539378 | 18.811941 | 1.190553 | 733.932425 | 47.901377 |\n\nfilter | clevel | codec | cspeed | dspeed | cratio | cratio * cspeed | cratio * dspeed | cratio * cspeed * dspeed |\n | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n0 | bitshuffle | 1 | BLOSCLZ | 12.761833 | 66.747672 | 9.173380 | 170.239436 | 675.753748 | 12870.859984 |\n1 | bitshuffle | 1 | LZ4 | 12.205809 | 73.292183 | 11.894671 | 222.119679 | 922.913309 | 17639.433252 |\n2 | bitshuffle | 1 | LZ4HC | 6.076772 | 67.928352 | 12.769271 | 98.755855 | 908.162400 | 7154.733080 |\n3 | bitshuffle | 1 | ZLIB | 7.298479 | 25.029979 | 11.200472 | 106.809085 | 330.309560 | 3332.657153 |\n4 | bitshuffle | 1 | ZSTD | 11.477392 | 44.646190 | 15.785637 | 273.428811 | 774.338758 | 13816.902657 |\n... | ... | ... | ... | ... | ... | ... | ... | ... | ... |\n75 | shuffle | 9 | BLOSCLZ | 10.061763 | 72.198181 | 11.338061 | 209.104856 | 1076.932715 | 22342.209134 |\n76 | shuffle | 9 | LZ4 | 15.022658 | 92.064490 | 10.963307 | 266.011167 | 1250.285500 | 32369.603352 |\n77 | shuffle | 9 | LZ4HC | 2.625860 | 94.784550 | 12.928206 | 61.242247 | 1482.265572 | 7769.986737 |\n78 | shuffle | 9 | ZLIB | 1.053539 | 11.222278 | 16.333023 | 25.617114 | 199.231475 | 319.643959 |\n79 | shuffle | 9 | ZSTD | 0.103401 | 41.698953 | 18.288814 | 1.900180 | 1087.433286 | 114.708453 |\n\nDate: 2023-02-22\nCategories: \nTags: \n\nSkip to main content 2023-02-22 10:32Introducing Blosc2 NDim\n\nIt contains both the data and metalayer that stores the dimensional info for the array. Blosc2 NDim has a managed internal context that stores the different properties of each array.\n\n## Context#\n\n* typedef struct b2nd_context_s b2nd_context_t#\n * \n\nGeneral parameters needed for the creation of a b2nd array.\n\n* b2nd_context_t *b2nd_create_ctx(const blosc2_storage *b2_storage, int8_t ndim, const int64_t *shape, const int32_t *chunkshape, const int32_t *blockshape, const char *dtype, int8_t dtype_format, const blosc2_metalayer *metalayers, int32_t nmetalayers)#\n * \n\nCreate b2nd params.\n\nb2_storage – The Blosc2 storage params.\n * \n\nndim – The dimensions.\n * \n\nshape – The shape.\n * \n\nchunkshape – The chunk shape.\n * \n\nblockshape – The block shape.\n * \n\ndtype – The data type expressed as a string version.\n * \n\ndtype_format – The data type format; default is DTYPE_NUMPY_FORMAT.\n * \n\nmetalayers – The memory pointer to the list of the metalayers desired.\n * \n\nnmetalayers – The number of metalayers.\n * Returns\n * \n\nA pointer to the new b2nd params. NULL is returned if this fails.\n\nThe pointer returned must be freed when not used anymore with b2nd_free_ctx.\n\n* int b2nd_free_ctx(b2nd_context_t *ctx)#\n * \n\nFree the resources associated with b2nd_context_t.\n\nctx – The b2nd context to free.\n * Returns\n * \n\nThis is safe in the sense that it will not free the schunk pointer in internal cparams.\n\n## Array#\n\nA Blosc2 NDim array is a n-dimensional object that can be managed by the associated functions. The functions let users to perform different operations with these arrays like copying, getting, setting or converting data into buffers or files and vice-versa. Furthermore, Blosc2 NDim only stores the type size (not the data type), and every item of an array has the same size.\n\nThe b2nd_array_t type struct is where all data and metadata for an array is stored:\n\n* struct b2nd_array_t#\n * \n\nA multidimensional array of data that can be compressed.\n\n# Constructors#\n\n* int b2nd_uninit(b2nd_context_t *ctx, b2nd_array_t **array)#\n * \n\nCreate an uninitialized array.\n\n* int b2nd_empty(b2nd_context_t *ctx, b2nd_array_t **array)#\n * \n\nCreate an empty array.\n\n* int b2nd_zeros(b2nd_context_t *ctx, b2nd_array_t **array)#\n * \n\n* int b2nd_full(b2nd_context_t *ctx, b2nd_array_t **array, const void *fill_value)#\n * \n\nfill_value – Default value for uninitialized portions of the array.\n * Returns\n * \n\n# From/To buffer#\n\n* int b2nd_from_cbuffer(b2nd_context_t *ctx, b2nd_array_t **array, const void *buffer, int64_t buffersize)#\n * \n\nCreate a b2nd array from a C buffer.\n\nbuffer – The buffer where source data is stored.\n * \n\n* int b2nd_to_cbuffer(const b2nd_array_t *array, void *buffer, int64_t buffersize)#\n * \n\nExtract the data from a b2nd array into a C buffer.\n\n# From/To file#\n\n* int b2nd_open(const char *urlpath, b2nd_array_t **array)#\n * \n\nOpen a b2nd array from a file.\n\n* int b2nd_open_offset(const char *urlpath, b2nd_array_t **array, int64_t offset)#\n * \n\nOpen a b2nd array from a file using an offset.\n\noffset – The offset in the file where the b2nd array frame starts.\n * Returns\n * \n\n* int b2nd_save(const b2nd_array_t *array, char *urlpath)#\n * \n\nSave b2nd array into a specific urlpath.\n\narray – The array to be saved.\n * \n\nurlpath – The urlpath where the array will be stored.\n * Returns\n * \n\n# From Blosc object#\n\n* int b2nd_from_schunk(blosc2_schunk *schunk, b2nd_array_t **array)#\n * \n\nIt can only be used if the array is backed by a blosc super-chunk.\n\nschunk – The blosc super-chunk where the b2nd array is stored.\n * \n\n* int b2nd_from_cframe(uint8_t *cframe, int64_t cframe_len, bool copy, b2nd_array_t **array)#\n * \n\ncframe – The buffer of the in-memory array.\n * \n\ncframe_len – The size (in bytes) of the in-memory array.\n * \n\ncopy – Whether b2nd should make a copy of the cframe data or not. The copy will be made to an internal sparse frame.\n * \n\n* int b2nd_to_cframe(const b2nd_array_t *array, uint8_t **cframe, int64_t *cframe_len, bool *needs_free)#\n * \n\nCreate a serialized super-chunk from a b2nd array.\n\narray – The b2nd array to be serialized.\n * \n\ncframe – The pointer of the buffer where the in-memory array will be copied.\n * \n\ncframe_len – The length of the in-memory array buffer.\n * \n\nneeds_free – Whether the buffer should be freed or not.\n * Returns\n * \n\n# Modify data#\n\n* int b2nd_insert(b2nd_array_t *array, const void *buffer, int64_t buffersize, int8_t axis, int64_t insert_start)#\n * \n\nInsert given buffer in an array extending the given axis.\n\narray – The array to insert the data in.\n * \n\nbuffer – The buffer data to be inserted.\n * \n\naxis – The axis that will be extended.\n * \n\ninsert_start – The position inside the axis to start inserting the data.\n * Returns\n * \n\n* int b2nd_append(b2nd_array_t *array, const void *buffer, int64_t buffersize, int8_t axis)#\n * \n\nAppend a buffer at the end of a b2nd array.\n\narray – The array to append the data in.\n * \n\nbuffer – The buffer data to be appended.\n * \n\naxis – The axis that will be extended to append the data.\n * Returns\n * \n\n* int b2nd_delete(b2nd_array_t *array, int8_t axis, int64_t delete_start, int64_t delete_len)#\n * \n\nDelete shrinking the given axis delete_len items.\n\naxis – The axis to shrink.\n * \n\ndelete_start – The start position from the axis to start deleting chunks.\n * \n\ndelete_len – The number of items to delete to the array->shape[axis]. The newshape[axis] will be the old array->shape[axis] - delete_len\n * Returns\n * \n\n### Copying#\n\n* int b2nd_copy(b2nd_context_t *ctx, const b2nd_array_t *src, b2nd_array_t **array)#\n * \n\nMake a copy of the array data.\n\nThe copy is done into a new b2nd array.\n\nsrc – The array from which data is copied.\n * \n\nThe ndim and shape in ctx will be overwritten by the src ctx.\n\n### Slicing#\n\n* int b2nd_get_slice(b2nd_context_t *ctx, b2nd_array_t **array, const b2nd_array_t *src, const int64_t *start, const int64_t *stop)#\n * \n\nGet a slice from an array and store it into a new array.\n\nsrc – The array from which the slice will be extracted\n * \n\nThe ndim and shape from ctx will be overwritten by the src and stop-start respectively.\n\n* int b2nd_get_slice_cbuffer(const b2nd_array_t *array, const int64_t *start, const int64_t *stop, void *buffer, const int64_t *buffershape, int64_t buffersize)#\n * \n\nGet a slice from an array and store it into a C buffer.\n\narray – The array from which the slice will be extracted.\n * \n\n* int b2nd_set_slice_cbuffer(const void *buffer, const int64_t *buffershape, int64_t buffersize, const int64_t *start, const int64_t *stop, b2nd_array_t *array)#\n * \n\nSet a slice in a b2nd array using a C buffer.\n\nbuffer – The buffer where the slice data is.\n * \n\narray – The b2nd array where the slice will be set\n * Returns\n * \n\n* int b2nd_get_orthogonal_selection(const b2nd_array_t *array, int64_t **selection, int64_t *selection_size, void *buffer, int64_t *buffershape, int64_t buffersize)#\n * \n\narray – The array to get the data from.\n * \n\nbuffer – The buffer for getting the data.\n * \n\nSee also b2nd_set_orthogonal_selection.\n\n* int b2nd_set_orthogonal_selection(b2nd_array_t *array, int64_t **selection, int64_t *selection_size, const void *buffer, int64_t *buffershape, int64_t buffersize)#\n * \n\narray – The array to set the data to.\n * \n\nbuffer – The buffer with the data for setting.\n * \n\nSee also b2nd_get_orthogonal_selection.\n\n* int b2nd_squeeze(b2nd_array_t *array)#\n * \n\n* int b2nd_squeeze_index(b2nd_array_t *array, const bool *index)#\n * \n\nindex – Indexes of the single-dimensional entries to remove.\n * Returns\n * \n\n### Utils#\n\n* int b2nd_print_meta(const b2nd_array_t *array)#\n * \n\nPrint metalayer parameters.\n\narray – The array where the metalayer is stored.\n * Returns\n * \n\n* int b2nd_serialize_meta(int8_t ndim, const int64_t *shape, const int32_t *chunkshape, const int32_t *blockshape, const char *dtype, int8_t dtype_format, uint8_t **smeta)#\n * \n\nCreate the metainfo for the b2nd metalayer.\n\nshape – The shape of the array.\n * \n\nchunkshape – The shape of the chunks in the array.\n * \n\nblockshape – The shape of the blocks in the array.\n * \n\ndtype – A string representation of the data type of the array.\n * \n\ndtype_format – The format of the dtype representation. 0 means NumPy.\n * \n\nsmeta – The msgpack buffer (output).\n * Returns\n * \n\n* static inline int b2nd_deserialize_meta(const uint8_t *smeta, int32_t smeta_len, int8_t *ndim, int64_t *shape, int32_t *chunkshape, int32_t *blockshape, char **dtype, int8_t *dtype_format)#\n * \n\nRead the metainfo in the b2nd metalayer.\n\nsmeta – The msgpack buffer (input).\n * \n\nsmeta_len – The length of the smeta buffer (input).\n * \n\nshape – The shape of the array (output).\n * \n\nchunkshape – The shape of the chunks in the array (output).\n * \n\nblockshape – The shape of the blocks in the array (output).\n * \n\ndtype – A string representation of the data type of the array (output).\n * \n\ndtype_format – The format of the dtype representation (output). 0 means NumPy (the default).\n * Returns\n * \n\nThis function is inlined and available even when not linking with libblosc2.\n\n* int b2nd_resize(b2nd_array_t *array, const int64_t *new_shape, const int64_t *start)#\n * \n\nResize the shape of an array.\n\nnew_shape – The new shape from the array.\n * \n\nstart – The position in which the array will be extended or shrunk.\n * Returns\n * \n\n* int b2nd_free(b2nd_array_t *array)#\n * \n\nFree an array.\n\n# Effect on (relatively small) datasets\n\nIn recently released PyTables 3.8.0 we gave support for an optimized path for writing and reading Table instances with Blosc2 cooperating with the HDF5 machinery. On the blog describing its implementation we have shown how it collaborates with the HDF5 library so as to get top-class I/O performance.\n\nSince then, we have been aware (thanks to <NAME>) of the introduction of the H5Dchunk_iter function in HDF5 1.14 series. This predates the functionality of H5Dget_chunk_info, and makes retrieving the offsets of the chunks in the HDF5 file way more efficiently, specially on files with a large number of chunks - H5Dchunk_iter cost is O(n), whereas H5Dget_chunk_info is O(n^2).\n\nAs we decided to implement support for H5Dchunk_iter in PyTables, we were curious on the sort of boost this could provide reading tables created from real data. Keep reading for the experiments we've conducted about this.\n\n## Effect on (relatively small) datasets\n\nWe start by reading a table with real data coming from our usual ERA5 database. We fetched one year (2000 to be specific) of data with five different ERA5 datasets with the same shape and the same coordinates (latitude, longitude and time). This data has been stored on a table with 8 columns with 32 bytes per row and with 9 millions rows (for a grand total of 270 GB); the number of chunks is about 8K.\n\nWhen using compression, the size is typically reduced between a factor of 6x (LZ4 + shuffle) and 9x (Zstd + bitshuffle); in any case, the resulting file size is larger than the RAM available in our box (32 GB), so we can safely exclude OS filesystem caching effects here. Let's have a look at the results on reading this dataset inside PyTables (using shuffle only; for bitshuffle results are just a bit slower):\n\nWe see how the improvement when using HDF5 1.14 (and hence H5Dchunk_iter) for reading data sequentially (via a PyTables query) is not that noticeable, but for random queries, the speedup is way more apparent. For comparison purposes, we added the figures for Blosc1+LZ4; one can notice the great job of Blosc2, specially in terms of random reads due to the double partitioning and HDF5 pipeline replacement.\n\n## A trillion rows table\n\nBut 8K chunks is not such a large figure, and we are interested in using datasets with a larger amount. As it is very time consuming to download large amounts of real data for our benchmarks purposes, we have decided to use synthetic data (basically, a bunch of zeros) just to explore how the new H5Dchunk_iter function scales when handling extremely large datasets in HDF5.\n\nNow we will be creating a large table with 1 trillion rows, with the same 8 fields than in the previous section, but whose values are zeros (remember, we are trying to push HDF5 / Blosc2 to their limits, so data content is not important here). With that, we are getting a table with 845K chunks, which is about 100x more than in the previous section.\n\nWith this, lets' have a look at the plots for the read speed:\n\nAs expected, we are getting significantly better results when using HDF5 1.14 (with H5Dchunk_iter) in both sequential and random cases. For comparison purposes, we have added Blosc1-Zstd which does not make use of the new functionality. In particular, note how Blosc1 gets better results for random reads than Blosc2 with HDF5 1.12; as this is somehow unexpected, if you have an explanation, please chime in.\n\nIt is worth noting that even though the data are made of zeros, Blosc2 still needs to compress/decompress the full 32 TB thing. And the same goes for numexpr, which is used internally to perform the computations for the query in the sequential read case. This is testimonial of the optimization efforts in the data flow (i.e. avoiding as much memory copies as possible) inside PyTables.\n\n## 100 trillion rows baby\n\nAs a final exercise, we took the previous experiment to the limit, and made a table with 100 trillion (that’s a 1 followed with 14 zeros!) rows and measured different interesting aspects. It is worth noting that the total size for this case is 2.8 PB (petabyte), and the number of chunks is around 85 millions (finally, large enough to fully demonstrate the scalability of the new H5Dchunk_iter functionality).\n\nHere it is the speed of random and sequential reads:\n\nAs we can see, despite the large amount of chunks, the sequential read speed actually improved up to more than 75 GB/s. Regarding the random read latency, it increased to 60 µs; this is not too bad actually, as in real life the latencies during random reads in such a large files are determined by the storage media, which is no less than 100 µs for the fastest SSDs nowadays.\n\nThe script that creates the table and reads it can be found at bench/100-trillion-rows-baby.py. For the curious, it took about 24 hours to run on a Linux box wearing an Intel 13900K CPU with 32 GB of RAM. The memory consumption during writing was about 110 MB, whereas for reading was 1.7 GB steadily (pretty good for a multi-petabyte table). The final size for the file has been 17 GB, for a compression ratio of more than 175000x.\n\nAs we have seen, the H5Dchunk_iter function recently introduced in HDF5 1.14 is confirmed to be of a big help in performing reads more efficiently. We have also demonstrated that scalability is excellent, reaching phenomenal sequential speeds (exceeding 75 GB/s with synthetic data) that cannot be easily achieved by the most modern I/O subsystems, and hence avoiding unnecessary bottlenecks.\n\nIndeed, the combo HDF5 / Blosc2 is able to handle monster sized tables (on the petabyte ballpark) without becoming a significant bottleneck in performance. Not that you need to handle such a sheer amount of data anytime soon, but it is always reassuring to use a tool that is not going to take a step back in daunting scenarios like this.\n\nDate: 2022-12-23\nCategories: \nTags: \n\n2022-12-23 12:32Blosc2 Meets PyTables: Making HDF5 I/O Performance Awesome 2022-03-11 10:32Announcing Support for Lossy ZFP Codec as a Plugin for C-Blosc2 2021-07-26 04:32Caterva Slicing Performance: A Study\n\nThis is the classic API from Blosc1 with 32-bit limited containers.\n\n## Main API#\n\n* void blosc2_init(void)#\n * \n\nInitialize the Blosc library environment.\n\nYou must call this previous to any other Blosc call, unless you want Blosc to be used simultaneously in a multi-threaded environment, in which case you can use the blosc2_compress_ctx blosc2_decompress_ctx pair.\n\n* void blosc2_destroy(void)#\n * \n\nDestroy the Blosc library environment.\n\nYou must call this after to you are done with all the Blosc calls, unless you have not used blosc2_init() before.\n\n* int blosc1_compress(int clevel, int doshuffle, size_t typesize, size_t nbytes, const void *src, void *dest, size_t destsize)#\n * \n\nCompress a block of data in the\n `src` buffer and returns the size of compressed block. \nRemark\n\nCompression is memory safe and guaranteed not to write\n `dest` more than what is specified in `destsize` . There is not a minimum for `src` buffer size `nbytes` . \n\nBLOSC_CLEVEL=(INTEGER): This will overwrite the\n `clevel` parameter before the compression process starts. * \n\nBLOSC_SHUFFLE=[NOSHUFFLE | SHUFFLE | BITSHUFFLE]: This will overwrite the\n `doshuffle` parameter before the compression process starts. * \n\nBLOSC_DELTA=(1|0): This will call blosc2_set_delta() before the compression process starts.\n * \n\nBLOSC_TYPESIZE=(INTEGER): This will overwrite the\n `typesize` parameter before the compression process starts. * \n\nBLOSC_COMPRESSOR=[BLOSCLZ | LZ4 | LZ4HC | ZLIB | ZSTD]: This will call blosc1_set_compressor before the compression process starts.\n * \n\nBLOSC_SPLITMODE=(ALWAYS | NEVER | AUTO | FORWARD_COMPAT): This will call blosc1_set_splitmode() before the compression process starts.\n * \n\nBLOSC_BLOCKSIZE=(INTEGER): This will call blosc1_set_blocksize before the compression process starts. NOTE: The blocksize is a critical parameter with important restrictions in the allowed values, so use this with care.\n * \n\nBLOSC_NOLOCK=(ANY VALUE): This will call blosc2_compress_ctx under the hood, with the compressor, blocksize and numinternalthreads parameters set to the same as the last calls to blosc1_set_compressor, blosc1_set_blocksize and blosc2_set_nthreads. BLOSC_CLEVEL, BLOSC_SHUFFLE, BLOSC_DELTA and BLOSC_TYPESIZE environment vars will also be honored.\n\nclevel – The desired compression level and must be a number between 0 (no compression) and 9 (maximum compression).\n * \n\ndoshuffle – Specifies whether the shuffle compression preconditioner should be applied or not. BLOSC_NOFILTER means not applying filters, BLOSC_SHUFFLE means applying shuffle at a byte level and BLOSC_BITSHUFFLE at a bit level (slower but may achieve better compression).\n * \n\ntypesize – Is the number of bytes for the atomic type in binary\n `src` buffer. This is mainly useful for the shuffle preconditioner. For implementation reasons, only a 1 < typesize < 256 will allow the shuffle filter to work. When typesize is not in this range, shuffle will be silently disabled. * \n\nnbytes – The number of bytes to compress in the\n `src` buffer. * \n\nsrc – The buffer containing the data to compress.\n * \n\ndest – The buffer where the compressed data will be put, must have at least the size of\n `destsize` . * \n\ndestsize – The size of the dest buffer. Blosc guarantees that if you set\n `destsize` to, at least, ( `nbytes` + BLOSC2_MAX_OVERHEAD), the compression will always succeed. * Returns\n * \n\nThe number of bytes compressed. If\n `src` buffer cannot be compressed into `destsize` , the return value is zero and you should discard the contents of the `dest` buffer. A negative return value means that an internal error happened. This should never happen. If you see this, please report it back together with the buffer data causing this and compression settings. \nWarning\n\n* int blosc1_decompress(const void *src, void *dest, size_t destsize)#\n * \n\nDecompress a block of compressed data in\n `src` , put the result in `dest` and returns the size of the decompressed block. \nRemark\n\nDecompression is memory safe and guaranteed not to write the\n `dest` buffer more than what is specified in `destsize` . \nRemark\n\nIn case you want to keep under control the number of bytes read from source, you can call blosc1_cbuffer_sizes first to check whether the\n `nbytes` (i.e. the number of bytes to be read from `src` buffer by this function) in the compressed buffer is ok with you. \n\nBLOSC_NOLOCK=(ANY VALUE): This will call blosc2_decompress_ctx under the hood, with the numinternalthreads parameter set to the same value as the last call to blosc2_set_nthreads.\n\nsrc – The buffer to be decompressed.\n * \n\ndest – The buffer where the decompressed data will be put.\n * \n\ndestsize – The size of the\n `dest` buffer. * Returns\n * \n\nThe number of bytes decompressed. If an error occurs, e.g. the compressed data is corrupted or the output buffer is not large enough, then a negative value will be returned instead.\n\n* int blosc1_getitem(const void *src, int start, int nitems, void *dest)#\n * \n\nGet\n `nitems` (of `typesize` size) in `src` buffer starting in `start` . \nThe items are returned in\n `dest` buffer, which has to have enough space for storing all items. \n\nsrc – The compressed buffer from data will be decompressed.\n * \n\nstart – The position of the first item (of\n `typesize` size) from where data will be retrieved. * \n\nnitems – The number of items (of\n `typesize` size) that will be retrieved. * \n\ndest – The buffer where the decompressed data retrieved will be put.\n * Returns\n * \n\nThe number of bytes copied to\n `dest` or a negative value if some error happens. \n\n* int16_t blosc2_get_nthreads(void)#\n * \n\nReturns the current number of threads that are used for compression/decompression.\n\n* int16_t blosc2_set_nthreads(int16_t nthreads)#\n * \n\nInitialize a pool of threads for compression/decompression.\n\nIf\n `nthreads` is 1, then the serial version is chosen and a possible previous existing pool is ended. If this is not called, `nthreads` is set to 1 internally. \n\nnthreads – The number of threads to use.\n * Returns\n * \n\nThe previous number of threads.\n\n* const char *blosc1_get_compressor(void)#\n * \n\nGet the current compressor that is used for compression.\n\nThe string identifying the compressor being used.\n\n* int blosc1_set_compressor(const char *compname)#\n * \n\nSelect the compressor to be used.\n\nThe supported ones are “blosclz”, “lz4”, “lz4hc”, “zlib” and “ztsd”. If this function is not called, then “blosclz” will be used.\n\ncompname – The name identifier of the compressor to be set.\n * Returns\n * \n\nThe code for the compressor (>=0). In case the compressor is not recognized, or there is not support for it in this build, it returns a -1.\n\n* void blosc2_set_delta(int dodelta)#\n * \n\nSelect the delta coding filter to be used.\n\nThis call should always succeed.\n\ndodelta – A value >0 will activate the delta filter. If 0, it will be de-activated\n\n* int blosc1_get_blocksize(void)#\n * \n\nGet the internal blocksize to be used during compression.\n\n0 means that an automatic blocksize is computed internally.\n\nThe size in bytes of the internal block size.\n\n* void blosc1_set_blocksize(size_t blocksize)#\n * \n\nForce the use of a specific blocksize.\n\nIf 0, an automatic blocksize will be used (the default).\n\nThe blocksize is a critical parameter with important restrictions in the allowed values, so use this with care.\n\n* void blosc1_set_splitmode(int splitmode)#\n * \n\nSet the split mode.\n\nBLOSC_FORWARD_COMPAT offers reasonably forward compatibility, BLOSC_AUTO_SPLIT is for nearly optimal results (based on heuristics), BLOSC_NEVER_SPLIT and BLOSC_ALWAYS_SPLIT are for the user experimenting when trying to get best compression ratios and/or speed.\n\nIf not called, the default mode is BLOSC_FORWARD_COMPAT_SPLIT.\n\nsplitmode – It can take the next values: BLOSC_FORWARD_COMPAT_SPLIT BLOSC_AUTO_SPLIT BLOSC_NEVER_SPLIT BLOSC_ALWAYS_SPLIT\n\n* int blosc2_free_resources(void)#\n * \n\nFree possible memory temporaries and thread resources.\n\nUse this when you are not going to use Blosc for a long while.\n\nA 0 if succeeds, in case of problems releasing the resources, it returns a negative number.\n\n## Compressed buffer information#\n\n* void blosc1_cbuffer_sizes(const void *cbuffer, size_t *nbytes, size_t *cbytes, size_t *blocksize)#\n * \n\nGet information about a compressed buffer, namely the number of uncompressed bytes (\n `nbytes` ) and compressed ( `cbytes` ). \nIt also returns the\n `blocksize` (which is used internally for doing the compression by blocks). \nYou only need to pass the first BLOSC_MIN_HEADER_LENGTH bytes of a compressed buffer for this call to work.\n\ncbytes – The pointer where the number of compressed bytes will be put.\n * \n\nblocksize – The pointer where the block size will be put.\n\n* void blosc1_cbuffer_metainfo(const void *cbuffer, size_t *typesize, int *flags)#\n * \n\nGet information about a compressed buffer, namely the type size (\n `typesize` ), as well as some internal `flags` . \nYou can use the\n `BLOSC_DOSHUFFLE` , `BLOSC_DOBITSHUFFLE` , `BLOSC_DODELTA` and `BLOSC_MEMCPYED` symbols for extracting the interesting bits (e.g. `flags` & `BLOSC_DOSHUFFLE` says whether the buffer is byte-shuffled or not). \nThis function should always succeed.\n\ntypesize – The pointer where the type size will be put.\n * \n\nflags – The pointer of the integer where the additional info is encoded. The\n `flags` is a set of bits, where the currently used ones are: \n\nbit 0: whether the shuffle filter has been applied or not\n * \n\nbit 1: whether the internal buffer is a pure memcpy or not\n * \n\nbit 2: whether the bitshuffle filter has been applied or not\n * \n\nbit 3: whether the delta coding filter has been applied or not\n\n* void blosc2_cbuffer_versions(const void *cbuffer, int *version, int *versionlz)#\n * \n\nGet information about a compressed buffer, namely the internal Blosc format version (\n `version` ) and the format for the internal Lempel-Ziv compressor used ( `versionlz` ). \nThis function should always succeed.\n\nversion – The pointer where the Blosc format version will be put.\n * \n\nversionlz – The pointer where the Lempel-Ziv version will be put.\n\n* const char *blosc2_cbuffer_complib(const void *cbuffer)#\n * \n\nGet the compressor library/format used in a compressed buffer.\n\nThe string identifying the compressor library/format used.\n\n* int blosc1_cbuffer_validate(const void *cbuffer, size_t cbytes, size_t *nbytes)#\n * \n\nChecks that the compressed buffer starting at\n `cbuffer` of length `cbytes` may contain valid blosc compressed data, and that it is safe to call blosc1_decompress/blosc1_getitem. \nOn success, returns 0 and sets\n `nbytes` to the size of the uncompressed data. This does not guarantee that the decompression function won’t return an error, but does guarantee that it is safe to attempt decompression. \n\ncbytes – The number of compressed bytes.\n * \n\nOn failure, returns negative value.\n\n## Utility functions#\n\n* int blosc2_compcode_to_compname(int compcode, const char **compname)#\n * \n\nGet the compressor name associated with the compressor code.\n\ncompcode – The code identifying the compressor\n * \n\ncompname – The pointer to a string where the compressor name will be put.\n * Returns\n * \n\nThe compressor code. If the compressor code is not recognized, or there is not support for it in this build, -1 is returned.\n\n* int blosc2_compname_to_compcode(const char *compname)#\n * \n\nGet the compressor code associated with the compressor name.\n\ncompname – The string containing the compressor name.\n * Returns\n * \n\nThe compressor code. If the compressor name is not recognized, or there is not support for it in this build, -1 is returned instead.\n\n* const char *blosc2_list_compressors(void)#\n * \n\nGet a list of compressors supported in the current build.\n\nThis function does not leak, so you should not free() the returned list.\n\nThe comma separated string with the list of compressor names supported.\n\n* const char *blosc2_get_version_string(void)#\n * \n\nGet the version of Blosc in string format.\n\nThe string with the current Blosc version. Useful for dynamic libraries.\n\n* int blosc2_get_complib_info(const char *compname, char **complib, char **version)#\n * \n\nGet info from compression libraries included in the current build.\n\ncompname – The compressor name that you want info from.\n * \n\ncomplib – The pointer to a string where the compression library name, if available, will be put.\n * \n\nversion – The pointer to a string where the compression library version, if available, will be put.\n * Returns\n * \n\nThe code for the compression library (>=0). If it is not supported, this function returns -1.\n\nYou are in charge of the\n `complib` and `version` strings, you should free() them so as to avoid leaks.\n\n# The Blosc2 pipeline\n\nThe Blosc Development Team is happy to announce that the latest version of Python-Blosc2 allows user-defined Python functions all throughout its compression pipeline: you can use Python for building prefilters, postfilters, filters, codecs for Blosc2 and explore all its capabilities. And if done correctly (by using e.g. NumPy, numba, numexpr...), most of the time you won't even need to translate those into C for speed.\n\n## The Blosc2 pipeline\n\nThe Blosc2 pipeline includes all the functions that are applied to the data until it is finally compressed (and decompressed back). As can be seen in the image below, during compression the first function that can be applied to the data is the prefilter (if any), then the filters pipeline (with a maximum of six filters) and, last but not least, the codec itself. For decompressing, the order will be the other way around: first the codec, then the filters pipeline and finally the postfilter (if any).\n\n## Defining prefilters and postfilters\n\nA prefilter is a function that is applied to the SChunk each time you add data into it (e.g. when appending or updating). It is executed for each data block and receives three parameters: input, output and offset. For convenience, the input and output are presented as NumPy arrays; the former is a view of the input data and the later is an empty NumPy array that must be filled (this is actually what the first filter in the filters pipeline will receive). Regarding the offset, it is an integer which indicates where the corresponding block begins inside the SChunk container.\n\nYou can easily set a prefilter to a specific SChunk through a decorator. For example:\n > schunk = blosc2.SChunk() @schunk.prefilter(np.int64, np.float64) def pref(input, output, offset): output[:] = input - np.pi + offset\n\nThis decorator requires the data types for the input (original data) and output NumPy arrays, which must be of same itemsize.\n\nIf you do not want the prefilter to be applied anymore, you can always remove it:\n > schunk.remove_prefilter(\"pref\")\n\nAs for the postfilters, they are applied at the end of the pipeline during decompression. A postfilter receives the same parameters as the prefilter and can be set in the same way:\n > @schunk.postfilter(np.float64, np.int64) def postf(input, output, offset): output[:] = input + np.pi - offset\n\nIn this case, the input data is the one from the buffer returned by the filter pipeline, and the output data type should be the same as the original data (for a good round-trip).\n\nYou can also remove postfilters whenever you want:\n > schunk.remove_postfilter(\"postf\")\n\n### Fillers\n\nBefore we move onto the next step in the pipeline, we need to introduce the fillers. A filler is similar to a prefilter but with a twist. It is used to fill an empty SChunk and you can pass to it any extra parameter you want, as long as it is a NumPy array, SChunk or Python Scalar. All these extra parameters will arrive to the filler function as a tuple containing just the corresponding block slice for each parameter (except for the scalars, that are passed untouched). To declare a filter, you will also need to pass the inputs along with its data type. For example:\n > @schunk.filler(((schunk0, dtype0), (ndarray1, dtype1), (py_scalar3, dtype2)), schunk_dtype) def filler(inputs_tuple, output, offset): output[:] = inputs_tuple[0] - inputs_tuple[1] * inputs_tuple[2]\n\nThis will automatically append the data to the schunk, but applying the filler function first. After that the schunk would be completely filled, the filler will be de-registered, so the next time you update some data the it would not be executed; a filler is meant to build new SChunk objects from other containers.\n\n## User-defined filters and codecs\n\nThe main difference between prefilters/postfilters and their filters/codecs counterparts is that the former ones are meant to run for an specific SChunk instance, whereas the later can be locally registered and hence, used in any SChunk.\n\nLet's start describing the user-defined filters. A filter is composed by two functions: one for the compression process (forward), and another one for the decompression process (backward). Such functions receive the input and output as NumPy arrays of type uint8 (bytes), plus the filter meta and the SChunk instance to which the data belongs to. The forward function will fill the output with the modified data from input. The backward will be responsible of reversing the changes done by forward so that the data returned at the end of the decompression should be the same as the one received at the beginning of the compression. Check the drawing below:\n\nSo, once we have the pair of forward and backward functions defined, they can be registered locally associating to a filter ID between 160 and 255:\n > blosc2.register_filter(id, forward, backward)\n\nNow, we can use the user-defined filter in any SChunk instance by choosing the new local ID in the filters pipeline:\n > schunk.cparams = {\"filters\": [id], \"filters_meta\": [meta]}\n\nRegarding the user-defined codecs, they do not differ too much from its filter counterparts. The main difference is that, because their goal is to actually compress data, the corresponding functions (in this case encoder and decoder) will need to return the size in bytes of the compressed/decompressed data respectively. This time the scheme would be:\n\nTo register a codec, you name it, assign an ID to it and pass the user-defined functions:\n > blosc2.register_codec(codec_name, id, encoder, decoder)\n\nAnd to use it you just use its ID in the cparams:\n > schunk.cparams = {\"codec\": id, \"codec_meta\": meta}\n\nWe have seen how easily you can define your own filters and codecs for the Blosc2 compression pipeline. They are very easy to use because they conveniently wrap input and output data as NumPy arrays. Now, you can start experimenting with different filter/compression algorithms straight from Python. You can even come with a library of such filters/codecs that can be used in all your data pipeline processing. Welcome to compression made easy!\n\nSee more examples in the repository.\n\nFind the complete documentation at: https://www.blosc.org/python-blosc2/python-blosc2.html.\n\nThis work has been made thanks to a Small Development Grant from NumFOCUS. NumFOCUS is a non-profit organization supporting open code for better science. If you like this, consider giving a donation to them (and if you like our work, you can nominate it to our project too!). Thanks!\n\nDate: 2022-12-15\nCategories: \nTags: \n\n2022-12-15 08:00User Defined Pipeline for Python-Blosc2 2021-05-10 07:32Wrapping C-Blosc2 in Python (a beginner's view) 2021-02-08 07:32Introducing Sparse Frames\n\n# Retrieve data with __getitem__ and get_slice\n\nDate: 2014-05-05\nCategories: \nTags: \n\nThe Blosc Development Team is happy to announce that the latest version of Python-Blosc2 0.4. It comes with new and exciting features, like a handier way of setting, expanding and getting the data and metadata from a super-chunk (SChunk) instance. Contrarily to chunks, a super-chunk can update and resize the data that it containes, supports user metadata, and it does not have the 2 GB storage limitation.\n\nAdditionally, you can now convert now a SChunk into a contiguous, serialized buffer (aka cframe) and vice-versa; as a bonus, this serialization process also works with a NumPy array at a blazing speed.\n\nContinue reading for knowing the new features a bit more in depth.\n\n## Retrieve data with __getitem__ and get_slice\n\nThe most general way to store data in Python-Blosc2 is through a SChunk (super-chunk) object. Here the data is split into chunks of the same size. So until now, the only way of working with it was chunk by chunk (see the basics tutorial).\n\nWith the new version, you can get general data slices with the handy __getitem__() method without having to mess with chunks manually. The only inconvenience is that this returns a bytes object, which is difficult to read by humans. To overcome this, we have also implemented the get_slice() method; it comes with two optional params: start and stop for selecting the slice you are interested in. Also, you can pass to out any Python object supporting the Buffer Protocol and it will be filled with the data slice. One common example is to pass a NumPy array in the out argument:\n > out_slice = numpy.empty(chunksize * nchunks, dtype=numpy.int32) schunk.get_slice(out=out_slice)\n\nWe have now the out_slice NumPy array filled with the schunk data. Easy and effective.\n\n## Set data with __setitem__\n\nSimilarly, if we would like to set data, we had different ways of doing it, e.g. with the update_chunk() or the update_data() methods. But those work, again, chunk by chunk, which was a bummer. That's why we also implemented the convenient __setitem__() method. In a similar way to the get_slice() method, the value to be set can be any Python object supporting the Buffer Protocol. In addition, this method is very flexible because it not only can set the data of an already existing slice of the SChunk, but it also can expand (and update at the same time) it.\n\nTo do so, the stop param will set the new number of items in SChunk:\n > start = schunk_nelems - 123 stop = start + new_value.size # new number of items schunk[start:stop] = new_value\n\nIn the code above, the data between start and the SChunk current size will be updated and then, the data between the previous SChunk size and the new stop will be appended automatically for you. This is very handy indeed (note that the step parameter is not yet supported though).\n\n## Serialize SChunk from/to a contiguous compressed buffer\n\nSuper-chunks can be serialized in two slightly different format frames: contiguous and sparse. A contiguous frame (aka cframe) serializes the whole super-chunk data and metadata into a sequential buffer, whereas the sparse frame (aka sframe) uses a contiguous frame for metadata and the data is stored separately in so-called chunks. Here it is how they look like:\n\nThe contiguous and sparse formats come with its own pros and cons. A contiguous frame is ideal for transmitting / storing data as a whole buffer / file, while the sparse one is better suited to act as a store while a super-chunk is being built.\n\nIn this new version of Python-Blosc2 we have added a method to convert from a SChunk to a contiguous, serialized buffer:\n > buf = schunk.to_cframe()\n\nas well as a function to build back a SChunk instance from that buffer:\n > schunk = schunk_from_cframe(buf)\n\nThis allows for a nice way to serialize / deserialize super-chunks for transmission / storage purposes. Also, and for performance reasons, and for reducing memory usage to a maximum, these functions avoid copies as much as possible. For example, the schunk_from_cframe function can build a SChunk instance without copying the data in cframe. Such a capability makes the use of cframes very desirable whenever you have to transmit and re-create data from one machine to another in a very efficient way.\n\n## Serializing NumPy arrays\n\nLast but not least, you can also serialize NumPy arrays with the new pair of functions pack_array2() / unpack_array2(). Although you could already do this with the existing pack_array() / unpack_array() functions, the new ones are much faster and do not have the 2 GB size limitation. To prove this, let's see its performance by looking at some benchmark results obtained with an Intel box (i9-10940X CPU @ 3.30GHz, 14 cores) running Ubuntu 22.04.\n\nIn this benchmark we are comparing a plain NumPy array copy against compression/decompression through different compressors and functions (compress() / decompress(), pack_array() / unpack_array() and pack_array2() / unpack_array2()). The data distribution for the plots below is for 3 different data distributions: arange, linspace and random:\n\nAs can be seen, different codecs offer different compression ratios for the different distributions. Note in particular how linear distributions (arange for int64 and linspace for float64) can reach really high compression ratios (very low entropy).\n\nLet's see the speed for compression / decompression; in order to not show too many info in this blog, we will show just the plots for the linspace linear distribution:\n\nHere we can see that the pair pack_array2() / unpack_array2() is consistently (much) faster than their previous version pack_array() / unpack_array(). Despite that, the fastest is the compress() / decompress() pair; however this is not serializing all the properties of a NumPy array, and has the limitation of not being able to compress data larger than 2 GB.\n\nYou can test the speed in your box by running the pack_compress bench.\n\nAlso, if you would like to store the contiguous buffer on-disk, you can directly use the pair of functions save_array(), load_array().\n\n## Native performance on Apple M1 processors\n\nContrariliy to Blosc1, Blosc2 comes with native support for ARM processors (it leverages the NEON SIMD instruction set there), and that means that it runs very fast in this architecture. As an example, let's see how the new pack_array2() / unpack_array2() works in an Apple M1 laptop (Macbook Air).\n\nAs can be seen, running Blosc2 in native arm64 mode on M1 offers quite a bit more performance (specially during compression) than using the i386 emulation. If speed is important to you, and you have a M1/M2 processor, make sure that you are running Blosc2 in native mode (arm64).\n\nThe new features added to python-blosc2 offer an easy way of creating, getting, setting and expanding data by using a SChunk instance. Furthermore, you can get a contiguous compressed representation (aka cframe) of it and re-create it again latter. And you can do the same with NumPy arrays (either in-memory or on-disk) faster than with the former functions, and even faster than a plain memcpy().\n\nFor more info on how to use these useful new features, see this Jupyter notebook tutorial.\n\nFinally, the complete documentation is at: https://www.blosc.org/python-blosc2/python-blosc2.html. Thanks to <NAME> (@datapythonista) for his fine work and enthusiasm in helping us in providing a better structure to the Blosc documentation!\n\nThis work has been possible thanks to a Small Development Grant from NumFOCUS. NumFOCUS is a non-profit organization supporting open code for better science. If you like the goal, consider giving a donation to NumFOCUS (you can optionally make it go to our project too, to which we would be very grateful indeed :-).\n\n# 404\n\nFile not found\n\nThe site configured at this address does not contain the requested file.\n If this is your site, make sure that the filename case matches the URL as well as any file permissions.For root URLs (like `http://example.com/` ) you must provide an `index.html` file. \nRead the full documentation for more information about using GitHub Pages.\n\n* blosc2.pack_array2(arr, chunksize=None, **kwargs)#\n * \n\nPack (compress) a NumPy array. This is faster, and it does not have a 2 GB limitation.\n\nout – The serialized version (cframe) of the array. If urlpath is provided, the number of bytes in file is returned instead.\n * Return type:\n * \n\nbytes | int\n\nExamples\n > >>> import numpy as np >>> a = np.arange(1e6) >>> cframe = blosc2.pack_array2(a) >>> len(cframe) < a.size * a.itemsize True\n\n* blosc2.unpack_array2(cframe)#\n * \n\nUnpack (decompress) a packed NumPy array via a cframe.\n\ncframe¶ (bytes) – The packed array to be restored.\n * Returns:\n * \n\nout – The unpacked NumPy array.\n * Return type:\n * \n\nTypeError – If\n `cframe` is not of type bytes, or not a cframe. * \n\nRunTimeError – If some other problem is detected.\n\nExamples\n > >>> import numpy as np >>> a = np.arange(1e6) >>> cframe = blosc2.pack_array2(a) >>> len(cframe) < a.size*a.itemsize True >>> a2 = blosc2.unpack_array2(cframe) >>> np.array_equal(a, a2) True\n\n* blosc2.pack_array(arr, clevel=9, filter=Filter.SHUFFLE, codec=Codec.BLOSCLZ)#\n * \n\nPack (compress) a NumPy array. It is equivalent to the pack function.\n\nclevel¶ (int (optional)) – The compression level from 0 (no compression) to 9 (maximum compression). The default is 9.\n * \n\nfilter¶ (\n `Filter` (optional)) – The filter to be activated. The default is `Filter.SHUFFLE` . * \n\ncodec¶ (\n `Codec` (optional)) – The compressor used internally in Blosc. The default is `Codec.BLOSCLZ` . * Returns:\n * \n\nout – The packed array in form of a Python str / bytes object.\n * Return type:\n * \n\nstr / bytes\n * Raises:\n * \n\nAttributeError – If\n `arr` does not have an itemsize attribute. If `arr` does not have a size attribute. * \n\nValueError – If typesize is not within the allowed range. If the pickled object size is larger than the maximum allowed buffer size. If\n `clevel` is not within the allowed range. If `codec` is not within the supported compressors. \nSee also\n\nExamples\n > >>> import numpy as np >>> a = np.arange(1e6) >>> parray = blosc2.pack_array(a) >>> len(parray) < a.size*a.itemsize True\n\n* blosc2.unpack_array(packed_array, **kwargs)#\n * \n\nRestore a packed NumPy array.\n\npacked_array¶ (str / bytes) – The packed array to be restored.\n * \n\n**kwargs¶ (fix_imports / encoding / errors) – Optional parameters that can be passed to the pickle.loads API.\n * Returns:\n * \n\nout – The decompressed data in form of a NumPy array.\n * Return type:\n * \n\nTypeError – If\n `packed_array` is not of type bytes or string. \nExamples\n > >>> import numpy as np >>> a = np.arange(1e6) >>> parray = blosc2.pack_array(a) >>> len(parray) < a.size*a.itemsize True >>> a2 = blosc2.unpack_array(parray) >>> np.array_equal(a, a2) True >>> a = np.array(['å', 'ç', 'ø']) >>> parray = blosc2.pack_array(a) >>> a2 = blosc2.unpack_array(parray) >>> np.array_equal(a, a2) True\n\n* blosc2.save_array(arr, urlpath, chunksize=None, **kwargs)#\n * \n\nSave a serialized NumPy array in urlpath.\n\narr¶ (ndarray) – The NumPy array to be saved.\n * \n\nurlpath¶ (str) – The path for the file where the array is saved.\n * \n\nout – The number of bytes of the saved array.\n * Return type:\n * \n\nint\n\nExamples\n > >>> import numpy as np >>> a = np.arange(1e6) >>> serial_size = blosc2.save_array(a, \"test.bl2\", mode=\"w\") >>> serial_size < a.size * a.itemsize True\n\n# Announcing Support for Lossy ZFP Codec as a Plugin for C-Blosc2\n\n## Announcing Support for Lossy ZFP Codec as a Plugin for C-Blosc2\n\nBlosc supports different filters and codecs for compressing data, like e.g. the lossless NDLZ codec and the NDCELL filter. These have been developed explicitly to be used in multidimensional datasets (via Caterva or ironArray Community Edition).\n\nHowever, a lossy codec like ZFP allows for much better compression ratios at the expense of loosing some precision in floating point data. Moreover, while NDLZ is only available for 2-dim datasets, ZFP can be used up to 4-dim datasets.\n\n### How ZFP works?\n\nZFP partitions datasets into cells of 4^(number of dimensions) values, i.e., 4, 16, 64, or 256 values for 1D, 2D, 3D, and 4D arrays, respectively. Each cell is then (de)compressed independently, and the resulting bit strings are concatenated into a single stream of bits.\n\nFurthermore, ZFP usually truncates each input value either to a fixed number of bits to meet a storage budget or to some variable length needed to meet a chosen error tolerance. For more info on how this works, see zfp overview docs.\n\n### ZFP implementation\n\nSimilarly to other registered Blosc2 official plugins, this codec is now available at the blosc2/plugins directory of the C-Blosc2 repository. However, as there are different modes for working with ZFP, there are several associated codec IDs (see later).\n\nSo, in order to use ZFP, users just have to choose the ID for the desired ZFP mode between the ones listed in blosc2/codecs-registry.h. For more info on how the plugin selection mechanism works, see https://www.blosc.org/posts/registering-plugins/.\n\n### ZFP modes\n\nZFP is a lossy codec, but it still lets the user to choose the degree of the data loss. There are different compression modes:\n\nBLOSC_CODEC_ZFP_FIXED_ACCURACY: The user can choose the absolute error in truncation. For example, if the desired absolute error is 0.01, each value loss must be less than or equal to 0.01. With that, if 23.0567 is a value of the original input, after compressing and decompressing this input with error=0.01, the new value must be between 23.0467 and 23.0667.\n * \n\nBLOSC_CODEC_ZFP_FIXED_PRECISION: The user specifies the maximum number of bit planes encoded during compression (relative error). This is, for each input value, the number of most significant bits that will be encoded.\n * \n\nBLOSC_CODEC_ZFP_FIXED_RATE: The user chooses the size that the compressed cells must have based on the input cell size. For example, if the cell size is 2000 bytes and user chooses ratio=50, the output cell size will be 50% of 2000 = 1000 bytes.\n\nFor more info, see: https://github.com/Blosc/c-blosc2/blob/main/plugins/codecs/zfp/README.md\n\n### Benchmark: ZFP FIXED-ACCURACY VS FIXED_PRECISION VS FIXED-RATE modes\n\nThe dataset used in this benchmark is called precipitation_amount_1hour_Accumulation.zarr and has been fetched from ERA5 database, which provides hourly estimates of a large number of atmospheric, land and oceanic climate variables.\n\nSpecifically, the downloaded dataset in Caterva format has this parameters:\n\nndim = 3\n * \n\ntype = float32\n * \n\nshape = [720, 721, 1440]\n * \n\nchunkshape = [128, 128, 256]\n * \n\nblockshape = [16, 32, 64]\n\nThe next plots represent the compression results obtained by using the different ZFP modes to compress the already mentioned dataset.\n\nNote: It is important to remark that this is a specific dataset and the codec may perform differently for other ones.\n\nBelow the bars it is annotated what parameter is used for each test. For example, for the first column, the different compression modes are setup like this:\n\nFIXED-ACCURACY: for each input value, the absolute error is 10^(-6) = 0.000001.\n * \n\nFIXED-PRECISION: for each input value, only the 20 most significant bits for the mantissa will be encoded.\n * \n\nFIXED-RATE: the size of the output cells is 30% of the input cell size.\n\nAlthough the FIXED-PRECISION mode does not obtain great results, we see that with the FIXED-ACCURACY mode we do get better performance as the absolute error increases. Similarly, we can see how the FIXED-RATE mode gets the requested ratios, which is cool but, in exchange, the amount of data loss is unknown.\n\nAlso, while FIXED-ACCURACY and FIXED-RATE modes consume similar times, the FIXED-PRECISION mode, which seems to have less data loss, also takes longer to compress. Generally speaking we can see how, the more data loss (more data truncation) achieved by a mode, the faster it operates.\n\n### \"Third partition\"\n\nOne of the most appealing features of Caterva besides supporting multi-dimensionality is its implementation of a second partition, making slicing more efficient. As one of the distinctive characteristics of ZFP is that it compresses data in independent (and small) cells, we have been toying with the idea of implementing a third partition so that slicing of thin selections or just single-point selection can be made faster.\n\nSo, as part of the current ZFP implementation, we have combined the Caterva/Blosc2 partitioning (chunking and blocking) with the independent cell handling of ZFP, allowing to extract single cells within the ZFP streams (blocks in Blosc jargon). Due to the properties and limitations of the different ZFP compression modes, we have been able to implement a sort of \"third partition\" just for the FIXED-RATE mode when used together with the blosc2_getitem_ctx() function.\n\nSuch a combination of the existing partitioning and single cell extraction is useful for selecting more narrowly the data to extract, saving time and memory. As an example, below you can see a comparison of the mean times that it takes to retrieve a bunch of single elements out of different multidimensional arrays from the ERA5 dataset (see above). Here we have used Blosc2 with a regular LZ4 codec compared against the FIXED-RATE mode of the new ZFP codec:\n\nAs you can see, using the ZFP codec in FIXED-RATE mode allows for a good improvement in speed (up to more than 2x) for retrieving single elements (or, in general an amount not exceeding the cell size) in comparison with the existing codecs (even the fastest ones, like LZ4) inside Blosc2. As the performance improvement is of the same order than random access time of modern SSDs, we anticipate that this could be a major win in scenarios where random access is important.\n\nIf you are curious on how this new functionality performs for your own datasets and computer, you can use/adapt our benchmark code.\n\n### Conclusions\n\nThe integration of ZFP as a codec plugin will greatly enhance the capabilities of lossy compression inside C-Blosc2. The current ZFP plugin supports different modes; if users want to specify data loss during compression, it is recommended to use the FIXED-ACCURACY or FIXED-PRECISION modes (and most specially the former because of its better compression performance).\n\nHowever, if the priority is to get specific compression ratios without paying too much attention to the amount of data loss, one should use the FIXED-RATE mode, which let choose the desired compression ratio. This mode also has the advantage that a \"third partition\" can be used for improving random elements access speed.\n\nThis work has been done thanks to a Small Development Grant from the NumFOCUS Foundation, to whom we are very grateful indeed. NumFOCUS is doing a excellent job in sponsoring scientific projects and you can donate to the Blosc project (or many others under the NumFOCUS umbrella) via its donation page.\n"}}},{"rowIdx":59467,"cells":{"project":{"kind":"string","value":"rkafkajars"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘rkafkajars’\n October 14, 2022\nType Package\nTitle External Jars Required for Package 'rkafka'\nVersion 1.2\nDate 2021-12-01\nAuthor <NAME> [aut,cre], <NAME> and Yammer Inc.[ctb,cph],Sun Microsys-\n tems Inc.[ctb,cph],<NAME>[ctb,cph],<NAME>[ctb],Junit[ctb,cph],The Apache Soft-\n ware Foundation [ctb,cph],Stefan Groschupf[ctb,cph],Taro L.Saito[ctb],EPFL Type-\n safe Inc.[ctb,cph],QOS.ch[ctb,cph]\nMaintainer <NAME> <<EMAIL>>\nDescription The 'rkafkajars' package collects all the external jars required for the 'rkafka' package.\nDepends rJava\nImports RUnit\nSystemRequirements Java JDK 1.7 or higher\nCopyright See file COPYRIGHTS\nLicense Apache License 2.0 | file LICENSE\nNeedsCompilation no\nRepository CRAN\nDate/Publication 2021-12-05 16:10:02 UTC\nR topics documented:\nrkafkajar... 2\n rkafkajars External Jars Required for Package ’rkafka’\nDescription\n The ’rkafkajars’ package collects all the external jars required for the ’rkafka’ package. These\n external jars are quite large in size (12MB) and have a slow release cycle. By separating the Java and\n R development, the storage footprint on CRAN is reduced. By using the ’rJava’ package that links\n R and Java, we can use the excellent work already done by the folks and provide the functionality\n of using ’KAFKA’ in R\nDetails\n Package: rkafkajars\n Type: Package\n Version: 1.2\n Date: 2021-12-01\n License: Apache License 2.0\nAuthor(s)\n <NAME>\n Maintainer: <NAME><<EMAIL>>"}}},{"rowIdx":59468,"cells":{"project":{"kind":"string","value":"rusoto_pinpoint_sms_voice"},"source":{"kind":"string","value":"rust"},"language":{"kind":"string","value":"Rust"},"content":{"kind":"string","value":"Crate rusoto_pinpoint_sms_voice\n===\n\nPinpoint SMS and Voice Messaging public facing APIs\n\nIf you’re using the service, you’re probably looking for PinpointSmsVoiceClient and PinpointSmsVoice.\n\nStructs\n---\n\nCallInstructionsMessageTypeAn object that defines a message that contains text formatted using Amazon Pinpoint Voice Instructions markup.\n\nCloudWatchLogsDestinationAn object that contains information about an event destination that sends data to Amazon CloudWatch Logs.\n\nCreateConfigurationSetEventDestinationRequestCreate a new event destination in a configuration set.\n\nCreateConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was created successfully.\n\nCreateConfigurationSetRequestA request to create a new configuration set.\n\nCreateConfigurationSetResponseAn empty object that indicates that the configuration set was successfully created.\n\nDeleteConfigurationSetEventDestinationRequestDeleteConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was deleted successfully.\n\nDeleteConfigurationSetRequestDeleteConfigurationSetResponseAn empty object that indicates that the configuration set was deleted successfully.\n\nEventDestinationAn object that defines an event destination.\n\nEventDestinationDefinitionAn object that defines a single event destination.\n\nGetConfigurationSetEventDestinationsRequestGetConfigurationSetEventDestinationsResponseAn object that contains information about an event destination.\n\nKinesisFirehoseDestinationAn object that contains information about an event destination that sends data to Amazon Kinesis Data Firehose.\n\nPinpointSmsVoiceClientA client for the Pinpoint SMS Voice API.\n\nPlainTextMessageTypeAn object that defines a message that contains unformatted text.\n\nSSMLMessageTypeAn object that defines a message that contains SSML-formatted text.\n\nSendVoiceMessageRequestSendVoiceMessageRequest\n\nSendVoiceMessageResponseAn object that that contains the Message ID of a Voice message that was sent successfully.\n\nSnsDestinationAn object that contains information about an event destination that sends data to Amazon SNS.\n\nUpdateConfigurationSetEventDestinationRequestUpdateConfigurationSetEventDestinationRequest\n\nUpdateConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was updated successfully.\n\nVoiceMessageContentAn object that contains a voice message and information about the recipient that you want to send it to.\n\nEnums\n---\n\nCreateConfigurationSetErrorErrors returned by CreateConfigurationSet\n\nCreateConfigurationSetEventDestinationErrorErrors returned by CreateConfigurationSetEventDestination\n\nDeleteConfigurationSetErrorErrors returned by DeleteConfigurationSet\n\nDeleteConfigurationSetEventDestinationErrorErrors returned by DeleteConfigurationSetEventDestination\n\nGetConfigurationSetEventDestinationsErrorErrors returned by GetConfigurationSetEventDestinations\n\nSendVoiceMessageErrorErrors returned by SendVoiceMessage\n\nUpdateConfigurationSetEventDestinationErrorErrors returned by UpdateConfigurationSetEventDestination\n\nTraits\n---\n\nPinpointSmsVoiceTrait representing the capabilities of the Pinpoint SMS Voice API. Pinpoint SMS Voice clients implement this trait.\n\nCrate rusoto_pinpoint_sms_voice\n===\n\nPinpoint SMS and Voice Messaging public facing APIs\n\nIf you’re using the service, you’re probably looking for PinpointSmsVoiceClient and PinpointSmsVoice.\n\nStructs\n---\n\nCallInstructionsMessageTypeAn object that defines a message that contains text formatted using Amazon Pinpoint Voice Instructions markup.\n\nCloudWatchLogsDestinationAn object that contains information about an event destination that sends data to Amazon CloudWatch Logs.\n\nCreateConfigurationSetEventDestinationRequestCreate a new event destination in a configuration set.\n\nCreateConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was created successfully.\n\nCreateConfigurationSetRequestA request to create a new configuration set.\n\nCreateConfigurationSetResponseAn empty object that indicates that the configuration set was successfully created.\n\nDeleteConfigurationSetEventDestinationRequestDeleteConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was deleted successfully.\n\nDeleteConfigurationSetRequestDeleteConfigurationSetResponseAn empty object that indicates that the configuration set was deleted successfully.\n\nEventDestinationAn object that defines an event destination.\n\nEventDestinationDefinitionAn object that defines a single event destination.\n\nGetConfigurationSetEventDestinationsRequestGetConfigurationSetEventDestinationsResponseAn object that contains information about an event destination.\n\nKinesisFirehoseDestinationAn object that contains information about an event destination that sends data to Amazon Kinesis Data Firehose.\n\nPinpointSmsVoiceClientA client for the Pinpoint SMS Voice API.\n\nPlainTextMessageTypeAn object that defines a message that contains unformatted text.\n\nSSMLMessageTypeAn object that defines a message that contains SSML-formatted text.\n\nSendVoiceMessageRequestSendVoiceMessageRequest\n\nSendVoiceMessageResponseAn object that that contains the Message ID of a Voice message that was sent successfully.\n\nSnsDestinationAn object that contains information about an event destination that sends data to Amazon SNS.\n\nUpdateConfigurationSetEventDestinationRequestUpdateConfigurationSetEventDestinationRequest\n\nUpdateConfigurationSetEventDestinationResponseAn empty object that indicates that the event destination was updated successfully.\n\nVoiceMessageContentAn object that contains a voice message and information about the recipient that you want to send it to.\n\nEnums\n---\n\nCreateConfigurationSetErrorErrors returned by CreateConfigurationSet\n\nCreateConfigurationSetEventDestinationErrorErrors returned by CreateConfigurationSetEventDestination\n\nDeleteConfigurationSetErrorErrors returned by DeleteConfigurationSet\n\nDeleteConfigurationSetEventDestinationErrorErrors returned by DeleteConfigurationSetEventDestination\n\nGetConfigurationSetEventDestinationsErrorErrors returned by GetConfigurationSetEventDestinations\n\nSendVoiceMessageErrorErrors returned by SendVoiceMessage\n\nUpdateConfigurationSetEventDestinationErrorErrors returned by UpdateConfigurationSetEventDestination\n\nTraits\n---\n\nPinpointSmsVoiceTrait representing the capabilities of the Pinpoint SMS Voice API. Pinpoint SMS Voice clients implement this trait.\n\nStruct rusoto_pinpoint_sms_voice::PinpointSmsVoiceClient\n===\n\n\n```\npub struct PinpointSmsVoiceClient { /* private fields */ }\n```\nA client for the Pinpoint SMS Voice API.\n\nImplementations\n---\n\nsource### impl PinpointSmsVoiceClient\n\nsource#### pub fn new(region: Region) -> PinpointSmsVoiceClient\n\nCreates a client backed by the default tokio event loop.\n\nThe client will use the default credentials provider and tls client.\n\nsource#### pub fn new_with<P, D>( request_dispatcher: D, credentials_provider: P, region: Region) -> PinpointSmsVoiceClient where P: ProvideAwsCredentials + Send + Sync + 'static, D: DispatchSignedRequest + Send + Sync + 'static,\n\nsource#### pub fn new_with_client(client: Client, region: Region) -> PinpointSmsVoiceClient\n\nTrait Implementations\n---\n\nsource### impl Clone for PinpointSmsVoiceClient\n\nsource#### fn clone(&self) -> PinpointSmsVoiceClient\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl PinpointSmsVoice for PinpointSmsVoiceClient\n\nsource#### fn create_configuration_set<'life0, 'async_trait>( &'life0 self, input: CreateConfigurationSetRequest) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetResponse, RusotoError<CreateConfigurationSetError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new configuration set. After you create the configuration set, you can add one or more event destinations to it.\n\nsource#### fn create_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: CreateConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetEventDestinationResponse, RusotoError<CreateConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new event destination in a configuration set.\n\nsource#### fn delete_configuration_set<'life0, 'async_trait>( &'life0 self, input: DeleteConfigurationSetRequest) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetResponse, RusotoError<DeleteConfigurationSetError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nDeletes an existing configuration set.\n\nsource#### fn delete_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: DeleteConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetEventDestinationResponse, RusotoError<DeleteConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nDeletes an event destination in a configuration set.\n\nsource#### fn get_configuration_set_event_destinations<'life0, 'async_trait>( &'life0 self, input: GetConfigurationSetEventDestinationsRequest) -> Pin<Box<dyn Future<Output = Result<GetConfigurationSetEventDestinationsResponse, RusotoError<GetConfigurationSetEventDestinationsError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nObtain information about an event destination, including the types of events it reports, the Amazon Resource Name (ARN) of the destination, and the name of the event destination.\n\nsource#### fn send_voice_message<'life0, 'async_trait>( &'life0 self, input: SendVoiceMessageRequest) -> Pin<Box<dyn Future<Output = Result<SendVoiceMessageResponse, RusotoError<SendVoiceMessageError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new voice message and send it to a recipient's phone number.\n\nsource#### fn update_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: UpdateConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<UpdateConfigurationSetEventDestinationResponse, RusotoError<UpdateConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nUpdate an event destination in a configuration set. An event destination is a location that you publish information about your voice calls to. For example, you can log an event to an Amazon CloudWatch destination when a call fails.\n\nAuto Trait Implementations\n---\n\n### impl !RefUnwindSafe for PinpointSmsVoiceClient\n\n### impl Send for PinpointSmsVoiceClient\n\n### impl Sync for PinpointSmsVoiceClient\n\n### impl Unpin for PinpointSmsVoiceClient\n\n### impl !UnwindSafe for PinpointSmsVoiceClient\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nTrait rusoto_pinpoint_sms_voice::PinpointSmsVoice\n===\n\n\n```\npub trait PinpointSmsVoice {\n fn create_configuration_set<'life0, 'async_trait>( \n &'life0 self, \n input: CreateConfigurationSetRequest \n ) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetResponse, RusotoError<CreateConfigurationSetError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn create_configuration_set_event_destination<'life0, 'async_trait>( \n &'life0 self, \n input: CreateConfigurationSetEventDestinationRequest \n ) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetEventDestinationResponse, RusotoError<CreateConfigurationSetEventDestinationError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn delete_configuration_set<'life0, 'async_trait>( \n &'life0 self, \n input: DeleteConfigurationSetRequest \n ) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetResponse, RusotoError<DeleteConfigurationSetError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn delete_configuration_set_event_destination<'life0, 'async_trait>( \n &'life0 self, \n input: DeleteConfigurationSetEventDestinationRequest \n ) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetEventDestinationResponse, RusotoError<DeleteConfigurationSetEventDestinationError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn get_configuration_set_event_destinations<'life0, 'async_trait>( \n &'life0 self, \n input: GetConfigurationSetEventDestinationsRequest \n ) -> Pin<Box<dyn Future<Output = Result<GetConfigurationSetEventDestinationsResponse, RusotoError<GetConfigurationSetEventDestinationsError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn send_voice_message<'life0, 'async_trait>( \n &'life0 self, \n input: SendVoiceMessageRequest \n ) -> Pin<Box<dyn Future<Output = Result<SendVoiceMessageResponse, RusotoError<SendVoiceMessageError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n fn update_configuration_set_event_destination<'life0, 'async_trait>( \n &'life0 self, \n input: UpdateConfigurationSetEventDestinationRequest \n ) -> Pin<Box<dyn Future<Output = Result<UpdateConfigurationSetEventDestinationResponse, RusotoError<UpdateConfigurationSetEventDestinationError>>> + Send + 'async_trait> where \n 'life0: 'async_trait, \n Self: 'async_trait;\n}\n```\nTrait representing the capabilities of the Pinpoint SMS Voice API. Pinpoint SMS Voice clients implement this trait.\n\nRequired Methods\n---\n\nsource#### fn create_configuration_set<'life0, 'async_trait>( &'life0 self, input: CreateConfigurationSetRequest) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetResponse, RusotoError<CreateConfigurationSetError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new configuration set. After you create the configuration set, you can add one or more event destinations to it.\n\nsource#### fn create_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: CreateConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<CreateConfigurationSetEventDestinationResponse, RusotoError<CreateConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new event destination in a configuration set.\n\nsource#### fn delete_configuration_set<'life0, 'async_trait>( &'life0 self, input: DeleteConfigurationSetRequest) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetResponse, RusotoError<DeleteConfigurationSetError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nDeletes an existing configuration set.\n\nsource#### fn delete_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: DeleteConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<DeleteConfigurationSetEventDestinationResponse, RusotoError<DeleteConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nDeletes an event destination in a configuration set.\n\nsource#### fn get_configuration_set_event_destinations<'life0, 'async_trait>( &'life0 self, input: GetConfigurationSetEventDestinationsRequest) -> Pin<Box<dyn Future<Output = Result<GetConfigurationSetEventDestinationsResponse, RusotoError<GetConfigurationSetEventDestinationsError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nObtain information about an event destination, including the types of events it reports, the Amazon Resource Name (ARN) of the destination, and the name of the event destination.\n\nsource#### fn send_voice_message<'life0, 'async_trait>( &'life0 self, input: SendVoiceMessageRequest) -> Pin<Box<dyn Future<Output = Result<SendVoiceMessageResponse, RusotoError<SendVoiceMessageError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nCreate a new voice message and send it to a recipient's phone number.\n\nsource#### fn update_configuration_set_event_destination<'life0, 'async_trait>( &'life0 self, input: UpdateConfigurationSetEventDestinationRequest) -> Pin<Box<dyn Future<Output = Result<UpdateConfigurationSetEventDestinationResponse, RusotoError<UpdateConfigurationSetEventDestinationError>>> + Send + 'async_trait>> where 'life0: 'async_trait, Self: 'async_trait,\n\nUpdate an event destination in a configuration set. An event destination is a location that you publish information about your voice calls to. For example, you can log an event to an Amazon CloudWatch destination when a call fails.\n\nImplementors\n---\n\nsource### impl PinpointSmsVoice for PinpointSmsVoiceClient\n\nStruct rusoto_pinpoint_sms_voice::CallInstructionsMessageType\n===\n\n\n```\npub struct CallInstructionsMessageType {\n pub text: Option<String>,\n}\n```\nAn object that defines a message that contains text formatted using Amazon Pinpoint Voice Instructions markup.\n\nFields\n---\n\n`text: Option<String>`The language to use when delivering the message. For a complete list of supported languages, see the Amazon Polly Developer Guide.\n\nTrait Implementations\n---\n\nsource### impl Clone for CallInstructionsMessageType\n\nsource#### fn clone(&self) -> CallInstructionsMessageType\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CallInstructionsMessageType\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CallInstructionsMessageType\n\nsource#### fn default() -> CallInstructionsMessageType\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<CallInstructionsMessageType> for CallInstructionsMessageType\n\nsource#### fn eq(&self, other: &CallInstructionsMessageType) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CallInstructionsMessageType) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for CallInstructionsMessageType\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for CallInstructionsMessageType\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CallInstructionsMessageType\n\n### impl Send for CallInstructionsMessageType\n\n### impl Sync for CallInstructionsMessageType\n\n### impl Unpin for CallInstructionsMessageType\n\n### impl UnwindSafe for CallInstructionsMessageType\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::CloudWatchLogsDestination\n===\n\n\n```\npub struct CloudWatchLogsDestination {\n pub iam_role_arn: Option<String>,\n pub log_group_arn: Option<String>,\n}\n```\nAn object that contains information about an event destination that sends data to Amazon CloudWatch Logs.\n\nFields\n---\n\n`iam_role_arn: Option<String>`The Amazon Resource Name (ARN) of an Amazon Identity and Access Management (IAM) role that is able to write event data to an Amazon CloudWatch destination.\n\n`log_group_arn: Option<String>`The name of the Amazon CloudWatch Log Group that you want to record events in.\n\nTrait Implementations\n---\n\nsource### impl Clone for CloudWatchLogsDestination\n\nsource#### fn clone(&self) -> CloudWatchLogsDestination\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CloudWatchLogsDestination\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CloudWatchLogsDestination\n\nsource#### fn default() -> CloudWatchLogsDestination\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for CloudWatchLogsDestination\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<CloudWatchLogsDestination> for CloudWatchLogsDestination\n\nsource#### fn eq(&self, other: &CloudWatchLogsDestination) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CloudWatchLogsDestination) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for CloudWatchLogsDestination\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for CloudWatchLogsDestination\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CloudWatchLogsDestination\n\n### impl Send for CloudWatchLogsDestination\n\n### impl Sync for CloudWatchLogsDestination\n\n### impl Unpin for CloudWatchLogsDestination\n\n### impl UnwindSafe for CloudWatchLogsDestination\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::CreateConfigurationSetEventDestinationRequest\n===\n\n\n```\npub struct CreateConfigurationSetEventDestinationRequest {\n pub configuration_set_name: String,\n pub event_destination: Option<EventDestinationDefinition>,\n pub event_destination_name: Option<String>,\n}\n```\nCreate a new event destination in a configuration set.\n\nFields\n---\n\n`configuration_set_name: String`ConfigurationSetName\n\n`event_destination: Option<EventDestinationDefinition>``event_destination_name: Option<String>`A name that identifies the event destination.\n\nTrait Implementations\n---\n\nsource### impl Clone for CreateConfigurationSetEventDestinationRequest\n\nsource#### fn clone(&self) -> CreateConfigurationSetEventDestinationRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CreateConfigurationSetEventDestinationRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CreateConfigurationSetEventDestinationRequest\n\nsource#### fn default() -> CreateConfigurationSetEventDestinationRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<CreateConfigurationSetEventDestinationRequest> for CreateConfigurationSetEventDestinationRequest\n\nsource#### fn eq(&self, other: &CreateConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CreateConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for CreateConfigurationSetEventDestinationRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for CreateConfigurationSetEventDestinationRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetEventDestinationRequest\n\n### impl Send for CreateConfigurationSetEventDestinationRequest\n\n### impl Sync for CreateConfigurationSetEventDestinationRequest\n\n### impl Unpin for CreateConfigurationSetEventDestinationRequest\n\n### impl UnwindSafe for CreateConfigurationSetEventDestinationRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::CreateConfigurationSetEventDestinationResponse\n===\n\n\n```\npub struct CreateConfigurationSetEventDestinationResponse {}\n```\nAn empty object that indicates that the event destination was created successfully.\n\nTrait Implementations\n---\n\nsource### impl Clone for CreateConfigurationSetEventDestinationResponse\n\nsource#### fn clone(&self) -> CreateConfigurationSetEventDestinationResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CreateConfigurationSetEventDestinationResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CreateConfigurationSetEventDestinationResponse\n\nsource#### fn default() -> CreateConfigurationSetEventDestinationResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for CreateConfigurationSetEventDestinationResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<CreateConfigurationSetEventDestinationResponse> for CreateConfigurationSetEventDestinationResponse\n\nsource#### fn eq(&self, other: &CreateConfigurationSetEventDestinationResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\n1.0.0 · source#### fn ne(&self, other: &Rhs) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for CreateConfigurationSetEventDestinationResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetEventDestinationResponse\n\n### impl Send for CreateConfigurationSetEventDestinationResponse\n\n### impl Sync for CreateConfigurationSetEventDestinationResponse\n\n### impl Unpin for CreateConfigurationSetEventDestinationResponse\n\n### impl UnwindSafe for CreateConfigurationSetEventDestinationResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::CreateConfigurationSetRequest\n===\n\n\n```\npub struct CreateConfigurationSetRequest {\n pub configuration_set_name: Option<String>,\n}\n```\nA request to create a new configuration set.\n\nFields\n---\n\n`configuration_set_name: Option<String>`The name that you want to give the configuration set.\n\nTrait Implementations\n---\n\nsource### impl Clone for CreateConfigurationSetRequest\n\nsource#### fn clone(&self) -> CreateConfigurationSetRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CreateConfigurationSetRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CreateConfigurationSetRequest\n\nsource#### fn default() -> CreateConfigurationSetRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<CreateConfigurationSetRequest> for CreateConfigurationSetRequest\n\nsource#### fn eq(&self, other: &CreateConfigurationSetRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CreateConfigurationSetRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for CreateConfigurationSetRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for CreateConfigurationSetRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetRequest\n\n### impl Send for CreateConfigurationSetRequest\n\n### impl Sync for CreateConfigurationSetRequest\n\n### impl Unpin for CreateConfigurationSetRequest\n\n### impl UnwindSafe for CreateConfigurationSetRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::CreateConfigurationSetResponse\n===\n\n\n```\npub struct CreateConfigurationSetResponse {}\n```\nAn empty object that indicates that the configuration set was successfully created.\n\nTrait Implementations\n---\n\nsource### impl Clone for CreateConfigurationSetResponse\n\nsource#### fn clone(&self) -> CreateConfigurationSetResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for CreateConfigurationSetResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for CreateConfigurationSetResponse\n\nsource#### fn default() -> CreateConfigurationSetResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for CreateConfigurationSetResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<CreateConfigurationSetResponse> for CreateConfigurationSetResponse\n\nsource#### fn eq(&self, other: &CreateConfigurationSetResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\n1.0.0 · source#### fn ne(&self, other: &Rhs) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for CreateConfigurationSetResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetResponse\n\n### impl Send for CreateConfigurationSetResponse\n\n### impl Sync for CreateConfigurationSetResponse\n\n### impl Unpin for CreateConfigurationSetResponse\n\n### impl UnwindSafe for CreateConfigurationSetResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::DeleteConfigurationSetEventDestinationRequest\n===\n\n\n```\npub struct DeleteConfigurationSetEventDestinationRequest {\n pub configuration_set_name: String,\n pub event_destination_name: String,\n}\n```\nFields\n---\n\n`configuration_set_name: String`ConfigurationSetName\n\n`event_destination_name: String`EventDestinationName\n\nTrait Implementations\n---\n\nsource### impl Clone for DeleteConfigurationSetEventDestinationRequest\n\nsource#### fn clone(&self) -> DeleteConfigurationSetEventDestinationRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for DeleteConfigurationSetEventDestinationRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for DeleteConfigurationSetEventDestinationRequest\n\nsource#### fn default() -> DeleteConfigurationSetEventDestinationRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<DeleteConfigurationSetEventDestinationRequest> for DeleteConfigurationSetEventDestinationRequest\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &DeleteConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for DeleteConfigurationSetEventDestinationRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetEventDestinationRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetEventDestinationRequest\n\n### impl Send for DeleteConfigurationSetEventDestinationRequest\n\n### impl Sync for DeleteConfigurationSetEventDestinationRequest\n\n### impl Unpin for DeleteConfigurationSetEventDestinationRequest\n\n### impl UnwindSafe for DeleteConfigurationSetEventDestinationRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::DeleteConfigurationSetEventDestinationResponse\n===\n\n\n```\npub struct DeleteConfigurationSetEventDestinationResponse {}\n```\nAn empty object that indicates that the event destination was deleted successfully.\n\nTrait Implementations\n---\n\nsource### impl Clone for DeleteConfigurationSetEventDestinationResponse\n\nsource#### fn clone(&self) -> DeleteConfigurationSetEventDestinationResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for DeleteConfigurationSetEventDestinationResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for DeleteConfigurationSetEventDestinationResponse\n\nsource#### fn default() -> DeleteConfigurationSetEventDestinationResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for DeleteConfigurationSetEventDestinationResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<DeleteConfigurationSetEventDestinationResponse> for DeleteConfigurationSetEventDestinationResponse\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetEventDestinationResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\n1.0.0 · source#### fn ne(&self, other: &Rhs) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetEventDestinationResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetEventDestinationResponse\n\n### impl Send for DeleteConfigurationSetEventDestinationResponse\n\n### impl Sync for DeleteConfigurationSetEventDestinationResponse\n\n### impl Unpin for DeleteConfigurationSetEventDestinationResponse\n\n### impl UnwindSafe for DeleteConfigurationSetEventDestinationResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::DeleteConfigurationSetRequest\n===\n\n\n```\npub struct DeleteConfigurationSetRequest {\n pub configuration_set_name: String,\n}\n```\nFields\n---\n\n`configuration_set_name: String`ConfigurationSetName\n\nTrait Implementations\n---\n\nsource### impl Clone for DeleteConfigurationSetRequest\n\nsource#### fn clone(&self) -> DeleteConfigurationSetRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for DeleteConfigurationSetRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for DeleteConfigurationSetRequest\n\nsource#### fn default() -> DeleteConfigurationSetRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<DeleteConfigurationSetRequest> for DeleteConfigurationSetRequest\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &DeleteConfigurationSetRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for DeleteConfigurationSetRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetRequest\n\n### impl Send for DeleteConfigurationSetRequest\n\n### impl Sync for DeleteConfigurationSetRequest\n\n### impl Unpin for DeleteConfigurationSetRequest\n\n### impl UnwindSafe for DeleteConfigurationSetRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::DeleteConfigurationSetResponse\n===\n\n\n```\npub struct DeleteConfigurationSetResponse {}\n```\nAn empty object that indicates that the configuration set was deleted successfully.\n\nTrait Implementations\n---\n\nsource### impl Clone for DeleteConfigurationSetResponse\n\nsource#### fn clone(&self) -> DeleteConfigurationSetResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for DeleteConfigurationSetResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for DeleteConfigurationSetResponse\n\nsource#### fn default() -> DeleteConfigurationSetResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for DeleteConfigurationSetResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<DeleteConfigurationSetResponse> for DeleteConfigurationSetResponse\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\n1.0.0 · source#### fn ne(&self, other: &Rhs) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetResponse\n\n### impl Send for DeleteConfigurationSetResponse\n\n### impl Sync for DeleteConfigurationSetResponse\n\n### impl Unpin for DeleteConfigurationSetResponse\n\n### impl UnwindSafe for DeleteConfigurationSetResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::EventDestination\n===\n\n\n```\npub struct EventDestination {\n pub cloud_watch_logs_destination: Option<CloudWatchLogsDestination>,\n pub enabled: Option<bool>,\n pub kinesis_firehose_destination: Option<KinesisFirehoseDestination>,\n pub matching_event_types: Option<Vec<String>>,\n pub name: Option<String>,\n pub sns_destination: Option<SnsDestination>,\n}\n```\nAn object that defines an event destination.\n\nFields\n---\n\n`cloud_watch_logs_destination: Option<CloudWatchLogsDestination>``enabled: Option<bool>`Indicates whether or not the event destination is enabled. If the event destination is enabled, then Amazon Pinpoint sends response data to the specified event destination.\n\n`kinesis_firehose_destination: Option<KinesisFirehoseDestination>``matching_event_types: Option<Vec<String>>``name: Option<String>`A name that identifies the event destination configuration.\n\n`sns_destination: Option<SnsDestination>`Trait Implementations\n---\n\nsource### impl Clone for EventDestination\n\nsource#### fn clone(&self) -> EventDestination\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for EventDestination\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for EventDestination\n\nsource#### fn default() -> EventDestination\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for EventDestination\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<EventDestination> for EventDestination\n\nsource#### fn eq(&self, other: &EventDestination) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &EventDestination) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for EventDestination\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for EventDestination\n\n### impl Send for EventDestination\n\n### impl Sync for EventDestination\n\n### impl Unpin for EventDestination\n\n### impl UnwindSafe for EventDestination\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::EventDestinationDefinition\n===\n\n\n```\npub struct EventDestinationDefinition {\n pub cloud_watch_logs_destination: Option<CloudWatchLogsDestination>,\n pub enabled: Option<bool>,\n pub kinesis_firehose_destination: Option<KinesisFirehoseDestination>,\n pub matching_event_types: Option<Vec<String>>,\n pub sns_destination: Option<SnsDestination>,\n}\n```\nAn object that defines a single event destination.\n\nFields\n---\n\n`cloud_watch_logs_destination: Option<CloudWatchLogsDestination>``enabled: Option<bool>`Indicates whether or not the event destination is enabled. If the event destination is enabled, then Amazon Pinpoint sends response data to the specified event destination.\n\n`kinesis_firehose_destination: Option<KinesisFirehoseDestination>``matching_event_types: Option<Vec<String>>``sns_destination: Option<SnsDestination>`Trait Implementations\n---\n\nsource### impl Clone for EventDestinationDefinition\n\nsource#### fn clone(&self) -> EventDestinationDefinition\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for EventDestinationDefinition\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for EventDestinationDefinition\n\nsource#### fn default() -> EventDestinationDefinition\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<EventDestinationDefinition> for EventDestinationDefinition\n\nsource#### fn eq(&self, other: &EventDestinationDefinition) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &EventDestinationDefinition) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for EventDestinationDefinition\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for EventDestinationDefinition\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for EventDestinationDefinition\n\n### impl Send for EventDestinationDefinition\n\n### impl Sync for EventDestinationDefinition\n\n### impl Unpin for EventDestinationDefinition\n\n### impl UnwindSafe for EventDestinationDefinition\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::GetConfigurationSetEventDestinationsRequest\n===\n\n\n```\npub struct GetConfigurationSetEventDestinationsRequest {\n pub configuration_set_name: String,\n}\n```\nFields\n---\n\n`configuration_set_name: String`ConfigurationSetName\n\nTrait Implementations\n---\n\nsource### impl Clone for GetConfigurationSetEventDestinationsRequest\n\nsource#### fn clone(&self) -> GetConfigurationSetEventDestinationsRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for GetConfigurationSetEventDestinationsRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for GetConfigurationSetEventDestinationsRequest\n\nsource#### fn default() -> GetConfigurationSetEventDestinationsRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<GetConfigurationSetEventDestinationsRequest> for GetConfigurationSetEventDestinationsRequest\n\nsource#### fn eq(&self, other: &GetConfigurationSetEventDestinationsRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &GetConfigurationSetEventDestinationsRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for GetConfigurationSetEventDestinationsRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for GetConfigurationSetEventDestinationsRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for GetConfigurationSetEventDestinationsRequest\n\n### impl Send for GetConfigurationSetEventDestinationsRequest\n\n### impl Sync for GetConfigurationSetEventDestinationsRequest\n\n### impl Unpin for GetConfigurationSetEventDestinationsRequest\n\n### impl UnwindSafe for GetConfigurationSetEventDestinationsRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::GetConfigurationSetEventDestinationsResponse\n===\n\n\n```\npub struct GetConfigurationSetEventDestinationsResponse {\n pub event_destinations: Option<Vec<EventDestination>>,\n}\n```\nAn object that contains information about an event destination.\n\nFields\n---\n\n`event_destinations: Option<Vec<EventDestination>>`Trait Implementations\n---\n\nsource### impl Clone for GetConfigurationSetEventDestinationsResponse\n\nsource#### fn clone(&self) -> GetConfigurationSetEventDestinationsResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for GetConfigurationSetEventDestinationsResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for GetConfigurationSetEventDestinationsResponse\n\nsource#### fn default() -> GetConfigurationSetEventDestinationsResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for GetConfigurationSetEventDestinationsResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<GetConfigurationSetEventDestinationsResponse> for GetConfigurationSetEventDestinationsResponse\n\nsource#### fn eq(&self, other: &GetConfigurationSetEventDestinationsResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &GetConfigurationSetEventDestinationsResponse) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for GetConfigurationSetEventDestinationsResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for GetConfigurationSetEventDestinationsResponse\n\n### impl Send for GetConfigurationSetEventDestinationsResponse\n\n### impl Sync for GetConfigurationSetEventDestinationsResponse\n\n### impl Unpin for GetConfigurationSetEventDestinationsResponse\n\n### impl UnwindSafe for GetConfigurationSetEventDestinationsResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::KinesisFirehoseDestination\n===\n\n\n```\npub struct KinesisFirehoseDestination {\n pub delivery_stream_arn: Option<String>,\n pub iam_role_arn: Option<String>,\n}\n```\nAn object that contains information about an event destination that sends data to Amazon Kinesis Data Firehose.\n\nFields\n---\n\n`delivery_stream_arn: Option<String>`The Amazon Resource Name (ARN) of an IAM role that can write data to an Amazon Kinesis Data Firehose stream.\n\n`iam_role_arn: Option<String>`The Amazon Resource Name (ARN) of the Amazon Kinesis Data Firehose destination that you want to use in the event destination.\n\nTrait Implementations\n---\n\nsource### impl Clone for KinesisFirehoseDestination\n\nsource#### fn clone(&self) -> KinesisFirehoseDestination\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for KinesisFirehoseDestination\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for KinesisFirehoseDestination\n\nsource#### fn default() -> KinesisFirehoseDestination\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for KinesisFirehoseDestination\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<KinesisFirehoseDestination> for KinesisFirehoseDestination\n\nsource#### fn eq(&self, other: &KinesisFirehoseDestination) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &KinesisFirehoseDestination) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for KinesisFirehoseDestination\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for KinesisFirehoseDestination\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for KinesisFirehoseDestination\n\n### impl Send for KinesisFirehoseDestination\n\n### impl Sync for KinesisFirehoseDestination\n\n### impl Unpin for KinesisFirehoseDestination\n\n### impl UnwindSafe for KinesisFirehoseDestination\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::PlainTextMessageType\n===\n\n\n```\npub struct PlainTextMessageType {\n pub language_code: Option<String>,\n pub text: Option<String>,\n pub voice_id: Option<String>,\n}\n```\nAn object that defines a message that contains unformatted text.\n\nFields\n---\n\n`language_code: Option<String>`The language to use when delivering the message. For a complete list of supported languages, see the Amazon Polly Developer Guide.\n\n`text: Option<String>`The plain (not SSML-formatted) text to deliver to the recipient.\n\n`voice_id: Option<String>`The name of the voice that you want to use to deliver the message. For a complete list of supported voices, see the Amazon Polly Developer Guide.\n\nTrait Implementations\n---\n\nsource### impl Clone for PlainTextMessageType\n\nsource#### fn clone(&self) -> PlainTextMessageType\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for PlainTextMessageType\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for PlainTextMessageType\n\nsource#### fn default() -> PlainTextMessageType\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<PlainTextMessageType> for PlainTextMessageType\n\nsource#### fn eq(&self, other: &PlainTextMessageType) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &PlainTextMessageType) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for PlainTextMessageType\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for PlainTextMessageType\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for PlainTextMessageType\n\n### impl Send for PlainTextMessageType\n\n### impl Sync for PlainTextMessageType\n\n### impl Unpin for PlainTextMessageType\n\n### impl UnwindSafe for PlainTextMessageType\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::SSMLMessageType\n===\n\n\n```\npub struct SSMLMessageType {\n pub language_code: Option<String>,\n pub text: Option<String>,\n pub voice_id: Option<String>,\n}\n```\nAn object that defines a message that contains SSML-formatted text.\n\nFields\n---\n\n`language_code: Option<String>`The language to use when delivering the message. For a complete list of supported languages, see the Amazon Polly Developer Guide.\n\n`text: Option<String>`The SSML-formatted text to deliver to the recipient.\n\n`voice_id: Option<String>`The name of the voice that you want to use to deliver the message. For a complete list of supported voices, see the Amazon Polly Developer Guide.\n\nTrait Implementations\n---\n\nsource### impl Clone for SSMLMessageType\n\nsource#### fn clone(&self) -> SSMLMessageType\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for SSMLMessageType\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for SSMLMessageType\n\nsource#### fn default() -> SSMLMessageType\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<SSMLMessageType> for SSMLMessageType\n\nsource#### fn eq(&self, other: &SSMLMessageType) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &SSMLMessageType) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for SSMLMessageType\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for SSMLMessageType\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for SSMLMessageType\n\n### impl Send for SSMLMessageType\n\n### impl Sync for SSMLMessageType\n\n### impl Unpin for SSMLMessageType\n\n### impl UnwindSafe for SSMLMessageType\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::SendVoiceMessageRequest\n===\n\n\n```\npub struct SendVoiceMessageRequest {\n pub caller_id: Option<String>,\n pub configuration_set_name: Option<String>,\n pub content: Option<VoiceMessageContent>,\n pub destination_phone_number: Option<String>,\n pub origination_phone_number: Option<String>,\n}\n```\nSendVoiceMessageRequest\n\nFields\n---\n\n`caller_id: Option<String>`The phone number that appears on recipients' devices when they receive the message.\n\n`configuration_set_name: Option<String>`The name of the configuration set that you want to use to send the message.\n\n`content: Option<VoiceMessageContent>``destination_phone_number: Option<String>`The phone number that you want to send the voice message to.\n\n`origination_phone_number: Option<String>`The phone number that Amazon Pinpoint should use to send the voice message. This isn't necessarily the phone number that appears on recipients' devices when they receive the message, because you can specify a CallerId parameter in the request.\n\nTrait Implementations\n---\n\nsource### impl Clone for SendVoiceMessageRequest\n\nsource#### fn clone(&self) -> SendVoiceMessageRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for SendVoiceMessageRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for SendVoiceMessageRequest\n\nsource#### fn default() -> SendVoiceMessageRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<SendVoiceMessageRequest> for SendVoiceMessageRequest\n\nsource#### fn eq(&self, other: &SendVoiceMessageRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &SendVoiceMessageRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for SendVoiceMessageRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for SendVoiceMessageRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for SendVoiceMessageRequest\n\n### impl Send for SendVoiceMessageRequest\n\n### impl Sync for SendVoiceMessageRequest\n\n### impl Unpin for SendVoiceMessageRequest\n\n### impl UnwindSafe for SendVoiceMessageRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::SendVoiceMessageResponse\n===\n\n\n```\npub struct SendVoiceMessageResponse {\n pub message_id: Option<String>,\n}\n```\nAn object that that contains the Message ID of a Voice message that was sent successfully.\n\nFields\n---\n\n`message_id: Option<String>`A unique identifier for the voice message.\n\nTrait Implementations\n---\n\nsource### impl Clone for SendVoiceMessageResponse\n\nsource#### fn clone(&self) -> SendVoiceMessageResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for SendVoiceMessageResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for SendVoiceMessageResponse\n\nsource#### fn default() -> SendVoiceMessageResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for SendVoiceMessageResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<SendVoiceMessageResponse> for SendVoiceMessageResponse\n\nsource#### fn eq(&self, other: &SendVoiceMessageResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &SendVoiceMessageResponse) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for SendVoiceMessageResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for SendVoiceMessageResponse\n\n### impl Send for SendVoiceMessageResponse\n\n### impl Sync for SendVoiceMessageResponse\n\n### impl Unpin for SendVoiceMessageResponse\n\n### impl UnwindSafe for SendVoiceMessageResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::SnsDestination\n===\n\n\n```\npub struct SnsDestination {\n pub topic_arn: Option<String>,\n}\n```\nAn object that contains information about an event destination that sends data to Amazon SNS.\n\nFields\n---\n\n`topic_arn: Option<String>`The Amazon Resource Name (ARN) of the Amazon SNS topic that you want to publish events to.\n\nTrait Implementations\n---\n\nsource### impl Clone for SnsDestination\n\nsource#### fn clone(&self) -> SnsDestination\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for SnsDestination\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for SnsDestination\n\nsource#### fn default() -> SnsDestination\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for SnsDestination\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<SnsDestination> for SnsDestination\n\nsource#### fn eq(&self, other: &SnsDestination) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &SnsDestination) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for SnsDestination\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for SnsDestination\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for SnsDestination\n\n### impl Send for SnsDestination\n\n### impl Sync for SnsDestination\n\n### impl Unpin for SnsDestination\n\n### impl UnwindSafe for SnsDestination\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::UpdateConfigurationSetEventDestinationRequest\n===\n\n\n```\npub struct UpdateConfigurationSetEventDestinationRequest {\n pub configuration_set_name: String,\n pub event_destination: Option<EventDestinationDefinition>,\n pub event_destination_name: String,\n}\n```\nUpdateConfigurationSetEventDestinationRequest\n\nFields\n---\n\n`configuration_set_name: String`ConfigurationSetName\n\n`event_destination: Option<EventDestinationDefinition>``event_destination_name: String`EventDestinationName\n\nTrait Implementations\n---\n\nsource### impl Clone for UpdateConfigurationSetEventDestinationRequest\n\nsource#### fn clone(&self) -> UpdateConfigurationSetEventDestinationRequest\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for UpdateConfigurationSetEventDestinationRequest\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for UpdateConfigurationSetEventDestinationRequest\n\nsource#### fn default() -> UpdateConfigurationSetEventDestinationRequest\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<UpdateConfigurationSetEventDestinationRequest> for UpdateConfigurationSetEventDestinationRequest\n\nsource#### fn eq(&self, other: &UpdateConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &UpdateConfigurationSetEventDestinationRequest) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for UpdateConfigurationSetEventDestinationRequest\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for UpdateConfigurationSetEventDestinationRequest\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for UpdateConfigurationSetEventDestinationRequest\n\n### impl Send for UpdateConfigurationSetEventDestinationRequest\n\n### impl Sync for UpdateConfigurationSetEventDestinationRequest\n\n### impl Unpin for UpdateConfigurationSetEventDestinationRequest\n\n### impl UnwindSafe for UpdateConfigurationSetEventDestinationRequest\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nStruct rusoto_pinpoint_sms_voice::UpdateConfigurationSetEventDestinationResponse\n===\n\n\n```\npub struct UpdateConfigurationSetEventDestinationResponse {}\n```\nAn empty object that indicates that the event destination was updated successfully.\n\nTrait Implementations\n---\n\nsource### impl Clone for UpdateConfigurationSetEventDestinationResponse\n\nsource#### fn clone(&self) -> UpdateConfigurationSetEventDestinationResponse\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for UpdateConfigurationSetEventDestinationResponse\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for UpdateConfigurationSetEventDestinationResponse\n\nsource#### fn default() -> UpdateConfigurationSetEventDestinationResponse\n\nReturns the “default value” for a type. Read more\n\nsource### impl<'de> Deserialize<'de> for UpdateConfigurationSetEventDestinationResponse\n\nsource#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where __D: Deserializer<'de>,\n\nDeserialize this value from the given Serde deserializer. Read more\n\nsource### impl PartialEq<UpdateConfigurationSetEventDestinationResponse> for UpdateConfigurationSetEventDestinationResponse\n\nsource#### fn eq(&self, other: &UpdateConfigurationSetEventDestinationResponse) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\n1.0.0 · source#### fn ne(&self, other: &Rhs) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for UpdateConfigurationSetEventDestinationResponse\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for UpdateConfigurationSetEventDestinationResponse\n\n### impl Send for UpdateConfigurationSetEventDestinationResponse\n\n### impl Sync for UpdateConfigurationSetEventDestinationResponse\n\n### impl Unpin for UpdateConfigurationSetEventDestinationResponse\n\n### impl UnwindSafe for UpdateConfigurationSetEventDestinationResponse\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource### impl<T> DeserializeOwned for T where T: for<'de> Deserialize<'de>,\n\nStruct rusoto_pinpoint_sms_voice::VoiceMessageContent\n===\n\n\n```\npub struct VoiceMessageContent {\n pub call_instructions_message: Option<CallInstructionsMessageType>,\n pub plain_text_message: Option<PlainTextMessageType>,\n pub ssml_message: Option<SSMLMessageType>,\n}\n```\nAn object that contains a voice message and information about the recipient that you want to send it to.\n\nFields\n---\n\n`call_instructions_message: Option<CallInstructionsMessageType>``plain_text_message: Option<PlainTextMessageType>``ssml_message: Option<SSMLMessageType>`Trait Implementations\n---\n\nsource### impl Clone for VoiceMessageContent\n\nsource#### fn clone(&self) -> VoiceMessageContent\n\nReturns a copy of the value. Read more\n\n1.0.0 · source#### fn clone_from(&mut self, source: &Self)\n\nPerforms copy-assignment from `source`. Read more\n\nsource### impl Debug for VoiceMessageContent\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Default for VoiceMessageContent\n\nsource#### fn default() -> VoiceMessageContent\n\nReturns the “default value” for a type. Read more\n\nsource### impl PartialEq<VoiceMessageContent> for VoiceMessageContent\n\nsource#### fn eq(&self, other: &VoiceMessageContent) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &VoiceMessageContent) -> bool\n\nThis method tests for `!=`.\n\nsource### impl Serialize for VoiceMessageContent\n\nsource#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where __S: Serializer,\n\nSerialize this value into the given Serde serializer. Read more\n\nsource### impl StructuralPartialEq for VoiceMessageContent\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for VoiceMessageContent\n\n### impl Send for VoiceMessageContent\n\n### impl Sync for VoiceMessageContent\n\n### impl Unpin for VoiceMessageContent\n\n### impl UnwindSafe for VoiceMessageContent\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToOwned for T where T: Clone,\n\n#### type Owned = T\n\nThe resulting type after obtaining ownership.\n\nsource#### fn to_owned(&self) -> T\n\nCreates owned data from borrowed data, usually by cloning. Read more\n\nsource#### fn clone_into(&self, target: &mutT)\n\n🔬 This is a nightly-only experimental API. (`toowned_clone_into`)Uses borrowed data to replace owned data, usually by cloning. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::CreateConfigurationSetError\n===\n\n\n```\npub enum CreateConfigurationSetError {\n AlreadyExists(String),\n BadRequest(String),\n InternalServiceError(String),\n LimitExceeded(String),\n TooManyRequests(String),\n}\n```\nErrors returned by CreateConfigurationSet\n\nVariants\n---\n\n### `AlreadyExists(String)`\n\nThe resource specified in your request already exists.\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `LimitExceeded(String)`\n\nThere are too many instances of the specified resource type.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl CreateConfigurationSetError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<CreateConfigurationSetErrorTrait Implementations\n---\n\nsource### impl Debug for CreateConfigurationSetError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for CreateConfigurationSetError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for CreateConfigurationSetError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<CreateConfigurationSetError> for CreateConfigurationSetError\n\nsource#### fn eq(&self, other: &CreateConfigurationSetError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CreateConfigurationSetError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for CreateConfigurationSetError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetError\n\n### impl Send for CreateConfigurationSetError\n\n### impl Sync for CreateConfigurationSetError\n\n### impl Unpin for CreateConfigurationSetError\n\n### impl UnwindSafe for CreateConfigurationSetError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::CreateConfigurationSetEventDestinationError\n===\n\n\n```\npub enum CreateConfigurationSetEventDestinationError {\n AlreadyExists(String),\n BadRequest(String),\n InternalServiceError(String),\n LimitExceeded(String),\n NotFound(String),\n TooManyRequests(String),\n}\n```\nErrors returned by CreateConfigurationSetEventDestination\n\nVariants\n---\n\n### `AlreadyExists(String)`\n\nThe resource specified in your request already exists.\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `LimitExceeded(String)`\n\nThere are too many instances of the specified resource type.\n\n### `NotFound(String)`\n\nThe resource you attempted to access doesn't exist.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl CreateConfigurationSetEventDestinationError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<CreateConfigurationSetEventDestinationErrorTrait Implementations\n---\n\nsource### impl Debug for CreateConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for CreateConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for CreateConfigurationSetEventDestinationError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<CreateConfigurationSetEventDestinationError> for CreateConfigurationSetEventDestinationError\n\nsource#### fn eq(&self, other: &CreateConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &CreateConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for CreateConfigurationSetEventDestinationError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for CreateConfigurationSetEventDestinationError\n\n### impl Send for CreateConfigurationSetEventDestinationError\n\n### impl Sync for CreateConfigurationSetEventDestinationError\n\n### impl Unpin for CreateConfigurationSetEventDestinationError\n\n### impl UnwindSafe for CreateConfigurationSetEventDestinationError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::DeleteConfigurationSetError\n===\n\n\n```\npub enum DeleteConfigurationSetError {\n BadRequest(String),\n InternalServiceError(String),\n NotFound(String),\n TooManyRequests(String),\n}\n```\nErrors returned by DeleteConfigurationSet\n\nVariants\n---\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `NotFound(String)`\n\nThe resource you attempted to access doesn't exist.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl DeleteConfigurationSetError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<DeleteConfigurationSetErrorTrait Implementations\n---\n\nsource### impl Debug for DeleteConfigurationSetError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for DeleteConfigurationSetError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for DeleteConfigurationSetError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<DeleteConfigurationSetError> for DeleteConfigurationSetError\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &DeleteConfigurationSetError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetError\n\n### impl Send for DeleteConfigurationSetError\n\n### impl Sync for DeleteConfigurationSetError\n\n### impl Unpin for DeleteConfigurationSetError\n\n### impl UnwindSafe for DeleteConfigurationSetError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::DeleteConfigurationSetEventDestinationError\n===\n\n\n```\npub enum DeleteConfigurationSetEventDestinationError {\n BadRequest(String),\n InternalServiceError(String),\n NotFound(String),\n TooManyRequests(String),\n}\n```\nErrors returned by DeleteConfigurationSetEventDestination\n\nVariants\n---\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `NotFound(String)`\n\nThe resource you attempted to access doesn't exist.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl DeleteConfigurationSetEventDestinationError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<DeleteConfigurationSetEventDestinationErrorTrait Implementations\n---\n\nsource### impl Debug for DeleteConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for DeleteConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for DeleteConfigurationSetEventDestinationError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<DeleteConfigurationSetEventDestinationError> for DeleteConfigurationSetEventDestinationError\n\nsource#### fn eq(&self, other: &DeleteConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &DeleteConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for DeleteConfigurationSetEventDestinationError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for DeleteConfigurationSetEventDestinationError\n\n### impl Send for DeleteConfigurationSetEventDestinationError\n\n### impl Sync for DeleteConfigurationSetEventDestinationError\n\n### impl Unpin for DeleteConfigurationSetEventDestinationError\n\n### impl UnwindSafe for DeleteConfigurationSetEventDestinationError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::GetConfigurationSetEventDestinationsError\n===\n\n\n```\npub enum GetConfigurationSetEventDestinationsError {\n BadRequest(String),\n InternalServiceError(String),\n NotFound(String),\n TooManyRequests(String),\n}\n```\nErrors returned by GetConfigurationSetEventDestinations\n\nVariants\n---\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `NotFound(String)`\n\nThe resource you attempted to access doesn't exist.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl GetConfigurationSetEventDestinationsError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<GetConfigurationSetEventDestinationsErrorTrait Implementations\n---\n\nsource### impl Debug for GetConfigurationSetEventDestinationsError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for GetConfigurationSetEventDestinationsError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for GetConfigurationSetEventDestinationsError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<GetConfigurationSetEventDestinationsError> for GetConfigurationSetEventDestinationsError\n\nsource#### fn eq(&self, other: &GetConfigurationSetEventDestinationsError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &GetConfigurationSetEventDestinationsError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for GetConfigurationSetEventDestinationsError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for GetConfigurationSetEventDestinationsError\n\n### impl Send for GetConfigurationSetEventDestinationsError\n\n### impl Sync for GetConfigurationSetEventDestinationsError\n\n### impl Unpin for GetConfigurationSetEventDestinationsError\n\n### impl UnwindSafe for GetConfigurationSetEventDestinationsError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::SendVoiceMessageError\n===\n\n\n```\npub enum SendVoiceMessageError {\n BadRequest(String),\n InternalServiceError(String),\n TooManyRequests(String),\n}\n```\nErrors returned by SendVoiceMessage\n\nVariants\n---\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl SendVoiceMessageError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<SendVoiceMessageErrorTrait Implementations\n---\n\nsource### impl Debug for SendVoiceMessageError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for SendVoiceMessageError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for SendVoiceMessageError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<SendVoiceMessageError> for SendVoiceMessageError\n\nsource#### fn eq(&self, other: &SendVoiceMessageError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &SendVoiceMessageError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for SendVoiceMessageError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for SendVoiceMessageError\n\n### impl Send for SendVoiceMessageError\n\n### impl Sync for SendVoiceMessageError\n\n### impl Unpin for SendVoiceMessageError\n\n### impl UnwindSafe for SendVoiceMessageError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nEnum rusoto_pinpoint_sms_voice::UpdateConfigurationSetEventDestinationError\n===\n\n\n```\npub enum UpdateConfigurationSetEventDestinationError {\n BadRequest(String),\n InternalServiceError(String),\n NotFound(String),\n TooManyRequests(String),\n}\n```\nErrors returned by UpdateConfigurationSetEventDestination\n\nVariants\n---\n\n### `BadRequest(String)`\n\nThe input you provided is invalid.\n\n### `InternalServiceError(String)`\n\nThe API encountered an unexpected error and couldn't complete the request. You might be able to successfully issue the request again in the future.\n\n### `NotFound(String)`\n\nThe resource you attempted to access doesn't exist.\n\n### `TooManyRequests(String)`\n\nYou've issued too many requests to the resource. Wait a few minutes, and then try again.\n\nImplementations\n---\n\nsource### impl UpdateConfigurationSetEventDestinationError\n\nsource#### pub fn from_response( res: BufferedHttpResponse) -> RusotoError<UpdateConfigurationSetEventDestinationErrorTrait Implementations\n---\n\nsource### impl Debug for UpdateConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Display for UpdateConfigurationSetEventDestinationError\n\nsource#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. Read more\n\nsource### impl Error for UpdateConfigurationSetEventDestinationError\n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more\n\nsource#### fn backtrace(&self) -> Option<&Backtrace🔬 This is a nightly-only experimental API. (`backtrace`)Returns a stack backtrace, if available, of where this error occurred. Read more\n\n1.0.0 · source#### fn description(&self) -> &str\n\n👎 Deprecated since 1.42.0: use the Display impl or to_string()\n\n Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎 Deprecated since 1.33.0: replaced by Error::source, which can support downcasting\n\nsource### impl PartialEq<UpdateConfigurationSetEventDestinationError> for UpdateConfigurationSetEventDestinationError\n\nsource#### fn eq(&self, other: &UpdateConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `self` and `other` values to be equal, and is used by `==`. Read more\n\nsource#### fn ne(&self, other: &UpdateConfigurationSetEventDestinationError) -> bool\n\nThis method tests for `!=`.\n\nsource### impl StructuralPartialEq for UpdateConfigurationSetEventDestinationError\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for UpdateConfigurationSetEventDestinationError\n\n### impl Send for UpdateConfigurationSetEventDestinationError\n\n### impl Sync for UpdateConfigurationSetEventDestinationError\n\n### impl Unpin for UpdateConfigurationSetEventDestinationError\n\n### impl UnwindSafe for UpdateConfigurationSetEventDestinationError\n\nBlanket Implementations\n---\n\nsource### impl<T> Any for T where T: 'static + ?Sized,\n\nsource#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. Read more\n\nsource### impl<T> Borrow<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. Read more\n\nsource### impl<T> BorrowMut<T> for T where T: ?Sized,\n\nconst: unstable · source#### fn borrow_mut(&mut self) -> &mutT\n\nMutably borrows from an owned value. Read more\n\nsource### impl<T> From<T> for T\n\nconst: unstable · source#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\nsource### impl<T> Instrument for T\n\nsource#### fn instrument(self, span: Span) -> Instrumented<SelfInstruments this type with the provided `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource#### fn in_current_span(self) -> Instrumented<SelfInstruments this type with the current `Span`, returning an\n`Instrumented` wrapper. Read more\n\nsource### impl<T, U> Into<U> for T where U: From<T>,\n\nconst: unstable · source#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\nsource### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`\n\nsource### impl<T> ToString for T where T: Display + ?Sized,\n\nsource#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. Read more\n\nsource### impl<T, U> TryFrom<U> for T where U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.\n\nsource### impl<T, U> TryInto<U> for T where U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.\n\nconst: unstable · source#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nsource### impl<T> WithSubscriber for T\n\nsource#### fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> where S: Into<Dispatch>,\n\nAttaches the provided `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more\n\nsource#### fn with_current_subscriber(self) -> WithDispatch<SelfAttaches the current default `Subscriber` to this type, returning a\n`WithDispatch` wrapper. Read more"}}},{"rowIdx":59469,"cells":{"project":{"kind":"string","value":"bisectr"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘bisectr’\n October 12, 2022\nTitle Tools to find bad commits with git bisect\nVersion 0.1.0\nAuthor <NAME> <<EMAIL>>\nMaintainer <NAME> <<EMAIL>>\nDescription Tools to find bad commits with git bisect. See\n https://github.com/wch/bisectr for examples and test script\n templates.\nURL https://github.com/wch/bisectr\nDepends R (>= 2.14)\nImports devtools\nLicense GPL-2\nCollate 'bisect.r'\nRepository CRAN\nDate/Publication 2012-06-15 03:45:00\nNeedsCompilation no\nR topics documented:\nbisect... 2\nbisect_instal... 2\nbisect_load_al... 3\nbisect_requir... 3\nbisect_return_interactiv... 4\nbisect_runtes... 4\nbisect_sourc... 5\n bisectr bisectr package\nDescription\n This package is used for creating test scripts to find bad commits with git bisect. For example test\n scripts, see https://github.com/wch/bisectr.\n bisect_install Install a package from source, for bisect tests.\nDescription\n If the installation fails, the default behavior is to mark this commit as skip.\nUsage\n bisect_install(pkgdir = \".\", on_fail = \"skip\")\nArguments\n pkgdir The directory to load from\n on_fail What to do if installation fails (default is to mark this commit as \"skip\")\nDetails\n This function is usually used together with bisect_require.\nSee Also\n bisect_require\n bisect_load_all\n bisect_source\n bisect_runtest\n bisect_return_interactive\n bisect_load_all Like load_all, but for bisect tests.\nDescription\n If the package fails to load, the default is to mark this commit as skip.\nUsage\n bisect_load_all(pkgdir = \".\", on_error = \"skip\")\nArguments\n pkgdir The directory to load from\n on_error What to do if loading throws an error (default is to mark this commit as \"skip\")\nSee Also\n bisect_source\n bisect_install\n bisect_runtest\n bisect_return_interactive\n bisect_require Load a package like require(), for bisect tests.\nDescription\n If the package fails to load, the default behavior is to mark this commit as skip.\nUsage\n bisect_require(package, on_fail = \"skip\")\nArguments\n package Name of package\n on_fail What to do if loading fails (default \"skip\")\nDetails\n This function is usually used together with bisect_install.\nSee Also\n bisect_install\n bisect_load_all\n bisect_source\n bisect_runtest\n bisect_return_interactive\n bisect_return_interactive\n Prompt the user for an interactive good/bad/skip response and return\n the appropriate value (to be passed to bisect_runtest).\nDescription\n Prompt the user for an interactive good/bad/skip response and return the appropriate value (to be\n passed to bisect_runtest).\nUsage\n bisect_return_interactive()\nSee Also\n bisect_runtest\n bisect_load_all\n bisect_install\n bisect_source\n bisect_runtest Run a test function for git bisect testing.\nDescription\n If the function fun returns \"good\" or TRUE, quit and return a code to mark this commit as good.\n If the function returns \"bad\" or FALSE, quit and return a code to mark this commit as bad. If the\n function returns \"skip\" or NA, quit and return a code to mark this commit as skip. If the function\n returns \"ignore\" or NULL, do nothing.\nUsage\n bisect_runtest(fun, on_error = \"skip\",\n msg = \"Running test...\")\nArguments\n fun The test function\n on_error What to do if running fun throws an error (default is to mark this commit as\n skip)\n msg A message to print to the console when running the test\nDetails\n It is also important to set on_error. This tells it what to do when the test function throws an error.\n The default behavior is to mark this commit as skip. However, in some cases, it makes sense to\n mark this commit as bad if an error is thrown.\nSee Also\n bisect_load_all\n bisect_install\n bisect_source\n bisect_return_interactive\n bisect_source Like source, but for bisect tests.\nDescription\n If the file fails to load, the default is mark this commit as skip.\nUsage\n bisect_source(file, ..., on_error = \"skip\")\nArguments\n file The file to load\n ... Other arguments to pass to source\n on_error What to do if loading throws an error (default is to mark this commit as \"skip\")\nSee Also\n source\n bisect_load_all\n bisect_install\n bisect_runtest\n bisect_return_interactive"}}},{"rowIdx":59470,"cells":{"project":{"kind":"string","value":"web-platform-compat"},"source":{"kind":"string","value":"readthedoc"},"language":{"kind":"string","value":"JSON"},"content":{"kind":"string","value":"web-platform-compat 0.1.0 documentation\n\nweb-platform-compat[¶](#web-platform-compat)\n===\n\nThe Web Platform Compatibility API will support compatibility data on the\n[Mozilla Developer Network](https://developer.mozilla.org). This currently takes the form of browser compatibility tables, such as the one on the [CSS display property](https://developer.mozilla.org/en-US/docs/Web/CSS/display#Browser_compatibility).\nThe API will help centralize this data, and allow it to be kept consistant across languages and different presentations.\n\n*Note: This project will be renamed to browsercompat in the near future, to syncronize the project name with the planned production domain name https://browsercompat.org.*\n\nThe project started in December 2013. The goals, requirements, and current status are documented on the [MozillaWiki](https://wiki.mozilla.org/index.php?title=MDN/Projects/Development/CompatibilityTables).\n\nThis project will implement the data store and API for compatibility data and related resources.\n\nStatus[¶](#status)\n---\n\nWe’re defining the API and the split between API-side and client-side functionality - see the [draft API docs](draft/intro.html).\n\nThe next step is to implement some of the API with sample data,\nas an aid to the discussion.\n\nDevelopment[¶](#development)\n---\n\n| Code: | <https://github.com/jwhitlock/web-platform-compat> |\n| Dev Server: | <https://browsercompat.herokuapp.com> (based on [jwhitlock/browsercompat-data](https://github.com/jwhitlock/browsercompat-data)) |\n| Issues: | <https://bugzilla.mozilla.org/buglist.cgi?quicksearch=compat-data> (tracking bug)\n<https://github.com/jwhitlock/web-platform-compat/issues?state=open> (documentation issues)\n<https://bugzilla.mozilla.org/showdependencytree.cgi?id=996570&hide_resolved=1> (blocking issues for v1) |\n| Dev Docs: | <https://web-platform-compat.readthedocs.org>\n<https://github.com/jwhitlock/web-platform-compat/wiki> |\n| Mailing list: | <https://lists.mozilla.org/listinfo/dev-mdn> |\n| IRC: | <irc://irc.mozilla.org/mdndev> |\n\nContents:\n\n### Installation[¶](#installation)\n\n#### Install Django Project[¶](#install-django-project)\n\nFor detailed local instation instructions, including OS-specific instructions, see the [Installation page on the wiki](https://www.python.org).\n\n1. Install system packages and libraries. The required packages are\n[Python](https://www.python.org) (2.7, 3.4, or both),\n[pip](https://pip.pypa.io/en/latest/) (latest), and\n[virtualenv](https://virtualenv.pypa.io/en/latest/) (latest).\nTo match production and for a smooth installation of Python packages,\ninstall\n[PostgreSQL](http://www.postgresql.org) (9.2 or later recommended) and\n[Memcached](http://memcached.org) (latest).\n[virtualenvwrapper](http://virtualenvwrapper.readthedocs.org/en/latest/) and [autoenv](https://github.com/kennethreitz/autoenv) will make your development life easier.\n2. Optionally, provision a PostgreSQL database, recommended to match production. The default Django database settings will use a\n[SQLite](http://sqlite.org) database named `db.sqlite3`.\n3. Optionally, run [Memcached](http://memcached.org) for improved read performance and to match production. The default settings will run without a cache.\n4. [Clone project locally](https://help.github.com/articles/which-remote-url-should-i-use/).\n5. [Create a virtualenv](https://virtualenv.pypa.io/en/latest/userguide.html).\n6. Install dependencies with\n`pip install -r requirements.txt -r requirements-dev.txt`.\n7. Customize the configuration with environment variables.\nSee `wpcsite/settings.py` and `env.dist` for advice and available settings.\n8. Initialize the database and a superuser account with\n`./manage.py migrate`.\n9. Verify that tests pass with `./manage,py test` or `make test`.\n10. Run it with `./manage.py runserver` or `./manage.py runserver_plus`.\n\n#### Install in Heroku[¶](#install-in-heroku)\n\n[Heroku](https://www.heroku.com/) allows you to quickly deploy web-platform-compat. Heroku hosts the beta version of the service at <https://browsercompat.herokuapp.com>, using the add-ons:\n\n* [heroku-postgresql](https://devcenter.heroku.com/articles/heroku-postgresql) ([hobby-basic tier](https://devcenter.heroku.com/articles/heroku-postgres-plans), $9/month, required for size of dataset)\n* [memcachier](https://devcenter.heroku.com/articles/memcachier) (free dev tier)\n\nTo deploy with Heroku, you’ll need to [signup for a free account](https://signup.heroku.com/) and install the [Heroku Toolbelt](http://toolbelt.heroku.com/). Then you can:\n\n1. Clone project locally 2. `heroku apps:create`\n3. `git push heroku master`\n4. See the current config with `heroku config`, and then customize with environment variables using `heroku config:set`\n(see `wpcsite/settings.py` and `env.dist`)\n5. Add superuser account (`heroku run ./manage.py createsuperuser`)\n\n#### Configuring authentication[¶](#configuring-authentication)\n\nThe project uses [django-allauth](http://www.intenct.nl/projects/django-allauth/) as a framework for local and social authentication. The [public service](https://browsercompat.herokuapp.com) uses username and password for local authentication, and [Firefox Accounts](https://developer.mozilla.org/en-US/Firefox_Accounts) (FxA) for social authentication.\n\ndjango-allauth supports multiple emails per user, with one primary email used for communication. Email addresses are validated by sending a confirmation link. For a public server, you’ll need to\n[configure Django to send email](https://docs.djangoproject.com/en/1.7/topics/email/), by configuring your mail server and setting environment variables. For local development, it is easiest to print emails to the console:\n```\nexport EMAIL_BACKEND=\"django.core.mail.backends.console.EmailBackend\"\n```\ndjango-allauth supports many social authentication providers. See the\n[providers documentation](http://django-allauth.readthedocs.org/en/latest/providers.html) for the current list and hints for configuration.\nUsing a authentication provider is not required, especially for local development. Instead, use local authentication with a username and password.\n\nIf you need FxA integration, see the [Firefox Accounts page on the wiki](https://github.com/jwhitlock/web-platform-compat/wiki/Firefox%20Accounts)\nfor install hints.\n\n#### Load Data[¶](#load-data)\n\nThere are several ways to get data into your API:\n\n1. Load data from the github export 2. Load data from another webcompat server 3. Load sample data from the [WebPlatform project](http://www.webplatform.org) and [MDN](https://developer.mozilla.org/en-US/)\n\n##### Load from GitHub[¶](#load-from-github)\n\nThe data on [browsercompat.herokuapp.com](https://browsercompat.herokuapp.com) is archived in the\n[browsercompat-data](https://github.com/jwhitlock/browsercompat-data) github repo, and this is the fastest way to get data into your empty API:\n\n1. Clone the github repo (`git clone https://github.com/jwhitlock/browsercompat-data.git`)\n2. Run the API (`./manage.py runserver`)\n3. Import the data (`tools/upload_data.py --data /path/to/browsercompat-data/data`)\n\n##### Load from another webcompat server[¶](#load-from-another-webcompat-server)\n\nIf you have read access to a webcompat server that you’d like to clone, you can grab the data for your own server.\n\n1. Download the data (`tools/download_data.py --api https://browsercompat.example.com`)\n2. Run the API (`./manage.py runserver`)\n3. Import the data (`tools/upload_data.py`)\n\n##### Load Sample Data[¶](#load-sample-data)\n\nThe [WebPlatform project](http://www.webplatform.org) imported data from [MDN](https://developer.mozilla.org/en-US/), and stored the formatted compatibility data in a [github project](https://github.com/webplatform/compatibility-data). There is a lot of data that was not imported, so it’s not a good data source for re-displaying on MDN.\nHowever, combining this data with specification data from MDN will create a good data set for testing the API at scale.\n\nTo load sample data:\n\n1. Run the API (`./manage.py runserver`)\n2. Load a subset of the WebPlatform data (`tools/load_webcompat_data.py`) or full set of data (`tools/load_webcompat.py --all-data`)\n3. Load specification data (`tools/load_spec_data.py`)\n\n### Contributing[¶](#contributing)\n\nContributions should follow the [MDN Contribution Guidelines](https://github.com/mozilla/kuma/blob/master/CONTRIBUTING.md):\n\n* You agree to license your contributions under [MPL 2](http://www.mozilla.org/MPL/2.0/)\n* Discuss large changes on the [dev-mdn mailing list](https://lists.mozilla.org/listinfo/dev-mdn) or on a [bugzilla bug](https://bugzilla.mozilla.org/show_bug.cgi?id=989448)\nbefore coding.\n* Python code style should follow [PEP8 standards](http://www.python.org/dev/peps/pep-0008/) whenever possible.\n* All commit messages must start with “bug NNNNNNN” or “fix bug NNNNNNN”\n\n\t+ Reason: Make it easy for someone to consume the commit log and reach\n\toriginating requests for all changes\n\t+ Exceptions: “Merge” and “Revert” commits\n\t+ Notes:\n\t\n\t\t- “fix bug NNNNNNN” - will trigger a github bot to automatically mark\n\t\tbug as “RESOLVED:FIXED”\n\t\t- If a pull request has multiple commits, we should squash commits\n\t\ttogether or re-word commit messages so that each commit message\n\t\tcontains a bug number\n* MDN module [owner or peer](https://wiki.mozilla.org/Modules/All#MDN) must review and merge all pull requests.\n\n\t+ Reason: Owner and peers are and accountable for the quality of MDN code\n\tchanges\n\t+ Exceptions: Owners/peers may commit directly to master for critical\n\tsecurity/down-time fixes; they must file a bug for follow-up review.\n* MDN reviewers must verify sufficient test coverage on all changes - either by new or existing tests.\n\n\t+ Reason: Automated tests reduce human error involved in reviews\n\t+ Notes: The Django site has [good testing docs](https://docs.djangoproject.com/en/dev/topics/testing/), and\n\t[Django REST framework](http://www.django-rest-framework.org) has some [additonal testing docs](http://www.django-rest-framework.org/api-guide/testing).\n\n#### What to work on[¶](#what-to-work-on)\n\nThere is a [tracking bug](https://bugzilla.mozilla.org/showdependencytree.cgi?id=989448&hide_resolved=1) for this project, and a [specific bug](https://bugzilla.mozilla.org/showdependencytree.cgi?id=996570&hide_resolved=1) for the data store, the primary purpose of this project. The dependant bugs represent areas of work, and are not exhaustive. If you want to contribute at this phase in development, take a look at the bugs and linked documents, to familiarize yourself with the project, and then get in touch with the team on IRC (#mdndev on irc.mozilla.org) to carve out a piece of the project.\n\n#### GitHub workflow[¶](#github-workflow)\n\n1. [Get your environment setup](installation.html)\n2. Set up mozilla remote\n(`$ git remote add mozilla git://github.com/mozilla/web-platform-compat.git`)\n3. Create a branch for a bug\n(`$ git checkout -b new-issue-888888`)\n4. Develop on bug branch.\n\nTime passes, the mozilla/web-platform-compat repository accumulates new commits 5. Commit changes to bug branch\n(`$ git add . ; git commit -m 'fix bug 888888 - commit message'`)\n6. Fetch mozilla\n(`$ git fetch mozilla`)\n7. Update local master\n(`$ git checkout master; git pull mozilla master`)\n\nRepeat steps 4-7 till dev is complete 8. Rebase issue branch\n(`$ git checkout new-issue-888888; git rebase master`)\n9. Push branch to GitHub\n(`$ git push origin new-issue-888888`)\n10. Issue pull request (Click Pull Request button)\n\n### API (DRAFT)[¶](#api-draft)\n\n**This is a draft document**\n\nThe [MDN community](http://developer.mozilla.org) maintains information about web technologies such as HTML and CSS. This includes information about which specifications define the technology, and what browsers support the technology.\n\nBrowser support is shown in **Browser compatibility** tables in the source. A simple example is for the [HTML element <address>](https://developer.mozilla.org/en-US/docs/Web/HTML/Element/address#Browser_compatibility). A more complex example is the [CSS property display](https://developer.mozilla.org/en-US/docs/Web/CSS/display#Browser_compatibility).\n\nThere are several issues with the table-based compatibility tables, some of which could be solved by having a database-backed representation of compatibilty data, readable and writable from an API.\n\n#### Entrypoints[¶](#entrypoints)\n\nThe API will be reachable at <https://browsersupports.org/api/v1/>. A non-SSL version will be reachable at <http://browsersupports.org/api/v1/>, and will redirect to the SSL version. This site is for applications that read,\ncreate, update, and delete compatibility resources. It includes a browsable API to ease application development, but not full documentation.\n\nThe API supports two representations:\n\n`application/vnd.api+json` *(default)*\nJSON mostly conforming to the [JSON API](http://jsonapi.org).\n`text/html`\nthe Django REST Framework browsable API.\n\nThe API supports user accounts with [Persona](http://www.mozilla.org/en-US/persona/) authentication. Persona credentials can be exchanged for an [OAuth 2.0](http://oauth.net/2/) token for server-side code changes.\n\nA developer-centered website will be available at <https://browsersupports.org/>.\nA non-SSL version will be available at <http://browsersupports.org> and will redirect to the HTTPS version. This site is for documentation, example code,\nand example presentations.\n\nThe documentation site is not editable from the browser. It uses gettext-style translations. en-US will be the first supported language.\n\n#### Proposed Technologies[¶](#proposed-technologies)\n\nThe two sites are served from a single codebase, at\n<https://github.com/mozilla/web-platform-compat>. Technologies include:\n\n* [Django 1.7](https://docs.djangoproject.com/en/1.7/), a web framework\n* [Django REST Framework](http://www.django-rest-framework.org), an API framework\n* [django-simple-history](https://django-simple-history.readthedocs.org/en/latest/index.html), for recording changes to models\n* [django-mptt](https://github.com/django-mptt/django-mptt/), for efficiently storing hierarchical data\n* [django-oauth2-provider](https://github.com/caffeinehit/django-oauth2-provider), for script-based updates of content\n\n#### [Resources](#id1)[¶](#resources)\n\nResources are simple objects supporting [CRUD](http://en.wikipedia.org/wiki/Create,_read,_update_and_delete) operations. Read operations can be done anonymously. Creating and updating require account permissions, and deleting requires admin account permissions.\n\nAll resources support similar operations using HTTP methods:\n\n* `GET /api/v1/<type>` - List instances (paginated)\n* `POST /api/v1/<type>` - Create new instance\n* `GET /api/v1/<type>/<id>` - Retrieve an instance\n* `PUT /api/v1/<type>/<id>` - Update an instance\n* `DELETE /api/v1/<type>/<id>` - Delete instance\n\nAdditional features may be added as needed. See the [JSON API docs](http://jsonapi.org/format/) for ideas and what format they will take.\n\nBecause the operations are similar, only [browsers](#browsers) has complete operations examples, and others just show retrieving an instance (`GET /api/v1/<type>/<id>`).\n\nContents\n\n* [Resources](#resources)\n\t+ [Browsers](#browsers)\n\t\t- [List](#list)\n\t\t- [Retrieve by ID](#retrieve-by-id)\n\t\t- [Retrieve by Slug](#retrieve-by-slug)\n\t\t- [Create](#create)\n\t\t- [Update](#update)\n\t\t- [Partial Update](#partial-update)\n\t\t- [Update order of related resources](#update-order-of-related-resources)\n\t\t- [Reverting to a previous instance](#reverting-to-a-previous-instance)\n\t\t- [Deletion](#deletion)\n\t\t- [Reverting a deletion](#reverting-a-deletion)\n\t+ [Versions](#versions)\n\t+ [Features](#features)\n\t+ [Supports](#supports)\n\t+ [Specifications](#specifications)\n\t+ [Sections](#sections)\n\t+ [Maturities](#maturities)\n\n##### [Browsers](#id2)[¶](#browsers)\n\nA **browser** is a brand of web client that has one or more versions. This follows most users’ understanding of browsers, i.e., `firefox` represents desktop Firefox, `safari` represents desktop Safari, and `firefox-mobile`\nrepresents Firefox Mobile.\n\nThe **browsers** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **slug** *(write-once)* - Unique, human-friendly slug\n\t+ **name** *(localized)* - Browser name\n\t+ **note** *(localized)* - Notes, intended for related data like\n\tOS, applicable device, engines, etc.\n* **links**\n\n\t+ **versions** *(many)* - Associated [versions](#versions), ordered roughly\n\tfrom earliest to latest. User can change the order.\n\t+ **history_current** *(one)* - Current [historical_browsers](history.html#historical-browsers). Can be\n\tset to a value from **history** to revert changes.\n\t+ **history** *(many)* - Associated [historical_browsers](history.html#historical-browsers) in time order\n\t(most recent first). Changes are ignored.\n\n###### [List](#id3)[¶](#list)\n\nTo request the paginated list of **browsers**:\n```\nGET /api/v1/browsers HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": [\n {\n \"id\": \"1\",\n \"slug\": \"android\",\n \"name\": {\n \"en\": \"Android\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"1\"\n ],\n \"history_current\": \"1\",\n \"versions\": [\n \"1\",\n \"2\",\n \"3\"\n ]\n }\n },\n {\n \"id\": \"2\",\n \"slug\": \"blackberry\",\n \"name\": {\n \"en\": \"BlackBerry\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"2\"\n ],\n \"history_current\": \"2\",\n \"versions\": [\n \"4\",\n \"5\",\n \"6\"\n ]\n }\n },\n {\n \"id\": \"3\",\n \"slug\": \"chrome\",\n \"name\": {\n \"en\": \"Chrome\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"3\"\n ],\n \"history_current\": \"3\",\n \"versions\": [\n \"7\",\n \"8\",\n \"9\"\n ]\n }\n },\n {\n \"id\": \"4\",\n \"slug\": \"chrome_for_android\",\n \"name\": {\n \"en\": \"Chrome for Android\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"4\"\n ],\n \"history_current\": \"4\",\n \"versions\": [\n \"10\",\n \"11\",\n \"12\"\n ]\n }\n },\n {\n \"id\": \"5\",\n \"slug\": \"chrome_mobile\",\n \"name\": {\n \"en\": \"Chrome Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"5\"\n ],\n \"history_current\": \"5\",\n \"versions\": [\n \"13\"\n ]\n }\n },\n {\n \"id\": \"6\",\n \"slug\": \"firefox\",\n \"name\": {\n \"en\": \"Firefox\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"6\"\n ],\n \"history_current\": \"6\",\n \"versions\": [\n \"14\",\n \"15\",\n \"16\",\n \"17\",\n \"18\"\n ]\n }\n },\n {\n \"id\": \"7\",\n \"slug\": \"firefox_mobile\",\n \"name\": {\n \"en\": \"Firefox Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"7\"\n ],\n \"history_current\": \"7\",\n \"versions\": [\n \"19\",\n \"20\",\n \"21\"\n ]\n }\n },\n {\n \"id\": \"8\",\n \"slug\": \"firefox_os\",\n \"name\": {\n \"en\": \"Firefox OS\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"8\"\n ],\n \"history_current\": \"8\",\n \"versions\": [\n \"22\",\n \"23\",\n \"24\"\n ]\n }\n },\n {\n \"id\": \"9\",\n \"slug\": \"ie_mobile\",\n \"name\": {\n \"en\": \"IE Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"9\"\n ],\n \"history_current\": \"9\",\n \"versions\": [\n \"25\",\n \"26\",\n \"27\"\n ]\n }\n },\n {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"Internet Explorer\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"10\"\n ],\n \"history_current\": \"10\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"31\",\n \"32\"\n ]\n }\n }\n ],\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n },\n \"meta\": {\n \"pagination\": {\n \"browsers\": {\n \"previous\": null,\n \"next\": \"https://browsercompat.org/api/v1/browsers?page=2\",\n \"count\": 15\n }\n }\n }\n}\n```\n###### [Retrieve by ID](#id4)[¶](#retrieve-by-id)\n\nTo request a single **browser** with a known ID:\n```\nGET /api/v1/browsers/6 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"6\",\n \"slug\": \"firefox\",\n \"name\": {\n \"en\": \"Firefox\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"6\"\n ],\n \"history_current\": \"6\",\n \"versions\": [\n \"14\",\n \"15\",\n \"16\",\n \"17\",\n \"18\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Retrieve by Slug](#id5)[¶](#retrieve-by-slug)\n\nTo request a **browser** by slug:\n```\nGET /api/v1/browsers?slug=firefox HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nThe response includes the desired browser, in list format:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": [\n {\n \"id\": \"6\",\n \"slug\": \"firefox\",\n \"name\": {\n \"en\": \"Firefox\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"6\"\n ],\n \"history_current\": \"6\",\n \"versions\": [\n \"14\",\n \"15\",\n \"16\",\n \"17\",\n \"18\"\n ]\n }\n }\n ],\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n },\n \"meta\": {\n \"pagination\": {\n \"browsers\": {\n \"previous\": null,\n \"next\": null,\n \"count\": 1\n }\n }\n }\n}\n```\n###### [Create](#id6)[¶](#create)\n\nCreating **browser** instances require authentication with create privileges.\nTo create a new **browser** instance, `POST` a representation with at least the required parameters. Some items (such as the `id` attribute and the\n`history_current` link) will be picked by the server, and will be ignored if included.\n\nHere’s an example of creating a **browser** instance:\n```\nPOST /api/v1/browsers HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 132 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: <KEY>\n```\n```\n{\n \"browsers\": {\n \"slug\": \"amazon-silk-mobile\",\n \"name\": {\n \"en\": \"Amazon Silk Mobile\"\n }\n }\n}\n```\nA sample response is:\n```\nHTTP/1.1 201 CREATED Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"16\",\n \"slug\": \"amazon-silk-mobile\",\n \"name\": {\n \"en\": \"Amazon Silk Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"16\"\n ],\n \"history_current\": \"16\",\n \"versions\": []\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\nThis, and other methods that change resources, will create a new [changeset](change-control.html#changesets),\nand associate the new [historical_browsers](history.html#historical-browsers) with that [changeset](change-control.html#changesets). To assign to an existing changeset, add it to the URI:\n```\nPOST /api/v1/browsers?changeset=4 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 220 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p<KEY>\n```\n```\n{\n \"browsers\": {\n \"slug\": \"nintendo-ds\",\n \"name\": {\n \"en\": \"Nintendo DS Browser\",\n \"ja\": \"\\u30cb\\u30f3\\u30c6\\u30f3\\u30c9\\u30fc\\uff24\\uff33\\u30d6\\u30e9\\u30a6\\u30b6\"\n }\n }\n}\n```\nA sample response is:\n```\nHTTP/1.1 201 CREATED Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"18\",\n \"slug\": \"nintendo-ds\",\n \"name\": {\n \"en\": \"Nintendo DS Browser\",\n \"ja\": \"ニンテンドーＤＳブラウザ\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"18\"\n ],\n \"history_current\": \"18\",\n \"versions\": []\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Update](#id7)[¶](#update)\n\nUpdating a **browser** instance require authentication with create privileges.\nSome items (such as the `id` attribute and `history` links) can not be changed, and will be ignored if included. A successful update will return a\n`200 OK`, add a new ID to the `history` links list, and update the\n`history_current` link.\n\nThis update changes the English name from “Internet Explorer” to “Microsoft Internet Explorer”:\n```\nPUT /api/v1/browsers/10 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 1010 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: <KEY>\n```\n```\n{\n \"browsers\": {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"Microsoft Internet Explorer\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"10\"\n ],\n \"history_current\": \"10\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"31\",\n \"32\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\nWith this response:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"Microsoft Internet Explorer\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"19\",\n \"10\"\n ],\n \"history_current\": \"19\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"31\",\n \"32\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Partial Update](#id8)[¶](#partial-update)\n\nAn update can just update the target fields. This is a further request to change the English name for the Internet Explorer browser.\n```\nPUT /api/v1/browsers/10 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 78 Content-Type: application/vnd.api+json Cookie: csrftoken=p7FqFyNp6hZS0FJYKyQxVmLrZILldjqn; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p7FqFyNp6hZS0FJYKyQxVmLrZILldjqn\n```\n```\n{\n \"browsers\": {\n \"name\": {\n \"en\": \"IE\"\n }\n }\n}\n```\nWith this response:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"IE\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"20\",\n \"19\",\n \"10\"\n ],\n \"history_current\": \"20\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"31\",\n \"32\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Update order of related resources](#id9)[¶](#update-order-of-related-resources)\n\nIn many cases, related resources (which appear in the “links” attribute”)\nare sorted by ID. In some cases, the order is significant, and is set on a related field. For example, **versions** for a **browser** are ordered by updating the order on the **browser** object:\n\nTo change just the [versions](#versions) order:\n```\nPUT /api/v1/browsers/10 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 205 Content-Type: application/vnd.api+json Cookie: csrftoken=p<KEY>0<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p<KEY>n\n```\n```\n{\n \"browsers\": {\n \"links\": {\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"32\",\n \"31\"\n ]\n }\n }\n}\n```\nWith this response:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"IE\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"21\",\n \"20\",\n \"19\",\n \"10\"\n ],\n \"history_current\": \"21\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"32\",\n \"31\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Reverting to a previous instance](#id10)[¶](#reverting-to-a-previous-instance)\n\nTo revert to an earlier instance, set the `history_current` link to a previous value. This resets the content and creates a new\n[historical_browsers](history.html#historical-browsers) object:\n```\nPUT /api/v1/browsers/10 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 92 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: <KEY>\n```\n```\n{\n \"browsers\": {\n \"links\": {\n \"history_current\": \"10\"\n }\n }\n}\n```\nWith this response:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"browsers\": {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"Internet Explorer\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"22\",\n \"21\",\n \"20\",\n \"19\",\n \"10\"\n ],\n \"history_current\": \"22\",\n \"versions\": [\n \"28\",\n \"29\",\n \"30\",\n \"32\",\n \"31\"\n ]\n }\n },\n \"links\": {\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"browsers.versions\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{browsers.versions}\"\n }\n }\n}\n```\n###### [Deletion](#id11)[¶](#deletion)\n\nTo delete a **browser**:\n```\nDELETE /api/v1/browsers/16 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 0 Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: <KEY>\n```\nThe response has no body:\n```\nHTTP/1.1 204 NO CONTENT\n```\n###### [Reverting a deletion](#id12)[¶](#reverting-a-deletion)\n\nReverting deletions is not currently possible.\n\n##### [Versions](#id13)[¶](#versions)\n\nA **version** is a specific release of a Browser.\n\nThe **versions** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **version** *(write-once)* - Version of browser. Numeric or text string,\n\tdepending on the status (see table below).\n\t+ **release_day** - Day that browser was released in [ISO 8601](http://en.wikipedia.org/wiki/ISO_8601) format, or\n\tnull if unknown.\n\t+ **retirement_day** - Approximate day the browser was “retired” (stopped\n\tbeing a current browser), in [ISO 8601](http://en.wikipedia.org/wiki/ISO_8601) format, or null if unknown.\n\t+ **status** - One of:\n\t`beta` (a numbered release candidate suggested for early adopters or\n\ttesters),\n\t`current` (current version, the preferred download or update for\n\tusers),\n\t`future` (a named but unnumbered planned future release),\n\t`retired-beta` (old beta version, replaced by a new beta or release),\n\t`retired` (old version, no longer the preferred download for any\n\tplatform), or\n\t`unknown` (status of this version is unknown)\n\t+ **release_notes_uri** *(localized)* - URI of release notes for this\n\tversion, or null if none.\n\t+ **note** *(localized)* - Engine, OS, etc. information, or null\n\t+ **order** *(read-only)* - The relative order amoung versions for this\n\tbrowser. The order can be changed on the **browser** resource.\n* **links**\n\n\t+ **browser** - The related **browser**\n\t+ **supports** *(many)* - Associated **supports**, in ID order. Changes\n\tare ignored; work on the **supports** to add, change, or remove.\n\t+ **history_current** *(one)* - Current **historical_versions**.\n\tSet to a value from **history** to revert to that version.\n\t+ **history** *(many)* - Associated **historical_versions**, in time\n\torder (most recent first). Changes are ignored.\n\nThe version is either a numeric value, such as `\"11.0\"`, or text, such as\n`\"Nightly\"`. The version format depends on the chosen status:\n\n| Status | Version |\n| --- | --- |\n| `beta` | numeric |\n| `current` | numeric or the text `\"current\"` |\n| `future` | text |\n| `retired-beta` | numeric |\n| `retired` | numeric |\n| `unknown` | numeric |\n\nTo get a single **version**:\n```\nGET /api/v1/versions/18 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"versions\": {\n \"id\": \"18\",\n \"version\": \"16.0\",\n \"release_day\": \"2012-10-09\",\n \"retirement_day\": \"2012-11-20\",\n \"status\": \"retired\",\n \"release_notes_uri\": {\n \"en\": \"https://developer.mozilla.org/en/Firefox/Releases/16\",\n \"de\": \"https://developer.mozilla.org/de/Firefox/Releases/16\",\n \"es\": \"https://developer.mozilla.org/es/Firefox/Releases/16\",\n \"fr\": \"https://developer.mozilla.org/fr/Firefox/Versions/16\",\n \"ja\": \"https://developer.mozilla.org/ja/Firefox/Releases/16\",\n \"ko\": \"https://developer.mozilla.org/ko/Firefox/Releases/16\",\n \"pl\": \"https://developer.mozilla.org/pl/Firefox/Releases/16\",\n \"pt-PT\": \"https://developer.mozilla.org/pt-PT/Firefox/Releases/16\",\n \"ru\": \"https://developer.mozilla.org/ru/Firefox/Releases/16\",\n \"zh-CN\": \"https://developer.mozilla.org/zh-CN/Firefox/Releases/16\",\n \"zh-TW\": \"https://developer.mozilla.org/zh-TW/Firefox/Releases/16\"\n },\n \"note\": null,\n \"order\": 4,\n \"links\": {\n \"browser\": \"6\",\n \"supports\": [\n \"12\",\n \"22\"\n ],\n \"history\": [\n \"18\"\n ],\n \"history_current\": \"18\"\n }\n },\n \"links\": {\n \"versions.browser\": {\n \"type\": \"browsers\",\n \"href\": \"https://browsercompat.org/api/v1/browsers/{versions.browser}\"\n },\n \"versions.supports\": {\n \"type\": \"supports\",\n \"href\": \"https://browsercompat.org/api/v1/supports/{versions.supports}\"\n },\n \"versions.history\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history}\"\n },\n \"versions.history_current\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history_current}\"\n }\n }\n}\n```\n##### [Features](#id14)[¶](#features)\n\nA **feature** is a web technology. This could be a precise technology, such as the value `cover` for the CSS `background-size` property. It could be a heirarchical group of related technologies, such as the CSS\n`background-size` property or the set of all CSS properties. Some features correspond to a page on [MDN](https://developer.mozilla.org), which will display the list of specifications and a browser compatibility table of the sub-features.\n\nThe **features** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **slug** *(write-once)* - Unique, human-friendly slug\n\t+ **mdn_uri** *(optional, localized)* - The URI of the language-specific\n\tMDN page that this feature was first scraped from. If the path contains\n\tunicode, it should be percent-encoded as in [RFC 3987](http://tools.ietf.org/html/rfc3987.html#section-3.1). May be used in\n\tUX or for debugging import scripts.\n\t+ **experimental** - True if a feature is considered experimental, such as\n\tbeing non-standard or part of an non-ratified spec.\n\t+ **standardized** - True if a feature is described in a standards-track\n\tspec, regardless of the spec’s maturity.\n\t+ **stable** - True if a feature is considered suitable for production\n\twebsites.\n\t+ **obsolete** - True if a feature should not be used in new development.\n\t+ **name** *(canonical or localized)* - Feature name. If the name is the\n\tcode used by a developer, then the value is a string, and should be\n\twrapped in a `<code>` block when displayed. If the name is a\n\tdescription of the feature, then the value is the available\n\ttranslations, including at least an `en` translation, and may include\n\tHTML markup. For example, `\"display\"` and `\"display: none\"` are\n\tcanonical names for the CSS display property and one of the values for\n\tthat property, while `\"Basic support\"`,\n\t`\"<code>none, inline</code> and <code>block</code>\"`, and\n\t`\"CSS Properties\"` are non-canonical names that should be translated.\n* **links**\n\n\t+ **sections** *(many)* - Associated [sections](#sections). Order can be changed by\n\tthe user.\n\t+ **supports** *(many)* - Associated [supports](#supports), Order is in ID order,\n\tchanges are ignored.\n\t+ **parent** *(one or null)* - The feature one level up, or null\n\tif top-level. Can be changed by user.\n\t+ **children** *(many)* - The features that have this feature as parent, in\n\tdisplay order. Can be an empty list, for “leaf” features. Can be\n\tre-ordered by the user.\n\t+ **history_current** *(one)* - Current [historical_features](history.html#historical-features). User can\n\tset to a valid **history** to revert to that version.\n\t+ **history** *(many)* - Associated [historical_features](history.html#historical-features), in time order\n\t(most recent first). Changes are ignored.\n\nTo get a specific **feature** (in this case, a leaf feature with a translated name):\n```\nGET /api/v1/features/13 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"features\": {\n \"id\": \"13\",\n \"slug\": \"web-css-transform-three-value-syntax\",\n \"mdn_uri\": null,\n \"experimental\": false,\n \"standardized\": true,\n \"stable\": true,\n \"obsolete\": false,\n \"name\": {\n \"en\": \"Three-value syntax\",\n \"es\": \"Sintaxis con tres valores\",\n \"ja\": \"3-値構文\"\n },\n \"links\": {\n \"sections\": [],\n \"supports\": [\n \"20\",\n \"21\",\n \"22\",\n \"23\",\n \"24\",\n \"25\",\n \"26\"\n ],\n \"parent\": \"10\",\n \"children\": [],\n \"history_current\": \"13\",\n \"history\": [\n \"13\"\n ]\n }\n },\n \"links\": {\n \"features.sections\": {\n \"type\": \"sections\",\n \"href\": \"https://browsercompat.org/api/v1/sections/{features.sections}\"\n },\n \"features.supports\": {\n \"type\": \"supports\",\n \"href\": \"https://browsercompat.org/api/v1/supports/{features.supports}\"\n },\n \"features.parent\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.parent}\"\n },\n \"features.children\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.children}\"\n },\n \"features.history_current\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history_current}\"\n },\n \"features.history\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history}\"\n }\n }\n}\n```\nHere’s an example of a branch feature with a canonical name (the parent of the previous example):\n```\nGET /api/v1/features/10 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"features\": {\n \"id\": \"10\",\n \"slug\": \"web-css-transform-origin\",\n \"mdn_uri\": {\n \"en\": \"https://developer.mozilla.org/en-US/docs/Web/CSS/transform-origin\",\n \"es\": \"https://developer.mozilla.org/es/docs/Web/CSS/transform-origin\",\n \"fr\": \"https://developer.mozilla.org/fr/docs/Web/CSS/transform-origin\",\n \"ja\": \"https://developer.mozilla.org/ja/docs/Web/CSS/transform-origin\"\n },\n \"experimental\": false,\n \"standardized\": true,\n \"stable\": true,\n \"obsolete\": false,\n \"name\": \"transform-origin\",\n \"links\": {\n \"sections\": [\n \"4\"\n ],\n \"supports\": [],\n \"parent\": \"2\",\n \"children\": [\n \"11\",\n \"13\"\n ],\n \"history_current\": \"10\",\n \"history\": [\n \"10\"\n ]\n }\n },\n \"links\": {\n \"features.sections\": {\n \"type\": \"sections\",\n \"href\": \"https://browsercompat.org/api/v1/sections/{features.sections}\"\n },\n \"features.supports\": {\n \"type\": \"supports\",\n \"href\": \"https://browsercompat.org/api/v1/supports/{features.supports}\"\n },\n \"features.parent\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.parent}\"\n },\n \"features.children\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.children}\"\n },\n \"features.history_current\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history_current}\"\n },\n \"features.history\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history}\"\n }\n }\n}\n```\n##### [Supports](#id15)[¶](#supports)\n\nA **support** is an assertion that a particular Version of a Browser supports\n(or does not support) a feature.\n\nThe **support** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **support** - Assertion of support of the [version](#versions) for the\n\t[feature](#features), one of `\"yes\"`, `\"no\"`, `\"partial\"`, or `\"unknown\"`\n\t+ **prefix** - Prefix used to enable support, such as “moz”\n\t+ **prefix_mandatory** - True if the prefix is required\n\t+ **alternate_name** - An alternate name associated with this feature,\n\tsuch as `\"RTCPeerConnectionIdentityEvent\"`\n\t+ **alternate_name_mandatory** - True if the alternate name is required\n\t+ **requires_config** - A configuration string\n\trequired to enable the feature, such as\n\t`\"media.peerconnection.enabled=on\"`\n\t+ **default_config** - The configuration string in the shipping\n\tbrowser, such as `\"media.peerconnection.enabled=off\"`\n\t+ **protected** - True if the feature requires additional steps to enable\n\tin order to protect the user’s security or privacy, such as geolocation\n\tand the Bluetooth API.\n\t+ **note** *(localized)* - Note on support, designed for\n\tdisplay after a compatibility table, can contain HTML\n* **links**\n\n\t+ **version** *(one)* - The associated [version](#versions). Cannot be changed by\n\tthe user after creation.\n\t+ **feature** *(one)* - The associated [feature](#features). Cannot be changed by\n\tthe user after creation. The version and feature combo must be unique.\n\t+ **history_current** *(one)* - Current\n\t[historical_supports](history.html#historical-supports). Can be changed to a valid\n\t**history** to revert to that version.\n\t+ **history** *(many)* - Associated [historical_supports](history.html#historical-supports)\n\tin time order (most recent first). Changes are ignored.\n\nTo get a single **support**:\n```\nGET /api/v1/supports/22 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"supports\": {\n \"id\": \"22\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"18\",\n \"feature\": \"13\",\n \"history_current\": \"22\",\n \"history\": [\n \"22\"\n ]\n }\n },\n \"links\": {\n \"supports.version\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{supports.version}\"\n },\n \"supports.feature\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{supports.feature}\"\n },\n \"supports.history_current\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history_current}\"\n },\n \"supports.history\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history}\"\n }\n }\n}\n```\n##### [Specifications](#id16)[¶](#specifications)\n\nA **specification** is a standards document that specifies a web technology.\n\nThe **specification** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **slug** - Unique, human-friendly key\n\t+ **mdn_key** - Key used in the KumaScript macros [SpecName](https://developer.mozilla.org/en-US/docs/Template:SpecName) and [Spec2](https://developer.mozilla.org/en-US/docs/Template:Spec2).\n\t+ **name** *(localized)* - Specification name\n\t+ **uri** *(localized)* - Specification URI, without subpath and anchor\n* **links**\n\n\t+ **maturity** *(one)* - Associated [maturity](#maturities).\n\tCan be changed by the user.\n\t+ **sections** *(many)* - Associated [sections](#sections). The order can be changed\n\tby the user.\n\t+ **history_current** *(one)* - Current\n\t[historical_specifications](history.html#historical-specifications). Can be changed to a valid\n\t**history** to revert to that version.\n\t+ **history** *(many)* - Associated [historical_specifications](history.html#historical-specifications)\n\tin time order (most recent first). Changes are ignored.\n\nTo get a single **specification**:\n```\nGET /api/v1/specifications/2 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"specifications\": {\n \"id\": \"2\",\n \"slug\": \"css2_1\",\n \"mdn_key\": \"CSS2.1\",\n \"name\": {\n \"en\": \"CSS Level 2 (Revision 1)\"\n },\n \"uri\": {\n \"en\": \"http://www.w3.org/TR/CSS2/\"\n },\n \"links\": {\n \"maturity\": \"1\",\n \"sections\": [\n \"2\"\n ],\n \"history_current\": \"2\",\n \"history\": [\n \"2\"\n ]\n }\n },\n \"links\": {\n \"specifications.maturity\": {\n \"type\": \"maturities\",\n \"href\": \"https://browsercompat.org/api/v1/maturities/{specifications.maturity}\"\n },\n \"specifications.sections\": {\n \"type\": \"sections\",\n \"href\": \"https://browsercompat.org/api/v1/sections/{specifications.sections}\"\n },\n \"specifications.history_current\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{specifications.history_current}\"\n },\n \"specifications.history\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{specifications.history}\"\n }\n }\n}\n```\n##### [Sections](#id17)[¶](#sections)\n\nA **section** refers to a specific area of a [specification](#specifications) document.\n\nThe **section** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **number** *(optional, localized)* - The section number\n\t+ **name** *(localized)* - Section name\n\t+ **subpath** *(localized, optional)* - A subpage (possibly with an\n\t#anchor) to get to the subsection in the doc. Can be empty string.\n\t+ **note** *(localized, optional)* - Notes for this section\n* **links**\n\n\t+ **specification** *(one)* - The [specification](#specifications). Can be changed by\n\tthe user.\n\t+ **features** *(many)* - The associated [features](#features). In ID order,\n\tchanges are ignored.\n\t+ **history_current** *(one)* - Current\n\t[historical_sections](history.html#historical-sections). Can be changed to a valid\n\t**history** to revert to that version.\n\t+ **history** *(many)* - Associated [historical_sections](history.html#historical-sections)\n\tin time order (most recent first). Changes are ignored.\n\nTo get a single **section**:\n```\nGET /api/v1/sections/3 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"sections\": {\n \"id\": \"3\",\n \"number\": {\n \"en\": \"16\"\n },\n \"name\": {\n \"en\": \"The float property\"\n },\n \"subpath\": {\n \"en\": \"#the-float-property\"\n },\n \"note\": {\n \"en\": \"Lots of new values, not all clearly defined yet. Any differences in behavior unrelated to new features are expected to be unintentional; please report.\"\n },\n \"links\": {\n \"specification\": \"3\",\n \"features\": [\n \"5\"\n ],\n \"history_current\": \"3\",\n \"history\": [\n \"3\"\n ]\n }\n },\n \"links\": {\n \"sections.specification\": {\n \"type\": \"specifications\",\n \"href\": \"https://browsercompat.org/api/v1/specifications/{sections.specification}\"\n },\n \"sections.features\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{sections.features}\"\n },\n \"sections.history_current\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{sections.history_current}\"\n },\n \"sections.history\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{sections.history}\"\n }\n }\n}\n```\n##### [Maturities](#id18)[¶](#maturities)\n\nA **maturity** refers to the maturity of a [specification](#specifications) document.\n\nThe **maturity** representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **slug** - A human-friendly identifier for this maturity. When applicabile,\n\tit match the key in the KumaScript macro [Spec2](https://developer.mozilla.org/en-US/docs/Template:Spec2)\n\t+ **name** *(localized)* - Status name\n* **links**\n\n\t+ **specifications** *(many)* - Associated [specifications](#specifications). In ID order,\n\tchanges are ignored.\n\t+ **history_current** *(one)* - Current\n\t[historical_maturities](history.html#historical-maturities). Can be changed to a valid\n\t**history** to revert to that version.\n\t+ **history** *(many)* - Associated [historical_maturities](history.html#historical-maturities)\n\tin time order (most recent first). Changes are ignored.\n\nTo get a single **maturity**:\n```\nGET /api/v1/maturities/1 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"maturities\": {\n \"id\": \"1\",\n \"slug\": \"REC\",\n \"name\": {\n \"en\": \"Recommendation\",\n \"de\": \"Empfehlung\",\n \"ja\": \"勧告\",\n \"ru\": \"Рекомендация\"\n },\n \"links\": {\n \"specifications\": [\n \"1\",\n \"2\"\n ],\n \"history_current\": \"1\",\n \"history\": [\n \"1\"\n ]\n }\n },\n \"links\": {\n \"maturities.specifications\": {\n \"type\": \"specifications\",\n \"href\": \"https://browsercompat.org/api/v1/specifications/{maturities.specifications}\"\n },\n \"maturities.history_current\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{maturities.history_current}\"\n },\n \"maturities.history\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{maturities.history}\"\n }\n }\n}\n```\n#### Change Control Resources[¶](#change-control-resources)\n\nChange Control Resources help manage changes to resources.\n\n##### Users[¶](#users)\n\nA **user** represents a person or process that creates, changes, or deletes a resource.\n\nThe representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **username** - The user’s email or ID\n\t+ **created** *(server selected)* - Time that the account was created, in\n\t[ISO 8601](http://en.wikipedia.org/wiki/ISO_8601) format.\n\t+ **agreement** - The version of the contribution agreement the\n\tuser has accepted. “0” for not agreed, “1” for first version, etc.\n\t+ **permissions** - A list of permissions. Permissions include\n\t`\"change-resource\"` (add or change any resource except [users](#users) or\n\thistory resources),\n\t`\"delete-resource\"` (delete any resource)\n\t`\"import-mdn\"` (setup import of an MDN page)\n* **links**\n\n\t+ **changesets** *(many)* - Associated [changesets](#changesets), in ID order, changes\n\tare ignored.\n\nTo get a single **user** representation:\n```\nGET /api/v1/users/1 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"users\": {\n \"id\": \"1\",\n \"username\": \"user\",\n \"created\": \"2015-04-20T18:06:48.567514Z\",\n \"agreement\": 0,\n \"permissions\": [\n \"change-resource\",\n \"delete-resource\"\n ],\n \"links\": {\n \"changesets\": [\n \"1\"\n ]\n }\n },\n \"links\": {\n \"users.changesets\": {\n \"type\": \"changesets\",\n \"href\": \"https://browsercompat.org/api/v1/changesets/{users.changesets}\"\n }\n }\n}\n```\nIf a client is authenticated, the logged-in user’s account can be retrieved with:\n```\nGET /api/v1/users/me HTTP/1.1 Host: browsersupports.org Accept: application/vnd.api+json\n```\n##### Changesets[¶](#changesets)\n\nA **changeset** collects history resources into a logical unit, allowing for faster reversions and better history display. The **changeset** can be auto-created through a `POST`, `PUT`, or `DELETE` to a resource, or it can be created independently and specified by adding `changeset=<ID>` URI parameter (i.e., `PUT /browsers/15?changeset=73`).\n\nThe representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **created** *(server selected)* - When the changeset was created, in\n\t[ISO 8601](http://en.wikipedia.org/wiki/ISO_8601) format.\n\t+ **modified** *(server selected)* - When the changeset was last modified,\n\tin [ISO 8601](http://en.wikipedia.org/wiki/ISO_8601) format.\n\t+ **target_resource_type** *(write-once, optional)* - The name of the\n\tprimary resource for this changeset, for example “browsers”, “versions”,\n\tetc.\n\t+ **target_resource_id** *(write-once, optional)* - The ID of the primary\n\tresource for this changeset.\n\t+ **closed** - True if the changeset is closed to new changes.\n\tAuto-created changesets are auto-closed, and cache invalidation is\n\tdelayed until manually created changesets are closed.\n* **links**\n\n\t+ **user** *(one)* - The user who initiated this changeset, can not be\n\tchanged.\n\t+ **historical_browsers** *(many)* - Associated [historical_browsers](history.html#historical-browsers), in ID\n\torder, changes are ignored.\n\t+ **historical_features** *(many)* - Associated [historical_features](history.html#historical-features),\n\tin ID order, changes are ignored.\n\t+ **historical_maturities** *(many)* - Associated [historical_maturities](history.html#historical-maturities),\n\tin ID order, changes are ignored.\n\t+ **historical_sections** *(many)* - Associated [historical_sections](history.html#historical-sections), in ID\n\torder, changes are ignored.\n\t+ **historical_specificationss** *(many)* - Associated\n\t[historical_specificationss](history.html#historical-specificationss), in ID order, changes are ignored.\n\t+ **historical_supports** *(many)* - Associated [historical_supports](history.html#historical-supports), in ID\n\torder, changes are ignored.\n\t+ **historical_versions** *(many)* - Associated\n\t[historical_versions](history.html#historical-versions), in ID order, changes are ignored.\n\nTo get a single **changeset** representation:\n```\nGET /api/v1/changesets/2 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"changesets\": {\n \"id\": \"2\",\n \"created\": \"2015-04-20T18:22:47.046692Z\",\n \"modified\": \"2015-04-20T18:22:47.056433Z\",\n \"closed\": true,\n \"target_resource_type\": null,\n \"target_resource_id\": null,\n \"links\": {\n \"user\": \"1\",\n \"historical_browsers\": [\n \"16\"\n ],\n \"historical_features\": [],\n \"historical_maturities\": [],\n \"historical_sections\": [],\n \"historical_specifications\": [],\n \"historical_supports\": [],\n \"historical_versions\": []\n }\n },\n \"links\": {\n \"changesets.user\": {\n \"type\": \"users\",\n \"href\": \"https://browsercompat.org/api/v1/users/{changesets.user}\"\n },\n \"changesets.historical_browsers\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{changesets.historical_browsers}\"\n },\n \"changesets.historical_features\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{changesets.historical_features}\"\n },\n \"changesets.historical_maturities\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{changesets.historical_maturities}\"\n },\n \"changesets.historical_sections\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{changesets.historical_sections}\"\n },\n \"changesets.historical_specifications\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{changesets.historical_specifications}\"\n },\n \"changesets.historical_supports\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{changesets.historical_supports}\"\n },\n \"changesets.historical_versions\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{changesets.historical_versions}\"\n }\n }\n}\n```\n#### History Resources[¶](#history-resources)\n\nHistory Resources are created when a Resource is created, updated, or deleted.\nBy navigating the history chain, a caller can see the changes of a resource over time.\n\nAll history representations are similar, so one example should be enough to determine the pattern.\n\n##### Historical Browsers[¶](#historical-browsers)\n\nA **historical_browser** resource represents the state of a [browser](resources.html#browsers) at a point in time, and who is responsible for that state. The representation includes:\n\n* **attributes**\n\n\t+ **id** *(server selected)* - Database ID\n\t+ **date** *(server selected)* - The time of this change in [ISO 8601](http://en.wikipedia.org/wiki/ISO_8601)\n\t+ **event** *(server selected)* - The type of event, one of `\"created\"`,\n\t`\"changed\"`, or `\"deleted\"`\n\t+ **browsers** - The **browsers** representation at this point in time\n* **links**\n\n\t+ **browser** *(one)* - Associated [browser](resources.html#browsers), can not be changed\n\t+ **changeset** *(one)* - Associated [changeset](change-control#changesets), can not be changed.\n\nTo get a single **historical_browsers** representation:\n```\nGET /api/v1/historical_browsers/6 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"historical_browsers\": {\n \"id\": \"6\",\n \"date\": \"2015-04-20T18:44:09.905824Z\",\n \"event\": \"created\",\n \"browsers\": {\n \"id\": \"6\",\n \"slug\": \"firefox\",\n \"name\": {\n \"en\": \"Firefox\"\n },\n \"note\": null,\n \"links\": {\n \"history_current\": \"6\"\n }\n },\n \"links\": {\n \"changeset\": \"1\",\n \"browser\": \"6\"\n }\n },\n \"links\": {\n \"historical_browsers.changeset\": {\n \"type\": \"changesets\",\n \"href\": \"https://browsercompat.org/api/v1/changesets/{historical_browsers.changeset}\"\n },\n \"historical_browsers.browser\": {\n \"type\": \"browsers\",\n \"href\": \"https://browsercompat.org/api/v1/browsers/{historical_browsers.browser}\"\n }\n }\n}\n```\n##### Historical Versions[¶](#historical-versions)\n\nA **historical_versions** resource represents the state of a\n[version](resources.html#versions) at a point in time, and who is responsible for that representation. See [historical_browsers](#historical-browsers) and [versions](resources.html#versions) for an idea of the represention.\n\n##### Historical Features[¶](#historical-features)\n\nA **historical_features** resource represents the state of a [feature](resources.html#features) at a point in time, and who is responsible for that representation. See\n[historical_browsers](#historical-browsers) and [features](resources.html#features) for an idea of the represention.\n\n##### Historical Sections[¶](#historical-sections)\n\nA **historical_sections** resource represents the state of a [section](resources.html#sections) at a point in time, and who is responsible for that representation. See\n[historical_browsers](#historical-browsers) and [sections](resources.html#sections) for an idea of the represention.\n\n##### Historical Specifications[¶](#historical-specifications)\n\nA **historical_specifications** resource represents the state of a [specification](resources.html#specifications) at a point in time, and who is responsible for that representation. See\n[historical_browsers](#historical-browsers) and [specifications](resources.html#specifications) for an idea of the represention.\n\n##### Historical Supports[¶](#historical-supports)\n\nA **historical_supports** resource represents the state of a [support](resources.html#supports) at a point in time, and who is responsible for that representation. See\n[historical_browsers](#historical-browsers) and [supports](resources.html#supports) for an idea of the represention.\n\n##### Historical Maturities[¶](#historical-maturities)\n\nA **historical_maturities** resource represents the state of a [maturity](resources.html#maturities) at a point in time, and who is responsible for that representation. See\n[historical_browsers](#historical-browsers) and [maturities](resources.html#maturities) for an idea of the represention.\n\n#### Views[¶](#views)\n\nA **View** is a combination of resources for a particular presentation. It is suitable for anonymous viewing of content.\n\nIt is possible that views are unnecessary, and could be constructed by supporting optional parts of the JSON API spec, such as [Inclusion of Linked Resources](http://jsonapi.org/format/#fetching-includes). These views are written as if they are aliases for a fully-fleshed implementation of JSON API.\n\n##### View a Feature[¶](#view-a-feature)\n\nThis view collects the data for a [feature](resources.html#features), including the related resources needed to display it on MDN.\n\nHere is a simple example, the view for the CSS property [float](https://developer.mozilla.org/en-US/docs/Web/CSS/float):\n```\nGET /api/v1/view_features/5 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json\n```\nA sample response is:\n```\nHTTP/1.1 200 OK Content-Type: application/vnd.api+json\n```\n```\n{\n \"features\": {\n \"id\": \"5\",\n \"slug\": \"web-css-float\",\n \"mdn_uri\": {\n \"en\": \"https://developer.mozilla.org/en-US/docs/Web/CSS/float\",\n \"de\": \"https://developer.mozilla.org/de/docs/Web/CSS/float\",\n \"es\": \"https://developer.mozilla.org/es/docs/Web/CSS/float\",\n \"ja\": \"https://developer.mozilla.org/ja/docs/Web/CSS/float\",\n \"ru\": \"https://developer.mozilla.org/ru/docs/Web/CSS/float\"\n },\n \"experimental\": false,\n \"standardized\": true,\n \"stable\": true,\n \"obsolete\": false,\n \"name\": \"float\",\n \"links\": {\n \"sections\": [\n \"1\",\n \"2\",\n \"3\"\n ],\n \"supports\": [],\n \"parent\": \"2\",\n \"children\": [\n \"6\"\n ],\n \"history_current\": \"5\",\n \"history\": [\n \"5\"\n ]\n }\n },\n \"links\": {\n \"features.sections\": {\n \"type\": \"sections\",\n \"href\": \"https://browsercompat.org/api/v1/sections/{features.sections}\"\n },\n \"features.supports\": {\n \"type\": \"supports\",\n \"href\": \"https://browsercompat.org/api/v1/supports/{features.supports}\"\n },\n \"features.parent\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.parent}\"\n },\n \"features.children\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{features.children}\"\n },\n \"features.history_current\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history_current}\"\n },\n \"features.history\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{features.history}\"\n },\n \"browsers.history\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history}\"\n },\n \"browsers.history_current\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{browsers.history_current}\"\n },\n \"versions.browser\": {\n \"type\": \"browsers\",\n \"href\": \"https://browsercompat.org/api/v1/browsers/{versions.browser}\"\n },\n \"versions.history\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history}\"\n },\n \"versions.history_current\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history_current}\"\n },\n \"supports.version\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{supports.version}\"\n },\n \"supports.feature\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{supports.feature}\"\n },\n \"supports.history_current\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history_current}\"\n },\n \"supports.history\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history}\"\n },\n \"maturities.history_current\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{maturities.history_current}\"\n },\n \"maturities.history\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{maturities.history}\"\n },\n \"specifications.maturity\": {\n \"type\": \"maturities\",\n \"href\": \"https://browsercompat.org/api/v1/maturities/{specifications.maturity}\"\n },\n \"specifications.history_current\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{specifications.history_current}\"\n },\n \"specifications.history\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{specifications.history}\"\n },\n \"sections.specification\": {\n \"type\": \"specifications\",\n \"href\": \"https://browsercompat.org/api/v1/specifications/{sections.specification}\"\n },\n \"sections.history_current\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{sections.history_current}\"\n },\n \"sections.history\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{sections.history}\"\n }\n },\n \"linked\": {\n \"browsers\": [\n {\n \"id\": \"1\",\n \"slug\": \"android\",\n \"name\": {\n \"en\": \"Android\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"1\"\n ],\n \"history_current\": \"1\"\n }\n },\n {\n \"id\": \"2\",\n \"slug\": \"blackberry\",\n \"name\": {\n \"en\": \"BlackBerry\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"2\"\n ],\n \"history_current\": \"2\"\n }\n },\n {\n \"id\": \"3\",\n \"slug\": \"chrome\",\n \"name\": {\n \"en\": \"Chrome\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"3\"\n ],\n \"history_current\": \"3\"\n }\n },\n {\n \"id\": \"6\",\n \"slug\": \"firefox\",\n \"name\": {\n \"en\": \"Firefox\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"6\"\n ],\n \"history_current\": \"6\"\n }\n },\n {\n \"id\": \"7\",\n \"slug\": \"firefox_mobile\",\n \"name\": {\n \"en\": \"Firefox Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"7\"\n ],\n \"history_current\": \"7\"\n }\n },\n {\n \"id\": \"9\",\n \"slug\": \"ie_mobile\",\n \"name\": {\n \"en\": \"IE Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"9\"\n ],\n \"history_current\": \"9\"\n }\n },\n {\n \"id\": \"10\",\n \"slug\": \"internet_explorer\",\n \"name\": {\n \"en\": \"Internet Explorer\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"22\",\n \"21\",\n \"20\",\n \"19\",\n \"10\"\n ],\n \"history_current\": \"22\"\n }\n },\n {\n \"id\": \"11\",\n \"slug\": \"opera\",\n \"name\": {\n \"en\": \"Opera\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"11\"\n ],\n \"history_current\": \"11\"\n }\n },\n {\n \"id\": \"14\",\n \"slug\": \"safari\",\n \"name\": {\n \"en\": \"Safari\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"14\"\n ],\n \"history_current\": \"14\"\n }\n },\n {\n \"id\": \"15\",\n \"slug\": \"safari_mobile\",\n \"name\": {\n \"en\": \"Safari Mobile\"\n },\n \"note\": null,\n \"links\": {\n \"history\": [\n \"15\"\n ],\n \"history_current\": \"15\"\n }\n }\n ],\n \"versions\": [\n {\n \"id\": \"2\",\n \"version\": \"1.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"1\",\n \"history\": [\n \"2\"\n ],\n \"history_current\": \"2\"\n }\n },\n {\n \"id\": \"4\",\n \"version\": \"current\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"current\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 0,\n \"links\": {\n \"browser\": \"2\",\n \"history\": [\n \"4\"\n ],\n \"history_current\": \"4\"\n }\n },\n {\n \"id\": \"8\",\n \"version\": \"1.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"3\",\n \"history\": [\n \"8\"\n ],\n \"history_current\": \"8\"\n }\n },\n {\n \"id\": \"15\",\n \"version\": \"1.0\",\n \"release_day\": \"2004-11-09\",\n \"retirement_day\": \"2005-11-29\",\n \"status\": \"retired\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"6\",\n \"history\": [\n \"15\"\n ],\n \"history_current\": \"15\"\n }\n },\n {\n \"id\": \"20\",\n \"version\": \"1.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"7\",\n \"history\": [\n \"20\"\n ],\n \"history_current\": \"20\"\n }\n },\n {\n \"id\": \"27\",\n \"version\": \"6.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 2,\n \"links\": {\n \"browser\": \"9\",\n \"history\": [\n \"27\"\n ],\n \"history_current\": \"27\"\n }\n },\n {\n \"id\": \"29\",\n \"version\": \"4.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"10\",\n \"history\": [\n \"29\"\n ],\n \"history_current\": \"29\"\n }\n },\n {\n \"id\": \"34\",\n \"version\": \"7.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"11\",\n \"history\": [\n \"34\"\n ],\n \"history_current\": \"34\"\n }\n },\n {\n \"id\": \"42\",\n \"version\": \"1.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"14\",\n \"history\": [\n \"42\"\n ],\n \"history_current\": \"42\"\n }\n },\n {\n \"id\": \"44\",\n \"version\": \"5.1\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 3,\n \"links\": {\n \"browser\": \"14\",\n \"history\": [\n \"44\"\n ],\n \"history_current\": \"44\"\n }\n },\n {\n \"id\": \"46\",\n \"version\": \"1.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"unknown\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 1,\n \"links\": {\n \"browser\": \"15\",\n \"history\": [\n \"46\"\n ],\n \"history_current\": \"46\"\n }\n }\n ],\n \"supports\": [\n {\n \"id\": \"1\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"2\",\n \"feature\": \"6\",\n \"history_current\": \"1\",\n \"history\": [\n \"1\"\n ]\n }\n },\n {\n \"id\": \"2\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"8\",\n \"feature\": \"6\",\n \"history_current\": \"2\",\n \"history\": [\n \"2\"\n ]\n }\n },\n {\n \"id\": \"3\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"15\",\n \"feature\": \"6\",\n \"history_current\": \"3\",\n \"history\": [\n \"3\"\n ]\n }\n },\n {\n \"id\": \"4\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"20\",\n \"feature\": \"6\",\n \"history_current\": \"4\",\n \"history\": [\n \"4\"\n ]\n }\n },\n {\n \"id\": \"5\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"27\",\n \"feature\": \"6\",\n \"history_current\": \"5\",\n \"history\": [\n \"5\"\n ]\n }\n },\n {\n \"id\": \"6\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"29\",\n \"feature\": \"6\",\n \"history_current\": \"6\",\n \"history\": [\n \"6\"\n ]\n }\n },\n {\n \"id\": \"7\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"34\",\n \"feature\": \"6\",\n \"history_current\": \"7\",\n \"history\": [\n \"7\"\n ]\n }\n },\n {\n \"id\": \"8\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"42\",\n \"feature\": \"6\",\n \"history_current\": \"8\",\n \"history\": [\n \"8\"\n ]\n }\n },\n {\n \"id\": \"9\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"44\",\n \"feature\": \"6\",\n \"history_current\": \"9\",\n \"history\": [\n \"9\"\n ]\n }\n },\n {\n \"id\": \"10\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"46\",\n \"feature\": \"6\",\n \"history_current\": \"10\",\n \"history\": [\n \"10\"\n ]\n }\n },\n {\n \"id\": \"27\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"4\",\n \"feature\": \"6\",\n \"history_current\": \"27\",\n \"history\": [\n \"27\"\n ]\n }\n }\n ],\n \"maturities\": [\n {\n \"id\": \"1\",\n \"slug\": \"REC\",\n \"name\": {\n \"en\": \"Recommendation\",\n \"de\": \"Empfehlung\",\n \"ja\": \"勧告\",\n \"ru\": \"Рекомендация\"\n },\n \"links\": {\n \"history_current\": \"1\",\n \"history\": [\n \"1\"\n ]\n }\n },\n {\n \"id\": \"2\",\n \"slug\": \"WD\",\n \"name\": {\n \"en\": \"Working Draft\",\n \"de\": \"Arbeitsentwurf\",\n \"ja\": \"草案\",\n \"ru\": \"Рабочий черновик\"\n },\n \"links\": {\n \"history_current\": \"2\",\n \"history\": [\n \"2\"\n ]\n }\n }\n ],\n \"specifications\": [\n {\n \"id\": \"1\",\n \"slug\": \"css1\",\n \"mdn_key\": \"CSS1\",\n \"name\": {\n \"en\": \"CSS Level 1\"\n },\n \"uri\": {\n \"en\": \"http://www.w3.org/TR/CSS1/\"\n },\n \"links\": {\n \"maturity\": \"1\",\n \"history_current\": \"1\",\n \"history\": [\n \"1\"\n ]\n }\n },\n {\n \"id\": \"2\",\n \"slug\": \"css2_1\",\n \"mdn_key\": \"CSS2.1\",\n \"name\": {\n \"en\": \"CSS Level 2 (Revision 1)\"\n },\n \"uri\": {\n \"en\": \"http://www.w3.org/TR/CSS2/\"\n },\n \"links\": {\n \"maturity\": \"1\",\n \"history_current\": \"2\",\n \"history\": [\n \"2\"\n ]\n }\n },\n {\n \"id\": \"3\",\n \"slug\": \"css3_box\",\n \"mdn_key\": \"CSS3 Box\",\n \"name\": {\n \"en\": \"CSS Basic Box Model\"\n },\n \"uri\": {\n \"en\": \"http://dev.w3.org/csswg/css3-box/\"\n },\n \"links\": {\n \"maturity\": \"2\",\n \"history_current\": \"3\",\n \"history\": [\n \"3\"\n ]\n }\n }\n ],\n \"sections\": [\n {\n \"id\": \"1\",\n \"number\": {\n \"en\": \"5.5.25\"\n },\n \"name\": {\n \"en\": \"'float'\"\n },\n \"subpath\": {\n \"en\": \"#float\"\n },\n \"note\": {\n \"en\": \"Initial definition.\"\n },\n \"links\": {\n \"specification\": \"1\",\n \"history_current\": \"1\",\n \"history\": [\n \"1\"\n ]\n }\n },\n {\n \"id\": \"2\",\n \"number\": {\n \"en\": \"9.5.1\"\n },\n \"name\": {\n \"en\": \"Positioning the float: the 'float' property\"\n },\n \"subpath\": {\n \"en\": \"visuren.html#float-position\"\n },\n \"note\": {\n \"en\": \"No change.\"\n },\n \"links\": {\n \"specification\": \"2\",\n \"history_current\": \"2\",\n \"history\": [\n \"2\"\n ]\n }\n },\n {\n \"id\": \"3\",\n \"number\": {\n \"en\": \"16\"\n },\n \"name\": {\n \"en\": \"The float property\"\n },\n \"subpath\": {\n \"en\": \"#the-float-property\"\n },\n \"note\": {\n \"en\": \"Lots of new values, not all clearly defined yet. Any differences in behavior unrelated to new features are expected to be unintentional; please report.\"\n },\n \"links\": {\n \"specification\": \"3\",\n \"history_current\": \"3\",\n \"history\": [\n \"3\"\n ]\n }\n }\n ],\n \"features\": [\n {\n \"id\": \"6\",\n \"slug\": \"web-css-float_basic-support\",\n \"mdn_uri\": null,\n \"experimental\": false,\n \"standardized\": true,\n \"stable\": true,\n \"obsolete\": false,\n \"name\": {\n \"en\": \"Basic Support\",\n \"ja\": \"基本サポート\"\n },\n \"links\": {\n \"sections\": [],\n \"supports\": [\n \"1\",\n \"2\",\n \"3\",\n \"4\",\n \"5\",\n \"6\",\n \"7\",\n \"8\",\n \"9\",\n \"10\",\n \"27\"\n ],\n \"parent\": \"5\",\n \"children\": [],\n \"history_current\": \"6\",\n \"history\": [\n \"6\"\n ]\n }\n }\n ]\n },\n \"meta\": {\n \"compat_table\": {\n \"supports\": {\n \"5\": {},\n \"6\": {\n \"1\": [\n \"1\"\n ],\n \"2\": [\n \"27\"\n ],\n \"3\": [\n \"2\"\n ],\n \"6\": [\n \"3\"\n ],\n \"7\": [\n \"4\"\n ],\n \"9\": [\n \"5\"\n ],\n \"10\": [\n \"6\"\n ],\n \"11\": [\n \"7\"\n ],\n \"14\": [\n \"8\"\n ],\n \"15\": [\n \"10\"\n ]\n }\n },\n \"tabs\": [\n {\n \"name\": {\n \"en\": \"Desktop Browsers\"\n },\n \"browsers\": [\n \"3\",\n \"6\",\n \"10\",\n \"11\",\n \"14\"\n ]\n },\n {\n \"name\": {\n \"en\": \"Mobile Browsers\"\n },\n \"browsers\": [\n \"1\",\n \"7\",\n \"9\",\n \"15\",\n \"2\"\n ]\n }\n ],\n \"pagination\": {\n \"linked.features\": {\n \"previous\": null,\n \"next\": null,\n \"count\": 1\n }\n },\n \"languages\": [\n \"en\",\n \"de\",\n \"es\",\n \"ja\",\n \"ru\"\n ],\n \"notes\": {}\n }\n }\n}\n```\nThe process for using this representation is:\n\n1. Parse into an in-memory object store,\n2. Create the “Specifications” section:\n\n\t1. Add the `Specifications` header\n\t2. Create an HTML table with a header row “Specification”, “Status”, “Comment”\n\t3. For each id in features.links.sections (`[\"746\", \"421\", \"70\"]`):\n\t\n\t\t* Add the first column: a link to specifications.uri.(lang or en) +\n\t\tsections.subpath.(lang or en), with link text\n\t\tspecifications.name.(lang or en), with title based on\n\t\tsections.name.(lang or en) or feature.name.(lang or en).\n\t\t* Add the second column: A span with class\n\t\t“spec-” + maturities.slug, and the text\n\t\tmaturities.name.(lang or en).\n\t\t* Add the third column:\n\t\tmaturities.notes.(lang or en), or empty string\n\t4. Close the table, and add an edit button.\n3. Create the Browser Compatibility section:\n\n\t1. Add The “Browser compatibility” header\n\t2. For each item in meta.compat-table.tabs, create a table with the proper\n\tname (“Desktop”, “Mobile”)\n\t3. For each browser id in meta.compat-table.tabs.browsers, add a column with\n\tthe translated browser name.\n\t4. For each feature in features.features:\n\t\n\t\t* Add the first column: the feature name. If it is a string, then wrap\n\t\tin `<code>`. Otherwise, use the best translation of feature.name,\n\t\tin a `lang=(lang)` block.\n\t\t* Add any feature flags, such as an obsolete or experimental icon,\n\t\tbased on the feature flags.\n\t\t* For each browser id in meta.compat-table-important:\n\t\t\n\t\t\t+ Get the important support IDs from\n\t\t\tmeta.compat-table-important.supports.<`feature ID`>.<`browser ID`>\n\t\t\t+ If null, then display ”?”\n\t\t\t+ If just one, display “<`version`>”, or “<`support`>”,\n\t\t\tdepending on the defined attributes\n\t\t\t+ If multiple, display as subcells\n\t\t\t+ Add prefixes, alternate names, config, ank notes link\n\t\t\tas appropriate\n\t5. Close each table, add an edit button\n\t6. Add notes for displayed supports\n\nThis may be done by including the JSON in the page as sent over the wire,\nor loaded asynchronously, with the tables built after initial page load.\n\nThis can also be used by a [“caniuse” table layout](https://wiki.mozilla.org/MDN/Development/CompatibilityTables/Data_Requirements#1._CanIUse_table_layout) by ignoring the meta section and displaying all the included data. This will require more client-side processing to generate, or additional data in the `<meta>`\nsection.\n\n###### Updating Views with Changesets[¶](#updating-views-with-changesets)\n\nUpdating the page requires a sequence of requests. For example, if a user wants to change Chrome support for `<address>` from an unknown version to version 1, you’ll have to create the [version](resources.html#versions) for that version,\nthen add the [support](resources.html#supports) for the support.\n\nThe first step is to create a [changeset](change-control#changeset) as an authenticated user:\n```\nPOST /api/v1/changesets HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 107 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p<KEY>\n```\n```\n{\n \"changesets\": {\n \"target_resource_type\": \"features\",\n \"target_resource_id\": \"5\"\n }\n}\n```\nA sample response is:\n```\nHTTP/1.1 201 CREATED Content-Type: application/vnd.api+json\n```\n```\n{\n \"changesets\": {\n \"id\": \"36\",\n \"created\": \"2015-04-20T20:36:06.794827Z\",\n \"modified\": \"2015-04-20T20:36:06.795315Z\",\n \"closed\": false,\n \"target_resource_type\": \"features\",\n \"target_resource_id\": 5,\n \"links\": {\n \"user\": \"1\",\n \"historical_browsers\": [],\n \"historical_features\": [],\n \"historical_maturities\": [],\n \"historical_sections\": [],\n \"historical_specifications\": [],\n \"historical_supports\": [],\n \"historical_versions\": []\n }\n },\n \"links\": {\n \"changesets.user\": {\n \"type\": \"users\",\n \"href\": \"https://browsercompat.org/api/v1/users/{changesets.user}\"\n },\n \"changesets.historical_browsers\": {\n \"type\": \"historical_browsers\",\n \"href\": \"https://browsercompat.org/api/v1/historical_browsers/{changesets.historical_browsers}\"\n },\n \"changesets.historical_features\": {\n \"type\": \"historical_features\",\n \"href\": \"https://browsercompat.org/api/v1/historical_features/{changesets.historical_features}\"\n },\n \"changesets.historical_maturities\": {\n \"type\": \"historical_maturities\",\n \"href\": \"https://browsercompat.org/api/v1/historical_maturities/{changesets.historical_maturities}\"\n },\n \"changesets.historical_sections\": {\n \"type\": \"historical_sections\",\n \"href\": \"https://browsercompat.org/api/v1/historical_sections/{changesets.historical_sections}\"\n },\n \"changesets.historical_specifications\": {\n \"type\": \"historical_specifications\",\n \"href\": \"https://browsercompat.org/api/v1/historical_specifications/{changesets.historical_specifications}\"\n },\n \"changesets.historical_supports\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{changesets.historical_supports}\"\n },\n \"changesets.historical_versions\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{changesets.historical_versions}\"\n }\n }\n}\n```\nNext, use the [changeset](change-control#changeset) ID when creating the [version](resources.html#versions):\n```\nPOST /api/v1/versions?changeset=36 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 138 Content-Type: application/vnd.api+json Cookie: csrftoken=p<KEY>n; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p<KEY>n\n```\n```\n{\n \"versions\": {\n \"version\": \"2.0\",\n \"status\": \"retired\",\n \"links\": {\n \"browser\": \"3\"\n }\n }\n}\n```\nA sample response is:\n```\nHTTP/1.1 201 CREATED Content-Type: application/vnd.api+json\n```\n```\n{\n \"versions\": {\n \"id\": \"50\",\n \"version\": \"2.0\",\n \"release_day\": null,\n \"retirement_day\": null,\n \"status\": \"retired\",\n \"release_notes_uri\": null,\n \"note\": null,\n \"order\": 3,\n \"links\": {\n \"browser\": \"3\",\n \"supports\": [],\n \"history\": [\n \"53\"\n ],\n \"history_current\": \"53\"\n }\n },\n \"links\": {\n \"versions.browser\": {\n \"type\": \"browsers\",\n \"href\": \"https://browsercompat.org/api/v1/browsers/{versions.browser}\"\n },\n \"versions.supports\": {\n \"type\": \"supports\",\n \"href\": \"https://browsercompat.org/api/v1/supports/{versions.supports}\"\n },\n \"versions.history\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history}\"\n },\n \"versions.history_current\": {\n \"type\": \"historical_versions\",\n \"href\": \"https://browsercompat.org/api/v1/historical_versions/{versions.history_current}\"\n }\n }\n}\n```\nFinally, create the [support](resources.html#supports):\n```\nPOST /api/v1/supports?changeset=36 HTTP/1.1 Host: browsercompat.org Accept: application/vnd.api+json Content-Length: 112 Content-Type: application/vnd.api+json Cookie: csrftoken=<KEY>; sessionid=wurexa2wq416ftlvd5plesngwa28183h X-Csrftoken: p<KEY>\n```\n```\n{\n \"supports\": {\n \"links\": {\n \"version\": \"50\",\n \"feature\": \"6\"\n }\n }\n}\n```\nA sample response is:\n```\nHTTP/1.1 201 CREATED Content-Type: application/vnd.api+json\n```\n```\n{\n \"supports\": {\n \"id\": \"29\",\n \"support\": \"yes\",\n \"prefix\": null,\n \"prefix_mandatory\": false,\n \"alternate_name\": null,\n \"alternate_mandatory\": false,\n \"requires_config\": null,\n \"default_config\": null,\n \"protected\": false,\n \"note\": null,\n \"links\": {\n \"version\": \"50\",\n \"feature\": \"6\",\n \"history_current\": \"32\",\n \"history\": [\n \"32\"\n ]\n }\n },\n \"links\": {\n \"supports.version\": {\n \"type\": \"versions\",\n \"href\": \"https://browsercompat.org/api/v1/versions/{supports.version}\"\n },\n \"supports.feature\": {\n \"type\": \"features\",\n \"href\": \"https://browsercompat.org/api/v1/features/{supports.feature}\"\n },\n \"supports.history_current\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history_current}\"\n },\n \"supports.history\": {\n \"type\": \"historical_supports\",\n \"href\": \"https://browsercompat.org/api/v1/historical_supports/{supports.history}\"\n }\n }\n}\n```\nThe [historical_versions](history.html#historical-versions) and [historical_supports](history.html#historical-supports)\nresources will both refer to [changeset](change-control#changeset) 36, and this [changeset](change-control#changeset) is linked to [feature](resources.html#features) 5, despite the fact that no changes were made to the [feature](resources.html#features). This will facilitate displaying a history of the compatibility tables, for the purpose of reviewing changes and reverting vandalism.\n\n###### Updating View with PUT[¶](#updating-view-with-put)\n\nview_features supports PUT for bulk updates of support data. Here is a simple example that adds a new subfeature without support:\n```\nPUT /api/v1/view_features/html-element-address HTTP/1.1 Host: browsersupports.org Content-Type: application/vnd.api+json Authorization: Bearer mF_9.B5f-4.1JqM\n```\n```\n{\n \"features\": {\n \"id\": \"816\",\n \"slug\": \"html-element-address\",\n \"mdn_uri\": {\n \"en\": \"https://developer.mozilla.org/en-US/docs/Web/HTML/Element/address\"\n },\n \"experimental\": false,\n \"standardized\": true,\n \"stable\": true,\n \"obsolete\": false,\n \"name\": \"address\",\n \"links\": {\n \"sections\": [\"746\", \"421\", \"70\"],\n \"supports\": [],\n \"parent\": \"800\",\n \"children\": [\"191\"],\n \"history_current\": \"216\",\n \"history\": [\"216\"]\n }\n },\n \"linked\": {\n \"features\": [\n {\n \"id\": \"_New Subfeature\",\n \"slug\": \"html-address-new-subfeature\",\n \"name\": {\n \"en\": \"New Subfeature\"\n },\n \"links\": {\n \"parent\": \"816\"\n }\n }\n ]\n }\n}\n```\nThe response is the feature view with new and updated items, or an error response.\n\nThis is a trivial use case, which would be better implemented by creating the\n[feature](resources.html#features) directly, but it can be extended to bulk updates of existing feature views, or for first-time importing of subfeatures and support data. It has some quirks:\n\n* New items should be identified with an ID starting with an underscore\n(`_`). Relations to new items should use the underscored IDs.\n* Only [feature](resources.html#features), [support](resources.html#supports), and [section](resources.html#sections) resources can be added or updated.\nFeatures must be the target feature or a descendant, and supports and sections are restricted to those features.\n* Deletions are not supported.\n* Other resources ([browsers](resources.html#browsers), [versions](resources.html#versions), etc) can not be added or changed.\nThis includes adding links to new resources.\n\nOnce the MDN import is complete, this PUT interface will be deprecated in favor of direct POST and PUT to the standard resource API.\n\n#### Services[¶](#services)\n\nA **Service** provides server functionality beyond basic manipulation of resources.\n\n##### Authentication[¶](#authentication)\n\nSeveral endpoint handle user authentication.\n\n<https://browsersupports.org/accounts/profile/> is an HTML page that summarizes the users’ account, which includes:\n\n* The username, which can’t be changed.\n* Changing or setting the password, which is optional if a linked account is used.\n* Viewing, adding, and removing linked accounts, which are optional if a password is set. The support linked account type is [Firefox Accounts](https://accounts.firefox.com/signup).\n* Viewing, adding, and removing emails. Emails can be verified (a link is clicked or a trusted linked accout says it is verified), and one is the primary email used for communication.\n\nAdditional endpoints for authentication:\n\n* `/accounts/` - Redirect to login or profile, depending on login state\n* `/accounts/signup/` - Create a new account, using username and password\n* `/accounts/login/` - Login to an existing account, using username and password or selecting a linked account\n* `/accounts/logout/` - Logout from site\n* `/accounts/password/change/` - Change an existing password\n* `/accounts/password/set/` - Set the password for an account using only a linked account\n* `/accounts/email/` - Manage associated email addresses\n* `/accounts/password/reset/` - Start a password reset via email\n* `/accounts/social/connections/` - Manage social accounts\n* `/accounts/fxa/login/` - Start a [Firefox Accounts](https://accounts.firefox.com/signup) login\n\n##### Browser Identification[¶](#browser-identification)\n\nThe `/browser_ident` endpoint provides browser identification based on the User Agent and other parameters.\n\nTwo potential sources for this information:\n\n* [WhichBrowser](https://github.com/NielsLeenheer/WhichBrowser) - Very detailed. Uses User Agent header and feature detection to distinguish between similar browsers. Written in PHP.\n* [ua-parser](https://github.com/tobie/ua-parser) - Parses the User Agent. The [reference parser](https://webplatform.github.io/browser-compat-model/#reference-user-agent-parser) for\n[WebPlatform.org](http://www.webplatform.org). Written in Python.\n\nThis endpoint will probably require the browser to visit it. It will be further speced as part of the UX around user contributions.\n\n#### [Issues](#id1)[¶](#issues)\n\nThis draft API reflects a good guess at a useful, efficent API for storing user-contributed compatibility data. Some of the guesses are better than others. This section highlights the areas where more experienced opinions are welcome, and areas where more work is expected.\n\nContents\n\n* [Issues](#issues)\n\t+ [Additions to Browser Compatibility Data Architecture](#additions-to-browser-compatibility-data-architecture)\n\t+ [Unresolved Issues](#unresolved-issues)\n\t+ [Interesting MDN Pages](#interesting-mdn-pages)\n\t+ [Translating from MDN wiki format](#translating-from-mdn-wiki-format)\n\t+ [Data sources for browser versions](#data-sources-for-browser-versions)\n\t+ [To Do](#to-do)\n\n##### [Additions to Browser Compatibility Data Architecture](#id2)[¶](#additions-to-browser-compatibility-data-architecture)\n\nThis spec includes changes to the [Browser Compatibility Data Architecture](https://docs.google.com/document/d/1YF7GJ6kgV5_hx6SJjyrgunqznQU1mKxp5FaLAEzMDl4/edit#)\ndeveloped around March 2014. These seemed like a good idea to me, based on list threads and thinking how to recreate Browser Compatibility tables live on MDN.\n\nThese changes are:\n\n* [browsers](resources.html#browsers)\n\n\t+ **slug** - human-friendly unique identifier\n\t+ **name** - converted to localized text.\n\t+ **note** - added for engine, OS, etc. information\n* [versions](resources.html#versions)\n\n\t+ Was browser-versions, but multi-word resources are problematic.\n\t+ **release_day** - Day of release\n\t+ **retirement_day** - Day of “retirement”, or when it was superceeded by\n\ta new release.\n\t+ **status** - One of “retired”, “retired-beta”, “current”, “beta”,\n\t“future”\n\t+ **relese_notes_uri** - For Mozilla releases, as specified in [CompatGeckoDesktop](https://developer.mozilla.org/en-US/docs/Template:CompatGeckoDesktop).\n\t+ **note** - added for engine version, etc.\n* [features](resources.html#features)\n\n\t+ **slug** - human-friendly unique identifier\n\t+ **mdn_uri** - MDN page that data was scraped from\n\t+ **experimental** - True if the feature is considered experimental due to\n\tbeing part of a unratified spec such as CSS Transitions, ES6, or the DOM\n\tLiving Standard. For example, see the run-in value of\n\t[Web/CSS/display](https://developer.mozilla.org/en-US/docs/Web/CSS/display#Specifications).\n\t+ **standardized** - True if the feature is described in a standards-track\n\tspecification, regardless of the maturity of the specification. Most\n\tfeatures are standardized, but some browser-specific features may be\n\tnon-standard, and some features like the left and right features\n\tof [Web/CSS/caption-side](https://developer.mozilla.org/en-US/docs/Web/CSS/caption-side#Specifications) were part of the CSS2 “wishlist” document\n\tthat was not standardized.\n\t+ **stable** - True if the feature is considered stable enough for\n\tproduction usage.\n\t+ **obsolete** - True if the feature should no longer be used in\n\tproduction code.\n\t+ **name** - converted to localized text, or a string if the name is\n\tcanonical\n\t+ **sections** - replaces spec link\n\t+ **parent**, **children** - tree relations for this feature\n* [supports](resources.html#supports)\n\n\t+ Was browser-version-features, but multi-word resources are problematic.\n\t+ **prefix** - string prefix to enable, or null if no prefix\n\t+ **prefix_mandatory** - True if the prefix is required\n\t+ **alternate_name** - An alternate name associated with this feature,\n\tsuch as “RTCPeerConnectionIdentityEvent”\n\t+ **alternate_name_mandatory** - True if the alternate name is required\n\t+ **requires_config** - A configuration string\n\trequired to enable the feature, such as\n\t“media.peerconnection.enabled=on”\n\t+ **default_config** - The configuration string in the shipping\n\tbrowser, such as “media.peerconnection.enabled=off”\n\t+ **note** - Note, which can be null, but if included, can be translated,\n\tand may contain HTML and code samples. Supports extended footnote in use\n\ton MDN. MDN inline notes are not supported, and must be converted to\n\tfootnotes.\n\nThere are also additional [Resources](resources.html):\n\n* [specifications](resources.html#specifications) - For referring to a specification, with translated titles and URIs.\n* [sections](resources.html#sections) - For referring to a section of a specification, with translated titles and anchors\n* [maturities](resources.html#maturities) - For identifying the process stage of a specification\n* All the [history](history.html) resources ([historical_browsers](history.html#historical-browsers),\n[historical_versions](history.html#historical-versions), etc.)\n* [users](change-control#users) - For identifying the user who made a change\n* [changesets](change-control#changesets) - Collect several history resources into a logical change\n\n##### [Unresolved Issues](#id3)[¶](#unresolved-issues)\n\n* We’ve been talking data models. This document talks about APIs.\n**The service will not have a working SQL interface**. Features like history require that changes are made through the API. Make sure your use case is supported by the API.\n* overholt wants [availability in Web Workers](https://bugzilla.mozilla.org/show_bug.cgi?id=996570#c14). Is an API enough to support that need?\n* I think <NAME> has good points about browsers being different across operating systems and OS versions - I’m considering adding this to the model:\n[Mapping browsers to 2.2.1 Dictionary Browser Members](http://lists.w3.org/Archives/Public/public-webplatform-tests/2013OctDec/0007.html).\n* How should we support versioning the API? There is no Internet concensus.\n\n\t+ I expect to break the API as needed while implementing. At some point\n\t(late 2014), we’ll call it v1.\n\t+ Additions, such as new attributes and links, will not cause an API bump\n\t+ Some people put the version in the URL (/v1/browsers, /v2/browsers)\n\t+ Some people use a custom header (`X-Api-Version: 2`)\n\t+ Some people use the Accept header\n\t(`Accept: application/vnd.api+json;version=2`)\n\t+ These people all hate each other. [Read a good blog post on the subject](http://www.troyhunt.com/2014/02/your-api-versioning-is-wrong-which-is.html).\n* What should be the default permissions for new users? What is the process for upgrading or downgrading permissions?\n* Is Persona a good fit for creating API accounts? There will need to be a process where an MDN user becomes an API user, and a way for an API user to authenticate directly with the API.\n* If we succeed, we’ll have a detailed history of browser support for each feature. For example, the datastore will know that every version of Firefox supported the `<h1>` tag. How should version history be summarized for the Browser Compatibility table? Should the API pick the “important” versions,\nand the KumaScript display them all? Or should the API send all known versions, and the KumaScript parse them for the significant versions, with UX for exposing known versions? The view doc proposes one implementation,\nwith a `<meta>` section for identifying the important bits.\n* Do we want to add more items to versions? Wikipedia has interesting data for [Chrome release history](http://en.wikipedia.org/wiki/Google_Chrome_complete_version_history#Release_history) and [Firefox release history](http://en.wikipedia.org/wiki/Firefox_release_history#Release_history).\nSome possibly useful additions: release date, retirement date, codename,\nJS engine version, operating system, notes. It feels like we should import the data from version-specific KumaScripts like [CompatGeckoDesktop](https://developer.mozilla.org/en-US/docs/Template:CompatGeckoDesktop)\n(versions, release dates, translations, links to release docs).\n* We’ll need additional models for automated browser testing. Things like user agents, test names, test results for a user / user agent. And, we’ll need a bunch of rules for mapping test results to features, required number of tests before we’ll say a browser supports a feature, what to do with test conflicts, etc. It might be easier to move all those wishlist items to a different project, that talks to this API when it’s ready to assert browser support for a feature.\n* We need to decide on the URIs for the API and the developer resources.\nThis is being tracked by [Bugzilla 1050458](https://bugzilla.mozilla.org/show_bug.cgi?id=1050458).\n* In [browsers](resources.html#browsers), it seems like icon won’t be generally useful. What format should the icon be? What size? It may be more useful to use the slug for deciding between icons designed for the local implementation.\n\n##### [Interesting MDN Pages](#id4)[¶](#interesting-mdn-pages)\n\nThese MDN pages represent use cases for compatibility data. They may suggest features to add, or existing features that will be dropped.\n\n* [Web/HTML/Element/address](https://developer.mozilla.org/en-US/docs/Web/HTML/Element/address#Specifications) - A typical “simple” example. However, the name is non-canonical (“Basic Features”) and must be translated, rather than a canonical form (“<address>”) that could be the same for all languages.\n* [Web/CSS/display](https://developer.mozilla.org/en-US/docs/Web/CSS/display#Specifications) - This complex page includes non-canonical names\n(“`none,inline` and `block`”), experimental features (`run-in`),\nsupport changes across versions, prefixes, etc. Everything that makes this project hard.\n* [Web/CSS/cursor](https://developer.mozilla.org/en-US/docs/Web/CSS/cursor#Specifications) - May be more complex than display.\n* [Web/HTML/Element/Input](https://developer.mozilla.org/en-US/docs/Web/HTML/Element/Input#Browser_compatibility) - Complex, with lots of attributes. Split by standard may not be as useful as other ways to split it.\n* [Web/CSS/animation-name](https://developer.mozilla.org/en-US/docs/Web/CSS/animation-name#Specifications) - New property that moved from prefixed support to standard support.\n* [Web/CSS/caption-side](https://developer.mozilla.org/en-US/docs/Web/CSS/caption-side#Specifications) - Rarely used ‘Non-standard’ tag. Also seen on\n[Web/CSS/text-align](https://developer.mozilla.org/en-US/docs/Web/CSS/text-align#Specifications).\n* [Web/CSS/@font-face](https://developer.mozilla.org/en-US/docs/Web/CSS/@font-face#Specifications) - Rarely used ‘Unimplemented’ tag as inline note. Also seen on [Web/CSS/text-decoration-line](https://developer.mozilla.org/en-US/docs/Web/CSS/text-decoration-line#Specifications).\n* [Web/CSS/length](https://developer.mozilla.org/en-US/docs/Web/CSS/length#Browser_compatibility) - Rarely used “warning” tag. Also seen on\n[Web/CSS/text-underline-position](https://developer.mozilla.org/en-US/docs/Web/CSS/text-underline-position#Specifications).\n* [Web/CSS/line-break](https://developer.mozilla.org/en-US/docs/Web/CSS/line-break#Specifications) - Rarely used “Fix Me” inline note\n* [Web/CSS/min-height](https://developer.mozilla.org/en-US/docs/Web/CSS/min-height#Specifications) - “Obsolete since Gecko 22” tag on auto, versus:\n* [Web/CSS/min-width](https://developer.mozilla.org/en-US/docs/Web/CSS/min-width#Specifications) - Obsolete trash can icon\n* [Web/CSS/text-transform](https://developer.mozilla.org/en-US/docs/Web/CSS/text-transform#Specifications) - Interesting use of non-ascii unicode in feature names, good test case.\n* [Web/CSS/transform-origin](https://developer.mozilla.org/en-US/docs/Web/CSS/transform-origin#Specifications) - IE may justify a ‘alternate’ value for supports.support, or just ‘no’ with a note.\n\nSome pages will require manual intervention to get them into the data store.\nHere’s a sample:\n\n* [Web/CSS/box-decoration-break](https://developer.mozilla.org/en-US/docs/Web/CSS/box-decoration-break#Specifications) - Broken formatting\n* [Web/CSS/box-sizing](https://developer.mozilla.org/en-US/docs/Web/CSS/box-sizing#Specifications) - In Safari column, link to engine version will become an inline note.\n* [Web/CSS/break-inside](https://developer.mozilla.org/en-US/docs/Web/CSS/break-inside#Specifications) - Will need to add a skeleton compatibility table.\n* [Web/CSS/@document](https://developer.mozilla.org/en-US/docs/Web/CSS/@document#Specifications) - Specification paragraph rather than normal table.\n* [Web/CSS/clip](https://developer.mozilla.org/en-US/docs/Web/CSS/clip#Specifications) - Long inline notes should be converted to notes.\n* [Web/CSS/:invalid](https://developer.mozilla.org/en-US/docs/Web/CSS/:invalid#Specifications) - Links in feature names to other MDN docs\n* [Web/CSS/outline-color](https://developer.mozilla.org/en-US/docs/Web/CSS/outline-color#Specifications) - Instead of version, long note about support.\nConvert to two versions and a footnote.\n* [Web/CSS/radial-gradient](https://developer.mozilla.org/en-US/docs/Web/CSS/radial-gradient#Specifications) - Evolving standard, used version notes instead of marking feature as experimental or deprecated.\n* [Web/CSS/ratio](https://developer.mozilla.org/en-US/docs/Web/CSS/ratio#Specifications) - Strange Chrome version\n* [Web/CSS/tab-size](https://developer.mozilla.org/en-US/docs/Web/CSS/tab-size#Specifications) - Lots of interesting versions, including Safari nightly.\n* [Web/CSS/text-rendering](https://developer.mozilla.org/en-US/docs/Web/CSS/text-rendering#Specifications) - convert to footnotes, other changes needed. Not sure if it belongs under CSS.\n* [Web/API/IDBObjectStore](https://developer.mozilla.org/en-US/docs/Web/API/IDBObjectStore#Specifications) - apoplectic warning of Chrome behaviour. Maybe convert to regular note, or add a Feature for Chrome prefix with non-standard tag?\n\n##### [Translating from MDN wiki format](#id5)[¶](#translating-from-mdn-wiki-format)\n\nThe current compatibility data on developer.mozilla.org in MDN wiki format, a combination of HTML and KumaScript.\n\nA MDN page will be imported as a feature with at least one child feature.\n\nHere’s the MDN wiki version of the Specifications section for\n[Web/CSS/border-image-width](http://developer.mozilla.org/en-US/docs/Web/CSS/border-image-width):\n```\n<h2 id=\"Specifications\" name=\"Specifications\">Specifications</h2>\n<table class=\"standard-table\">\n <thead>\n <tr>\n <th scope=\"col\">Specification</th>\n <th scope=\"col\">Status</th>\n <th scope=\"col\">Comment</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <td>{{SpecName('CSS3 Backgrounds', '#border-image-width', 'border-image-width')}}</td>\n <td>{{Spec2('CSS3 Backgrounds')}}</td>\n <td>Initial specification</td>\n </tr>\n </tbody>\n</table>\n```\nThe elements of this table are converted into API data:\n\n* **Body row, first column** - Format is `SpecName('KEY', 'PATH', 'NAME')`.\n`KEY` is the specification.mdn_key, `PATH` is section.subpath, in the page language, and `NAME` is section.name, in the page language. The macro [SpecName](https://developer.mozilla.org/en-US/docs/Template:SpecName) has additional lookups on `KEY` for specification.name and specification.uri\n(en language only).\n* **Body row, second column** - Format is `Spec2('KEY')`. `KEY` is the specification.mdn_key, and should match the one from column one. The macro\n[Spec2](https://developer.mozilla.org/en-US/docs/Template:Spec2) has additional lookups on `KEY` for maturity.mdn_key,\nand maturity.name (multiple languages).\n* **Body row, third column** - Format is a text fragment which may include HTML markup, becomes the section.name associated with this feature.\n\nand here’s the Browser compatibility section:\n```\n<h2 id=\"Browser_compatibility\">Browser compatibility</h2>\n<div>{{CompatibilityTable}}</div>\n <div id=\"compat-desktop\">\n <table class=\"compat-table\">\n <tbody>\n <tr>\n <th>Feature</th>\n <th>Chrome</th>\n <th>Firefox (Gecko)</th>\n <th>Internet Explorer</th>\n <th>Opera</th>\n <th>Safari</th>\n </tr>\n <tr>\n <td>Basic support</td>\n <td>15.0</td>\n <td>{{CompatGeckoDesktop(\"13.0\")}}</td>\n <td>11</td>\n <td>15</td>\n <td>6</td>\n </tr>\n </tbody>\n </table>\n </div>\n <div id=\"compat-mobile\">\n <table class=\"compat-table\">\n <tbody>\n <tr>\n <th>Feature</th>\n <th>Android</th>\n <th>Firefox Mobile (Gecko)</th>\n <th>IE Phone</th>\n <th>Opera Mobile</th>\n <th>Safari Mobile</th>\n </tr>\n <tr>\n <td>Basic support</td>\n <td>{{CompatUnknown}}</td>\n <td>{{CompatGeckoMobile(\"13.0\")}}</td>\n <td>{{CompatNo}}</td>\n <td>{{CompatUnknown}}</td>\n <td>{{CompatUnknown}}</td>\n </tr>\n </tbody>\n </table>\n </div>\n</div>\n```\nThis will be converted to API resources:\n\n* **Table class** - one of `\"compat-desktop\"` or `\"compat-mobile\"`.\nRepresentation in API is TBD.\n* **Header row, all but the first column** - format is either `Browser Name\n(Engine Name)` or `Browser Name`. Used for browser.name, engine name is discarded. Other formats or KumaScript halt import.\n* **Non-header rows, first column** - If the format is `<code>some text</code>`, then feature.canonical=true and the string is the canonical name. If the format is text w/o KumaScript, it is the non-canonocial name.\nIf there is also KumaScript, it varies. **TODO:** doc KumaScript.\n* **Non-header rows, remaining columns** - Usually Kumascript:\n\n\t+ `{{CompatUnknown}}` - version.version is `null`, and\n\tsupport.support is `\"unknown\"`\n\t+ `{{CompatVersionUnknown}}` - version.version and are `null`,\n\tand support.support in `\"yes\"`\n\t+ `{{CompatNo}}` - version.version and are `null`, and\n\tsupport.support is `\"no\"`\n\t+ `{{CompatGeckoDesktop(\"VAL\")}}` - version.version is set to\n\t`\"VAL\"`, support.support is `\"yes\"`. and\n\tversion.release_day is set by logic in [CompatGeckoDesktop](https://developer.mozilla.org/en-US/docs/Template:CompatGeckoDesktop).\n\t+ `{{CompatGeckoMobile(\"VAL\")}}` - version.version is set to\n\t`\"VAL\"`, support.support is `\"yes\"`. is set by logic\n\tin [CompatGeckoMobile](https://developer.mozilla.org/en-US/docs/Template:CompatGeckoMobile).\n\t+ Numeric string, such as `6`, `15.0`. This becomes the\n\tversion.version, and support.support is\n\t`\"yes\"`.\n* **Content after table** - This is usually formatted as a paragraph,\ncontaining HTML. If it resembles a footnote, it will be converted to supports.notes.\n\nOnce the initial conversion has been done for a page, it may be useful to perform additional steps:\n\n1. Split large [features](resources.html#features) into smaller ones. For example,\nhere’s one way to reorganize [Web/CSS/display](https://developer.mozilla.org/en-US/docs/Web/CSS/display#Specifications):\n\n##### [Data sources for browser versions](#id6)[¶](#data-sources-for-browser-versions)\n\nThe **version** model currently supports a release date and a retirement date, as well as other version data. Some sources for this data include:\n\n* Google Chrome - [Google Chrome Release History](http://en.wikipedia.org/wiki/Google_Chrome#Release_history) on Wikipedia\n* Mozilla Firefox - [Firefox Release History](http://en.wikipedia.org/wiki/Firefox_release_history#Release_history) on Wikipedia and KumaScript macro [CompatGeckoDesktop](https://developer.mozilla.org/en-US/docs/Template:CompatGeckoDesktop)\n* Microsoft Internet Explorer - [Release History of IE](http://en.wikipedia.org/wiki/Internet_Explorer_1#Release_history_for_desktop_Windows_OS_version) on Wikipedia\n* Opera - [Current Opera version history](http://www.opera.com/docs/history/) and [Presto history](http://www.opera.com/docs/history/presto/) on opera.com\n* Safari - [Safari version history](http://en.wikipedia.org/wiki/Safari_version_history#Release_history) on Wikipedia\n\n##### [To Do](#id7)[¶](#to-do)\n\n* Add multi-get to browser doc, after deciding on `GET\n/versions/1,2,3,4` vs. `GET /browser/1/versions`\n* Look at additional MDN content for items in common use\n* Move to developers.mozilla.org subpath, auth changes\n* Jeremie’s suggested changes (*italics are done*)\n\n\t+ *Add browsers.notes, localized, to note things like engine, applicable\n\tOS, execution contexts (web workers, XUL, etc.).*\n\t+ *Drop browsers.engine attribute. Not important for searching or\n\tfiltering, instead free text in browsers.notes*\n\t+ *Add versions.notes, localized, to note things like OS, devices,\n\tengines, etc.*\n\t+ *Drop versions.engine-version, not important for searching or\n\tsorting.*\n\t+ Drop versions.status. Doesn’t think the MDN team will be able\n\tto keep up with browser releases. Will instead rely on users\n\tfiguring out if a browser version is the current release.\n\t+ *Drop feature.canonical. Instead, name=”string” means it is\n\tcanonical, and name={“lang”: “translation”} means it is non-canonical.*\n\t+ Feature-sets is a cloud, not a heirarchy. “color=red” is the same\n\tfeature as “background-color=red”, so needs to be multiply assigned.\n\t+ *A feature-set can either have sub-feature sets (middle of cloud), or\n\tfeatures (edge of cloud).* - Note - implemented by merging features and\n\tfeature sets.\n\t+ *Add support-sets, to make positive assertions about\n\ta version supporting a feature-set. Only negative assertions\n\tcan be made based on features.* - Note - implemented by merging features\n\tand feature sets\n\t+ Drop order of features by feature set. Client will alpha-sort.\n\t+ *supports.support, drop “prefixed” status. If prefixed,\n\tsupport = ‘yes’, and prefix is set.*\n\t+ Add examples of filtering (browser versions in 2010, firefox versions\n\tbefore version X).\n* Holly’s suggestions\n\n\t+ Nail down the data, so she has something solid to build a UX on.\n\t+ sheppy or jms will have experience with how users use tables and\n\tcontribute to them, how frequently.\n* Add history resources for specifications, etc.\n* Add empty resource for deleted items?\n\n### Tools[¶](#tools)\n\nSome potentially useful scripts can be found in the /tools folder:\n\n#### download_data.py[¶](#download-data-py)\n\nDownload data from API. Usage:\n```\n$ tools/download_data.py [--api API] [-vq] [--data DATA]\n```\n* `--api <API>` (optional): Set the base URL of the API\n(default: http://localhost:8000)\n* `-v` (optional): Print debug information\n* `-q` (optional): Only print warnings\n* `--data <DATA>` (optional): Set the output data folder\n(default: data subfolder in the working copy)\n\nThis will create several files (browsers.json, versions.json, etc.) that represent the API resources without pagination.\n\n#### import_mdn.py[¶](#import-mdn-py)\n\nImport features from MDN, or reparse imported features. Usage:\n```\n$ tools/import_mdn.py [--api API] [--user USER] [-vq]\n```\n* `--api <API>` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--user <USER>` (optional): Set the username to use on the API\n(default: prompt for username)\n* `-v` (optional): Print debug information\n* `-q` (optional): Only print warnings\n\n#### load_spec_data.py[¶](#load-spec-data-py)\n\nImport specification data from MDN’s [SpecName](https://developer.mozilla.org/en-US/docs/Template:SpecName) and [Spec2](https://developer.mozilla.org/en-US/docs/Template:Spec2). Usage:\n```\n$ tools/load_spec_data.py [--api <API>] [--user <USER>]\n [-vq] [--all-data]\n```\n* `--api <API>` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--user <USER>` (optional): Set the username to use on the API\n(default: prompt for username)\n* `-v` (optional): Print debug information\n* `-q` (optional): Only print warnings\n\n#### load_webcompat_data.py[¶](#load-webcompat-data-py)\n\nInitialize with compatibility data from the [WebPlatform](https://github.com/webplatform/compatibility-data) project. Usage:\n```\n$ tools/load_webcompat_data.py [--api <API>] [--user <USER>]\n [-vq] [--all-data]\n```\n* `--api <API>` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--user <USER>` (optional): Set the username to use on the API\n(default: prompt for username)\n* `-v` (optional): Print debug information\n* `-q` (optional): Only print warnings\n* `--all-data` (optional): Import all data, rather than a subset\n\n#### make_doc_requests.py[¶](#make-doc-requests-py)\n\nMake documentation/integration requests against an API. Used by tools/run_integration_tests.sh. Usage:\n```\n$ tools/integration_requests.py [--mode {display,generate,verify}]\n [--api API]\n [--raw RAW] [--cases CASES]\n [--user USER] [--password PASSWORD]\n [--include-mod] [-vq]\n [case name [case name ...]]\n```\n* `--mode {display,generate,verify}` (optional): Set the mode. Values are:\n\n\t+ `display` (default): Run GET requests against an API, printing the\n\tactual requests and responses.\n\t+ `generate`: Run all requests against an API. Throw away some headers,\n\tsuch as `Allow` and `Server`. Modify other headers, such as\n\t`Cookies`, to make them consistant from run to run. Standardize some\n\tresponse data, such as creation and modification times. Store the\n\tcleaned-up requests and responses in the docs folder, for documentation\n\tand integration testing.\n\t+ `verify`: Run all requests against an API, standardizing the requests\n\tand responses and comparing them to those in the docs folder.\n* `--api API` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--raw RAW` (optional): Set the path to the folder containing raw requests and responses (default: `docs/raw`)\n* `--cases CASES` (optional): Set the path to the documentation cases JSON file (default `docs/doc_cases.json`)\n* `--user USER`: Set the username to use for requests (default anonymous requests)\n* `--password PASSWORD`: Set the password to use for requests (default is prompt if `--user` set, otherwise use anonymous requests)\n* `--include-mod`: If `--mode display`, then include requests that would modify the data, such as `POST`, `PUT`, and `DELETE`.\n* `-v`: Be more verbose\n* `-q`: Be quieter\n* `case name`: Run the listed cases, not the full suite of cases\n\n#### mirror_mdn_features.py[¶](#mirror-mdn-features-py)\n\nCreate and update API features for MDN pages. This will create the branch features, and then import_mdn.py can be used to generate the leaf features.\nUsage:\n```\n$ tools/mirror_mdn_features.py [--api API] [--data DATA]\n [--user USER] [--password PASSWORD]\n```\n* `--api API` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--user USER`: Set the username to use for requests (default is prompt for username)\n* `--password PASSWORD`: Set the password to use for requests (default is prompt for username)\n* `--data DATA`: Set the data folder for caching MDN page JSON\n\n#### run_integration_tests.sh[¶](#run-integration-tests-sh)\n\nRun a local API server with known data, make requests against it, and look for issues in the response. Usage:\n```\n$ tools/run_integration_tests.sh [-ghqv]\n```\n* `-g`: Generate documentation / integration test samples. If omitted, then responses are checked against the documentation samples. Useful for adding new documentation cases, or updating when the API changes.\n* `-h`: Show a usage statement\n* `-q`: Show less output\n* `-v`: Show more output\n\n#### sample_mdn.py[¶](#sample-mdn-py)\n\nLoad random pages from MDN in your browser. Usage:\n```\n$ tools/sample_mdn.py\n```\n#### upload_data.py[¶](#upload-data-py)\n\nUpload data to the API. Usage:\n```\n$ tools/upload_data.py [--api API] [--user USER]\n [-vq] [--data DATA]\n```\n* `--api <API>` (optional): Set the base URL of the API\n(default: `http://localhost:8000`)\n* `--user <USER>` (optional): Set the username to use on the API\n(default: prompt for username)\n* `-v` (optional): Print debug information\n* `-q` (optional): Only print warnings\n* `--data <DATA>` (optional): Set the output data folder\n(default: data subfolder in the working copy)\n\nThis will load the local resources from files (browsers.json, versions.json, etc),\ndownload the resources from the API, and upload the changes to make the API match the local resource files.\n\n### History[¶](#history)\n\nweb-platform-compat has not been released to production yet. The blocking issues for version 1 are tracked on [Bugzilla](https://bugzilla.mozilla.org/showdependencytree.cgi?id=996570&hide_resolved=1).\n\nIn-progess versions are periodically deployed to Heroku at\n<https://browsercompat.herokuapp.com>.\n\nHere are some of the development deployments:\n\n* 2015-02 - Added MDN importer\n* 2014-12 - Added rest of resources, sample displays.\nDropped versioning pre-release.\n* 0.2.0 - 2014-10-13 - Add features, supports, pagination\n* 0.1.0d - 2014-09-29 - Add resource-level caching\n* 0.1.0c - 2014-09-16 - Add sample feature view, simplify draft API\n* 0.1.0b - 2014-09-05 - Add filtering, more JSON API tuning.\n* 0.1.0a - 2014-09-02 - First Heroku deployment. Browser and Version data.\n\n### Indices and tables[¶](#indices-and-tables)\n\n* [Index](genindex.html)\n* [Module Index](py-modindex.html)\n* [Search Page](search.html)\n\n### [Table Of Contents](index.html#document-index)\n\n* [Installation](index.html#document-installation)\n\t+ [Install Django Project](index.html#install-django-project)\n\t+ [Install in Heroku](index.html#install-in-heroku)\n\t+ [Configuring authentication](index.html#configuring-authentication)\n\t+ [Load Data](index.html#load-data)\n\t\t- [Load from GitHub](index.html#load-from-github)\n\t\t- [Load from another webcompat server](index.html#load-from-another-webcompat-server)\n\t\t- [Load Sample Data](index.html#load-sample-data)\n* [Contributing](index.html#document-contributing)\n\t+ [What to work on](index.html#what-to-work-on)\n\t+ [GitHub workflow](index.html#github-workflow)\n* [API (DRAFT)](index.html#document-draft/intro)\n\t+ [Entrypoints](index.html#document-draft/entrypoints)\n\t+ [Proposed Technologies](index.html#document-draft/technologies)\n\t+ [Resources](index.html#document-draft/resources)\n\t\t- [Browsers](index.html#browsers)\n\t\t- [Versions](index.html#versions)\n\t\t- [Features](index.html#features)\n\t\t- [Supports](index.html#supports)\n\t\t- [Specifications](index.html#specifications)\n\t\t- [Sections](index.html#sections)\n\t\t- [Maturities](index.html#maturities)\n\t+ [Change Control Resources](index.html#document-draft/change-control)\n\t\t- [Users](index.html#users)\n\t\t- [Changesets](index.html#changesets)\n\t+ [History Resources](index.html#document-draft/history)\n\t\t- [Historical Browsers](index.html#historical-browsers)\n\t\t- [Historical Versions](index.html#historical-versions)\n\t\t- [Historical Features](index.html#historical-features)\n\t\t- [Historical Sections](index.html#historical-sections)\n\t\t- [Historical Specifications](index.html#historical-specifications)\n\t\t- [Historical Supports](index.html#historical-supports)\n\t\t- [Historical Maturities](index.html#historical-maturities)\n\t+ [Views](index.html#document-draft/views)\n\t\t- [View a Feature](index.html#view-a-feature)\n\t+ [Services](index.html#document-draft/services)\n\t\t- [Authentication](index.html#authentication)\n\t\t- [Browser Identification](index.html#browser-identification)\n\t+ [Issues](index.html#document-draft/issues)\n\t\t- [Additions to Browser Compatibility Data Architecture](index.html#additions-to-browser-compatibility-data-architecture)\n\t\t- [Unresolved Issues](index.html#unresolved-issues)\n\t\t- [Interesting MDN Pages](index.html#interesting-mdn-pages)\n\t\t- [Translating from MDN wiki format](index.html#translating-from-mdn-wiki-format)\n\t\t- [Data sources for browser versions](index.html#data-sources-for-browser-versions)\n\t\t- [To Do](index.html#to-do)\n* [Tools](index.html#document-tools)\n\t+ [download_data.py](index.html#download-data-py)\n\t+ [import_mdn.py](index.html#import-mdn-py)\n\t+ [load_spec_data.py](index.html#load-spec-data-py)\n\t+ [load_webcompat_data.py](index.html#load-webcompat-data-py)\n\t+ [make_doc_requests.py](index.html#make-doc-requests-py)\n\t+ [mirror_mdn_features.py](index.html#mirror-mdn-features-py)\n\t+ [run_integration_tests.sh](index.html#run-integration-tests-sh)\n\t+ [sample_mdn.py](index.html#sample-mdn-py)\n\t+ [upload_data.py](index.html#upload-data-py)\n* [History](index.html#document-history)\n\n### Related Topics\n\n* [Documentation overview](index.html#document-index)\n\n### Quick search\n\n Enter search terms or a module, class or function name."}}},{"rowIdx":59471,"cells":{"project":{"kind":"string","value":"github.com/docker/docker/pkg/chrootarchive"},"source":{"kind":"string","value":"go"},"language":{"kind":"string","value":"Go"},"content":{"kind":"string","value":"None\n\nDocumentation\n [¶](#section-documentation)\n---\n\n[Rendered for](https://go.dev/about#build-context)\n\nlinux/amd64 windows/amd64 darwin/amd64 js/wasm\n\n \n### Index [¶](#pkg-index)\n\n* [func ApplyLayer(dest string, layer io.Reader) (size int64, err error)](#ApplyLayer)\n* [func ApplyUncompressedLayer(dest string, layer io.Reader, options *archive.TarOptions) (int64, error)](#ApplyUncompressedLayer)\n* [func NewArchiver(idMapping idtools.IdentityMapping) *archive.Archiver](#NewArchiver)\n* [func Tar(srcPath string, options *archive.TarOptions, root string) (io.ReadCloser, error)](#Tar)\n* [func Untar(tarArchive io.Reader, dest string, options *archive.TarOptions) error](#Untar)\n* [func UntarUncompressed(tarArchive io.Reader, dest string, options *archive.TarOptions) error](#UntarUncompressed)\n* [func UntarWithRoot(tarArchive io.Reader, dest string, options *archive.TarOptions, root string) error](#UntarWithRoot)\n\n### Constants [¶](#pkg-constants)\n\nThis section is empty.\n\n### Variables [¶](#pkg-variables)\n\nThis section is empty.\n\n### Functions [¶](#pkg-functions)\n\n#### \nfunc [ApplyLayer](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/diff.go#L13) [¶](#ApplyLayer)\n```\nfunc ApplyLayer(dest [string](/builtin#string), layer [io](/io).[Reader](/io#Reader)) (size [int64](/builtin#int64), err [error](/builtin#error))\n```\nApplyLayer parses a diff in the standard layer format from `layer`,\nand applies it to the directory `dest`. The stream `layer` can only be uncompressed.\nReturns the size in bytes of the contents of the layer.\n\n#### \nfunc [ApplyUncompressedLayer](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/diff.go#L21) [¶](#ApplyUncompressedLayer)\n\nadded in v1.8.0\n```\nfunc ApplyUncompressedLayer(dest [string](/builtin#string), layer [io](/io).[Reader](/io#Reader), options *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[TarOptions](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#TarOptions)) ([int64](/builtin#int64), [error](/builtin#error))\n```\nApplyUncompressedLayer parses a diff in the standard layer format from\n`layer`, and applies it to the directory `dest`. The stream `layer`\ncan only be uncompressed.\nReturns the size in bytes of the contents of the layer.\n\n#### \nfunc [NewArchiver](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/archive.go#L14) [¶](#NewArchiver)\n```\nfunc NewArchiver(idMapping [idtools](/github.com/docker/docker@v24.0.6+incompatible/pkg/idtools).[IdentityMapping](/github.com/docker/docker@v24.0.6+incompatible/pkg/idtools#IdentityMapping)) *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[Archiver](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#Archiver)\n```\nNewArchiver returns a new Archiver which uses chrootarchive.Untar\n\n#### \nfunc [Tar](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/archive.go#L91) [¶](#Tar)\n```\nfunc Tar(srcPath [string](/builtin#string), options *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[TarOptions](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#TarOptions), root [string](/builtin#string)) ([io](/io).[ReadCloser](/io#ReadCloser), [error](/builtin#error))\n```\nTar tars the requested path while chrooted to the specified root.\n\n#### \nfunc [Untar](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/archive.go#L25) [¶](#Untar)\n```\nfunc Untar(tarArchive [io](/io).[Reader](/io#Reader), dest [string](/builtin#string), options *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[TarOptions](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#TarOptions)) [error](/builtin#error)\n```\nUntar reads a stream of bytes from `archive`, parses it as a tar archive,\nand unpacks it into the directory at `dest`.\nThe archive may be compressed with one of the following algorithms:\nidentity (uncompressed), gzip, bzip2, xz.\n\n#### \nfunc [UntarUncompressed](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/archive.go#L48) [¶](#UntarUncompressed)\n\nadded in v1.8.0\n```\nfunc UntarUncompressed(tarArchive [io](/io).[Reader](/io#Reader), dest [string](/builtin#string), options *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[TarOptions](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#TarOptions)) [error](/builtin#error)\n```\nUntarUncompressed reads a stream of bytes from `archive`, parses it as a tar archive,\nand unpacks it into the directory at `dest`.\nThe archive must be an uncompressed stream.\n\n#### \nfunc [UntarWithRoot](https://github.com/docker/docker/blob/v24.0.6/pkg/chrootarchive/archive.go#L41) [¶](#UntarWithRoot)\n```\nfunc UntarWithRoot(tarArchive [io](/io).[Reader](/io#Reader), dest [string](/builtin#string), options *[archive](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive).[TarOptions](/github.com/docker/docker@v24.0.6+incompatible/pkg/archive#TarOptions), root [string](/builtin#string)) [error](/builtin#error)\n```\nUntarWithRoot is the same as `Untar`, but allows you to pass in a root directory The root directory is the directory that will be chrooted to.\n`dest` must be a path within `root`, if it is not an error will be returned.\n\n`root` should set to a directory which is not controlled by any potentially malicious process.\n\nThis should be used to prevent a potential attacker from manipulating `dest`\nsuch that it would provide access to files outside of `dest` through things like symlinks. Normally `ResolveSymlinksInScope` would handle this, however sanitizing symlinks in this manner is inherrently racey:\nref: CVE-2018-15664\n\n### Types [¶](#pkg-types)\n\nThis section is empty."}}},{"rowIdx":59472,"cells":{"project":{"kind":"string","value":"capnproto.org/go/capnp/v3"},"source":{"kind":"string","value":"go"},"language":{"kind":"string","value":"Go"},"content":{"kind":"string","value":"README\n [¶](#section-readme)\n---\n\n### Cap'n Proto bindings for Go\n\n\n[](https://goreportcard.com/report/capnproto.org/go/capnp/v3)\n[](https://github.com/capnproto/go-capnproto2/actions/workflows/go.yml)\n[](http://pkg.go.dev/capnproto.org/go/capnp/v3)\n[](https://matrix.to/#/%23go-capnp:matrix.org)\n\nDocumentation\n [¶](#section-documentation)\n---\n\n \n### Overview [¶](#pkg-overview)\n\n* [Generating code](#hdr-Generating_code)\n* [Messages and Segments](#hdr-Messages_and_Segments)\n* [Pointers](#hdr-Pointers)\n* [Structs](#hdr-Structs)\n* [Groups](#hdr-Groups)\n* [Unions](#hdr-Unions)\n* [Enums](#hdr-Enums)\n* [Interfaces](#hdr-Interfaces)\n\nPackage capnp is a Cap'n Proto library for Go.\n<https://capnproto.org/Read the Getting Started guide for a tutorial on how to use this package. <https://github.com/capnproto/go-capnproto2/wiki/Getting-Started#### Generating code [¶](#hdr-Generating_code)\n\ncapnpc-go provides the compiler backend for capnp.\n```\n# First, install capnpc-go to $PATH.\ngo install capnproto.org/go/capnp/v3/capnpc-go\n# Then, check out the go-capnp source code:\ngit clone https://github.com/capnproto/go-capnp /desired/path/to/go-capnp\n# Then, generate Go files.\ncapnp compile -I /desired/path/to/go-capnp/std -ogo *.capnp\n```\ncapnpc-go requires two annotations for all files: package and import.\npackage is needed to know what package to place at the head of the generated file and what identifier to use when referring to the type from another package. import should be the fully qualified import path and is used to generate import statement from other packages and to detect when two types are in the same package. For example:\n```\nusing Go = import \"/go.capnp\";\n$Go.package(\"main\");\n$Go.import(\"capnproto.org/go/capnp/v3/example\");\n```\nFor adding documentation comments to the generated code, there's the doc annotation. This annotation adds the comment to a struct, enum or field so that godoc will pick it up. For example:\n```\nstruct Zdate $Go.doc(\"Zdate represents a calendar date\") {\n year @0 :Int16;\n month @1 :UInt8;\n day @2 :UInt8 ;\n}\n```\n#### Messages and Segments [¶](#hdr-Messages_and_Segments)\n\nIn Cap'n Proto, the unit of communication is a message. A message consists of one or more segments -- contiguous blocks of memory. This allows large messages to be split up and loaded independently or lazily.\nTypically you will use one segment per message. Logically, a message is organized in a tree of objects, with the root always being a struct (as opposed to a list or primitive). Messages can be read from and written to a stream.\n\nThe Message and Segment types are the main types that application code will use from this package. The Message type has methods for marshaling and unmarshaling its segments to the wire format. If the application needs to read or write from a stream, it should use the Encoder and Decoder types.\n\n#### Pointers [¶](#hdr-Pointers)\n\nThe type for a generic reference to a Cap'n Proto object is Ptr. A Ptr can refer to a struct, a list, or an interface. Ptr, Struct, List, and Interface (the pointer types) have value semantics and refer to data in a single segment. All of the pointer types have a notion of \"valid\".\nAn invalid pointer will return the default value from any accessor and panic when any setter is called.\n\nIn previous versions of this package, the Pointer interface was used instead of the Ptr struct. This interface and functions that use it are now deprecated. See <https://github.com/capnproto/go-capnproto2/wiki/New-Ptr-Type>\nfor details about this API change.\n\nData accessors and setters (i.e. struct primitive fields and list elements) do not return errors, but pointer accessors and setters do.\nThere are a few reasons that a read or write of a pointer can fail, but the most common are bad pointers or allocation failures. For accessors,\nan invalid object will be returned in case of an error.\n\nSince Go doesn't have generics, wrapper types provide type safety on lists. This package provides lists of basic types, and capnpc-go generates list wrappers for named types. However, if you need to use deeper nesting of lists (e.g. List(List(UInt8))), you will need to use a PointerList and wrap the elements.\n\n#### Structs [¶](#hdr-Structs)\n\nFor the following schema:\n```\nstruct Foo @0x8423424e9b01c0af {\n num @0 :UInt32;\n bar @1 :Foo;\n}\n```\ncapnpc-go will generate:\n```\n// Foo is a pointer to a Foo struct in a segment.\n// Member functions are provided to get/set members in the\n// struct.\ntype Foo struct{ capnp.Struct }\n\n// Foo_TypeID is the unique identifier for the type Foo.\n// It remains the same across languages and schema changes.\nconst Foo_TypeID = 0x8423424e9b01c0af\n\n// NewFoo creates a new orphaned Foo struct, preferring placement in\n// s. If there isn't enough space, then another segment in the\n// message will be used or allocated. You can set a field of type Foo\n// to this new message, but usually you will want to use the\n// NewBar()-style method shown below.\nfunc NewFoo(s *capnp.Segment) (Foo, error)\n\n// NewRootFoo creates a new Foo struct and sets the message's root to\n// it.\nfunc NewRootFoo(s *capnp.Segment) (Foo, error)\n\n// ReadRootFoo reads the message's root pointer and converts it to a\n// Foo struct.\nfunc ReadRootFoo(msg *capnp.Message) (Foo, error)\n\n// Num returns the value of the num field.\nfunc (s Foo) Num() uint32\n\n// SetNum sets the value of the num field to v.\nfunc (s Foo) SetNum(v uint32)\n\n// Bar returns the value of the bar field. This can return an error\n// if the pointer goes beyond the segment's range, the segment fails\n// to load, or the pointer recursion limit has been reached.\nfunc (s Foo) Bar() (Foo, error)\n\n// HasBar reports whether the bar field was initialized (non-null).\nfunc (s Foo) HasBar() bool\n\n// SetBar sets the value of the bar field to v.\nfunc (s Foo) SetBar(v Foo) error\n\n// NewBar sets the bar field to a newly allocated Foo struct,\n// preferring placement in s's segment.\nfunc (s Foo) NewBar() (Foo, error)\n\n// Foo_List is a value with pointer semantics. It is created for all\n// structs, and is used for List(Foo) in the capnp file.\ntype Foo_List struct{ capnp.List }\n\n// NewFoo_List creates a new orphaned List(Foo), preferring placement\n// in s. This can then be added to a message by using a Set function\n// which takes a Foo_List. sz specifies the number of elements in the\n// list. The list's size cannot be changed after creation.\nfunc NewFoo_List(s *capnp.Segment, sz int32) Foo_List\n\n// Len returns the number of elements in the list.\nfunc (s Foo_List) Len() int\n\n// At returns a pointer to the i'th element. If i is an invalid index,\n// this will return an invalid Foo (all getters will return default\n// values, setters will fail).\nfunc (s Foo_List) At(i int) Foo\n\n// Foo_Promise is a promise for a Foo. Methods are provided to get\n// promises of struct and interface fields.\ntype Foo_Promise struct{ *capnp.Pipeline }\n\n// Get waits until the promise is resolved and returns the result.\nfunc (p Foo_Promise) Get() (Foo, error)\n\n// Bar returns a promise for that bar field.\nfunc (p Foo_Promise) Bar() Foo_Promise\n```\n#### Groups [¶](#hdr-Groups)\n\nFor each group a typedef is created with a different method set for just the groups fields:\n```\nstruct Foo {\n\tgroup :Group {\n\t\tfield @0 :Bool;\n\t}\n}\n```\ngenerates the following:\n```\ntype Foo struct{ capnp.Struct }\ntype Foo_group Foo\n\nfunc (s Foo) Group() Foo_group func (s Foo_group) Field() bool\n```\nThat way the following may be used to access a field in a group:\n```\nvar f Foo value := f.Group().Field()\n```\nNote that group accessors just convert the type and so have no overhead.\n\n#### Unions [¶](#hdr-Unions)\n\nNamed unions are treated as a group with an inner unnamed union. Unnamed unions generate an enum Type_Which and a corresponding Which() function:\n```\nstruct Foo {\n\tunion {\n\t\ta @0 :Bool;\n\t\tb @1 :Bool;\n\t}\n}\n```\ngenerates the following:\n```\ntype Foo_Which uint16\n\nconst (\n\tFoo_Which_a Foo_Which = 0\n\tFoo_Which_b Foo_Which = 1\n)\n\nfunc (s Foo) A() bool func (s Foo) B() bool func (s Foo) SetA(v bool)\nfunc (s Foo) SetB(v bool)\nfunc (s Foo) Which() Foo_Which\n```\nWhich() should be checked before using the getters, and the default case must always be handled.\n\nSetters for single values will set the union discriminator as well as set the value.\n\nFor voids in unions, there is a void setter that just sets the discriminator.\nFor example:\n```\nstruct Foo {\n\tunion {\n\t\ta @0 :Void;\n\t\tb @1 :Void;\n\t}\n}\n```\ngenerates the following:\n```\nfunc (s Foo) SetA() // Set that we are using A func (s Foo) SetB() // Set that we are using B\n```\nSimilarly, for groups in unions, there is a group setter that just sets the discriminator. This must be called before the group getter can be used to set values. For example:\n```\nstruct Foo {\n\tunion {\n\t\ta :group {\n\t\t\tv :Bool\n\t\t}\n\t\tb :group {\n\t\t\tv :Bool\n\t\t}\n\t}\n}\n```\nand in usage:\n```\nf.SetA() // Set that we are using group A f.A().SetV(true) // then we can use the group A getter to set the inner values\n```\n#### Enums [¶](#hdr-Enums)\n\ncapnpc-go generates enum values as constants. For example in the capnp file:\n```\nenum ElementSize {\n empty @0;\n bit @1;\n byte @2;\n twoBytes @3;\n fourBytes @4;\n eightBytes @5;\n pointer @6;\n inlineComposite @7;\n}\n```\nIn the generated capnp.go file:\n```\ntype ElementSize uint16\n\nconst (\n\tElementSize_empty ElementSize = 0\n\tElementSize_bit ElementSize = 1\n\tElementSize_byte ElementSize = 2\n\tElementSize_twoBytes ElementSize = 3\n\tElementSize_fourBytes ElementSize = 4\n\tElementSize_eightBytes ElementSize = 5\n\tElementSize_pointer ElementSize = 6\n\tElementSize_inlineComposite ElementSize = 7\n)\n```\nIn addition an enum.String() function is generated that will convert the constants to a string for debugging or logging purposes. By default, the enum name is used as the tag value,\nbut the tags can be customized with a $Go.tag or $Go.notag annotation.\n\nFor example:\n```\nenum ElementSize {\n\tempty @0 $Go.tag(\"void\");\n\tbit @1 $Go.tag(\"1 bit\");\n\tbyte @2 $Go.tag(\"8 bits\");\n\tinlineComposite @7 $Go.notag;\n}\n```\nIn the generated go file:\n```\nfunc (c ElementSize) String() string {\n\tswitch c {\n\tcase ElementSize_empty:\n\t\treturn \"void\"\n\tcase ElementSize_bit:\n\t\treturn \"1 bit\"\n\tcase ElementSize_byte:\n\t\treturn \"8 bits\"\n\tdefault:\n\t\treturn \"\"\n\t}\n}\n```\n#### Interfaces [¶](#hdr-Interfaces)\n\ncapnpc-go generates type-safe Client wrappers for interfaces. For parameter lists and result lists, structs are generated as described above with the names Interface_method_Params and Interface_method_Results, unless a single struct type is used. For example, for this interface:\n```\ninterface Calculator {\n\tevaluate @0 (expression :Expression) -> (value :Value);\n}\n```\ncapnpc-go generates the following Go code (along with the structs Calculator_evaluate_Params and Calculator_evaluate_Results):\n```\n// Calculator is a client to a Calculator interface.\ntype Calculator struct{ Client capnp.Client }\n\n// Evaluate calls `evaluate` on the client. params is called on a newly\n// allocated Calculator_evaluate_Params struct to fill in the parameters.\nfunc (c Calculator) Evaluate(\n\tctx context.Context,\n\tparams func(Calculator_evaluate_Params) error,\n\topts ...capnp.CallOption) *Calculator_evaluate_Results_Promise\n```\ncapnpc-go also generates code to implement the interface:\n```\n// A Calculator_Server implements the Calculator interface.\ntype Calculator_Server interface {\n\tEvaluate(context.Context, Calculator_evaluate_Call) error\n}\n\n// Calculator_evaluate_Call holds the arguments for a Calculator.evaluate server call.\ntype Calculator_evaluate_Call struct {\n\tParams Calculator_evaluate_Params\n\tResults Calculator_evaluate_Results\n\tOptions capnp.CallOptions\n}\n\n// Calculator_ServerToClient is equivalent to calling:\n// NewCalculator(capnp.NewServer(Calculator_Methods(nil, s), s))\n// If s does not implement the Close method, then nil is used.\nfunc Calculator_ServerToClient(s Calculator_Server) Calculator\n\n// Calculator_Methods appends methods from Calculator that call to server and\n// returns the methods. If methods is nil or the capacity of the underlying\n// slice is too small, a new slice is returned.\nfunc Calculator_Methods(methods []server.Method, s Calculator_Server) []server.Method\n```\nSince a single capability may want to implement many interfaces, you can use multiple *_Methods functions to build a single slice to send to NewServer.\n\nAn example of combining the client/server code to communicate with a locally implemented Calculator:\n```\nvar srv Calculator_Server calc := Calculator_ServerToClient(srv)\nresult := calc.Evaluate(ctx, func(params Calculator_evaluate_Params) {\n\tparams.SetExpression(expr)\n})\nval := result.Value().Get()\n```\nA note about message ordering: by default, only one method per server will be invoked at a time; when implementing a server method which blocks or takes a long time, you calling the server.Go function to unblock future calls.\n\nExample [¶](#example-package)\n```\n// Make a brand new empty message.\nmsg, seg, err := capnp.NewMessage(capnp.SingleSegment(nil))\nif err != nil {\n\tpanic(err)\n}\n\n// If you want runtime-type identification, this is easily obtained. Just\n// wrap everything in a struct that contains a single anoymous union (e.g. struct Z).\n// Then always set a Z as the root object in you message/first segment.\n// The cost of the extra word of storage is usually worth it, as\n// then human readable output is easily obtained via a shell command such as\n//\n// $ cat binary.cpz | capnp decode aircraft.capnp Z\n//\n// If you need to conserve space, and know your content in advance, it\n// isn't necessary to use an anonymous union. Just supply the type name\n// in place of 'Z' in the decode command above.\n\n// There can only be one root. Subsequent NewRoot* calls will set the root\n// pointer and orphan the previous root.\nz, err := air.NewRootZ(seg)\nif err != nil {\n\tpanic(err)\n}\n\n// then non-root objects:\naircraft, err := z.NewAircraft()\nif err != nil {\n\tpanic(err)\n}\nb737, err := aircraft.NewB737()\nif err != nil {\n\tpanic(err)\n}\nplanebase, err := b737.NewBase()\nif err != nil {\n\tpanic(err)\n}\n\n// Set primitive fields planebase.SetCanFly(true)\nplanebase.SetName(\"Henrietta\")\nplanebase.SetRating(100)\nplanebase.SetMaxSpeed(876) // km/hr\n// if we don't set capacity, it will get the default value, in this case 0.\n//planebase.SetCapacity(26020) // Liters fuel\n\n// Creating a list homes, err := planebase.NewHomes(2)\nif err != nil {\n\tpanic(err)\n}\nhomes.Set(0, air.Airport_jfk)\nhomes.Set(1, air.Airport_lax)\n\n// Ready to write!\n\n// You can write to memory...\nbuf, err := msg.Marshal()\nif err != nil {\n\tpanic(err)\n}\n_ = buf\n\n// ... or write to an io.Writer.\nfile, err := os.CreateTemp(\"\", \"go-capnproto\")\nif err != nil {\n\tpanic(err)\n}\ndefer file.Close()\ndefer os.Remove(file.Name())\nerr = capnp.NewEncoder(file).Encode(msg)\nif err != nil {\n\tpanic(err)\n}\n```\n```\nOutput:\n```\n### Index [¶](#pkg-index)\n\n* [func Canonicalize(s Struct) ([]byte, error)](#Canonicalize)\n* [func Disconnected(s string) error](#Disconnected)\n* [func Equal(p1, p2 Ptr) (bool, error)](#Equal)\n* [func IsDisconnected(e error) bool](#IsDisconnected)\n* [func IsUnimplemented(e error) bool](#IsUnimplemented)\n* [func NewMessage(arena Arena) (*Message, *Segment, error)](#NewMessage)\n* [func NewMultiSegmentMessage(b [][]byte) (msg *Message, first *Segment)](#NewMultiSegmentMessage)\n* [func NewPromisedClient(hook ClientHook) (Client, Resolver[Client])](#NewPromisedClient)\n* [func NewSingleSegmentMessage(b []byte) (msg *Message, first *Segment)](#NewSingleSegmentMessage)\n* [func SamePtr(p, q Ptr) bool](#SamePtr)\n* [func SetClientLeakFunc(clientLeakFunc func(msg string))](#SetClientLeakFunc)\n* [func Unimplemented(s string) error](#Unimplemented)\n* [type Answer](#Answer)\n* + [func ErrorAnswer(m Method, e error) *Answer](#ErrorAnswer)\n\t+ [func ImmediateAnswer(m Method, ptr Ptr) *Answer](#ImmediateAnswer)\n* + [func (ans *Answer) Client() Client](#Answer.Client)\n\t+ [func (ans *Answer) Done() <-chan struct{}](#Answer.Done)\n\t+ [func (ans *Answer) Field(off uint16, def []byte) *Future](#Answer.Field)\n\t+ [func (ans *Answer) Future() *Future](#Answer.Future)\n\t+ [func (ans *Answer) List() (List, error)](#Answer.List)\n\t+ [func (ans *Answer) Metadata() *Metadata](#Answer.Metadata)\n\t+ [func (ans *Answer) PipelineRecv(ctx context.Context, transform []PipelineOp, r Recv) PipelineCaller](#Answer.PipelineRecv)\n\t+ [func (ans *Answer) PipelineSend(ctx context.Context, transform []PipelineOp, s Send) (*Answer, ReleaseFunc)](#Answer.PipelineSend)\n\t+ [func (ans *Answer) Struct() (Struct, error)](#Answer.Struct)\n* [type AnswerQueue](#AnswerQueue)\n* + [func NewAnswerQueue(m Method) *AnswerQueue](#NewAnswerQueue)\n* + [func (aq *AnswerQueue) Fulfill(ptr Ptr)](#AnswerQueue.Fulfill)\n\t+ [func (aq *AnswerQueue) PipelineRecv(ctx context.Context, transform []PipelineOp, r Recv) PipelineCaller](#AnswerQueue.PipelineRecv)\n\t+ [func (aq *AnswerQueue) PipelineSend(ctx context.Context, transform []PipelineOp, r Send) (*Answer, ReleaseFunc)](#AnswerQueue.PipelineSend)\n\t+ [func (aq *AnswerQueue) Reject(e error)](#AnswerQueue.Reject)\n* [type Arena](#Arena)\n* [type BitList](#BitList)\n* + [func NewBitList(s *Segment, n int32) (BitList, error)](#NewBitList)\n* + [func (p BitList) At(i int) bool](#BitList.At)\n\t+ [func (BitList) DecodeFromPtr(p Ptr) BitList](#BitList.DecodeFromPtr)\n\t+ [func (l BitList) EncodeAsPtr(seg *Segment) Ptr](#BitList.EncodeAsPtr)\n\t+ [func (l BitList) IsValid() bool](#BitList.IsValid)\n\t+ [func (l BitList) Len() int](#BitList.Len)\n\t+ [func (l BitList) Message() *Message](#BitList.Message)\n\t+ [func (l BitList) Segment() *Segment](#BitList.Segment)\n\t+ [func (p BitList) Set(i int, v bool)](#BitList.Set)\n\t+ [func (p BitList) String() string](#BitList.String)\n\t+ [func (l BitList) ToPtr() Ptr](#BitList.ToPtr)\n* [type BitOffset](#BitOffset)\n* + [func (bit BitOffset) GoString() string](#BitOffset.GoString)\n\t+ [func (bit BitOffset) String() string](#BitOffset.String)\n* [type Brand](#Brand)\n* [type CapList](#CapList)\n* + [func (c CapList[T]) At(i int) (T, error)](#CapList.At)\n\t+ [func (CapList[T]) DecodeFromPtr(p Ptr) CapList[T]](#CapList.DecodeFromPtr)\n\t+ [func (l CapList[T]) EncodeAsPtr(seg *Segment) Ptr](#CapList.EncodeAsPtr)\n\t+ [func (l CapList[T]) IsValid() bool](#CapList.IsValid)\n\t+ [func (l CapList[T]) Len() int](#CapList.Len)\n\t+ [func (l CapList[T]) Message() *Message](#CapList.Message)\n\t+ [func (l CapList[T]) Segment() *Segment](#CapList.Segment)\n\t+ [func (c CapList[T]) Set(i int, v T) error](#CapList.Set)\n\t+ [func (l CapList[T]) ToPtr() Ptr](#CapList.ToPtr)\n* [type CapTable](#CapTable)\n* + [func (ct *CapTable) Add(c Client) CapabilityID](#CapTable.Add)\n\t+ [func (ct CapTable) At(i int) Client](#CapTable.At)\n\t+ [func (ct CapTable) Contains(ifc Interface) bool](#CapTable.Contains)\n\t+ [func (ct CapTable) Get(ifc Interface) (c Client)](#CapTable.Get)\n\t+ [func (ct CapTable) Len() int](#CapTable.Len)\n\t+ [func (ct *CapTable) Reset(cs ...Client)](#CapTable.Reset)\n\t+ [func (ct CapTable) Set(id CapabilityID, c Client)](#CapTable.Set)\n* [type CapabilityID](#CapabilityID)\n* + [func (id CapabilityID) GoString() string](#CapabilityID.GoString)\n\t+ [func (id CapabilityID) String() string](#CapabilityID.String)\n* [type Client](#Client)\n* + [func ErrorClient(e error) Client](#ErrorClient)\n\t+ [func NewClient(hook ClientHook) Client](#NewClient)\n* + [func (c Client) AddRef() Client](#Client.AddRef)\n\t+ [func (Client) DecodeFromPtr(p Ptr) Client](#Client.DecodeFromPtr)\n\t+ [func (c Client) EncodeAsPtr(seg *Segment) Ptr](#Client.EncodeAsPtr)\n\t+ [func (c Client) GetFlowLimiter() flowcontrol.FlowLimiter](#Client.GetFlowLimiter)\n\t+ [func (c Client) IsSame(c2 Client) bool](#Client.IsSame)\n\t+ [func (c Client) IsValid() bool](#Client.IsValid)\n\t+ [func (c Client) RecvCall(ctx context.Context, r Recv) PipelineCaller](#Client.RecvCall)\n\t+ [func (c Client) Release()](#Client.Release)\n\t+ [func (c Client) Resolve(ctx context.Context) error](#Client.Resolve)\n\t+ [func (c Client) SendCall(ctx context.Context, s Send) (*Answer, ReleaseFunc)](#Client.SendCall)\n\t+ [func (c Client) SendStreamCall(ctx context.Context, s Send) error](#Client.SendStreamCall)\n\t+ [func (c Client) SetFlowLimiter(lim flowcontrol.FlowLimiter)](#Client.SetFlowLimiter)\n\t+ [func (c Client) State() ClientState](#Client.State)\n\t+ [func (c Client) String() string](#Client.String)\n\t+ [func (c Client) WaitStreaming() error](#Client.WaitStreaming)\n\t+ [func (c Client) WeakRef() *WeakClient](#Client.WeakRef)\n* [type ClientHook](#ClientHook)\n* [type ClientKind](#ClientKind)\n* [type ClientState](#ClientState)\n* [type DataList](#DataList)\n* + [func NewDataList(s *Segment, n int32) (DataList, error)](#NewDataList)\n* + [func (l DataList) At(i int) ([]byte, error)](#DataList.At)\n\t+ [func (DataList) DecodeFromPtr(p Ptr) DataList](#DataList.DecodeFromPtr)\n\t+ [func (l DataList) EncodeAsPtr(seg *Segment) Ptr](#DataList.EncodeAsPtr)\n\t+ [func (l DataList) IsValid() bool](#DataList.IsValid)\n\t+ [func (l DataList) Len() int](#DataList.Len)\n\t+ [func (l DataList) Message() *Message](#DataList.Message)\n\t+ [func (l DataList) Segment() *Segment](#DataList.Segment)\n\t+ [func (l DataList) Set(i int, v []byte) error](#DataList.Set)\n\t+ [func (l DataList) String() string](#DataList.String)\n\t+ [func (l DataList) ToPtr() Ptr](#DataList.ToPtr)\n* [type DataOffset](#DataOffset)\n* + [func (off DataOffset) GoString() string](#DataOffset.GoString)\n\t+ [func (off DataOffset) String() string](#DataOffset.String)\n* [type Decoder](#Decoder)\n* + [func NewDecoder(r io.Reader) *Decoder](#NewDecoder)\n\t+ [func NewPackedDecoder(r io.Reader) *Decoder](#NewPackedDecoder)\n* + [func (d *Decoder) Decode() (*Message, error)](#Decoder.Decode)\n* [type Encoder](#Encoder)\n* + [func NewEncoder(w io.Writer) *Encoder](#NewEncoder)\n\t+ [func NewPackedEncoder(w io.Writer) *Encoder](#NewPackedEncoder)\n* + [func (e *Encoder) Encode(m *Message) error](#Encoder.Encode)\n* [type EnumList](#EnumList)\n* + [func NewEnumList(s *Segment, n int32) (EnumList[T], error)](#NewEnumList)\n* + [func (l EnumList[T]) At(i int) T](#EnumList.At)\n\t+ [func (EnumList[T]) DecodeFromPtr(p Ptr) EnumList[T]](#EnumList.DecodeFromPtr)\n\t+ [func (l EnumList[T]) EncodeAsPtr(seg *Segment) Ptr](#EnumList.EncodeAsPtr)\n\t+ [func (l EnumList[T]) IsValid() bool](#EnumList.IsValid)\n\t+ [func (l EnumList[T]) Len() int](#EnumList.Len)\n\t+ [func (l EnumList[T]) Message() *Message](#EnumList.Message)\n\t+ [func (l EnumList[T]) Segment() *Segment](#EnumList.Segment)\n\t+ [func (l EnumList[T]) Set(i int, v T)](#EnumList.Set)\n\t+ [func (l EnumList[T]) String() string](#EnumList.String)\n\t+ [func (l EnumList[T]) ToPtr() Ptr](#EnumList.ToPtr)\n* [type Float32List](#Float32List)\n* + [func NewFloat32List(s *Segment, n int32) (Float32List, error)](#NewFloat32List)\n* + [func (l Float32List) At(i int) float32](#Float32List.At)\n\t+ [func (Float32List) DecodeFromPtr(p Ptr) Float32List](#Float32List.DecodeFromPtr)\n\t+ [func (l Float32List) EncodeAsPtr(seg *Segment) Ptr](#Float32List.EncodeAsPtr)\n\t+ [func (l Float32List) IsValid() bool](#Float32List.IsValid)\n\t+ [func (l Float32List) Len() int](#Float32List.Len)\n\t+ [func (l Float32List) Message() *Message](#Float32List.Message)\n\t+ [func (l Float32List) Segment() *Segment](#Float32List.Segment)\n\t+ [func (l Float32List) Set(i int, v float32)](#Float32List.Set)\n\t+ [func (l Float32List) String() string](#Float32List.String)\n\t+ [func (l Float32List) ToPtr() Ptr](#Float32List.ToPtr)\n* [type Float64List](#Float64List)\n* + [func NewFloat64List(s *Segment, n int32) (Float64List, error)](#NewFloat64List)\n* + [func (l Float64List) At(i int) float64](#Float64List.At)\n\t+ [func (Float64List) DecodeFromPtr(p Ptr) Float64List](#Float64List.DecodeFromPtr)\n\t+ [func (l Float64List) EncodeAsPtr(seg *Segment) Ptr](#Float64List.EncodeAsPtr)\n\t+ [func (l Float64List) IsValid() bool](#Float64List.IsValid)\n\t+ [func (l Float64List) Len() int](#Float64List.Len)\n\t+ [func (l Float64List) Message() *Message](#Float64List.Message)\n\t+ [func (l Float64List) Segment() *Segment](#Float64List.Segment)\n\t+ [func (l Float64List) Set(i int, v float64)](#Float64List.Set)\n\t+ [func (l Float64List) String() string](#Float64List.String)\n\t+ [func (l Float64List) ToPtr() Ptr](#Float64List.ToPtr)\n* [type Future](#Future)\n* + [func (f *Future) Client() Client](#Future.Client)\n\t+ [func (f *Future) Done() <-chan struct{}](#Future.Done)\n\t+ [func (f *Future) Field(off uint16, def []byte) *Future](#Future.Field)\n\t+ [func (f *Future) List() (List, error)](#Future.List)\n\t+ [func (f *Future) Ptr() (Ptr, error)](#Future.Ptr)\n\t+ [func (f *Future) Struct() (Struct, error)](#Future.Struct)\n* [type Int16List](#Int16List)\n* + [func NewInt16List(s *Segment, n int32) (Int16List, error)](#NewInt16List)\n* + [func (l Int16List) At(i int) int16](#Int16List.At)\n\t+ [func (Int16List) DecodeFromPtr(p Ptr) Int16List](#Int16List.DecodeFromPtr)\n\t+ [func (l Int16List) EncodeAsPtr(seg *Segment) Ptr](#Int16List.EncodeAsPtr)\n\t+ [func (l Int16List) IsValid() bool](#Int16List.IsValid)\n\t+ [func (l Int16List) Len() int](#Int16List.Len)\n\t+ [func (l Int16List) Message() *Message](#Int16List.Message)\n\t+ [func (l Int16List) Segment() *Segment](#Int16List.Segment)\n\t+ [func (l Int16List) Set(i int, v int16)](#Int16List.Set)\n\t+ [func (l Int16List) String() string](#Int16List.String)\n\t+ [func (l Int16List) ToPtr() Ptr](#Int16List.ToPtr)\n* [type Int32List](#Int32List)\n* + [func NewInt32List(s *Segment, n int32) (Int32List, error)](#NewInt32List)\n* + [func (l Int32List) At(i int) int32](#Int32List.At)\n\t+ [func (Int32List) DecodeFromPtr(p Ptr) Int32List](#Int32List.DecodeFromPtr)\n\t+ [func (l Int32List) EncodeAsPtr(seg *Segment) Ptr](#Int32List.EncodeAsPtr)\n\t+ [func (l Int32List) IsValid() bool](#Int32List.IsValid)\n\t+ [func (l Int32List) Len() int](#Int32List.Len)\n\t+ [func (l Int32List) Message() *Message](#Int32List.Message)\n\t+ [func (l Int32List) Segment() *Segment](#Int32List.Segment)\n\t+ [func (l Int32List) Set(i int, v int32)](#Int32List.Set)\n\t+ [func (l Int32List) String() string](#Int32List.String)\n\t+ [func (l Int32List) ToPtr() Ptr](#Int32List.ToPtr)\n* [type Int64List](#Int64List)\n* + [func NewInt64List(s *Segment, n int32) (Int64List, error)](#NewInt64List)\n* + [func (l Int64List) At(i int) int64](#Int64List.At)\n\t+ [func (Int64List) DecodeFromPtr(p Ptr) Int64List](#Int64List.DecodeFromPtr)\n\t+ [func (l Int64List) EncodeAsPtr(seg *Segment) Ptr](#Int64List.EncodeAsPtr)\n\t+ [func (l Int64List) IsValid() bool](#Int64List.IsValid)\n\t+ [func (l Int64List) Len() int](#Int64List.Len)\n\t+ [func (l Int64List) Message() *Message](#Int64List.Message)\n\t+ [func (l Int64List) Segment() *Segment](#Int64List.Segment)\n\t+ [func (l Int64List) Set(i int, v int64)](#Int64List.Set)\n\t+ [func (l Int64List) String() string](#Int64List.String)\n\t+ [func (l Int64List) ToPtr() Ptr](#Int64List.ToPtr)\n* [type Int8List](#Int8List)\n* + [func NewInt8List(s *Segment, n int32) (Int8List, error)](#NewInt8List)\n* + [func (l Int8List) At(i int) int8](#Int8List.At)\n\t+ [func (Int8List) DecodeFromPtr(p Ptr) Int8List](#Int8List.DecodeFromPtr)\n\t+ [func (l Int8List) EncodeAsPtr(seg *Segment) Ptr](#Int8List.EncodeAsPtr)\n\t+ [func (l Int8List) IsValid() bool](#Int8List.IsValid)\n\t+ [func (l Int8List) Len() int](#Int8List.Len)\n\t+ [func (l Int8List) Message() *Message](#Int8List.Message)\n\t+ [func (l Int8List) Segment() *Segment](#Int8List.Segment)\n\t+ [func (l Int8List) Set(i int, v int8)](#Int8List.Set)\n\t+ [func (l Int8List) String() string](#Int8List.String)\n\t+ [func (l Int8List) ToPtr() Ptr](#Int8List.ToPtr)\n* [type Interface](#Interface)\n* + [func NewInterface(s *Segment, cap CapabilityID) Interface](#NewInterface)\n* + [func (i Interface) Capability() CapabilityID](#Interface.Capability)\n\t+ [func (i Interface) Client() (c Client)](#Interface.Client)\n\t+ [func (Interface) DecodeFromPtr(p Ptr) Interface](#Interface.DecodeFromPtr)\n\t+ [func (i Interface) EncodeAsPtr(*Segment) Ptr](#Interface.EncodeAsPtr)\n\t+ [func (i Interface) IsValid() bool](#Interface.IsValid)\n\t+ [func (i Interface) Message() *Message](#Interface.Message)\n\t+ [func (i Interface) ToPtr() Ptr](#Interface.ToPtr)\n* [type List](#List)\n* + [func NewCompositeList(s *Segment, sz ObjectSize, n int32) (List, error)](#NewCompositeList)\n* + [func (List) DecodeFromPtr(p Ptr) List](#List.DecodeFromPtr)\n\t+ [func (l List) EncodeAsPtr(*Segment) Ptr](#List.EncodeAsPtr)\n\t+ [func (p List) IsValid() bool](#List.IsValid)\n\t+ [func (p List) Len() int](#List.Len)\n\t+ [func (p List) Message() *Message](#List.Message)\n\t+ [func (p List) Segment() *Segment](#List.Segment)\n\t+ [func (p List) SetStruct(i int, s Struct) error](#List.SetStruct)\n\t+ [func (p List) Struct(i int) Struct](#List.Struct)\n\t+ [func (p List) ToPtr() Ptr](#List.ToPtr)\n* [type ListKind](#ListKind)\n* [type Message](#Message)\n* + [func Unmarshal(data []byte) (*Message, error)](#Unmarshal)\n\t+ [func UnmarshalPacked(data []byte) (*Message, error)](#UnmarshalPacked)\n* + [func (m *Message) CapTable() *CapTable](#Message.CapTable)\n\t+ [func (m *Message) Marshal() ([]byte, error)](#Message.Marshal)\n\t+ [func (m *Message) MarshalPacked() ([]byte, error)](#Message.MarshalPacked)\n\t+ [func (m *Message) NumSegments() int64](#Message.NumSegments)\n\t+ [func (m *Message) Release()](#Message.Release)\n\t+ [func (m *Message) Reset(arena Arena) (first *Segment, err error)](#Message.Reset)\n\t+ [func (m *Message) ResetReadLimit(limit uint64)](#Message.ResetReadLimit)\n\t+ [func (m *Message) Root() (Ptr, error)](#Message.Root)\n\t+ [func (m *Message) Segment(id SegmentID) (*Segment, error)](#Message.Segment)\n\t+ [func (m *Message) SetRoot(p Ptr) error](#Message.SetRoot)\n\t+ [func (m *Message) TotalSize() (uint64, error)](#Message.TotalSize)\n\t+ [func (m *Message) Unread(sz Size)](#Message.Unread)\n\t+ [func (m *Message) WriteTo(w io.Writer) (int64, error)](#Message.WriteTo)\n* [type Metadata](#Metadata)\n* + [func NewMetadata() *Metadata](#NewMetadata)\n* + [func (m *Metadata) Delete(key any)](#Metadata.Delete)\n\t+ [func (m *Metadata) Get(key any) (value any, ok bool)](#Metadata.Get)\n\t+ [func (m *Metadata) Lock()](#Metadata.Lock)\n\t+ [func (m *Metadata) Put(key, value any)](#Metadata.Put)\n\t+ [func (m *Metadata) Unlock()](#Metadata.Unlock)\n* [type Method](#Method)\n* + [func (m *Method) String() string](#Method.String)\n* [type MultiSegmentArena](#MultiSegmentArena)\n* + [func MultiSegment(b [][]byte) *MultiSegmentArena](#MultiSegment)\n* + [func (msa *MultiSegmentArena) Allocate(sz Size, segs map[SegmentID]*Segment) (SegmentID, []byte, error)](#MultiSegmentArena.Allocate)\n\t+ [func (msa *MultiSegmentArena) Data(id SegmentID) ([]byte, error)](#MultiSegmentArena.Data)\n\t+ [func (msa *MultiSegmentArena) NumSegments() int64](#MultiSegmentArena.NumSegments)\n\t+ [func (msa *MultiSegmentArena) Release()](#MultiSegmentArena.Release)\n\t+ [func (msa *MultiSegmentArena) String() string](#MultiSegmentArena.String)\n* [type ObjectSize](#ObjectSize)\n* + [func (sz ObjectSize) GoString() string](#ObjectSize.GoString)\n\t+ [func (sz ObjectSize) String() string](#ObjectSize.String)\n* [type PipelineCaller](#PipelineCaller)\n* [type PipelineClient](#PipelineClient)\n* + [func (pc PipelineClient) Answer() *Answer](#PipelineClient.Answer)\n\t+ [func (pc PipelineClient) Brand() Brand](#PipelineClient.Brand)\n\t+ [func (pc PipelineClient) Recv(ctx context.Context, r Recv) PipelineCaller](#PipelineClient.Recv)\n\t+ [func (pc PipelineClient) Send(ctx context.Context, s Send) (*Answer, ReleaseFunc)](#PipelineClient.Send)\n\t+ [func (pc PipelineClient) Shutdown()](#PipelineClient.Shutdown)\n\t+ [func (pc PipelineClient) String() string](#PipelineClient.String)\n\t+ [func (pc PipelineClient) Transform() []PipelineOp](#PipelineClient.Transform)\n* [type PipelineOp](#PipelineOp)\n* + [func (op PipelineOp) String() string](#PipelineOp.String)\n* [type PointerList](#PointerList)\n* + [func NewPointerList(s *Segment, n int32) (PointerList, error)](#NewPointerList)\n* + [func (p PointerList) At(i int) (Ptr, error)](#PointerList.At)\n\t+ [func (PointerList) DecodeFromPtr(p Ptr) PointerList](#PointerList.DecodeFromPtr)\n\t+ [func (l PointerList) EncodeAsPtr(seg *Segment) Ptr](#PointerList.EncodeAsPtr)\n\t+ [func (l PointerList) IsValid() bool](#PointerList.IsValid)\n\t+ [func (l PointerList) Len() int](#PointerList.Len)\n\t+ [func (l PointerList) Message() *Message](#PointerList.Message)\n\t+ [func (l PointerList) Segment() *Segment](#PointerList.Segment)\n\t+ [func (p PointerList) Set(i int, v Ptr) error](#PointerList.Set)\n\t+ [func (l PointerList) ToPtr() Ptr](#PointerList.ToPtr)\n* [type Promise](#Promise)\n* + [func NewPromise(m Method, pc PipelineCaller) *Promise](#NewPromise)\n* + [func (p *Promise) Answer() *Answer](#Promise.Answer)\n\t+ [func (p *Promise) Fulfill(result Ptr)](#Promise.Fulfill)\n\t+ [func (p *Promise) Reject(e error)](#Promise.Reject)\n\t+ [func (p *Promise) ReleaseClients()](#Promise.ReleaseClients)\n\t+ [func (p *Promise) Resolve(r Ptr, e error)](#Promise.Resolve)\n* [type Ptr](#Ptr)\n* + [func MustUnmarshalRoot(data []byte) Ptr](#MustUnmarshalRoot)\n\t+ [func Transform(p Ptr, transform []PipelineOp) (Ptr, error)](#Transform)\n* + [func (p Ptr) Data() []byte](#Ptr.Data)\n\t+ [func (p Ptr) DataDefault(def []byte) []byte](#Ptr.DataDefault)\n\t+ [func (Ptr) DecodeFromPtr(p Ptr) Ptr](#Ptr.DecodeFromPtr)\n\t+ [func (p Ptr) Default(def []byte) (Ptr, error)](#Ptr.Default)\n\t+ [func (p Ptr) EncodeAsPtr(*Segment) Ptr](#Ptr.EncodeAsPtr)\n\t+ [func (p Ptr) Interface() Interface](#Ptr.Interface)\n\t+ [func (p Ptr) IsValid() bool](#Ptr.IsValid)\n\t+ [func (p Ptr) List() List](#Ptr.List)\n\t+ [func (p Ptr) ListDefault(def []byte) (List, error)](#Ptr.ListDefault)\n\t+ [func (p Ptr) Message() *Message](#Ptr.Message)\n\t+ [func (p Ptr) Segment() *Segment](#Ptr.Segment)\n\t+ [func (p Ptr) Struct() Struct](#Ptr.Struct)\n\t+ [func (p Ptr) StructDefault(def []byte) (Struct, error)](#Ptr.StructDefault)\n\t+ [func (p Ptr) Text() string](#Ptr.Text)\n\t+ [func (p Ptr) TextBytes() []byte](#Ptr.TextBytes)\n\t+ [func (p Ptr) TextBytesDefault(def string) []byte](#Ptr.TextBytesDefault)\n\t+ [func (p Ptr) TextDefault(def string) string](#Ptr.TextDefault)\n* [type Recv](#Recv)\n* + [func (r Recv) AllocResults(sz ObjectSize) (Struct, error)](#Recv.AllocResults)\n\t+ [func (r Recv) Reject(e error)](#Recv.Reject)\n\t+ [func (r Recv) Return()](#Recv.Return)\n* [type ReleaseFunc](#ReleaseFunc)\n* [type Request](#Request)\n* + [func NewRequest(client Client, method Method, argsSize ObjectSize) (*Request, error)](#NewRequest)\n* + [func (r *Request) Args() Struct](#Request.Args)\n\t+ [func (r *Request) Future() *Future](#Request.Future)\n\t+ [func (r *Request) Release()](#Request.Release)\n\t+ [func (r *Request) Send(ctx context.Context) *Future](#Request.Send)\n\t+ [func (r *Request) SendStream(ctx context.Context) error](#Request.SendStream)\n* [type Resolver](#Resolver)\n* + [func NewLocalPromise() (C, Resolver[C])](#NewLocalPromise)\n* [type Returner](#Returner)\n* [type Segment](#Segment)\n* + [func (s *Segment) Data() []byte](#Segment.Data)\n\t+ [func (s *Segment) ID() SegmentID](#Segment.ID)\n\t+ [func (s *Segment) Message() *Message](#Segment.Message)\n* [type SegmentID](#SegmentID)\n* [type Send](#Send)\n* [type SingleSegmentArena](#SingleSegmentArena)\n* + [func SingleSegment(b []byte) *SingleSegmentArena](#SingleSegment)\n* + [func (ssa *SingleSegmentArena) Allocate(sz Size, segs map[SegmentID]*Segment) (SegmentID, []byte, error)](#SingleSegmentArena.Allocate)\n\t+ [func (ssa SingleSegmentArena) Data(id SegmentID) ([]byte, error)](#SingleSegmentArena.Data)\n\t+ [func (ssa SingleSegmentArena) NumSegments() int64](#SingleSegmentArena.NumSegments)\n\t+ [func (ssa *SingleSegmentArena) Release()](#SingleSegmentArena.Release)\n\t+ [func (ssa SingleSegmentArena) String() string](#SingleSegmentArena.String)\n* [type Size](#Size)\n* + [func (sz Size) GoString() string](#Size.GoString)\n\t+ [func (sz Size) String() string](#Size.String)\n* [type Struct](#Struct)\n* + [func NewRootStruct(s *Segment, sz ObjectSize) (Struct, error)](#NewRootStruct)\n\t+ [func NewStruct(s *Segment, sz ObjectSize) (Struct, error)](#NewStruct)\n* + [func (p Struct) Bit(n BitOffset) bool](#Struct.Bit)\n\t+ [func (p Struct) CopyFrom(other Struct) error](#Struct.CopyFrom)\n\t+ [func (Struct) DecodeFromPtr(p Ptr) Struct](#Struct.DecodeFromPtr)\n\t+ [func (s Struct) EncodeAsPtr(*Segment) Ptr](#Struct.EncodeAsPtr)\n\t+ [func (p Struct) HasPtr(i uint16) bool](#Struct.HasPtr)\n\t+ [func (p Struct) IsValid() bool](#Struct.IsValid)\n\t+ [func (p Struct) Message() *Message](#Struct.Message)\n\t+ [func (p Struct) Ptr(i uint16) (Ptr, error)](#Struct.Ptr)\n\t+ [func (p Struct) Segment() *Segment](#Struct.Segment)\n\t+ [func (p Struct) SetBit(n BitOffset, v bool)](#Struct.SetBit)\n\t+ [func (p Struct) SetData(i uint16, v []byte) error](#Struct.SetData)\n\t+ [func (p Struct) SetNewText(i uint16, v string) error](#Struct.SetNewText)\n\t+ [func (p Struct) SetPtr(i uint16, src Ptr) error](#Struct.SetPtr)\n\t+ [func (p Struct) SetText(i uint16, v string) error](#Struct.SetText)\n\t+ [func (p Struct) SetTextFromBytes(i uint16, v []byte) error](#Struct.SetTextFromBytes)\n\t+ [func (p Struct) SetUint16(off DataOffset, v uint16)](#Struct.SetUint16)\n\t+ [func (p Struct) SetUint32(off DataOffset, v uint32)](#Struct.SetUint32)\n\t+ [func (p Struct) SetUint64(off DataOffset, v uint64)](#Struct.SetUint64)\n\t+ [func (p Struct) SetUint8(off DataOffset, v uint8)](#Struct.SetUint8)\n\t+ [func (p Struct) Size() ObjectSize](#Struct.Size)\n\t+ [func (p Struct) ToPtr() Ptr](#Struct.ToPtr)\n\t+ [func (p Struct) Uint16(off DataOffset) uint16](#Struct.Uint16)\n\t+ [func (p Struct) Uint32(off DataOffset) uint32](#Struct.Uint32)\n\t+ [func (p Struct) Uint64(off DataOffset) uint64](#Struct.Uint64)\n\t+ [func (p Struct) Uint8(off DataOffset) uint8](#Struct.Uint8)\n* [type StructKind](#StructKind)\n* [type StructList](#StructList)\n* + [func (s StructList[T]) At(i int) T](#StructList.At)\n\t+ [func (StructList[T]) DecodeFromPtr(p Ptr) StructList[T]](#StructList.DecodeFromPtr)\n\t+ [func (l StructList[T]) EncodeAsPtr(seg *Segment) Ptr](#StructList.EncodeAsPtr)\n\t+ [func (l StructList[T]) IsValid() bool](#StructList.IsValid)\n\t+ [func (l StructList[T]) Len() int](#StructList.Len)\n\t+ [func (l StructList[T]) Message() *Message](#StructList.Message)\n\t+ [func (l StructList[T]) Segment() *Segment](#StructList.Segment)\n\t+ [func (s StructList[T]) Set(i int, v T) error](#StructList.Set)\n\t+ [func (l StructList[T]) ToPtr() Ptr](#StructList.ToPtr)\n* [type StructReturner](#StructReturner)\n* + [func (sr *StructReturner) AllocResults(sz ObjectSize) (Struct, error)](#StructReturner.AllocResults)\n\t+ [func (sr *StructReturner) Answer(m Method, pcall PipelineCaller) (*Answer, ReleaseFunc)](#StructReturner.Answer)\n\t+ [func (sr *StructReturner) PrepareReturn(e error)](#StructReturner.PrepareReturn)\n\t+ [func (sr *StructReturner) ReleaseResults()](#StructReturner.ReleaseResults)\n\t+ [func (sr *StructReturner) Return()](#StructReturner.Return)\n* [type TextList](#TextList)\n* + [func NewTextList(s *Segment, n int32) (TextList, error)](#NewTextList)\n* + [func (l TextList) At(i int) (string, error)](#TextList.At)\n\t+ [func (l TextList) BytesAt(i int) ([]byte, error)](#TextList.BytesAt)\n\t+ [func (TextList) DecodeFromPtr(p Ptr) TextList](#TextList.DecodeFromPtr)\n\t+ [func (l TextList) EncodeAsPtr(seg *Segment) Ptr](#TextList.EncodeAsPtr)\n\t+ [func (l TextList) IsValid() bool](#TextList.IsValid)\n\t+ [func (l TextList) Len() int](#TextList.Len)\n\t+ [func (l TextList) Message() *Message](#TextList.Message)\n\t+ [func (l TextList) Segment() *Segment](#TextList.Segment)\n\t+ [func (l TextList) Set(i int, v string) error](#TextList.Set)\n\t+ [func (l TextList) String() string](#TextList.String)\n\t+ [func (l TextList) ToPtr() Ptr](#TextList.ToPtr)\n* [type TypeParam](#TypeParam)\n* [type UInt16List](#UInt16List)\n* + [func NewUInt16List(s *Segment, n int32) (UInt16List, error)](#NewUInt16List)\n* + [func (l UInt16List) At(i int) uint16](#UInt16List.At)\n\t+ [func (UInt16List) DecodeFromPtr(p Ptr) UInt16List](#UInt16List.DecodeFromPtr)\n\t+ [func (l UInt16List) EncodeAsPtr(seg *Segment) Ptr](#UInt16List.EncodeAsPtr)\n\t+ [func (l UInt16List) IsValid() bool](#UInt16List.IsValid)\n\t+ [func (l UInt16List) Len() int](#UInt16List.Len)\n\t+ [func (l UInt16List) Message() *Message](#UInt16List.Message)\n\t+ [func (l UInt16List) Segment() *Segment](#UInt16List.Segment)\n\t+ [func (l UInt16List) Set(i int, v uint16)](#UInt16List.Set)\n\t+ [func (l UInt16List) String() string](#UInt16List.String)\n\t+ [func (l UInt16List) ToPtr() Ptr](#UInt16List.ToPtr)\n* [type UInt32List](#UInt32List)\n* + [func NewUInt32List(s *Segment, n int32) (UInt32List, error)](#NewUInt32List)\n* + [func (l UInt32List) At(i int) uint32](#UInt32List.At)\n\t+ [func (UInt32List) DecodeFromPtr(p Ptr) UInt32List](#UInt32List.DecodeFromPtr)\n\t+ [func (l UInt32List) EncodeAsPtr(seg *Segment) Ptr](#UInt32List.EncodeAsPtr)\n\t+ [func (l UInt32List) IsValid() bool](#UInt32List.IsValid)\n\t+ [func (l UInt32List) Len() int](#UInt32List.Len)\n\t+ [func (l UInt32List) Message() *Message](#UInt32List.Message)\n\t+ [func (l UInt32List) Segment() *Segment](#UInt32List.Segment)\n\t+ [func (l UInt32List) Set(i int, v uint32)](#UInt32List.Set)\n\t+ [func (l UInt32List) String() string](#UInt32List.String)\n\t+ [func (l UInt32List) ToPtr() Ptr](#UInt32List.ToPtr)\n* [type UInt64List](#UInt64List)\n* + [func NewUInt64List(s *Segment, n int32) (UInt64List, error)](#NewUInt64List)\n* + [func (l UInt64List) At(i int) uint64](#UInt64List.At)\n\t+ [func (UInt64List) DecodeFromPtr(p Ptr) UInt64List](#UInt64List.DecodeFromPtr)\n\t+ [func (l UInt64List) EncodeAsPtr(seg *Segment) Ptr](#UInt64List.EncodeAsPtr)\n\t+ [func (l UInt64List) IsValid() bool](#UInt64List.IsValid)\n\t+ [func (l UInt64List) Len() int](#UInt64List.Len)\n\t+ [func (l UInt64List) Message() *Message](#UInt64List.Message)\n\t+ [func (l UInt64List) Segment() *Segment](#UInt64List.Segment)\n\t+ [func (l UInt64List) Set(i int, v uint64)](#UInt64List.Set)\n\t+ [func (l UInt64List) String() string](#UInt64List.String)\n\t+ [func (l UInt64List) ToPtr() Ptr](#UInt64List.ToPtr)\n* [type UInt8List](#UInt8List)\n* + [func NewData(s *Segment, v []byte) (UInt8List, error)](#NewData)\n\t+ [func NewText(s *Segment, v string) (UInt8List, error)](#NewText)\n\t+ [func NewTextFromBytes(s *Segment, v []byte) (UInt8List, error)](#NewTextFromBytes)\n\t+ [func NewUInt8List(s *Segment, n int32) (UInt8List, error)](#NewUInt8List)\n* + [func (l UInt8List) At(i int) uint8](#UInt8List.At)\n\t+ [func (UInt8List) DecodeFromPtr(p Ptr) UInt8List](#UInt8List.DecodeFromPtr)\n\t+ [func (l UInt8List) EncodeAsPtr(seg *Segment) Ptr](#UInt8List.EncodeAsPtr)\n\t+ [func (l UInt8List) IsValid() bool](#UInt8List.IsValid)\n\t+ [func (l UInt8List) Len() int](#UInt8List.Len)\n\t+ [func (l UInt8List) Message() *Message](#UInt8List.Message)\n\t+ [func (l UInt8List) Segment() *Segment](#UInt8List.Segment)\n\t+ [func (l UInt8List) Set(i int, v uint8)](#UInt8List.Set)\n\t+ [func (l UInt8List) String() string](#UInt8List.String)\n\t+ [func (l UInt8List) ToPtr() Ptr](#UInt8List.ToPtr)\n* [type VoidList](#VoidList)\n* + [func NewVoidList(s *Segment, n int32) VoidList](#NewVoidList)\n* + [func (VoidList) DecodeFromPtr(p Ptr) VoidList](#VoidList.DecodeFromPtr)\n\t+ [func (l VoidList) EncodeAsPtr(seg *Segment) Ptr](#VoidList.EncodeAsPtr)\n\t+ [func (l VoidList) IsValid() bool](#VoidList.IsValid)\n\t+ [func (l VoidList) Len() int](#VoidList.Len)\n\t+ [func (l VoidList) Message() *Message](#VoidList.Message)\n\t+ [func (l VoidList) Segment() *Segment](#VoidList.Segment)\n\t+ [func (l VoidList) String() string](#VoidList.String)\n\t+ [func (l VoidList) ToPtr() Ptr](#VoidList.ToPtr)\n* [type WeakClient](#WeakClient)\n* + [func (wc *WeakClient) AddRef() (c Client, ok bool)](#WeakClient.AddRef)\n\n#### Examples [¶](#pkg-examples)\n\n* [Package](#example-package)\n* [Unmarshal](#example-Unmarshal)\n\n### Constants [¶](#pkg-constants)\n\nThis section is empty.\n\n### Variables [¶](#pkg-variables)\n\nThis section is empty.\n\n### Functions [¶](#pkg-functions)\n\n#### \nfunc [Canonicalize](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/canonical.go#L12) [¶](#Canonicalize)\n```\nfunc Canonicalize(s [Struct](#Struct)) ([][byte](/builtin#byte), [error](/builtin#error))\n```\nCanonicalize encodes a struct into its canonical form: a single-\nsegment blob without a segment table. The result will be identical for equivalent structs, even as the schema evolves. The blob is suitable for hashing or signing.\n\n#### \nfunc [Disconnected](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/error.go#L23) [¶](#Disconnected)\n```\nfunc Disconnected(s [string](/builtin#string)) [error](/builtin#error)\n```\nDisconnected returns an error that formats as the given text and will report true when passed to IsDisconnected.\n\n#### \nfunc [Equal](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L287) [¶](#Equal)\n```\nfunc Equal(p1, p2 [Ptr](#Ptr)) ([bool](/builtin#bool), [error](/builtin#error))\n```\nEqual returns true iff p1 and p2 are equal.\n\nEquality is defined to be:\n\n* Two structs are equal iff all of their fields are equal. If one struct has more fields than the other, the extra fields must all be zero.\n* Two lists are equal iff they have the same length and their corresponding elements are equal. If one list is a list of primitives and the other is a list of structs, then the list of primitives is treated as if it was a list of structs with the element value as the sole field.\n* Two interfaces are equal iff they point to a capability created by the same call to NewClient or they are referring to the same capability table index in the same message. The latter is significant when the message's capability table has not been populated.\n* Two null pointers are equal.\n* All other combinations of things are not equal.\n\n#### \nfunc [IsDisconnected](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/error.go#L28) [¶](#IsDisconnected)\n```\nfunc IsDisconnected(e [error](/builtin#error)) [bool](/builtin#bool)\n```\nIsDisconnected reports whether e indicates a failure due to loss of a necessary capability.\n\n#### \nfunc [IsUnimplemented](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/error.go#L17) [¶](#IsUnimplemented)\n```\nfunc IsUnimplemented(e [error](/builtin#error)) [bool](/builtin#bool)\n```\nIsUnimplemented reports whether e indicates that functionality is unimplemented.\n\n#### \nfunc [NewMessage](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L63) [¶](#NewMessage)\n```\nfunc NewMessage(arena [Arena](#Arena)) (*[Message](#Message), *[Segment](#Segment), [error](/builtin#error))\n```\nNewMessage creates a message with a new root and returns the first segment. It is an error to call NewMessage on an arena with data in it.\n\n#### \nfunc [NewMultiSegmentMessage](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L82) [¶](#NewMultiSegmentMessage)\n```\nfunc NewMultiSegmentMessage(b [][][byte](/builtin#byte)) (msg *[Message](#Message), first *[Segment](#Segment))\n```\nAnalogous to NewSingleSegmentMessage, but using MultiSegment.\n\n#### \nfunc [NewPromisedClient](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L190) [¶](#NewPromisedClient)\n```\nfunc NewPromisedClient(hook [ClientHook](#ClientHook)) ([Client](#Client), [Resolver](#Resolver)[[Client](#Client)])\n```\nNewPromisedClient creates the first reference to a capability that can resolve to a different capability. The hook will be shut down when the promise is resolved or the client has no more references,\nwhichever comes first.\n\nTypically the RPC system will create a client for the application.\nMost applications will not need to use this directly.\n\n#### \nfunc [NewSingleSegmentMessage](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L73) [¶](#NewSingleSegmentMessage)\n```\nfunc NewSingleSegmentMessage(b [][byte](/builtin#byte)) (msg *[Message](#Message), first *[Segment](#Segment))\n```\nNewSingleSegmentMessage(b) is equivalent to NewMessage(SingleSegment(b)), except that it panics instead of returning an error. This can only happen if the passed slice contains data, so the caller is responsible for ensuring that it has a length of zero.\n\n#### \nfunc [SamePtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L202) [¶](#SamePtr)\n```\nfunc SamePtr(p, q [Ptr](#Ptr)) [bool](/builtin#bool)\n```\nSamePtr reports whether p and q refer to the same object.\n\n#### \nfunc [SetClientLeakFunc](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L696) [¶](#SetClientLeakFunc)\n```\nfunc SetClientLeakFunc(clientLeakFunc func(msg [string](/builtin#string)))\n```\nSetClientLeakFunc sets a callback for reporting Clients that went out of scope without being released. The callback is not guaranteed to be called and must be safe to call concurrently from multiple goroutines. The exact format of the message is unspecified.\n\nSetClientLeakFunc must not be called after any calls to NewClient or NewPromisedClient.\n\n#### \nfunc [Unimplemented](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/error.go#L12) [¶](#Unimplemented)\n```\nfunc Unimplemented(s [string](/builtin#string)) [error](/builtin#error)\n```\nUnimplemented returns an error that formats as the given text and will report true when passed to IsUnimplemented.\n\n### Types [¶](#pkg-types)\n\n#### \ntype [Answer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L233) [¶](#Answer)\n```\ntype Answer struct {\n\t// contains filtered or unexported fields\n}\n```\nAn Answer is a deferred result of a client call. Conceptually, this is a future. It is safe to use from multiple goroutines.\n\n#### \nfunc [ErrorAnswer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L239) [¶](#ErrorAnswer)\n```\nfunc ErrorAnswer(m [Method](#Method), e [error](/builtin#error)) *[Answer](#Answer)\n```\nErrorAnswer returns a Answer that always returns error e.\n\n#### \nfunc [ImmediateAnswer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L252) [¶](#ImmediateAnswer)\n```\nfunc ImmediateAnswer(m [Method](#Method), ptr [Ptr](#Ptr)) *[Answer](#Answer)\n```\nImmediateAnswer returns an Answer that accesses ptr.\n\n#### \nfunc (*Answer) [Client](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L297) [¶](#Answer.Client)\n```\nfunc (ans *[Answer](#Answer)) Client() [Client](#Client)\n```\nClient returns the answer as a client. If the answer's originating call has not completed, then calls will be queued until the original call's completion. The client reference is borrowed: the caller should not call Close.\n\n#### \nfunc (*Answer) [Done](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L277) [¶](#Answer.Done)\n```\nfunc (ans *[Answer](#Answer)) Done() <-chan struct{}\n```\nDone returns a channel that is closed when the answer's call is finished.\n\n#### \nfunc (*Answer) [Field](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L303) [¶](#Answer.Field)\n```\nfunc (ans *[Answer](#Answer)) Field(off [uint16](/builtin#uint16), def [][byte](/builtin#byte)) *[Future](#Future)\n```\nField returns a derived future which yields the pointer field given,\ndefaulting to the value given.\n\n#### \nfunc (*Answer) [Future](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L266) [¶](#Answer.Future)\n```\nfunc (ans *[Answer](#Answer)) Future() *[Future](#Future)\n```\nFuture returns a future that is equivalent to ans.\n\n#### \nfunc (*Answer) [List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L289) [¶](#Answer.List)\n```\nfunc (ans *[Answer](#Answer)) List() ([List](#List), [error](/builtin#error))\n```\nList waits until the answer is resolved and returns the list this answer represents.\n\n#### \nfunc (*Answer) [Metadata](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L272) [¶](#Answer.Metadata)\n```\nfunc (ans *[Answer](#Answer)) Metadata() *[Metadata](#Metadata)\n```\nMetadata returns a metadata map where callers can store information about the answer\n\n#### \nfunc (*Answer) [PipelineRecv](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L336) [¶](#Answer.PipelineRecv)\n```\nfunc (ans *[Answer](#Answer)) PipelineRecv(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n```\nPipelineRecv starts a pipelined call.\n\n#### \nfunc (*Answer) [PipelineSend](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L308) [¶](#Answer.PipelineSend)\n```\nfunc (ans *[Answer](#Answer)) PipelineSend(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), s [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n```\nPipelineSend starts a pipelined call.\n\n#### \nfunc (*Answer) [Struct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L283) [¶](#Answer.Struct)\n```\nfunc (ans *[Answer](#Answer)) Struct() ([Struct](#Struct), [error](/builtin#error))\n```\nStruct waits until the answer is resolved and returns the struct this answer represents.\n\n#### \ntype [AnswerQueue](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L23) [¶](#AnswerQueue)\n```\ntype AnswerQueue struct {\n\t// contains filtered or unexported fields\n}\n```\nAnswerQueue is a queue of method calls to make after an earlier method call finishes. The queue is unbounded; it is the caller's responsibility to manage/impose backpressure.\n\nAn AnswerQueue can be in one of three states:\n\n1. Queueing. Incoming method calls will be added to the queue.\n2. Draining, entered by calling Fulfill or Reject. Queued method calls will be delivered in sequence, and new incoming method calls will block until the AnswerQueue enters the Drained state.\n3. Drained, entered once all queued methods have been delivered.\nIncoming methods are passthrough.\n\n#### \nfunc [NewAnswerQueue](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L47) [¶](#NewAnswerQueue)\n```\nfunc NewAnswerQueue(m [Method](#Method)) *[AnswerQueue](#AnswerQueue)\n```\nNewAnswerQueue creates a new answer queue.\n\n#### \nfunc (*AnswerQueue) [Fulfill](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L61) [¶](#AnswerQueue.Fulfill)\n```\nfunc (aq *[AnswerQueue](#AnswerQueue)) Fulfill(ptr [Ptr](#Ptr))\n```\nFulfill empties the queue, delivering the method calls on the given pointer. After fulfill returns, pipeline calls will be immediately delivered instead of being queued.\n\n#### \nfunc (*AnswerQueue) [PipelineRecv](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L114) [¶](#AnswerQueue.PipelineRecv)\n```\nfunc (aq *[AnswerQueue](#AnswerQueue)) PipelineRecv(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n```\n#### \nfunc (*AnswerQueue) [PipelineSend](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L118) [¶](#AnswerQueue.PipelineSend)\n```\nfunc (aq *[AnswerQueue](#AnswerQueue)) PipelineSend(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), r [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n```\n#### \nfunc (*AnswerQueue) [Reject](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L85) [¶](#AnswerQueue.Reject)\n```\nfunc (aq *[AnswerQueue](#AnswerQueue)) Reject(e [error](/builtin#error))\n```\nReject empties the queue, returning errors on all the method calls.\n\n#### \ntype [Arena](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L12) [¶](#Arena)\n```\ntype Arena interface {\n // NumSegments returns the number of segments in the arena.\n\t// This must not be larger than 1<<32.\n\tNumSegments() [int64](/builtin#int64)\n\n // Data loads the data for the segment with the given ID. IDs are in\n\t// the range [0, NumSegments()).\n\t// must be tightly packed in the range [0, NumSegments()).\n\tData(id [SegmentID](#SegmentID)) ([][byte](/builtin#byte), [error](/builtin#error))\n\n // Allocate selects a segment to place a new object in, creating a\n\t// segment or growing the capacity of a previously loaded segment if\n\t// necessary. If Allocate does not return an error, then the\n\t// difference of the capacity and the length of the returned slice\n\t// must be at least minsz. segs is a map of segments keyed by ID\n\t// using arrays returned by the Data method (although the length of\n\t// these slices may have changed by previous allocations). Allocate\n\t// must not modify segs.\n\t//\n\t// If Allocate creates a new segment, the ID must be one larger than\n\t// the last segment's ID or zero if it is the first segment.\n\t//\n\t// If Allocate returns an previously loaded segment's ID, then the\n\t// arena is responsible for preserving the existing data in the\n\t// returned byte slice.\n\tAllocate(minsz [Size](#Size), segs map[[SegmentID](#SegmentID)]*[Segment](#Segment)) ([SegmentID](#SegmentID), [][byte](/builtin#byte), [error](/builtin#error))\n\n // Release all resources associated with the Arena. Callers MUST NOT\n\t// use the Arena after it has been released.\n\t//\n\t// Calling Release() is OPTIONAL, but may reduce allocations.\n\t//\n\t// Implementations MAY use Release() as a signal to return resources\n\t// to free lists, or otherwise reuse the Arena. However, they MUST\n\t// NOT assume Release() will be called.\n\tRelease()\n}\n```\nAn Arena loads and allocates segments for a Message.\n\n#### \ntype [BitList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L250) [¶](#BitList)\n```\ntype BitList [List](#List)\n```\nA BitList is a reference to a list of booleans.\n\n#### \nfunc [NewBitList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L255) [¶](#NewBitList)\n```\nfunc NewBitList(s *[Segment](#Segment), n [int32](/builtin#int32)) ([BitList](#BitList), [error](/builtin#error))\n```\nNewBitList creates a new bit list, preferring placement in s.\n\n#### \nfunc (BitList) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L279) [¶](#BitList.At)\n```\nfunc (p [BitList](#BitList)) At(i [int](/builtin#int)) [bool](/builtin#bool)\n```\nAt returns the i'th bit.\n\n#### \nfunc (BitList) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L49) [¶](#BitList.DecodeFromPtr)\n```\nfunc ([BitList](#BitList)) DecodeFromPtr(p [Ptr](#Ptr)) [BitList](#BitList)\n```\n#### \nfunc (BitList) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L45) [¶](#BitList.EncodeAsPtr)\n```\nfunc (l [BitList](#BitList)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (BitList) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L37) [¶](#BitList.IsValid)\n```\nfunc (l [BitList](#BitList)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (BitList) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L41) [¶](#BitList.Len)\n```\nfunc (l [BitList](#BitList)) Len() [int](/builtin#int)\n```\n#### \nfunc (BitList) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L53) [¶](#BitList.Message)\n```\nfunc (l [BitList](#BitList)) Message() *[Message](#Message)\n```\n#### \nfunc (BitList) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L57) [¶](#BitList.Segment)\n```\nfunc (l [BitList](#BitList)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (BitList) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L293) [¶](#BitList.Set)\n```\nfunc (p [BitList](#BitList)) Set(i [int](/builtin#int), v [bool](/builtin#bool))\n```\nSet sets the i'th bit to v.\n\n#### \nfunc (BitList) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L313) [¶](#BitList.String)\n```\nfunc (p [BitList](#BitList)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[true, false]\").\n\n#### \nfunc (BitList) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L61) [¶](#BitList.ToPtr)\n```\nfunc (l [BitList](#BitList)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [BitOffset](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L197) [¶](#BitOffset)\n```\ntype BitOffset [uint32](/builtin#uint32)\n```\nBitOffset is an offset in bits from the beginning of a struct's data section. It is bounded to [0, 1<<22).\n\n#### \nfunc (BitOffset) [GoString](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L215) [¶](#BitOffset.GoString)\n```\nfunc (bit [BitOffset](#BitOffset)) GoString() [string](/builtin#string)\n```\nGoString returns the offset as a Go expression.\n\n#### \nfunc (BitOffset) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L210) [¶](#BitOffset.String)\n```\nfunc (bit [BitOffset](#BitOffset)) String() [string](/builtin#string)\n```\nString returns the offset in the format \"bit X\".\n\n#### \ntype [Brand](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L573) [¶](#Brand)\n```\ntype Brand struct {\n Value [any](/builtin#any)\n}\n```\nA Brand is an opaque value used to identify a capability.\n\n#### \ntype [CapList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1082) [¶](#CapList)\n```\ntype CapList[T ~[ClientKind](#ClientKind)] [PointerList](#PointerList)\n```\nA list of some Cap'n Proto capability type T.\n\n#### \nfunc (CapList[T]) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1084) [¶](#CapList.At)\n```\nfunc (c [CapList](#CapList)[T]) At(i [int](/builtin#int)) (T, [error](/builtin#error))\n```\n#### \nfunc (CapList[T]) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L305) [¶](#CapList.DecodeFromPtr)\n```\nfunc ([CapList](#CapList)[T]) DecodeFromPtr(p [Ptr](#Ptr)) [CapList](#CapList)[T]\n```\n#### \nfunc (CapList[T]) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L301) [¶](#CapList.EncodeAsPtr)\n```\nfunc (l [CapList](#CapList)[T]) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (CapList[T]) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L293) [¶](#CapList.IsValid)\n```\nfunc (l [CapList](#CapList)[T]) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (CapList[T]) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L297) [¶](#CapList.Len)\n```\nfunc (l [CapList](#CapList)[T]) Len() [int](/builtin#int)\n```\n#### \nfunc (CapList[T]) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L309) [¶](#CapList.Message)\n```\nfunc (l [CapList](#CapList)[T]) Message() *[Message](#Message)\n```\n#### \nfunc (CapList[T]) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L313) [¶](#CapList.Segment)\n```\nfunc (l [CapList](#CapList)[T]) Segment() *[Segment](#Segment)\n```\n#### \nfunc (CapList[T]) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1092) [¶](#CapList.Set)\n```\nfunc (c [CapList](#CapList)[T]) Set(i [int](/builtin#int), v T) [error](/builtin#error)\n```\n#### \nfunc (CapList[T]) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L317) [¶](#CapList.ToPtr)\n```\nfunc (l [CapList](#CapList)[T]) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [CapTable](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L9) [¶](#CapTable)\n```\ntype CapTable struct {\n\t// contains filtered or unexported fields\n}\n```\nCapTable is the indexed list of the clients referenced in the message. Capability pointers inside the message will use this table to map pointers to Clients. The table is populated by the RPC system.\n\n<https://capnproto.org/encoding.html#capabilities-interfaces#### \nfunc (*CapTable) [Add](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L61) [¶](#CapTable.Add)\n```\nfunc (ct *[CapTable](#CapTable)) Add(c [Client](#Client)) [CapabilityID](#CapabilityID)\n```\nAdd appends a capability to the message's capability table and returns its ID. It \"steals\" c's reference: the Message will release the client when calling Reset.\n\n#### \nfunc (CapTable) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L30) [¶](#CapTable.At)\n```\nfunc (ct [CapTable](#CapTable)) At(i [int](/builtin#int)) [Client](#Client)\n```\nAt returns the capability at the given index of the table.\n\n#### \nfunc (CapTable) [Contains](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L36) [¶](#CapTable.Contains)\n```\nfunc (ct [CapTable](#CapTable)) Contains(ifc [Interface](#Interface)) [bool](/builtin#bool)\n```\nContains returns true if the supplied interface corresponds to a client already present in the table.\n\n#### \nfunc (CapTable) [Get](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L43) [¶](#CapTable.Get)\n```\nfunc (ct [CapTable](#CapTable)) Get(ifc [Interface](#Interface)) (c [Client](#Client))\n```\nGet the client corresponding to the supplied interface. It returns a null client if the interface's CapabilityID isn't in the table.\n\n#### \nfunc (CapTable) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L25) [¶](#CapTable.Len)\n```\nfunc (ct [CapTable](#CapTable)) Len() [int](/builtin#int)\n```\nLen returns the number of capabilities in the table.\n\n#### \nfunc (*CapTable) [Reset](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L16) [¶](#CapTable.Reset)\n```\nfunc (ct *[CapTable](#CapTable)) Reset(cs ...[Client](#Client))\n```\nReset the cap table, releasing all capabilities and setting the length to zero. Clients passed as arguments are added to the table after zeroing, such that ct.Len() == len(cs).\n\n#### \nfunc (CapTable) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/captable.go#L54) [¶](#CapTable.Set)\n```\nfunc (ct [CapTable](#CapTable)) Set(id [CapabilityID](#CapabilityID), c [Client](#Client))\n```\nSet the client for the supplied capability ID. If a client for the given ID already exists, it will be replaced without releasing.\n\n#### \ntype [CapabilityID](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L91) [¶](#CapabilityID)\n```\ntype CapabilityID [uint32](/builtin#uint32)\n```\nA CapabilityID is an index into a message's capability table.\n\n#### \nfunc (CapabilityID) [GoString](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L99) [¶](#CapabilityID.GoString)\n```\nfunc (id [CapabilityID](#CapabilityID)) GoString() [string](/builtin#string)\n```\nGoString returns the ID as a Go expression.\n\n#### \nfunc (CapabilityID) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L94) [¶](#CapabilityID.String)\n```\nfunc (id [CapabilityID](#CapabilityID)) String() [string](/builtin#string)\n```\nString returns the ID in the format \"capability X\".\n\n#### \ntype [Client](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L106) [¶](#Client)\n```\ntype Client [ClientKind](#ClientKind)\n```\nA Client is a reference to a Cap'n Proto capability.\nThe zero value is a null capability reference.\nIt is safe to use from multiple goroutines.\n\n#### \nfunc [ErrorClient](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L1002) [¶](#ErrorClient)\n```\nfunc ErrorClient(e [error](/builtin#error)) [Client](#Client)\n```\nErrorClient returns a Client that always returns error e.\nAn ErrorClient does not need to be released: it is a sentinel like a nil Client.\n\nThe returned client's State() method returns a State with its Brand.Value set to e.\n\n#### \nfunc [NewClient](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L161) [¶](#NewClient)\n```\nfunc NewClient(hook [ClientHook](#ClientHook)) [Client](#Client)\n```\nNewClient creates the first reference to a capability.\nIf hook is nil, then NewClient returns nil.\n\nTypically the RPC system will create a client for the application.\nMost applications will not need to use this directly.\n\n#### \nfunc (Client) [AddRef](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L517) [¶](#Client.AddRef)\n```\nfunc (c [Client](#Client)) AddRef() [Client](#Client)\n```\nAddRef creates a new Client that refers to the same capability as c.\nIf c is nil or has resolved to null, then AddRef returns nil.\n\n#### \nfunc (Client) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L671) [¶](#Client.DecodeFromPtr)\n```\nfunc ([Client](#Client)) DecodeFromPtr(p [Ptr](#Ptr)) [Client](#Client)\n```\n#### \nfunc (Client) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L666) [¶](#Client.EncodeAsPtr)\n```\nfunc (c [Client](#Client)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Client) [GetFlowLimiter](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L289) [¶](#Client.GetFlowLimiter)\n```\nfunc (c [Client](#Client)) GetFlowLimiter() [flowcontrol](/capnproto.org/go/capnp/v3@v3.0.0-alpha-29/flowcontrol).[FlowLimiter](/capnproto.org/go/capnp/v3@v3.0.0-alpha-29/flowcontrol#FlowLimiter)\n```\nGet the current flowcontrol.FlowLimiter used to manage flow control for this client.\n\n#### \nfunc (Client) [IsSame](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L477) [¶](#Client.IsSame)\n```\nfunc (c [Client](#Client)) IsSame(c2 [Client](#Client)) [bool](/builtin#bool)\n```\nIsSame reports whether c and c2 refer to a capability created by the same call to NewClient. This can return false negatives if c or c2 are not fully resolved: use Resolve if this is an issue. If either c or c2 are released, then IsSame panics.\n\n#### \nfunc (Client) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L468) [¶](#Client.IsValid)\n```\nfunc (c [Client](#Client)) IsValid() [bool](/builtin#bool)\n```\nIsValid reports whether c is a valid reference to a capability.\nA reference is invalid if it is nil, has resolved to null, or has been released.\n\n#### \nfunc (Client) [RecvCall](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L451) [¶](#Client.RecvCall)\n```\nfunc (c [Client](#Client)) RecvCall(ctx [context](/context).[Context](/context#Context), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n```\nRecvCall starts executing a method with the referenced arguments and returns an answer that will hold the result. The hook will call a.Release when it no longer needs to reference the parameters. The caller must call the returned release function when it no longer needs the answer's data.\n\nNote that unlike SendCall, this method does *not* respect the flow control policy configured with SetFlowLimiter.\n\n#### \nfunc (Client) [Release](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L632) [¶](#Client.Release)\n```\nfunc (c [Client](#Client)) Release()\n```\nRelease releases a capability reference. If this is the last reference to the capability, then the underlying resources associated with the capability will be released.\n\nRelease has no effect if c has already been released, or if c is nil or resolved to null.\n\n#### \nfunc (Client) [Resolve](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L492) [¶](#Client.Resolve)\n```\nfunc (c [Client](#Client)) Resolve(ctx [context](/context).[Context](/context#Context)) [error](/builtin#error)\n```\nResolve blocks until the capability is fully resolved or the Context is Done.\nResolve only returns an error if the context is canceled; it returns nil even if the capability resolves to an error.\n\n#### \nfunc (Client) [SendCall](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L319) [¶](#Client.SendCall)\n```\nfunc (c [Client](#Client)) SendCall(ctx [context](/context).[Context](/context#Context), s [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n```\nSendCall allocates space for parameters, calls args.Place to fill out the parameters, then starts executing a method, returning an answer that will hold the result. The caller must call the returned release function when it no longer needs the answer's data.\n\nThis method respects the flow control policy configured with SetFlowLimiter;\nit may block if the sender is sending too fast.\n\n#### \nfunc (Client) [SendStreamCall](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L403) [¶](#Client.SendStreamCall)\n```\nfunc (c [Client](#Client)) SendStreamCall(ctx [context](/context).[Context](/context#Context), s [Send](#Send)) [error](/builtin#error)\n```\nSendStreamCall is like SendCall except that:\n\n1. It does not return an answer for the eventual result.\n2. If the call returns an error, all future calls on this client will return the same error (without starting the method or calling PlaceArgs).\n\n#### \nfunc (Client) [SetFlowLimiter](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L306) [¶](#Client.SetFlowLimiter)\n```\nfunc (c [Client](#Client)) SetFlowLimiter(lim [flowcontrol](/capnproto.org/go/capnp/v3@v3.0.0-alpha-29/flowcontrol).[FlowLimiter](/capnproto.org/go/capnp/v3@v3.0.0-alpha-29/flowcontrol#FlowLimiter))\n```\nUpdate the flowcontrol.FlowLimiter used to manage flow control for this client. This affects all future calls, but not calls already waiting to send. Passing nil sets the value to flowcontrol.NopLimiter,\nwhich is also the default.\n\nWhen .Release() is called on the client, it will call .Release() on the FlowLimiter in turn.\n\n#### \nfunc (Client) [State](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L557) [¶](#Client.State)\n```\nfunc (c [Client](#Client)) State() [ClientState](#ClientState)\n```\nState reads the current state of the client. It returns the zero ClientState if c is nil, has resolved to null, or has been released.\n\n#### \nfunc (Client) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L596) [¶](#Client.String)\n```\nfunc (c [Client](#Client)) String() [string](/builtin#string)\n```\nString returns a string that identifies this capability for debugging purposes. Its format should not be depended on: in particular, it should not be used to compare clients. Use IsSame to compare clients for equality.\n\n#### \nfunc (Client) [WaitStreaming](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L433) [¶](#Client.WaitStreaming)\n```\nfunc (c [Client](#Client)) WaitStreaming() [error](/builtin#error)\n```\nWaitStreaming waits for all outstanding streaming calls (i.e. calls started with SendStreamCall) to complete, and then returns an error if any streaming call has failed.\n\n#### \nfunc (Client) [WeakRef](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L544) [¶](#Client.WeakRef)\n```\nfunc (c [Client](#Client)) WeakRef() *[WeakClient](#WeakClient)\n```\nWeakRef creates a new WeakClient that refers to the same capability as c. If c is nil or has resolved to null, then WeakRef returns nil.\n\n#### \ntype [ClientHook](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L829) [¶](#ClientHook)\n```\ntype ClientHook interface {\n // Send allocates space for parameters, calls s.PlaceArgs to fill out\n\t// the arguments, then starts executing a method, returning an answer\n\t// that will hold the result. The hook must call s.PlaceArgs at most\n\t// once, and if it does call s.PlaceArgs, it must return before Send\n\t// returns. The caller must call the returned release function when\n\t// it no longer needs the answer's data.\n\t//\n\t// Send is typically used when application code is making a call.\n\tSend(ctx [context](/context).[Context](/context#Context), s [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n\n // Recv starts executing a method with the referenced arguments\n\t// and places the result in a message controlled by the caller.\n\t// The hook will call r.ReleaseArgs when it no longer needs to\n\t// reference the parameters and use r.Returner to complete the method\n\t// call. If Recv does not call r.Returner.Return before it returns,\n\t// then it must return a non-nil PipelineCaller.\n\t//\n\t// Recv is typically used when the RPC system has received a call.\n\tRecv(ctx [context](/context).[Context](/context#Context), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n\n // Brand returns an implementation-specific value. This can be used\n\t// to introspect and identify kinds of clients.\n\tBrand() [Brand](#Brand)\n\n // Shutdown releases any resources associated with this capability.\n\t// The behavior of calling any methods on the receiver after calling\n\t// Shutdown is undefined. It is expected for the ClientHook to reject\n\t// any outstanding call futures.\n\tShutdown()\n\n // String formats the hook as a string (same as fmt.Stringer)\n\tString() [string](/builtin#string)\n}\n```\nA ClientHook represents a Cap'n Proto capability. Application code should not pass around ClientHooks; applications should pass around Clients. A ClientHook must be safe to use from multiple goroutines.\n\nCalls must be delivered to the capability in the order they are made.\nThis guarantee is based on the concept of a capability acknowledging delivery of a call: this is specific to an implementation of ClientHook.\nA type that implements ClientHook must guarantee that if foo() then bar()\nis called on a client, then the capability acknowledging foo() happens before the capability observing bar().\n\nClientHook is an internal interface. Users generally SHOULD NOT supply their own implementations.\n\n#### \ntype [ClientKind](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L111) [¶](#ClientKind)\n```\ntype ClientKind = struct {\n\t// contains filtered or unexported fields\n}\n```\nThe underlying type of Client. We expose this so that we can use ~ClientKind as a constraint in generics to capture any capability type.\n\n#### \ntype [ClientState](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L578) [¶](#ClientState)\n```\ntype ClientState struct {\n // Brand is the value returned from the hook's Brand method.\n\tBrand [Brand](#Brand)\n // IsPromise is true if the client has not resolved yet.\n\tIsPromise [bool](/builtin#bool)\n // Arbitrary metadata. Note that, if a Client is a promise,\n\t// when it resolves its metadata will be replaced with that\n\t// of its resolution.\n\t//\n\t// TODO: this might change before the v3 API is stabilized;\n\t// we are not sure the above is the correct semantics.\n\tMetadata *[Metadata](#Metadata)\n}\n```\nClientState is a snapshot of a client's identity.\n\n#### \ntype [DataList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L450) [¶](#DataList)\n```\ntype DataList [List](#List)\n```\nDataList is an array of pointers to data.\n\n#### \nfunc [NewDataList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L455) [¶](#NewDataList)\n```\nfunc NewDataList(s *[Segment](#Segment), n [int32](/builtin#int32)) ([DataList](#DataList), [error](/builtin#error))\n```\nNewDataList allocates a new list of data pointers, preferring placement in s.\n\n#### \nfunc (DataList) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L464) [¶](#DataList.At)\n```\nfunc (l [DataList](#DataList)) At(i [int](/builtin#int)) ([][byte](/builtin#byte), [error](/builtin#error))\n```\nAt returns the i'th data in the list.\n\n#### \nfunc (DataList) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L177) [¶](#DataList.DecodeFromPtr)\n```\nfunc ([DataList](#DataList)) DecodeFromPtr(p [Ptr](#Ptr)) [DataList](#DataList)\n```\n#### \nfunc (DataList) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L173) [¶](#DataList.EncodeAsPtr)\n```\nfunc (l [DataList](#DataList)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (DataList) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L165) [¶](#DataList.IsValid)\n```\nfunc (l [DataList](#DataList)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (DataList) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L169) [¶](#DataList.Len)\n```\nfunc (l [DataList](#DataList)) Len() [int](/builtin#int)\n```\n#### \nfunc (DataList) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L181) [¶](#DataList.Message)\n```\nfunc (l [DataList](#DataList)) Message() *[Message](#Message)\n```\n#### \nfunc (DataList) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L185) [¶](#DataList.Segment)\n```\nfunc (l [DataList](#DataList)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (DataList) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L477) [¶](#DataList.Set)\n```\nfunc (l [DataList](#DataList)) Set(i [int](/builtin#int), v [][byte](/builtin#byte)) [error](/builtin#error)\n```\nSet sets the i'th data in the list to v.\n\n#### \nfunc (DataList) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L493) [¶](#DataList.String)\n```\nfunc (l [DataList](#DataList)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. `[\"foo\", \"bar\"]`).\n\n#### \nfunc (DataList) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L189) [¶](#DataList.ToPtr)\n```\nfunc (l [DataList](#DataList)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [DataOffset](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L122) [¶](#DataOffset)\n```\ntype DataOffset [uint32](/builtin#uint32)\n```\nDataOffset is an offset in bytes from the beginning of a struct's data section. It is bounded to [0, 1<<19).\n\n#### \nfunc (DataOffset) [GoString](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L133) [¶](#DataOffset.GoString)\n```\nfunc (off [DataOffset](#DataOffset)) GoString() [string](/builtin#string)\n```\nGoString returns the offset as a Go expression.\n\n#### \nfunc (DataOffset) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L125) [¶](#DataOffset.String)\n```\nfunc (off [DataOffset](#DataOffset)) String() [string](/builtin#string)\n```\nString returns the offset in the format \"+X bytes\".\n\n#### \ntype [Decoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L18) [¶](#Decoder)\n```\ntype Decoder struct {\n\n // Maximum number of bytes that can be read per call to Decode.\n\t// If not set, a reasonable default is used.\n\tMaxMessageSize [uint64](/builtin#uint64)\n\t// contains filtered or unexported fields\n}\n```\nA Decoder represents a framer that deserializes a particular Cap'n Proto input stream.\n\n#### \nfunc [NewDecoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L32) [¶](#NewDecoder)\n```\nfunc NewDecoder(r [io](/io).[Reader](/io#Reader)) *[Decoder](#Decoder)\n```\nNewDecoder creates a new Cap'n Proto framer that reads from r.\nThe returned decoder will only read as much data as necessary to decode the message.\n\n#### \nfunc [NewPackedDecoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L39) [¶](#NewPackedDecoder)\n```\nfunc NewPackedDecoder(r [io](/io).[Reader](/io#Reader)) *[Decoder](#Decoder)\n```\nNewPackedDecoder creates a new Cap'n Proto framer that reads from a packed stream r. The returned decoder may read more data than necessary from r.\n\n#### \nfunc (*Decoder) [Decode](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L45) [¶](#Decoder.Decode)\n```\nfunc (d *[Decoder](#Decoder)) Decode() (*[Message](#Message), [error](/builtin#error))\n```\nDecode reads a message from the decoder stream. The error is io.EOF only if no bytes were read.\n\n#### \ntype [Encoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L200) [¶](#Encoder)\n```\ntype Encoder struct {\n\t// contains filtered or unexported fields\n}\n```\nAn Encoder represents a framer for serializing a particular Cap'n Proto stream.\n\n#### \nfunc [NewEncoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L207) [¶](#NewEncoder)\n```\nfunc NewEncoder(w [io](/io).[Writer](/io#Writer)) *[Encoder](#Encoder)\n```\nNewEncoder creates a new Cap'n Proto framer that writes to w.\n\n#### \nfunc [NewPackedEncoder](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L213) [¶](#NewPackedEncoder)\n```\nfunc NewPackedEncoder(w [io](/io).[Writer](/io#Writer)) *[Encoder](#Encoder)\n```\nNewPackedEncoder creates a new Cap'n Proto framer that writes to a packed stream w.\n\n#### \nfunc (*Encoder) [Encode](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L218) [¶](#Encoder.Encode)\n```\nfunc (e *[Encoder](#Encoder)) Encode(m *[Message](#Message)) [error](/builtin#error)\n```\nEncode writes a message to the encoder stream.\n\n#### \ntype [EnumList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1041) [¶](#EnumList)\n```\ntype EnumList[T ~[uint16](/builtin#uint16)] [UInt16List](#UInt16List)\n```\nA list of some Cap'n Proto enum type T.\n\n#### \nfunc [NewEnumList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1046) [¶](#NewEnumList)\n```\nfunc NewEnumList[T ~[uint16](/builtin#uint16)](s *[Segment](#Segment), n [int32](/builtin#int32)) ([EnumList](#EnumList)[T], [error](/builtin#error))\n```\nNewEnumList creates a new list of T, preferring placement in s.\n\n#### \nfunc (EnumList[T]) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1052) [¶](#EnumList.At)\n```\nfunc (l [EnumList](#EnumList)[T]) At(i [int](/builtin#int)) T\n```\nAt returns the i'th element.\n\n#### \nfunc (EnumList[T]) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L241) [¶](#EnumList.DecodeFromPtr)\n```\nfunc ([EnumList](#EnumList)[T]) DecodeFromPtr(p [Ptr](#Ptr)) [EnumList](#EnumList)[T]\n```\n#### \nfunc (EnumList[T]) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L237) [¶](#EnumList.EncodeAsPtr)\n```\nfunc (l [EnumList](#EnumList)[T]) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (EnumList[T]) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L229) [¶](#EnumList.IsValid)\n```\nfunc (l [EnumList](#EnumList)[T]) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (EnumList[T]) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L233) [¶](#EnumList.Len)\n```\nfunc (l [EnumList](#EnumList)[T]) Len() [int](/builtin#int)\n```\n#### \nfunc (EnumList[T]) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L245) [¶](#EnumList.Message)\n```\nfunc (l [EnumList](#EnumList)[T]) Message() *[Message](#Message)\n```\n#### \nfunc (EnumList[T]) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L249) [¶](#EnumList.Segment)\n```\nfunc (l [EnumList](#EnumList)[T]) Segment() *[Segment](#Segment)\n```\n#### \nfunc (EnumList[T]) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1057) [¶](#EnumList.Set)\n```\nfunc (l [EnumList](#EnumList)[T]) Set(i [int](/builtin#int), v T)\n```\nSet sets the i'th element to v.\n\n#### \nfunc (EnumList[T]) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1062) [¶](#EnumList.String)\n```\nfunc (l [EnumList](#EnumList)[T]) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (EnumList[T]) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L253) [¶](#EnumList.ToPtr)\n```\nfunc (l [EnumList](#EnumList)[T]) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Float32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L949) [¶](#Float32List)\n```\ntype Float32List [List](#List)\n```\nFloat32List is an array of Float32 values.\n\n#### \nfunc [NewFloat32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L954) [¶](#NewFloat32List)\n```\nfunc NewFloat32List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Float32List](#Float32List), [error](/builtin#error))\n```\nNewFloat32List creates a new list of Float32, preferring placement in s.\n\n#### \nfunc (Float32List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L963) [¶](#Float32List.At)\n```\nfunc (l [Float32List](#Float32List)) At(i [int](/builtin#int)) [float32](/builtin#float32)\n```\nAt returns the i'th element.\n\n#### \nfunc (Float32List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L81) [¶](#Float32List.DecodeFromPtr)\n```\nfunc ([Float32List](#Float32List)) DecodeFromPtr(p [Ptr](#Ptr)) [Float32List](#Float32List)\n```\n#### \nfunc (Float32List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L77) [¶](#Float32List.EncodeAsPtr)\n```\nfunc (l [Float32List](#Float32List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Float32List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L69) [¶](#Float32List.IsValid)\n```\nfunc (l [Float32List](#Float32List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Float32List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L73) [¶](#Float32List.Len)\n```\nfunc (l [Float32List](#Float32List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Float32List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L85) [¶](#Float32List.Message)\n```\nfunc (l [Float32List](#Float32List)) Message() *[Message](#Message)\n```\n#### \nfunc (Float32List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L89) [¶](#Float32List.Segment)\n```\nfunc (l [Float32List](#Float32List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Float32List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L972) [¶](#Float32List.Set)\n```\nfunc (l [Float32List](#Float32List)) Set(i [int](/builtin#int), v [float32](/builtin#float32))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Float32List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L981) [¶](#Float32List.String)\n```\nfunc (l [Float32List](#Float32List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Float32List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L93) [¶](#Float32List.ToPtr)\n```\nfunc (l [Float32List](#Float32List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Float64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L995) [¶](#Float64List)\n```\ntype Float64List [List](#List)\n```\nFloat64List is an array of Float64 values.\n\n#### \nfunc [NewFloat64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1000) [¶](#NewFloat64List)\n```\nfunc NewFloat64List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Float64List](#Float64List), [error](/builtin#error))\n```\nNewFloat64List creates a new list of Float64, preferring placement in s.\n\n#### \nfunc (Float64List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1009) [¶](#Float64List.At)\n```\nfunc (l [Float64List](#Float64List)) At(i [int](/builtin#int)) [float64](/builtin#float64)\n```\nAt returns the i'th element.\n\n#### \nfunc (Float64List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L113) [¶](#Float64List.DecodeFromPtr)\n```\nfunc ([Float64List](#Float64List)) DecodeFromPtr(p [Ptr](#Ptr)) [Float64List](#Float64List)\n```\n#### \nfunc (Float64List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L109) [¶](#Float64List.EncodeAsPtr)\n```\nfunc (l [Float64List](#Float64List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Float64List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L101) [¶](#Float64List.IsValid)\n```\nfunc (l [Float64List](#Float64List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Float64List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L105) [¶](#Float64List.Len)\n```\nfunc (l [Float64List](#Float64List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Float64List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L117) [¶](#Float64List.Message)\n```\nfunc (l [Float64List](#Float64List)) Message() *[Message](#Message)\n```\n#### \nfunc (Float64List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L121) [¶](#Float64List.Segment)\n```\nfunc (l [Float64List](#Float64List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Float64List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1018) [¶](#Float64List.Set)\n```\nfunc (l [Float64List](#Float64List)) Set(i [int](/builtin#int), v [float64](/builtin#float64))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Float64List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1027) [¶](#Float64List.String)\n```\nfunc (l [Float64List](#Float64List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Float64List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L125) [¶](#Float64List.ToPtr)\n```\nfunc (l [Float64List](#Float64List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Future](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L366) [¶](#Future)\n```\ntype Future struct {\n\t// contains filtered or unexported fields\n}\n```\nA Future accesses a portion of an Answer. It is safe to use from multiple goroutines.\n\n#### \nfunc (*Future) [Client](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L423) [¶](#Future.Client)\n```\nfunc (f *[Future](#Future)) Client() [Client](#Client)\n```\nClient returns the future as a client. If the answer's originating call has not completed, then calls will be queued until the original call's completion. The client reference is borrowed: the caller should not call Release.\n\n#### \nfunc (*Future) [Done](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L390) [¶](#Future.Done)\n```\nfunc (f *[Future](#Future)) Done() <-chan struct{}\n```\nDone returns a channel that is closed when the answer's call is finished.\n\n#### \nfunc (*Future) [Field](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L459) [¶](#Future.Field)\n```\nfunc (f *[Future](#Future)) Field(off [uint16](/builtin#uint16), def [][byte](/builtin#byte)) *[Future](#Future)\n```\nField returns a derived future which yields the pointer field given,\ndefaulting to the value given.\n\n#### \nfunc (*Future) [List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L414) [¶](#Future.List)\n```\nfunc (f *[Future](#Future)) List() ([List](#List), [error](/builtin#error))\n```\nList waits until the answer is resolved and returns the list this answer represents.\n\n#### \nfunc (*Future) [Ptr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L396) [¶](#Future.Ptr)\n```\nfunc (f *[Future](#Future)) Ptr() ([Ptr](#Ptr), [error](/builtin#error))\n```\nPtr waits until the answer is resolved and returns the pointer this future represents.\n\n#### \nfunc (*Future) [Struct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L407) [¶](#Future.Struct)\n```\nfunc (f *[Future](#Future)) Struct() ([Struct](#Struct), [error](/builtin#error))\n```\nStruct waits until the answer is resolved and returns the struct this answer represents.\n\n#### \ntype [Int16List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L719) [¶](#Int16List)\n```\ntype Int16List [List](#List)\n```\nInt16List is an array of Int16 values.\n\n#### \nfunc [NewInt16List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L724) [¶](#NewInt16List)\n```\nfunc NewInt16List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Int16List](#Int16List), [error](/builtin#error))\n```\nNewInt16List creates a new list of Int16, preferring placement in s.\n\n#### \nfunc (Int16List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L733) [¶](#Int16List.At)\n```\nfunc (l [Int16List](#Int16List)) At(i [int](/builtin#int)) [int16](/builtin#int16)\n```\nAt returns the i'th element.\n\n#### \nfunc (Int16List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L401) [¶](#Int16List.DecodeFromPtr)\n```\nfunc ([Int16List](#Int16List)) DecodeFromPtr(p [Ptr](#Ptr)) [Int16List](#Int16List)\n```\n#### \nfunc (Int16List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L397) [¶](#Int16List.EncodeAsPtr)\n```\nfunc (l [Int16List](#Int16List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Int16List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L389) [¶](#Int16List.IsValid)\n```\nfunc (l [Int16List](#Int16List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Int16List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L393) [¶](#Int16List.Len)\n```\nfunc (l [Int16List](#Int16List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Int16List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L405) [¶](#Int16List.Message)\n```\nfunc (l [Int16List](#Int16List)) Message() *[Message](#Message)\n```\n#### \nfunc (Int16List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L409) [¶](#Int16List.Segment)\n```\nfunc (l [Int16List](#Int16List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Int16List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L742) [¶](#Int16List.Set)\n```\nfunc (l [Int16List](#Int16List)) Set(i [int](/builtin#int), v [int16](/builtin#int16))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Int16List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L751) [¶](#Int16List.String)\n```\nfunc (l [Int16List](#Int16List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Int16List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L413) [¶](#Int16List.ToPtr)\n```\nfunc (l [Int16List](#Int16List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Int32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L811) [¶](#Int32List)\n```\ntype Int32List [List](#List)\n```\nInt32List is an array of Int32 values.\n\n#### \nfunc [NewInt32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L816) [¶](#NewInt32List)\n```\nfunc NewInt32List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Int32List](#Int32List), [error](/builtin#error))\n```\nNewInt32List creates a new list of Int32, preferring placement in s.\n\n#### \nfunc (Int32List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L825) [¶](#Int32List.At)\n```\nfunc (l [Int32List](#Int32List)) At(i [int](/builtin#int)) [int32](/builtin#int32)\n```\nAt returns the i'th element.\n\n#### \nfunc (Int32List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L465) [¶](#Int32List.DecodeFromPtr)\n```\nfunc ([Int32List](#Int32List)) DecodeFromPtr(p [Ptr](#Ptr)) [Int32List](#Int32List)\n```\n#### \nfunc (Int32List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L461) [¶](#Int32List.EncodeAsPtr)\n```\nfunc (l [Int32List](#Int32List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Int32List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L453) [¶](#Int32List.IsValid)\n```\nfunc (l [Int32List](#Int32List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Int32List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L457) [¶](#Int32List.Len)\n```\nfunc (l [Int32List](#Int32List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Int32List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L469) [¶](#Int32List.Message)\n```\nfunc (l [Int32List](#Int32List)) Message() *[Message](#Message)\n```\n#### \nfunc (Int32List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L473) [¶](#Int32List.Segment)\n```\nfunc (l [Int32List](#Int32List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Int32List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L834) [¶](#Int32List.Set)\n```\nfunc (l [Int32List](#Int32List)) Set(i [int](/builtin#int), v [int32](/builtin#int32))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Int32List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L843) [¶](#Int32List.String)\n```\nfunc (l [Int32List](#Int32List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Int32List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L477) [¶](#Int32List.ToPtr)\n```\nfunc (l [Int32List](#Int32List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Int64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L903) [¶](#Int64List)\n```\ntype Int64List [List](#List)\n```\nInt64List is an array of Int64 values.\n\n#### \nfunc [NewInt64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L908) [¶](#NewInt64List)\n```\nfunc NewInt64List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Int64List](#Int64List), [error](/builtin#error))\n```\nNewInt64List creates a new list of Int64, preferring placement in s.\n\n#### \nfunc (Int64List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L917) [¶](#Int64List.At)\n```\nfunc (l [Int64List](#Int64List)) At(i [int](/builtin#int)) [int64](/builtin#int64)\n```\nAt returns the i'th element.\n\n#### \nfunc (Int64List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L529) [¶](#Int64List.DecodeFromPtr)\n```\nfunc ([Int64List](#Int64List)) DecodeFromPtr(p [Ptr](#Ptr)) [Int64List](#Int64List)\n```\n#### \nfunc (Int64List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L525) [¶](#Int64List.EncodeAsPtr)\n```\nfunc (l [Int64List](#Int64List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Int64List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L517) [¶](#Int64List.IsValid)\n```\nfunc (l [Int64List](#Int64List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Int64List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L521) [¶](#Int64List.Len)\n```\nfunc (l [Int64List](#Int64List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Int64List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L533) [¶](#Int64List.Message)\n```\nfunc (l [Int64List](#Int64List)) Message() *[Message](#Message)\n```\n#### \nfunc (Int64List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L537) [¶](#Int64List.Segment)\n```\nfunc (l [Int64List](#Int64List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Int64List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L926) [¶](#Int64List.Set)\n```\nfunc (l [Int64List](#Int64List)) Set(i [int](/builtin#int), v [int64](/builtin#int64))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Int64List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L935) [¶](#Int64List.String)\n```\nfunc (l [Int64List](#Int64List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Int64List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L541) [¶](#Int64List.ToPtr)\n```\nfunc (l [Int64List](#Int64List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Int8List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L627) [¶](#Int8List)\n```\ntype Int8List [List](#List)\n```\nInt8List is an array of Int8 values.\n\n#### \nfunc [NewInt8List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L632) [¶](#NewInt8List)\n```\nfunc NewInt8List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([Int8List](#Int8List), [error](/builtin#error))\n```\nNewInt8List creates a new list of Int8, preferring placement in s.\n\n#### \nfunc (Int8List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L641) [¶](#Int8List.At)\n```\nfunc (l [Int8List](#Int8List)) At(i [int](/builtin#int)) [int8](/builtin#int8)\n```\nAt returns the i'th element.\n\n#### \nfunc (Int8List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L337) [¶](#Int8List.DecodeFromPtr)\n```\nfunc ([Int8List](#Int8List)) DecodeFromPtr(p [Ptr](#Ptr)) [Int8List](#Int8List)\n```\n#### \nfunc (Int8List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L333) [¶](#Int8List.EncodeAsPtr)\n```\nfunc (l [Int8List](#Int8List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (Int8List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L325) [¶](#Int8List.IsValid)\n```\nfunc (l [Int8List](#Int8List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (Int8List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L329) [¶](#Int8List.Len)\n```\nfunc (l [Int8List](#Int8List)) Len() [int](/builtin#int)\n```\n#### \nfunc (Int8List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L341) [¶](#Int8List.Message)\n```\nfunc (l [Int8List](#Int8List)) Message() *[Message](#Message)\n```\n#### \nfunc (Int8List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L345) [¶](#Int8List.Segment)\n```\nfunc (l [Int8List](#Int8List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (Int8List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L650) [¶](#Int8List.Set)\n```\nfunc (l [Int8List](#Int8List)) Set(i [int](/builtin#int), v [int8](/builtin#int8))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (Int8List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L659) [¶](#Int8List.String)\n```\nfunc (l [Int8List](#Int8List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (Int8List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L349) [¶](#Int8List.ToPtr)\n```\nfunc (l [Int8List](#Int8List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Interface](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L22) [¶](#Interface)\n```\ntype Interface struct {\n\t// contains filtered or unexported fields\n}\n```\nAn Interface is a reference to a client in a message's capability table.\n\n#### \nfunc [NewInterface](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L40) [¶](#NewInterface)\n```\nfunc NewInterface(s *[Segment](#Segment), cap [CapabilityID](#CapabilityID)) [Interface](#Interface)\n```\nNewInterface creates a new interface pointer.\n\nNo allocation is performed in the given segment: it is used purely to associate the interface pointer with a message.\n\n#### \nfunc (Interface) [Capability](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L68) [¶](#Interface.Capability)\n```\nfunc (i [Interface](#Interface)) Capability() [CapabilityID](#CapabilityID)\n```\nCapability returns the capability ID of the interface.\n\n#### \nfunc (Interface) [Client](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L82) [¶](#Interface.Client)\n```\nfunc (i [Interface](#Interface)) Client() (c [Client](#Client))\n```\nClient returns the client stored in the message's capability table or nil if the pointer is invalid.\n\n#### \nfunc (Interface) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L32) [¶](#Interface.DecodeFromPtr)\n```\nfunc ([Interface](#Interface)) DecodeFromPtr(p [Ptr](#Ptr)) [Interface](#Interface)\n```\nDecodeFromPtr(p) is equivalent to p.Interface(); for implementing TypeParam.\n\n#### \nfunc (Interface) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L29) [¶](#Interface.EncodeAsPtr)\n```\nfunc (i [Interface](#Interface)) EncodeAsPtr(*[Segment](#Segment)) [Ptr](#Ptr)\n```\ni.EncodeAsPtr is equivalent to i.ToPtr(); for implementing TypeParam.\nThe segment argument is ignored.\n\n#### \nfunc (Interface) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L63) [¶](#Interface.IsValid)\n```\nfunc (i [Interface](#Interface)) IsValid() [bool](/builtin#bool)\n```\nIsValid returns whether the interface is valid.\n\n#### \nfunc (Interface) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L55) [¶](#Interface.Message)\n```\nfunc (i [Interface](#Interface)) Message() *[Message](#Message)\n```\nMessage returns the message whose capability table the interface references or nil if the pointer is invalid.\n\n#### \nfunc (Interface) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L45) [¶](#Interface.ToPtr)\n```\nfunc (i [Interface](#Interface)) ToPtr() [Ptr](#Ptr)\n```\nToPtr converts the interface to a generic pointer.\n\n#### \ntype [List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L14) [¶](#List)\n```\ntype List [ListKind](#ListKind)\n```\nA List is a reference to an array of values.\n\n#### \nfunc [NewCompositeList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L51) [¶](#NewCompositeList)\n```\nfunc NewCompositeList(s *[Segment](#Segment), sz [ObjectSize](#ObjectSize), n [int32](/builtin#int32)) ([List](#List), [error](/builtin#error))\n```\nNewCompositeList creates a new composite list, preferring placement in s.\n\n#### \nfunc (List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L245) [¶](#List.DecodeFromPtr)\n```\nfunc ([List](#List)) DecodeFromPtr(p [Ptr](#Ptr)) [List](#List)\n```\nDecodeFromPtr(p) is equivalent to p.List; for implementing TypeParam.\n\n#### \nfunc (List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L242) [¶](#List.EncodeAsPtr)\n```\nfunc (l [List](#List)) EncodeAsPtr(*[Segment](#Segment)) [Ptr](#Ptr)\n```\nl.EncodeAsPtr is equivalent to l.ToPtr(); for implementing TypeParam.\nThe segment argument is ignored.\n\n#### \nfunc (List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L107) [¶](#List.IsValid)\n```\nfunc (p [List](#List)) IsValid() [bool](/builtin#bool)\n```\nIsValid returns whether the list is valid.\n\n#### \nfunc (List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L178) [¶](#List.Len)\n```\nfunc (p [List](#List)) Len() [int](/builtin#int)\n```\nLen returns the length of the list.\n\n#### \nfunc (List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L99) [¶](#List.Message)\n```\nfunc (p [List](#List)) Message() *[Message](#Message)\n```\nMessage returns the message the referenced list is stored in or nil if the pointer is invalid.\n\n#### \nfunc (List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L93) [¶](#List.Segment)\n```\nfunc (p [List](#List)) Segment() *[Segment](#Segment)\n```\nSegment returns the segment the referenced list is stored in or nil if the pointer is invalid.\n\n#### \nfunc (List) [SetStruct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L230) [¶](#List.SetStruct)\n```\nfunc (p [List](#List)) SetStruct(i [int](/builtin#int), s [Struct](#Struct)) [error](/builtin#error)\n```\nSetStruct set the i'th element to the value in s.\n\n#### \nfunc (List) [Struct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L208) [¶](#List.Struct)\n```\nfunc (p [List](#List)) Struct(i [int](/builtin#int)) [Struct](#Struct)\n```\nStruct returns the i'th element as a struct.\n\n#### \nfunc (List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L80) [¶](#List.ToPtr)\n```\nfunc (p [List](#List)) ToPtr() [Ptr](#Ptr)\n```\nToPtr converts the list to a generic pointer.\n\n#### \ntype [ListKind](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L19) [¶](#ListKind)\n```\ntype ListKind = struct {\n\t// contains filtered or unexported fields\n}\n```\nThe underlying type of List. We expose this so that we can use ~ListKind as a constraint in generics to capture any list type.\n\n#### \ntype [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L30) [¶](#Message)\n```\ntype Message struct {\n Arena [Arena](#Arena)\n\n // TraverseLimit limits how many total bytes of data are allowed to be\n\t// traversed while reading. Traversal is counted when a Struct or\n\t// List is obtained. This means that calling a getter for the same\n\t// sub-struct multiple times will cause it to be double-counted. Once\n\t// the traversal limit is reached, pointer accessors will report\n\t// errors. See <https://capnproto.org/encoding.html#amplification-attack>\n\t// for more details on this security measure.\n\t//\n\t// If not set, this defaults to 64 MiB.\n\tTraverseLimit [uint64](/builtin#uint64)\n\n // DepthLimit limits how deeply-nested a message structure can be.\n\t// If not set, this defaults to 64.\n\tDepthLimit [uint](/builtin#uint)\n\t// contains filtered or unexported fields\n}\n```\nA Message is a tree of Cap'n Proto objects, split into one or more segments of contiguous memory. The only required field is Arena.\nA Message is safe to read from multiple goroutines.\n\n#### \nfunc [Unmarshal](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L144) [¶](#Unmarshal)\n```\nfunc Unmarshal(data [][byte](/builtin#byte)) (*[Message](#Message), [error](/builtin#error))\n```\nUnmarshal reads an unpacked serialized stream into a message. No copying is performed, so the objects in the returned message read directly from data.\n\nExample [¶](#example-Unmarshal)\n```\nmsg, s, err := capnp.NewMessage(capnp.SingleSegment(nil))\nif err != nil {\n\tfmt.Printf(\"allocation error %v\\n\", err)\n\treturn\n}\nd, err := air.NewRootZdate(s)\nif err != nil {\n\tfmt.Printf(\"root error %v\\n\", err)\n\treturn\n}\nd.SetYear(2004)\nd.SetMonth(12)\nd.SetDay(7)\ndata, err := msg.Marshal()\nif err != nil {\n\tfmt.Printf(\"marshal error %v\\n\", err)\n\treturn\n}\n\n// Read msg, err = capnp.Unmarshal(data)\nif err != nil {\n\tfmt.Printf(\"unmarshal error %v\\n\", err)\n\treturn\n}\nd, err = air.ReadRootZdate(msg)\nif err != nil {\n\tfmt.Printf(\"read root error %v\\n\", err)\n\treturn\n}\nfmt.Printf(\"year %d, month %d, day %d\\n\", d.Year(), d.Month(), d.Day())\n```\n```\nOutput:\n\nyear 2004, month 12, day 7\n```\n#### \nfunc [UnmarshalPacked](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L173) [¶](#UnmarshalPacked)\n```\nfunc UnmarshalPacked(data [][byte](/builtin#byte)) (*[Message](#Message), [error](/builtin#error))\n```\nUnmarshalPacked reads a packed serialized stream into a message.\n\n#### \nfunc (*Message) [CapTable](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L221) [¶](#Message.CapTable)\n```\nfunc (m *[Message](#Message)) CapTable() *[CapTable](#CapTable)\n```\nCapTable is the indexed list of the clients referenced in the message. Capability pointers inside the message will use this table to map pointers to Clients. The table is populated by the RPC system.\n\n<https://capnproto.org/encoding.html#capabilities-interfaces#### \nfunc (*Message) [Marshal](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L351) [¶](#Message.Marshal)\n```\nfunc (m *[Message](#Message)) Marshal() ([][byte](/builtin#byte), [error](/builtin#error))\n```\nMarshal concatenates the segments in the message into a single byte slice including framing.\n\n#### \nfunc (*Message) [MarshalPacked](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L411) [¶](#Message.MarshalPacked)\n```\nfunc (m *[Message](#Message)) MarshalPacked() ([][byte](/builtin#byte), [error](/builtin#error))\n```\nMarshalPacked marshals the message in packed form.\n\n#### \nfunc (*Message) [NumSegments](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L249) [¶](#Message.NumSegments)\n```\nfunc (m *[Message](#Message)) NumSegments() [int64](/builtin#int64)\n```\nNumSegments returns the number of segments in the message.\n\n#### \nfunc (*Message) [Release](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L92) [¶](#Message.Release)\n```\nfunc (m *[Message](#Message)) Release()\n```\nRelease is syntactic sugar for Message.Reset(nil). See docstring for Reset for an important warning.\n\n#### \nfunc (*Message) [Reset](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L100) [¶](#Message.Reset)\n```\nfunc (m *[Message](#Message)) Reset(arena [Arena](#Arena)) (first *[Segment](#Segment), err [error](/builtin#error))\n```\nReset the message to use a different arena, allowing it to be reused. This invalidates any existing pointers in the Message, releases all clients in the cap table, and releases the current Arena, so use with caution.\n\n#### \nfunc (*Message) [ResetReadLimit](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L179) [¶](#Message.ResetReadLimit)\n```\nfunc (m *[Message](#Message)) ResetReadLimit(limit [uint64](/builtin#uint64))\n```\nResetReadLimit sets the number of bytes allowed to be read from this message.\n\n#### \nfunc (*Message) [Root](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L191) [¶](#Message.Root)\n```\nfunc (m *[Message](#Message)) Root() ([Ptr](#Ptr), [error](/builtin#error))\n```\nRoot returns the pointer to the message's root object.\n\n#### \nfunc (*Message) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L254) [¶](#Message.Segment)\n```\nfunc (m *[Message](#Message)) Segment(id [SegmentID](#SegmentID)) (*[Segment](#Segment), [error](/builtin#error))\n```\nSegment returns the segment with the given ID.\n\n#### \nfunc (*Message) [SetRoot](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L204) [¶](#Message.SetRoot)\n```\nfunc (m *[Message](#Message)) SetRoot(p [Ptr](#Ptr)) [error](/builtin#error)\n```\nSetRoot sets the message's root object to p.\n\n#### \nfunc (*Message) [TotalSize](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L228) [¶](#Message.TotalSize)\n```\nfunc (m *[Message](#Message)) TotalSize() ([uint64](/builtin#uint64), [error](/builtin#error))\n```\nCompute the total size of the message in bytes, when serialized as a stream. This is the same as the length of the slice returned by m.Marshal()\n\n#### \nfunc (*Message) [Unread](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L185) [¶](#Message.Unread)\n```\nfunc (m *[Message](#Message)) Unread(sz [Size](#Size))\n```\nUnread increases the read limit by sz.\n\n#### \nfunc (*Message) [WriteTo](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/message.go#L343) [¶](#Message.WriteTo)\n```\nfunc (m *[Message](#Message)) WriteTo(w [io](/io).[Writer](/io#Writer)) ([int64](/builtin#int64), [error](/builtin#error))\n```\n#### \ntype [Metadata](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L13) [¶](#Metadata)\n```\ntype Metadata struct {\n\t// contains filtered or unexported fields\n}\n```\nMetadata is a morally a map[any]any which implements sync.Locker; it is used by the rpc system to attach bookkeeping information to various objects.\n\nThe zero value is not meaningful, and the Metadata must not be copied after its first use.\n\n#### \nfunc [NewMetadata](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L46) [¶](#NewMetadata)\n```\nfunc NewMetadata() *[Metadata](#Metadata)\n```\nAllocate and return a freshly initialized Metadata.\n\n#### \nfunc (*Metadata) [Delete](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L41) [¶](#Metadata.Delete)\n```\nfunc (m *[Metadata](#Metadata)) Delete(key [any](/builtin#any))\n```\nDelete the key from the map.\n\n#### \nfunc (*Metadata) [Get](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L30) [¶](#Metadata.Get)\n```\nfunc (m *[Metadata](#Metadata)) Get(key [any](/builtin#any)) (value [any](/builtin#any), ok [bool](/builtin#bool))\n```\nLook up key in the map. Returns the value, and a boolean which is false if the key was not present.\n\n#### \nfunc (*Metadata) [Lock](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L19) [¶](#Metadata.Lock)\n```\nfunc (m *[Metadata](#Metadata)) Lock()\n```\nLock the metadata map.\n\n#### \nfunc (*Metadata) [Put](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L36) [¶](#Metadata.Put)\n```\nfunc (m *[Metadata](#Metadata)) Put(key, value [any](/builtin#any))\n```\nInsert the key, value pair into the map.\n\n#### \nfunc (*Metadata) [Unlock](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/metadata.go#L24) [¶](#Metadata.Unlock)\n```\nfunc (m *[Metadata](#Metadata)) Unlock()\n```\nUnlock the metadata map.\n\n#### \ntype [Method](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L961) [¶](#Method)\n```\ntype Method struct {\n InterfaceID [uint64](/builtin#uint64)\n MethodID [uint16](/builtin#uint16)\n\n // Canonical name of the interface. May be empty.\n\tInterfaceName [string](/builtin#string)\n // Method name as it appears in the schema. May be empty.\n\tMethodName [string](/builtin#string)\n}\n```\nA Method identifies a method along with an optional human-readable description of the method.\n\n#### \nfunc (*Method) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L974) [¶](#Method.String)\n```\nfunc (m *[Method](#Method)) String() [string](/builtin#string)\n```\nString returns a formatted string containing the interface name or the method name if present, otherwise it uses the raw IDs.\nThis is suitable for use in error messages and logs.\n\n#### \ntype [MultiSegmentArena](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L118) [¶](#MultiSegmentArena)\n```\ntype MultiSegmentArena struct {\n\t// contains filtered or unexported fields\n}\n```\nMultiSegment is an arena that stores object data across multiple []byte buffers, allocating new buffers of exponentially-increasing size when full. This avoids the potentially-expensive slice copying of SingleSegment.\n\n#### \nfunc [MultiSegment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L127) [¶](#MultiSegment)\n```\nfunc MultiSegment(b [][][byte](/builtin#byte)) *[MultiSegmentArena](#MultiSegmentArena)\n```\nMultiSegment returns a new arena that allocates new segments when they are full. b MAY be nil. Callers MAY use b to populate the buffer for reading or to reserve memory of a specific size.\n\n#### \nfunc (*MultiSegmentArena) [Allocate](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L209) [¶](#MultiSegmentArena.Allocate)\n```\nfunc (msa *[MultiSegmentArena](#MultiSegmentArena)) Allocate(sz [Size](#Size), segs map[[SegmentID](#SegmentID)]*[Segment](#Segment)) ([SegmentID](#SegmentID), [][byte](/builtin#byte), [error](/builtin#error))\n```\n#### \nfunc (*MultiSegmentArena) [Data](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L201) [¶](#MultiSegmentArena.Data)\n```\nfunc (msa *[MultiSegmentArena](#MultiSegmentArena)) Data(id [SegmentID](#SegmentID)) ([][byte](/builtin#byte), [error](/builtin#error))\n```\n#### \nfunc (*MultiSegmentArena) [NumSegments](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L197) [¶](#MultiSegmentArena.NumSegments)\n```\nfunc (msa *[MultiSegmentArena](#MultiSegmentArena)) NumSegments() [int64](/builtin#int64)\n```\n#### \nfunc (*MultiSegmentArena) [Release](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L143) [¶](#MultiSegmentArena.Release)\n```\nfunc (msa *[MultiSegmentArena](#MultiSegmentArena)) Release()\n```\nReturn this arena to an internal sync.Pool of arenas that can be re-used. Any time MultiSegment(nil) is called, arenas from this pool will be used if available, which can help reduce memory allocations.\n\nAll segments will be zeroed before re-use.\n\nCalling Release is optional; if not done the garbage collector will release the memory per usual.\n\n#### \nfunc (*MultiSegmentArena) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L240) [¶](#MultiSegmentArena.String)\n```\nfunc (msa *[MultiSegmentArena](#MultiSegmentArena)) String() [string](/builtin#string)\n```\n#### \ntype [ObjectSize](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L138) [¶](#ObjectSize)\n```\ntype ObjectSize struct {\n DataSize [Size](#Size) // must be <= 1<<19 - 8\n PointerCount [uint16](/builtin#uint16)\n}\n```\nObjectSize records section sizes for a struct or list.\n\n#### \nfunc (ObjectSize) [GoString](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L190) [¶](#ObjectSize.GoString)\n```\nfunc (sz [ObjectSize](#ObjectSize)) GoString() [string](/builtin#string)\n```\nGoString formats the ObjectSize as a keyed struct literal.\n\n#### \nfunc (ObjectSize) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L185) [¶](#ObjectSize.String)\n```\nfunc (sz [ObjectSize](#ObjectSize)) String() [string](/builtin#string)\n```\nString returns a short, human readable representation of the object size.\n\n#### \ntype [PipelineCaller](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L226) [¶](#PipelineCaller)\n```\ntype PipelineCaller interface {\n PipelineSend(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), s [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n PipelineRecv(ctx [context](/context).[Context](/context#Context), transform [][PipelineOp](#PipelineOp), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n}\n```\nA PipelineCaller implements promise pipelining.\n\nSee the counterpart methods in ClientHook for a description.\n\n#### \ntype [PipelineClient](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L471) [¶](#PipelineClient)\n```\ntype PipelineClient struct {\n\t// contains filtered or unexported fields\n}\n```\nPipelineClient implements ClientHook by calling to the pipeline's answer.\n\n#### \nfunc (PipelineClient) [Answer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L476) [¶](#PipelineClient.Answer)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Answer() *[Answer](#Answer)\n```\n#### \nfunc (PipelineClient) [Brand](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L492) [¶](#PipelineClient.Brand)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Brand() [Brand](#Brand)\n```\n#### \nfunc (PipelineClient) [Recv](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L488) [¶](#PipelineClient.Recv)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Recv(ctx [context](/context).[Context](/context#Context), r [Recv](#Recv)) [PipelineCaller](#PipelineCaller)\n```\n#### \nfunc (PipelineClient) [Send](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L484) [¶](#PipelineClient.Send)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Send(ctx [context](/context).[Context](/context#Context), s [Send](#Send)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n```\n#### \nfunc (PipelineClient) [Shutdown](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L504) [¶](#PipelineClient.Shutdown)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Shutdown()\n```\n#### \nfunc (PipelineClient) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L507) [¶](#PipelineClient.String)\n```\nfunc (pc [PipelineClient](#PipelineClient)) String() [string](/builtin#string)\n```\n#### \nfunc (PipelineClient) [Transform](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L480) [¶](#PipelineClient.Transform)\n```\nfunc (pc [PipelineClient](#PipelineClient)) Transform() [][PipelineOp](#PipelineOp)\n```\n#### \ntype [PipelineOp](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L516) [¶](#PipelineOp)\n```\ntype PipelineOp struct {\n Field [uint16](/builtin#uint16)\n DefaultValue [][byte](/builtin#byte)\n}\n```\nA PipelineOp describes a step in transforming a pipeline.\nIt maps closely with the PromisedAnswer.Op struct in rpc.capnp.\n\n#### \nfunc (PipelineOp) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L522) [¶](#PipelineOp.String)\n```\nfunc (op [PipelineOp](#PipelineOp)) String() [string](/builtin#string)\n```\nString returns a human-readable description of op.\n\n#### \ntype [PointerList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L331) [¶](#PointerList)\n```\ntype PointerList [List](#List)\n```\nA PointerList is a reference to an array of pointers.\n\n#### \nfunc [NewPointerList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L336) [¶](#NewPointerList)\n```\nfunc NewPointerList(s *[Segment](#Segment), n [int32](/builtin#int32)) ([PointerList](#PointerList), [error](/builtin#error))\n```\nNewPointerList allocates a new list of pointers, preferring placement in s.\n\n#### \nfunc (PointerList) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L355) [¶](#PointerList.At)\n```\nfunc (p [PointerList](#PointerList)) At(i [int](/builtin#int)) ([Ptr](#Ptr), [error](/builtin#error))\n```\nAt returns the i'th pointer in the list.\n\n#### \nfunc (PointerList) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L209) [¶](#PointerList.DecodeFromPtr)\n```\nfunc ([PointerList](#PointerList)) DecodeFromPtr(p [Ptr](#Ptr)) [PointerList](#PointerList)\n```\n#### \nfunc (PointerList) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L205) [¶](#PointerList.EncodeAsPtr)\n```\nfunc (l [PointerList](#PointerList)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (PointerList) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L197) [¶](#PointerList.IsValid)\n```\nfunc (l [PointerList](#PointerList)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (PointerList) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L201) [¶](#PointerList.Len)\n```\nfunc (l [PointerList](#PointerList)) Len() [int](/builtin#int)\n```\n#### \nfunc (PointerList) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L213) [¶](#PointerList.Message)\n```\nfunc (l [PointerList](#PointerList)) Message() *[Message](#Message)\n```\n#### \nfunc (PointerList) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L217) [¶](#PointerList.Segment)\n```\nfunc (l [PointerList](#PointerList)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (PointerList) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L365) [¶](#PointerList.Set)\n```\nfunc (p [PointerList](#PointerList)) Set(i [int](/builtin#int), v [Ptr](#Ptr)) [error](/builtin#error)\n```\nSet sets the i'th pointer in the list to v.\n\n#### \nfunc (PointerList) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L221) [¶](#PointerList.ToPtr)\n```\nfunc (l [PointerList](#PointerList)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [Promise](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L21) [¶](#Promise)\n```\ntype Promise struct {\n\t// contains filtered or unexported fields\n}\n```\nA Promise holds the result of an RPC call. Only one of Fulfill or Reject can be called on a Promise. Before the result is written, calls can be queued up using the Answer methods — this is promise pipelining.\n\nPromise is most useful for implementing ClientHook.\nMost applications will use Answer, since that what is returned by a Client.\n\n#### \nfunc [NewPromise](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L67) [¶](#NewPromise)\n```\nfunc NewPromise(m [Method](#Method), pc [PipelineCaller](#PipelineCaller)) *[Promise](#Promise)\n```\nNewPromise creates a new unresolved promise. The PipelineCaller will be used to make pipelined calls before the promise resolves.\n\n#### \nfunc (*Promise) [Answer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L200) [¶](#Promise.Answer)\n```\nfunc (p *[Promise](#Promise)) Answer() *[Answer](#Answer)\n```\nAnswer returns a read-only view of the promise.\nAnswer may be called concurrently by multiple goroutines.\n\n#### \nfunc (*Promise) [Fulfill](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L117) [¶](#Promise.Fulfill)\n```\nfunc (p *[Promise](#Promise)) Fulfill(result [Ptr](#Ptr))\n```\nFulfill resolves the promise with a successful result.\n\nFulfill will wait for any outstanding calls to the underlying PipelineCaller to yield Answers and any pipelined clients to be fulfilled.\n\n#### \nfunc (*Promise) [Reject](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L126) [¶](#Promise.Reject)\n```\nfunc (p *[Promise](#Promise)) Reject(e [error](/builtin#error))\n```\nReject resolves the promise with a failure.\n\nReject will wait for any outstanding calls to the underlying PipelineCaller to yield Answers and any pipelined clients to be fulfilled.\n\n#### \nfunc (*Promise) [ReleaseClients](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L211) [¶](#Promise.ReleaseClients)\n```\nfunc (p *[Promise](#Promise)) ReleaseClients()\n```\nReleaseClients waits until p is resolved and then closes any proxy clients created by the promise's answer. Failure to call this method will result in capability leaks. After the first call, subsequent calls to ReleaseClients do nothing. It is safe to call ReleaseClients concurrently from multiple goroutines.\n\nThis method is typically used in a ReleaseFunc.\n\n#### \nfunc (*Promise) [Resolve](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L137) [¶](#Promise.Resolve)\n```\nfunc (p *[Promise](#Promise)) Resolve(r [Ptr](#Ptr), e [error](/builtin#error))\n```\nResolve resolves the promise.\n\nIf e != nil, then this is equivalent to p.Reject(e).\nOtherwise, it is equivalent to p.Fulfill(r).\n\n#### \ntype [Ptr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L12) [¶](#Ptr)\n```\ntype Ptr struct {\n\t// contains filtered or unexported fields\n}\n```\nA Ptr is a reference to a Cap'n Proto struct, list, or interface.\nThe zero value is a null pointer.\n\n#### \nfunc [MustUnmarshalRoot](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/codec.go#L186) [¶](#MustUnmarshalRoot)\n```\nfunc MustUnmarshalRoot(data [][byte](/builtin#byte)) [Ptr](#Ptr)\n```\nMustUnmarshalRoot reads an unpacked serialized stream and returns its root pointer. If there is any error, it panics.\n\n#### \nfunc [Transform](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answer.go#L535) [¶](#Transform)\n```\nfunc Transform(p [Ptr](#Ptr), transform [][PipelineOp](#PipelineOp)) ([Ptr](#Ptr), [error](/builtin#error))\n```\nTransform applies a sequence of pipeline operations to a pointer and returns the result.\n\n#### \nfunc (Ptr) [Data](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L155) [¶](#Ptr.Data)\n```\nfunc (p [Ptr](#Ptr)) Data() [][byte](/builtin#byte)\n```\nData attempts to convert p into Data, returning nil if p is not a valid 1-byte list pointer.\n\n#### \nfunc (Ptr) [DataDefault](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L161) [¶](#Ptr.DataDefault)\n```\nfunc (p [Ptr](#Ptr)) DataDefault(def [][byte](/builtin#byte)) [][byte](/builtin#byte)\n```\nDataDefault attempts to convert p into Data, returning def if p is not a valid 1-byte list pointer.\n\n#### \nfunc (Ptr) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L211) [¶](#Ptr.DecodeFromPtr)\n```\nfunc ([Ptr](#Ptr)) DecodeFromPtr(p [Ptr](#Ptr)) [Ptr](#Ptr)\n```\nDecodeFromPtr returns its argument; for implementing TypeParam.\n\n#### \nfunc (Ptr) [Default](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L194) [¶](#Ptr.Default)\n```\nfunc (p [Ptr](#Ptr)) Default(def [][byte](/builtin#byte)) ([Ptr](#Ptr), [error](/builtin#error))\n```\nDefault returns p if it is valid, otherwise it unmarshals def.\n\n#### \nfunc (Ptr) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L208) [¶](#Ptr.EncodeAsPtr)\n```\nfunc (p [Ptr](#Ptr)) EncodeAsPtr(*[Segment](#Segment)) [Ptr](#Ptr)\n```\nEncodeAsPtr returns the receiver; for implementing TypeParam.\nThe segment argument is ignored.\n\n#### \nfunc (Ptr) [Interface](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L88) [¶](#Ptr.Interface)\n```\nfunc (p [Ptr](#Ptr)) Interface() [Interface](#Interface)\n```\nInterface converts p to an Interface. If p does not hold a List pointer, the zero value is returned.\n\n#### \nfunc (Ptr) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L174) [¶](#Ptr.IsValid)\n```\nfunc (p [Ptr](#Ptr)) IsValid() [bool](/builtin#bool)\n```\nIsValid reports whether p is valid.\n\n#### \nfunc (Ptr) [List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L55) [¶](#Ptr.List)\n```\nfunc (p [Ptr](#Ptr)) List() [List](#List)\n```\nList converts p to a List. If p does not hold a List pointer,\nthe zero value is returned.\n\n#### \nfunc (Ptr) [ListDefault](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L71) [¶](#Ptr.ListDefault)\n```\nfunc (p [Ptr](#Ptr)) ListDefault(def [][byte](/builtin#byte)) ([List](#List), [error](/builtin#error))\n```\nListDefault attempts to convert p into a list, reading the default value from def if p is not a list.\n\n#### \nfunc (Ptr) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L186) [¶](#Ptr.Message)\n```\nfunc (p [Ptr](#Ptr)) Message() *[Message](#Message)\n```\nMessage returns the message the referenced data is stored in or nil if the pointer is invalid.\n\n#### \nfunc (Ptr) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L180) [¶](#Ptr.Segment)\n```\nfunc (p [Ptr](#Ptr)) Segment() *[Segment](#Segment)\n```\nSegment returns the segment that the referenced data is stored in or nil if the pointer is invalid.\n\n#### \nfunc (Ptr) [Struct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L23) [¶](#Ptr.Struct)\n```\nfunc (p [Ptr](#Ptr)) Struct() [Struct](#Struct)\n```\nStruct converts p to a Struct. If p does not hold a Struct pointer,\nthe zero value is returned.\n\n#### \nfunc (Ptr) [StructDefault](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L38) [¶](#Ptr.StructDefault)\n```\nfunc (p [Ptr](#Ptr)) StructDefault(def [][byte](/builtin#byte)) ([Struct](#Struct), [error](/builtin#error))\n```\nStructDefault attempts to convert p into a struct, reading the default value from def if p is not a struct.\n\n#### \nfunc (Ptr) [Text](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L100) [¶](#Ptr.Text)\n```\nfunc (p [Ptr](#Ptr)) Text() [string](/builtin#string)\n```\nText attempts to convert p into Text, returning an empty string if p is not a valid 1-byte list pointer.\n\n#### \nfunc (Ptr) [TextBytes](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L121) [¶](#Ptr.TextBytes)\n```\nfunc (p [Ptr](#Ptr)) TextBytes() [][byte](/builtin#byte)\n```\nTextBytes attempts to convert p into Text, returning nil if p is not a valid 1-byte list pointer. It returns a slice directly into the segment.\n\n#### \nfunc (Ptr) [TextBytesDefault](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L132) [¶](#Ptr.TextBytesDefault)\n```\nfunc (p [Ptr](#Ptr)) TextBytesDefault(def [string](/builtin#string)) [][byte](/builtin#byte)\n```\nTextBytesDefault attempts to convert p into Text, returning def if p is not a valid 1-byte list pointer. It returns a slice directly into the segment.\n\n#### \nfunc (Ptr) [TextDefault](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/pointer.go#L110) [¶](#Ptr.TextDefault)\n```\nfunc (p [Ptr](#Ptr)) TextDefault(def [string](/builtin#string)) [string](/builtin#string)\n```\nTextDefault attempts to convert p into Text, returning def if p is not a valid 1-byte list pointer.\n\n#### \ntype [Recv](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L878) [¶](#Recv)\n```\ntype Recv struct {\n // Method must have InterfaceID and MethodID filled in.\n\tMethod [Method](#Method)\n\n // Args is the set of arguments for the RPC.\n\tArgs [Struct](#Struct)\n\n // ReleaseArgs is called after Args is no longer referenced.\n\t// Must not be nil. If called more than once, subsequent calls\n\t// must silently no-op.\n\tReleaseArgs [ReleaseFunc](#ReleaseFunc)\n\n // Returner manages the results.\n\tReturner [Returner](#Returner)\n}\n```\nRecv is the input to ClientHook.Recv.\n\n#### \nfunc (Recv) [AllocResults](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L896) [¶](#Recv.AllocResults)\n```\nfunc (r [Recv](#Recv)) AllocResults(sz [ObjectSize](#ObjectSize)) ([Struct](#Struct), [error](/builtin#error))\n```\nAllocResults allocates a result struct. It is the same as calling r.Returner.AllocResults(sz).\n\n#### \nfunc (Recv) [Reject](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L908) [¶](#Recv.Reject)\n```\nfunc (r [Recv](#Recv)) Reject(e [error](/builtin#error))\n```\nReject ends the method call with an error, releasing the arguments.\n\n#### \nfunc (Recv) [Return](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L901) [¶](#Recv.Return)\n```\nfunc (r [Recv](#Recv)) Return()\n```\nReturn ends the method call successfully, releasing the arguments.\n\n#### \ntype [ReleaseFunc](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L957) [¶](#ReleaseFunc)\n```\ntype ReleaseFunc func()\n```\nA ReleaseFunc tells the RPC system that a parameter or result struct is no longer in use and may be reclaimed. After the first call,\nsubsequent calls to a ReleaseFunc do nothing. A ReleaseFunc should not be called concurrently.\n\n#### \ntype [Request](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L10) [¶](#Request)\n```\ntype Request struct {\n\t// contains filtered or unexported fields\n}\n```\nA Request is a method call to be sent. Create one with NewReqeust, and send it with Request.Send().\n\n#### \nfunc [NewRequest](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L20) [¶](#NewRequest)\n```\nfunc NewRequest(client [Client](#Client), method [Method](#Method), argsSize [ObjectSize](#ObjectSize)) (*[Request](#Request), [error](/builtin#error))\n```\nNewRequest creates a new request calling the specified method on the specified client.\nargsSize is the size of the arguments struct.\n\n#### \nfunc (*Request) [Args](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L35) [¶](#Request.Args)\n```\nfunc (r *[Request](#Request)) Args() [Struct](#Struct)\n```\nArgs returns the arguments struct for this request. The arguments must not be accessed after the request is sent.\n\n#### \nfunc (*Request) [Future](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L74) [¶](#Request.Future)\n```\nfunc (r *[Request](#Request)) Future() *[Future](#Future)\n```\nFuture returns a future for the requests results. Returns nil if called before the request is sent.\n\n#### \nfunc (*Request) [Release](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L83) [¶](#Request.Release)\n```\nfunc (r *[Request](#Request)) Release()\n```\nRelease resources associated with the request. In particular:\n\n* Release the arguments if they have not yet been released.\n* If the request has been sent, wait for the result and release the results.\n\n#### \nfunc (*Request) [Send](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L52) [¶](#Request.Send)\n```\nfunc (r *[Request](#Request)) Send(ctx [context](/context).[Context](/context#Context)) *[Future](#Future)\n```\nSend sends the request, returning a future for its results.\n\n#### \nfunc (*Request) [SendStream](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/request.go#L64) [¶](#Request.SendStream)\n```\nfunc (r *[Request](#Request)) SendStream(ctx [context](/context).[Context](/context#Context)) [error](/builtin#error)\n```\nSendStream is to send as Client.SendStreamCall is to Client.SendCall\n\n#### \ntype [Resolver](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/resolver.go#L4) [¶](#Resolver)\n```\ntype Resolver[T [any](/builtin#any)] interface {\n // Fulfill supplies the value for the corresponding\n\t// Promise\n\tFulfill(T)\n\n // Reject rejects the corresponding promise, with\n\t// the specified error.\n\tReject([error](/builtin#error))\n}\n```\nA Resolver supplies a value for a pending promise.\n\n#### \nfunc [NewLocalPromise](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/localpromise.go#L16) [¶](#NewLocalPromise)\n```\nfunc NewLocalPromise[C ~[ClientKind](#ClientKind)]() (C, [Resolver](#Resolver)[C])\n```\nNewLocalPromise returns a client that will eventually resolve to a capability,\nsupplied via the fulfiller.\n\n#### \ntype [Returner](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L919) [¶](#Returner)\n```\ntype Returner interface {\n // AllocResults allocates the results struct that will be sent using\n\t// Return. It can be called at most once, and only before calling\n\t// Return. The struct returned by AllocResults must not be mutated\n\t// after Return is called, and may not be accessed after\n\t// ReleaseResults is called.\n\tAllocResults(sz [ObjectSize](#ObjectSize)) ([Struct](#Struct), [error](/builtin#error))\n\n // PrepareReturn finalizes the return message. The method call will\n\t// resolve successfully if e is nil, or otherwise it will return an\n\t// exception to the caller.\n\t//\n\t// PrepareReturn must be called once.\n\t//\n\t// After PrepareReturn is invoked, no goroutine may modify the message\n\t// containing the results.\n\tPrepareReturn(e [error](/builtin#error))\n\n // Return resolves the method call, using the results finalized in\n\t// PrepareReturn. Return must be called once.\n\t//\n\t// Return must wait for all ongoing pipelined calls to be delivered,\n\t// and after it returns, no new calls can be sent to the PipelineCaller\n\t// returned from Recv.\n\tReturn()\n\n // ReleaseResults relinquishes the caller's access to the message\n\t// containing the results; once this is called the message may be\n\t// released or reused, and it is not safe to access.\n\t//\n\t// If AllocResults has not been called, then this is a no-op.\n\tReleaseResults()\n}\n```\nA Returner allocates and sends the results from a received capability method call.\n\n#### \ntype [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/segment.go#L17) [¶](#Segment)\n```\ntype Segment struct {\n\t// contains filtered or unexported fields\n}\n```\nA Segment is an allocation arena for Cap'n Proto objects.\nIt is part of a Message, which can contain other segments that reference each other.\n\n#### \nfunc (*Segment) [Data](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/segment.go#L34) [¶](#Segment.Data)\n```\nfunc (s *[Segment](#Segment)) Data() [][byte](/builtin#byte)\n```\nData returns the raw byte slice for the segment.\n\n#### \nfunc (*Segment) [ID](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/segment.go#L29) [¶](#Segment.ID)\n```\nfunc (s *[Segment](#Segment)) ID() [SegmentID](#SegmentID)\n```\nID returns the segment's ID.\n\n#### \nfunc (*Segment) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/segment.go#L24) [¶](#Segment.Message)\n```\nfunc (s *[Segment](#Segment)) Message() *[Message](#Message)\n```\nMessage returns the message that contains s.\n\n#### \ntype [SegmentID](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/segment.go#L12) [¶](#SegmentID)\n```\ntype SegmentID [uint32](/builtin#uint32)\n```\nA SegmentID is a numeric identifier for a Segment.\n\n#### \ntype [Send](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L865) [¶](#Send)\n```\ntype Send struct {\n // Method must have InterfaceID and MethodID filled in.\n\tMethod [Method](#Method)\n\n // PlaceArgs is a function that will be called at most once before Send\n\t// returns to populate the arguments for the RPC. PlaceArgs may be nil.\n\tPlaceArgs func([Struct](#Struct)) [error](/builtin#error)\n\n // ArgsSize specifies the size of the struct to pass to PlaceArgs.\n\tArgsSize [ObjectSize](#ObjectSize)\n}\n```\nSend is the input to ClientHook.Send.\n\n#### \ntype [SingleSegmentArena](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L54) [¶](#SingleSegmentArena)\n```\ntype SingleSegmentArena [][byte](/builtin#byte)\n```\nSingleSegmentArena is an Arena implementation that stores message data in a continguous slice. Allocation is performed by first allocating a new slice and copying existing data. SingleSegment arena does not fail unless the caller attempts to access another segment.\n\n#### \nfunc [SingleSegment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L59) [¶](#SingleSegment)\n```\nfunc SingleSegment(b [][byte](/builtin#byte)) *[SingleSegmentArena](#SingleSegmentArena)\n```\nSingleSegment constructs a SingleSegmentArena from b. b MAY be nil.\nCallers MAY use b to populate the segment for reading, or to reserve memory of a specific size.\n\n#### \nfunc (*SingleSegmentArena) [Allocate](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L74) [¶](#SingleSegmentArena.Allocate)\n```\nfunc (ssa *[SingleSegmentArena](#SingleSegmentArena)) Allocate(sz [Size](#Size), segs map[[SegmentID](#SegmentID)]*[Segment](#Segment)) ([SegmentID](#SegmentID), [][byte](/builtin#byte), [error](/builtin#error))\n```\n#### \nfunc (SingleSegmentArena) [Data](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L67) [¶](#SingleSegmentArena.Data)\n```\nfunc (ssa [SingleSegmentArena](#SingleSegmentArena)) Data(id [SegmentID](#SegmentID)) ([][byte](/builtin#byte), [error](/builtin#error))\n```\n#### \nfunc (SingleSegmentArena) [NumSegments](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L63) [¶](#SingleSegmentArena.NumSegments)\n```\nfunc (ssa [SingleSegmentArena](#SingleSegmentArena)) NumSegments() [int64](/builtin#int64)\n```\n#### \nfunc (*SingleSegmentArena) [Release](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L110) [¶](#SingleSegmentArena.Release)\n```\nfunc (ssa *[SingleSegmentArena](#SingleSegmentArena)) Release()\n```\nReturn this arena to an internal sync.Pool of arenas that can be re-used. Any time SingleSegment(nil) is called, arenas from this pool will be used if available, which can help reduce memory allocations.\n\nAll segments will be zeroed before re-use.\n\nCalling Release is optional; if not done the garbage collector will release the memory per usual.\n\n#### \nfunc (SingleSegmentArena) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/arena.go#L97) [¶](#SingleSegmentArena.String)\n```\nfunc (ssa [SingleSegmentArena](#SingleSegmentArena)) String() [string](/builtin#string)\n```\n#### \ntype [Size](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L57) [¶](#Size)\n```\ntype Size [uint32](/builtin#uint32)\n```\nA Size is a size (in bytes).\n\n#### \nfunc (Size) [GoString](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L71) [¶](#Size.GoString)\n```\nfunc (sz [Size](#Size)) GoString() [string](/builtin#string)\n```\nGoString returns the size as a Go expression.\n\n#### \nfunc (Size) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/address.go#L63) [¶](#Size.String)\n```\nfunc (sz [Size](#Size)) String() [string](/builtin#string)\n```\nString returns the size in the format \"X bytes\".\n\n#### \ntype [Struct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L11) [¶](#Struct)\n```\ntype Struct [StructKind](#StructKind)\n```\nStruct is a pointer to a struct.\n\n#### \nfunc [NewRootStruct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L44) [¶](#NewRootStruct)\n```\nfunc NewRootStruct(s *[Segment](#Segment), sz [ObjectSize](#ObjectSize)) ([Struct](#Struct), [error](/builtin#error))\n```\nNewRootStruct creates a new struct, preferring placement in s, then sets the message's root to the new struct.\n\n#### \nfunc [NewStruct](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L25) [¶](#NewStruct)\n```\nfunc NewStruct(s *[Segment](#Segment), sz [ObjectSize](#ObjectSize)) ([Struct](#Struct), [error](/builtin#error))\n```\nNewStruct creates a new struct, preferring placement in s.\n\n#### \nfunc (Struct) [Bit](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L190) [¶](#Struct.Bit)\n```\nfunc (p [Struct](#Struct)) Bit(n [BitOffset](#BitOffset)) [bool](/builtin#bool)\n```\nBit returns the bit that is n bits from the start of the struct.\n\n#### \nfunc (Struct) [CopyFrom](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L95) [¶](#Struct.CopyFrom)\n```\nfunc (p [Struct](#Struct)) CopyFrom(other [Struct](#Struct)) [error](/builtin#error)\n```\nCopyFrom copies content from another struct. If the other struct's sections are larger than this struct's, the extra data is not copied,\nmeaning there is a risk of data loss when copying from messages built with future versions of the protocol.\n\n#### \nfunc (Struct) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L367) [¶](#Struct.DecodeFromPtr)\n```\nfunc ([Struct](#Struct)) DecodeFromPtr(p [Ptr](#Ptr)) [Struct](#Struct)\n```\nDecodeFromPtr(p) is equivalent to p.Struct() (the receiver is ignored).\nfor implementing TypeParam.\n\n#### \nfunc (Struct) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L363) [¶](#Struct.EncodeAsPtr)\n```\nfunc (s [Struct](#Struct)) EncodeAsPtr(*[Segment](#Segment)) [Ptr](#Ptr)\n```\ns.EncodeAsPtr is equivalent to s.ToPtr(); for implementing TypeParam.\nThe segment argument is ignored.\n\n#### \nfunc (Struct) [HasPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L121) [¶](#Struct.HasPtr)\n```\nfunc (p [Struct](#Struct)) HasPtr(i [uint16](/builtin#uint16)) [bool](/builtin#bool)\n```\nHasPtr reports whether the i'th pointer in the struct is non-null.\nIt does not affect the read limit.\n\n#### \nfunc (Struct) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L82) [¶](#Struct.IsValid)\n```\nfunc (p [Struct](#Struct)) IsValid() [bool](/builtin#bool)\n```\nIsValid returns whether the struct is valid.\n\n#### \nfunc (Struct) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L74) [¶](#Struct.Message)\n```\nfunc (p [Struct](#Struct)) Message() *[Message](#Message)\n```\nMessage returns the message the referenced struct is stored in or nil if the pointer is invalid.\n\n#### \nfunc (Struct) [Ptr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L112) [¶](#Struct.Ptr)\n```\nfunc (p [Struct](#Struct)) Ptr(i [uint16](/builtin#uint16)) ([Ptr](#Ptr), [error](/builtin#error))\n```\nPtr returns the i'th pointer in the struct.\n\n#### \nfunc (Struct) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L68) [¶](#Struct.Segment)\n```\nfunc (p [Struct](#Struct)) Segment() *[Segment](#Segment)\n```\nSegment returns the segment the referenced struct is stored in or nil if the pointer is invalid.\n\n#### \nfunc (Struct) [SetBit](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L199) [¶](#Struct.SetBit)\n```\nfunc (p [Struct](#Struct)) SetBit(n [BitOffset](#BitOffset), v [bool](/builtin#bool))\n```\nSetBit sets the bit that is n bits from the start of the struct to v.\n\n#### \nfunc (Struct) [SetData](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L166) [¶](#Struct.SetData)\n```\nfunc (p [Struct](#Struct)) SetData(i [uint16](/builtin#uint16), v [][byte](/builtin#byte)) [error](/builtin#error)\n```\nSetData sets the i'th pointer to a newly allocated data or null if v is nil.\n\n#### \nfunc (Struct) [SetNewText](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L145) [¶](#Struct.SetNewText)\n```\nfunc (p [Struct](#Struct)) SetNewText(i [uint16](/builtin#uint16), v [string](/builtin#string)) [error](/builtin#error)\n```\nSetNewText sets the i'th pointer to a newly allocated text.\n\n#### \nfunc (Struct) [SetPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L129) [¶](#Struct.SetPtr)\n```\nfunc (p [Struct](#Struct)) SetPtr(i [uint16](/builtin#uint16), src [Ptr](#Ptr)) [error](/builtin#error)\n```\nSetPtr sets the i'th pointer in the struct to src.\n\n#### \nfunc (Struct) [SetText](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L137) [¶](#Struct.SetText)\n```\nfunc (p [Struct](#Struct)) SetText(i [uint16](/builtin#uint16), v [string](/builtin#string)) [error](/builtin#error)\n```\nSetText sets the i'th pointer to a newly allocated text or null if v is empty.\n\n#### \nfunc (Struct) [SetTextFromBytes](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L154) [¶](#Struct.SetTextFromBytes)\n```\nfunc (p [Struct](#Struct)) SetTextFromBytes(i [uint16](/builtin#uint16), v [][byte](/builtin#byte)) [error](/builtin#error)\n```\nSetTextFromBytes sets the i'th pointer to a newly allocated text or null if v is nil.\n\n#### \nfunc (Struct) [SetUint16](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L266) [¶](#Struct.SetUint16)\n```\nfunc (p [Struct](#Struct)) SetUint16(off [DataOffset](#DataOffset), v [uint16](/builtin#uint16))\n```\nSetUint16 sets the 16-bit integer that is off bytes from the start of the struct to v.\n\n#### \nfunc (Struct) [SetUint32](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L275) [¶](#Struct.SetUint32)\n```\nfunc (p [Struct](#Struct)) SetUint32(off [DataOffset](#DataOffset), v [uint32](/builtin#uint32))\n```\nSetUint32 sets the 32-bit integer that is off bytes from the start of the struct to v.\n\n#### \nfunc (Struct) [SetUint64](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L284) [¶](#Struct.SetUint64)\n```\nfunc (p [Struct](#Struct)) SetUint64(off [DataOffset](#DataOffset), v [uint64](/builtin#uint64))\n```\nSetUint64 sets the 64-bit integer that is off bytes from the start of the struct to v.\n\n#### \nfunc (Struct) [SetUint8](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L257) [¶](#Struct.SetUint8)\n```\nfunc (p [Struct](#Struct)) SetUint8(off [DataOffset](#DataOffset), v [uint8](/builtin#uint8))\n```\nSetUint8 sets the 8-bit integer that is off bytes from the start of the struct to v.\n\n#### \nfunc (Struct) [Size](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L87) [¶](#Struct.Size)\n```\nfunc (p [Struct](#Struct)) Size() [ObjectSize](#ObjectSize)\n```\nSize returns the size of the struct.\n\n#### \nfunc (Struct) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L56) [¶](#Struct.ToPtr)\n```\nfunc (p [Struct](#Struct)) ToPtr() [Ptr](#Ptr)\n```\nToPtr converts the struct to a generic pointer.\n\n#### \nfunc (Struct) [Uint16](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L230) [¶](#Struct.Uint16)\n```\nfunc (p [Struct](#Struct)) Uint16(off [DataOffset](#DataOffset)) [uint16](/builtin#uint16)\n```\nUint16 returns a 16-bit integer from the struct's data section.\n\n#### \nfunc (Struct) [Uint32](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L239) [¶](#Struct.Uint32)\n```\nfunc (p [Struct](#Struct)) Uint32(off [DataOffset](#DataOffset)) [uint32](/builtin#uint32)\n```\nUint32 returns a 32-bit integer from the struct's data section.\n\n#### \nfunc (Struct) [Uint64](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L248) [¶](#Struct.Uint64)\n```\nfunc (p [Struct](#Struct)) Uint64(off [DataOffset](#DataOffset)) [uint64](/builtin#uint64)\n```\nUint64 returns a 64-bit integer from the struct's data section.\n\n#### \nfunc (Struct) [Uint8](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L221) [¶](#Struct.Uint8)\n```\nfunc (p [Struct](#Struct)) Uint8(off [DataOffset](#DataOffset)) [uint8](/builtin#uint8)\n```\nUint8 returns an 8-bit integer from the struct's data section.\n\n#### \ntype [StructKind](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/struct.go#L16) [¶](#StructKind)\n```\ntype StructKind = struct {\n\t// contains filtered or unexported fields\n}\n```\nThe underlying type of Struct. We expose this so that we can use ~StructKind as a constraint in generics to capture any struct type.\n\n#### \ntype [StructList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1067) [¶](#StructList)\n```\ntype StructList[T ~[StructKind](#StructKind)] [List](#List)\n```\nA list of some Cap'n Proto struct type T.\n\n#### \nfunc (StructList[T]) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1072) [¶](#StructList.At)\n```\nfunc (s [StructList](#StructList)[T]) At(i [int](/builtin#int)) T\n```\nAt returns the i'th element.\n\n#### \nfunc (StructList[T]) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L273) [¶](#StructList.DecodeFromPtr)\n```\nfunc ([StructList](#StructList)[T]) DecodeFromPtr(p [Ptr](#Ptr)) [StructList](#StructList)[T]\n```\n#### \nfunc (StructList[T]) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L269) [¶](#StructList.EncodeAsPtr)\n```\nfunc (l [StructList](#StructList)[T]) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (StructList[T]) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L261) [¶](#StructList.IsValid)\n```\nfunc (l [StructList](#StructList)[T]) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (StructList[T]) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L265) [¶](#StructList.Len)\n```\nfunc (l [StructList](#StructList)[T]) Len() [int](/builtin#int)\n```\n#### \nfunc (StructList[T]) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L277) [¶](#StructList.Message)\n```\nfunc (l [StructList](#StructList)[T]) Message() *[Message](#Message)\n```\n#### \nfunc (StructList[T]) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L281) [¶](#StructList.Segment)\n```\nfunc (l [StructList](#StructList)[T]) Segment() *[Segment](#Segment)\n```\n#### \nfunc (StructList[T]) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L1077) [¶](#StructList.Set)\n```\nfunc (s [StructList](#StructList)[T]) Set(i [int](/builtin#int), v T) [error](/builtin#error)\n```\nSet sets the i'th element to v.\n\n#### \nfunc (StructList[T]) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L285) [¶](#StructList.ToPtr)\n```\nfunc (l [StructList](#StructList)[T]) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [StructReturner](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L181) [¶](#StructReturner)\n```\ntype StructReturner struct {\n\t// contains filtered or unexported fields\n}\n```\nA StructReturner implements Returner by allocating an in-memory message. It is safe to use from multiple goroutines. The zero value is a Returner in its initial state.\n\n#### \nfunc (*StructReturner) [AllocResults](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L194) [¶](#StructReturner.AllocResults)\n```\nfunc (sr *[StructReturner](#StructReturner)) AllocResults(sz [ObjectSize](#ObjectSize)) ([Struct](#Struct), [error](/builtin#error))\n```\n#### \nfunc (*StructReturner) [Answer](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L265) [¶](#StructReturner.Answer)\n```\nfunc (sr *[StructReturner](#StructReturner)) Answer(m [Method](#Method), pcall [PipelineCaller](#PipelineCaller)) (*[Answer](#Answer), [ReleaseFunc](#ReleaseFunc))\n```\nAnswer returns an Answer that will be resolved when Return is called.\nanswer must only be called once per StructReturner.\n\n#### \nfunc (*StructReturner) [PrepareReturn](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L210) [¶](#StructReturner.PrepareReturn)\n```\nfunc (sr *[StructReturner](#StructReturner)) PrepareReturn(e [error](/builtin#error))\n```\n#### \nfunc (*StructReturner) [ReleaseResults](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L238) [¶](#StructReturner.ReleaseResults)\n```\nfunc (sr *[StructReturner](#StructReturner)) ReleaseResults()\n```\n#### \nfunc (*StructReturner) [Return](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/answerqueue.go#L216) [¶](#StructReturner.Return)\n```\nfunc (sr *[StructReturner](#StructReturner)) Return()\n```\n#### \ntype [TextList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L374) [¶](#TextList)\n```\ntype TextList [List](#List)\n```\nTextList is an array of pointers to strings.\n\n#### \nfunc [NewTextList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L379) [¶](#NewTextList)\n```\nfunc NewTextList(s *[Segment](#Segment), n [int32](/builtin#int32)) ([TextList](#TextList), [error](/builtin#error))\n```\nNewTextList allocates a new list of text pointers, preferring placement in s.\n\n#### \nfunc (TextList) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L388) [¶](#TextList.At)\n```\nfunc (l [TextList](#TextList)) At(i [int](/builtin#int)) ([string](/builtin#string), [error](/builtin#error))\n```\nAt returns the i'th string in the list.\n\n#### \nfunc (TextList) [BytesAt](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L402) [¶](#TextList.BytesAt)\n```\nfunc (l [TextList](#TextList)) BytesAt(i [int](/builtin#int)) ([][byte](/builtin#byte), [error](/builtin#error))\n```\nBytesAt returns the i'th element in the list as a byte slice.\nThe underlying array of the slice is the segment data.\n\n#### \nfunc (TextList) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L145) [¶](#TextList.DecodeFromPtr)\n```\nfunc ([TextList](#TextList)) DecodeFromPtr(p [Ptr](#Ptr)) [TextList](#TextList)\n```\n#### \nfunc (TextList) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L141) [¶](#TextList.EncodeAsPtr)\n```\nfunc (l [TextList](#TextList)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (TextList) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L133) [¶](#TextList.IsValid)\n```\nfunc (l [TextList](#TextList)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (TextList) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L137) [¶](#TextList.Len)\n```\nfunc (l [TextList](#TextList)) Len() [int](/builtin#int)\n```\n#### \nfunc (TextList) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L149) [¶](#TextList.Message)\n```\nfunc (l [TextList](#TextList)) Message() *[Message](#Message)\n```\n#### \nfunc (TextList) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L153) [¶](#TextList.Segment)\n```\nfunc (l [TextList](#TextList)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (TextList) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L415) [¶](#TextList.Set)\n```\nfunc (l [TextList](#TextList)) Set(i [int](/builtin#int), v [string](/builtin#string)) [error](/builtin#error)\n```\nSet sets the i'th string in the list to v.\n\n#### \nfunc (TextList) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L431) [¶](#TextList.String)\n```\nfunc (l [TextList](#TextList)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. `[\"foo\", \"bar\"]`).\n\n#### \nfunc (TextList) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L157) [¶](#TextList.ToPtr)\n```\nfunc (l [TextList](#TextList)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [TypeParam](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/typeparam.go#L7) [¶](#TypeParam)\n```\ntype TypeParam[T [any](/builtin#any)] interface {\n // Convert the receiver to a Ptr, storing it in seg if it is not\n\t// already associated with some message (only true for Clients and\n\t// wrappers around them.\n\tEncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n\n // Decode the pointer as the type of the receiver. Generally,\n\t// the receiver will be the zero value for the type.\n\tDecodeFromPtr(p [Ptr](#Ptr)) T\n}\n```\nThe TypeParam interface must be satisified by a type to be used as a capnproto type parameter. This is satisified by all capnproto pointer types. T should be instantiated by the type itself; in type parameter lists you will typically see parameter/constraints like T TypeParam[T].\n\n#### \ntype [UInt16List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L673) [¶](#UInt16List)\n```\ntype UInt16List [List](#List)\n```\nA UInt16List is an array of UInt16 values.\n\n#### \nfunc [NewUInt16List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L678) [¶](#NewUInt16List)\n```\nfunc NewUInt16List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([UInt16List](#UInt16List), [error](/builtin#error))\n```\nNewUInt16List creates a new list of UInt16, preferring placement in s.\n\n#### \nfunc (UInt16List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L687) [¶](#UInt16List.At)\n```\nfunc (l [UInt16List](#UInt16List)) At(i [int](/builtin#int)) [uint16](/builtin#uint16)\n```\nAt returns the i'th element.\n\n#### \nfunc (UInt16List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L433) [¶](#UInt16List.DecodeFromPtr)\n```\nfunc ([UInt16List](#UInt16List)) DecodeFromPtr(p [Ptr](#Ptr)) [UInt16List](#UInt16List)\n```\n#### \nfunc (UInt16List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L429) [¶](#UInt16List.EncodeAsPtr)\n```\nfunc (l [UInt16List](#UInt16List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (UInt16List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L421) [¶](#UInt16List.IsValid)\n```\nfunc (l [UInt16List](#UInt16List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (UInt16List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L425) [¶](#UInt16List.Len)\n```\nfunc (l [UInt16List](#UInt16List)) Len() [int](/builtin#int)\n```\n#### \nfunc (UInt16List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L437) [¶](#UInt16List.Message)\n```\nfunc (l [UInt16List](#UInt16List)) Message() *[Message](#Message)\n```\n#### \nfunc (UInt16List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L441) [¶](#UInt16List.Segment)\n```\nfunc (l [UInt16List](#UInt16List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (UInt16List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L696) [¶](#UInt16List.Set)\n```\nfunc (l [UInt16List](#UInt16List)) Set(i [int](/builtin#int), v [uint16](/builtin#uint16))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (UInt16List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L705) [¶](#UInt16List.String)\n```\nfunc (l [UInt16List](#UInt16List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (UInt16List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L445) [¶](#UInt16List.ToPtr)\n```\nfunc (l [UInt16List](#UInt16List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [UInt32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L765) [¶](#UInt32List)\n```\ntype UInt32List [List](#List)\n```\nUInt32List is an array of UInt32 values.\n\n#### \nfunc [NewUInt32List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L770) [¶](#NewUInt32List)\n```\nfunc NewUInt32List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([UInt32List](#UInt32List), [error](/builtin#error))\n```\nNewUInt32List creates a new list of UInt32, preferring placement in s.\n\n#### \nfunc (UInt32List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L779) [¶](#UInt32List.At)\n```\nfunc (l [UInt32List](#UInt32List)) At(i [int](/builtin#int)) [uint32](/builtin#uint32)\n```\nAt returns the i'th element.\n\n#### \nfunc (UInt32List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L497) [¶](#UInt32List.DecodeFromPtr)\n```\nfunc ([UInt32List](#UInt32List)) DecodeFromPtr(p [Ptr](#Ptr)) [UInt32List](#UInt32List)\n```\n#### \nfunc (UInt32List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L493) [¶](#UInt32List.EncodeAsPtr)\n```\nfunc (l [UInt32List](#UInt32List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (UInt32List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L485) [¶](#UInt32List.IsValid)\n```\nfunc (l [UInt32List](#UInt32List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (UInt32List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L489) [¶](#UInt32List.Len)\n```\nfunc (l [UInt32List](#UInt32List)) Len() [int](/builtin#int)\n```\n#### \nfunc (UInt32List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L501) [¶](#UInt32List.Message)\n```\nfunc (l [UInt32List](#UInt32List)) Message() *[Message](#Message)\n```\n#### \nfunc (UInt32List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L505) [¶](#UInt32List.Segment)\n```\nfunc (l [UInt32List](#UInt32List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (UInt32List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L788) [¶](#UInt32List.Set)\n```\nfunc (l [UInt32List](#UInt32List)) Set(i [int](/builtin#int), v [uint32](/builtin#uint32))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (UInt32List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L797) [¶](#UInt32List.String)\n```\nfunc (l [UInt32List](#UInt32List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (UInt32List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L509) [¶](#UInt32List.ToPtr)\n```\nfunc (l [UInt32List](#UInt32List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [UInt64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L857) [¶](#UInt64List)\n```\ntype UInt64List [List](#List)\n```\nUInt64List is an array of UInt64 values.\n\n#### \nfunc [NewUInt64List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L862) [¶](#NewUInt64List)\n```\nfunc NewUInt64List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([UInt64List](#UInt64List), [error](/builtin#error))\n```\nNewUInt64List creates a new list of UInt64, preferring placement in s.\n\n#### \nfunc (UInt64List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L871) [¶](#UInt64List.At)\n```\nfunc (l [UInt64List](#UInt64List)) At(i [int](/builtin#int)) [uint64](/builtin#uint64)\n```\nAt returns the i'th element.\n\n#### \nfunc (UInt64List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L561) [¶](#UInt64List.DecodeFromPtr)\n```\nfunc ([UInt64List](#UInt64List)) DecodeFromPtr(p [Ptr](#Ptr)) [UInt64List](#UInt64List)\n```\n#### \nfunc (UInt64List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L557) [¶](#UInt64List.EncodeAsPtr)\n```\nfunc (l [UInt64List](#UInt64List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (UInt64List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L549) [¶](#UInt64List.IsValid)\n```\nfunc (l [UInt64List](#UInt64List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (UInt64List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L553) [¶](#UInt64List.Len)\n```\nfunc (l [UInt64List](#UInt64List)) Len() [int](/builtin#int)\n```\n#### \nfunc (UInt64List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L565) [¶](#UInt64List.Message)\n```\nfunc (l [UInt64List](#UInt64List)) Message() *[Message](#Message)\n```\n#### \nfunc (UInt64List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L569) [¶](#UInt64List.Segment)\n```\nfunc (l [UInt64List](#UInt64List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (UInt64List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L880) [¶](#UInt64List.Set)\n```\nfunc (l [UInt64List](#UInt64List)) Set(i [int](/builtin#int), v [uint64](/builtin#uint64))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (UInt64List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L889) [¶](#UInt64List.String)\n```\nfunc (l [UInt64List](#UInt64List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (UInt64List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L573) [¶](#UInt64List.ToPtr)\n```\nfunc (l [UInt64List](#UInt64List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [UInt8List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L544) [¶](#UInt8List)\n```\ntype UInt8List [List](#List)\n```\nA UInt8List is an array of UInt8 values.\n\n#### \nfunc [NewData](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L580) [¶](#NewData)\n```\nfunc NewData(s *[Segment](#Segment), v [][byte](/builtin#byte)) ([UInt8List](#UInt8List), [error](/builtin#error))\n```\nNewData creates a new list of UInt8 from a byte slice.\n\n#### \nfunc [NewText](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L558) [¶](#NewText)\n```\nfunc NewText(s *[Segment](#Segment), v [string](/builtin#string)) ([UInt8List](#UInt8List), [error](/builtin#error))\n```\nNewText creates a new list of UInt8 from a string.\n\n#### \nfunc [NewTextFromBytes](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L569) [¶](#NewTextFromBytes)\n```\nfunc NewTextFromBytes(s *[Segment](#Segment), v [][byte](/builtin#byte)) ([UInt8List](#UInt8List), [error](/builtin#error))\n```\nNewTextFromBytes creates a NUL-terminated list of UInt8 from a byte slice.\n\n#### \nfunc [NewUInt8List](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L549) [¶](#NewUInt8List)\n```\nfunc NewUInt8List(s *[Segment](#Segment), n [int32](/builtin#int32)) ([UInt8List](#UInt8List), [error](/builtin#error))\n```\nNewUInt8List creates a new list of UInt8, preferring placement in s.\n\n#### \nfunc (UInt8List) [At](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L595) [¶](#UInt8List.At)\n```\nfunc (l [UInt8List](#UInt8List)) At(i [int](/builtin#int)) [uint8](/builtin#uint8)\n```\nAt returns the i'th element.\n\n#### \nfunc (UInt8List) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L369) [¶](#UInt8List.DecodeFromPtr)\n```\nfunc ([UInt8List](#UInt8List)) DecodeFromPtr(p [Ptr](#Ptr)) [UInt8List](#UInt8List)\n```\n#### \nfunc (UInt8List) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L365) [¶](#UInt8List.EncodeAsPtr)\n```\nfunc (l [UInt8List](#UInt8List)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (UInt8List) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L357) [¶](#UInt8List.IsValid)\n```\nfunc (l [UInt8List](#UInt8List)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (UInt8List) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L361) [¶](#UInt8List.Len)\n```\nfunc (l [UInt8List](#UInt8List)) Len() [int](/builtin#int)\n```\n#### \nfunc (UInt8List) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L373) [¶](#UInt8List.Message)\n```\nfunc (l [UInt8List](#UInt8List)) Message() *[Message](#Message)\n```\n#### \nfunc (UInt8List) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L377) [¶](#UInt8List.Segment)\n```\nfunc (l [UInt8List](#UInt8List)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (UInt8List) [Set](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L604) [¶](#UInt8List.Set)\n```\nfunc (l [UInt8List](#UInt8List)) Set(i [int](/builtin#int), v [uint8](/builtin#uint8))\n```\nSet sets the i'th element to v.\n\n#### \nfunc (UInt8List) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L613) [¶](#UInt8List.String)\n```\nfunc (l [UInt8List](#UInt8List)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[1, 2, 3]\").\n\n#### \nfunc (UInt8List) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L381) [¶](#UInt8List.ToPtr)\n```\nfunc (l [UInt8List](#UInt8List)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [VoidList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L512) [¶](#VoidList)\n```\ntype VoidList [List](#List)\n```\nA VoidList is a list of zero-sized elements.\n\n#### \nfunc [NewVoidList](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L518) [¶](#NewVoidList)\n```\nfunc NewVoidList(s *[Segment](#Segment), n [int32](/builtin#int32)) [VoidList](#VoidList)\n```\nNewVoidList creates a list of voids. No allocation is performed;\ns is only used for Segment()'s return value.\n\n#### \nfunc (VoidList) [DecodeFromPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L17) [¶](#VoidList.DecodeFromPtr)\n```\nfunc ([VoidList](#VoidList)) DecodeFromPtr(p [Ptr](#Ptr)) [VoidList](#VoidList)\n```\n#### \nfunc (VoidList) [EncodeAsPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L13) [¶](#VoidList.EncodeAsPtr)\n```\nfunc (l [VoidList](#VoidList)) EncodeAsPtr(seg *[Segment](#Segment)) [Ptr](#Ptr)\n```\n#### \nfunc (VoidList) [IsValid](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L5) [¶](#VoidList.IsValid)\n```\nfunc (l [VoidList](#VoidList)) IsValid() [bool](/builtin#bool)\n```\n#### \nfunc (VoidList) [Len](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L9) [¶](#VoidList.Len)\n```\nfunc (l [VoidList](#VoidList)) Len() [int](/builtin#int)\n```\n#### \nfunc (VoidList) [Message](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L21) [¶](#VoidList.Message)\n```\nfunc (l [VoidList](#VoidList)) Message() *[Message](#Message)\n```\n#### \nfunc (VoidList) [Segment](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L25) [¶](#VoidList.Segment)\n```\nfunc (l [VoidList](#VoidList)) Segment() *[Segment](#Segment)\n```\n#### \nfunc (VoidList) [String](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list.go#L530) [¶](#VoidList.String)\n```\nfunc (l [VoidList](#VoidList)) String() [string](/builtin#string)\n```\nString returns the list in Cap'n Proto schema format (e.g. \"[void, void, void]\").\n\n#### \nfunc (VoidList) [ToPtr](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/list-gen.go#L29) [¶](#VoidList.ToPtr)\n```\nfunc (l [VoidList](#VoidList)) ToPtr() [Ptr](#Ptr)\n```\n#### \ntype [WeakClient](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L786) [¶](#WeakClient)\n```\ntype WeakClient struct {\n\t// contains filtered or unexported fields\n}\n```\nA WeakClient is a weak reference to a capability: it refers to a capability without preventing it from being shut down. The zero value is a null reference.\n\n#### \nfunc (*WeakClient) [AddRef](https://github.com/capnproto/go-capnproto2/blob/v3.0.0-alpha-29/capability.go#L792) [¶](#WeakClient.AddRef)\n```\nfunc (wc *[WeakClient](#WeakClient)) AddRef() (c [Client](#Client), ok [bool](/builtin#bool))\n```\nAddRef creates a new Client that refers to the same capability as c as long as the capability hasn't already been shut down."}}},{"rowIdx":59473,"cells":{"project":{"kind":"string","value":"npm_@kolyaventuri_covid_act_now.jsonl"},"source":{"kind":"string","value":"personal_doc"},"language":{"kind":"string","value":"Unknown"},"content":{"kind":"string","value":"# Register#\n\nThe Covid Act Now API provides access to all of our COVID data tracking US states, counties, and metros.\n\nIt includes data and metrics for cases, vaccinations, tests, hospitalizations, and deaths. See data definitions for all included data.\n\nThe API provides the same data that powers Covid Act Now but in easily digestible CSV or JSON files, intended for consumption by other COVID websites, models, and tools.\n\nRegister \n\nData endpoints In the examples below, replace `YOUR_KEY_HERE` with the API key from Step 1 above. \nThe Covid Act Now API has coverage for states, counties, and metro areas (CBSAs). You can query the data in CSV or JSON formats.\n\nLearn how to query:\n\n* Current data for all states, counties, and metros\n * Historic data for all states, counties, and metros\n * Data for an individual state, county, or metro area\n * Aggregated US data\n\nDetails on the contents of each endpoint are available in the API Reference\n\nCurrent data for all states, counties, or metros \nThese endpoints contain the latest available data (a single, scalar value per field) for all states, counties, and CBSAs (metros).\n Each file contains all locations in the region type. For example,\n\n```\nhttps://api.covidactnow.org/v2/counties.csv?apiKey=YOUR_KEY_HERE\n```\n\ncontains all US counties. \n\nCSV format \nRead the API Reference for /v2/states.csv, /v2/counties.csv, /v2/cbsas.csv.\n\nHistoric data for all states, counties, or metros \nThese files contain the entire history (a timeseries for every field) for all states, counties, and cbsas (metros).\n\nCSV format \nRead the API reference for /v2/states.timeseries.csv, /v2/counties.timeseries.csv, /v2/cbsas.timeseries.csv\n\n# note\n\n As\n\n```\n/v2/counties.timeseries.json\n```\n\ncontains historic data for every county, it is very large. If you are looking for counties in a single state, consider\ndownloading counties for a single state. \n\nData for individual locations \nIt's easy to query a single state, county, or metro area.\n\nCurrent data \n\nHistoric data \n\nData for all counties in a state \nYou can also query all counties for a single state.\n\nAggregated US data \nWe also calculate country-wide data for the entire US.\n\nLicense \nData is licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.\n\nWe are a volunteer-driven 501(c)3 non-profit whose mission is to provide reliable and trustworthy COVID data, with a focus on U.S. counties. Since we started on March 20th, we’ve made our model and data open-source and freely available to the public.\n\nThis data requires a non-trivial amount of work to organize, sanitize, maintain, and develop, especially given the fast-changing nature of COVID and health data in the U.S. In order to ensure that we can continue to deliver best-in-class open-source COVID data, our tiny, volunteer-driven team appreciates donations here.\n\nWe also ask that, as legally required by our license, all commercial entities wishing to access our API contact <EMAIL> to acquire a commercial license. We define commercial users as any individual or entity engaged in commercial activities, such as selling goods or services.\n\nOur non-commercial users can freely download, use, share, modify, or build upon our source code.\n\nDate: 2019-08-24\nCategories: \nTags: \n\nThe Covid Act Now API provides historical covid projections updated daily.\n\n## API Key\n\nAn API key is required.\n\nRegister for an API key here.\n\nSecurity Scheme Type | API Key |\n | --- | --- |\nQuery parameter name: | apiKey |\n\n## Single State Summary\n\nRegion Summary object for a single state.\n\n## All states summary (json)\n\n## All states summary (csv)\n\n## Single County Summary\n\nRegion Summary object for a single county.\n\n## Single County Timeseries\n\nRegion Summary with Timeseries for a single county.\n\n## All counties summary (json)\n\n## All counties summary (csv)\n\n## Counties summary in state (json)\n\n## Counties summary in state (csv)\n\nAggregated data for all core-based statistical areas (CBSA).\n\nCBSAs represent collections of counties that are socioeconomically linked.\n\nThey are used to represent metropolitan and micropolitan (at least 10,000 people and fewer than 50,000 people) areas.\n\nFor example, the Seattle-Tacoma-Bellevue, WA CBSA is an aggregation of King County, Pierce County, and Snohomish County.\n\nCBSAs are currently in beta and may not contain all metrics or data.\n\n## Single CBSA Summary\n\nRegion Summary object for a single CBSA.\n\n## Single CBSA Timeseries\n\nRegion Summary with Timeseries for a single CBSA.\n\n## All CBSAs summary (json)\n\n## All CBSAs summary (csv)\n\n## US Summary\n\nRegion Summary object for US.\n\noverall | |\n | --- | --- |\ntestPositivityRatio | |\ncaseDensity | |\ncontactTracerCapacityRatio | |\ninfectionRate | |\nicuCapacityRatio | |\n\n* \"overall\": 0,\n * \"testPositivityRatio\": 0,\n * \"caseDensity\": 0,\n * \"contactTracerCapacityRatio\": 0,\n * \"infectionRate\": 0,\n * \"icuCapacityRatio\": 0\n} \n\n# Cases#\n\nDate: 2022-01-01\nCategories: \nTags: \n\nRead more about the data included in the Covid Act Now API.\n\nCases \n\nCases \nCumulative confirmed or suspected cases.\n\n* CSV column names:\n `actuals.cases` * JSON file fields:\n `actuals.cases` , \n\n```\nactualsTimeseries.*.cases\n```\n\nNew Cases \nNew confirmed or suspected cases.\n\nNew cases are a processed timeseries of cases - summing new cases may not equal the cumulative case count.\n\nProcessing steps:\n\n* If a region does not report cases for a period of time but then begins reporting again, we will exclude the first day that reporting recommences. This first day likely includes multiple days worth of cases and can be misleading to the overall series.\n * We remove any days with negative new cases.\n * We apply an outlier detection filter to the timeseries, which removes any data points that seem improbable given recent numbers. Many times this is due to backfill of previously unreported cases.\n\n```\nactualsTimeseries.*.newCases\n```\n\nCase Density \nThe number of cases per 100k population calculated using a 7-day rolling average.\n\n* CSV column names:\n `metrics.caseDensity` * JSON file fields:\n `metrics.caseDensity` , \n\n```\nmetricsTimeseries.*.caseDensity\n```\n\nInfection Rate \nR_t, or the estimated number of infections arising from a typical case.\n\n```\nmetricsTimeseries.*.infectionRate\n```\n\nInfection Rate Ci90 \n90th percentile confidence interval upper endpoint of the infection rate.\n\n```\nmetricsTimeseries.*.infectionRateCI90\n```\n\nWeekly New Cases Per100K \nThe number of new cases per 100k population over the last week.\n\n```\nmetricsTimeseries.*.weeklyNewCasesPer100k\n```\n\nTests \n\nPositive Tests \nCumulative positive test results to date\n\n```\nactualsTimeseries.*.positiveTests\n```\n\nNegative Tests \nCumulative negative test results to date\n\n```\nactualsTimeseries.*.negativeTests\n```\n\nTest Positivity Ratio \nRatio of people who test positive calculated using a 7-day rolling average.\n\n```\nmetricsTimeseries.*.testPositivityRatio\n```\n\nTest Positivity Ratio Details \nWhere to access\n\n```\nmetricsTimeseries.*.testPositivityRatioDetails\n```\n\nHospitalizations \n\nIcu Beds \nInformation about ICU bed utilization details.\n\n* capacity - Current staffed ICU bed capacity.\n * currentUsageTotal - Total number of ICU beds currently in use\n * currentUsageCovid - Number of ICU beds currently in use by COVID patients.\n\n```\nactualsTimeseries.*.icuBeds\n```\n\nHospital Beds \nInformation about acute bed utilization details.\n\n* capacity - Current staffed acute bed capacity.\n * currentUsageTotal - Total number of acute beds currently in use\n * currentUsageCovid - Number of acute beds currently in use by COVID patients.\n * weeklyCovidAdmissions - Number of COVID patients admitted in the past week.\n\n```\nactualsTimeseries.*.hospitalBeds\n```\n\nIcu Capacity Ratio \nRatio of staffed intensive care unit (ICU) beds that are currently in use.\n\n```\nmetricsTimeseries.*.icuCapacityRatio\n```\n\nBeds With Covid Patients Ratio \nRatio of staffed hospital beds that are currently in use by COVID patients. For counties, this is calculated using HSA-level data for the corresponding area. For more on HSAs, see https://apidocs.covidactnow.org/data-definitions/#health-service-areas\n\n```\nmetricsTimeseries.*.bedsWithCovidPatientsRatio\n```\n\nWeekly Covid Admissions Per100K \nNumber of COVID patients per 100k population admitted in the past week. For counties, this is calculated using HSA-level data for the corresponding area. For more on HSAs, see https://apidocs.covidactnow.org/data-definitions/#health-service-areas\n\n```\nmetricsTimeseries.*.weeklyCovidAdmissionsPer100k\n```\n\nVaccinations \n\nVaccines Distributed \nNumber of vaccine doses distributed.\n\n```\nactualsTimeseries.*.vaccinesDistributed\n```\n\nVaccinations Initiated \nNumber of vaccinations initiated.\n\n```\nactualsTimeseries.*.vaccinationsInitiated\n```\n\nVaccinations Completed \nNumber of vaccinations completed.\n\n```\nactualsTimeseries.*.vaccinationsCompleted\n```\n\nVaccinations Additional Dose \nNumber of individuals who are fully vaccinated and have received a booster (or additional) dose.\n\n```\nactualsTimeseries.*.vaccinationsAdditionalDose\n```\n\nVaccinations Fall 2022 Bivalent Booster \nNumber of individuals who have received a bivalent vaccine dose.\n\n```\nactualsTimeseries.*.vaccinationsFall2022BivalentBooster\n```\n\nVaccines Administered \nTotal number of vaccine doses administered.\n\n```\nactualsTimeseries.*.vaccinesAdministered\n```\n\nVaccines Administered Demographics \nDemographic distributions for administered vaccines.\n\nVaccinations Initiated Demographics \nDemographic distributions for initiated vaccinations.\n\nVaccinations Initiated Ratio \nRatio of population that has initiated vaccination.\n\n```\nmetricsTimeseries.*.vaccinationsInitiatedRatio\n```\n\nVaccinations Completed Ratio \nRatio of population that has completed vaccination.\n\n```\nmetricsTimeseries.*.vaccinationsCompletedRatio\n```\n\nVaccinations Additional Dose Ratio \nRatio of population that are fully vaccinated and have received a booster (or additional) dose.\n\n```\nmetricsTimeseries.*.vaccinationsAdditionalDoseRatio\n```\n\nVaccinations Fall 2022 Bivalent Booster Ratio \nRatio of population that have received a bivalent vaccine dose.\n\n```\nmetricsTimeseries.*.vaccinationsFall2022BivalentBoosterRatio\n```\n\nDeaths \n\nDeaths \nCumulative deaths that are suspected or confirmed to have been caused by COVID-19.\n\n```\nactualsTimeseries.*.deaths\n```\n\nCommunity Levels \nCommunity level for region.\n\nSee https://www.cdc.gov/coronavirus/2019-ncov/science/community-levels.html for details about how the Community Level is calculated and should be interpreted.\n\nThe values correspond to the following levels:\n\nAPI value | Community Level |\n | --- | --- |\n0 | Low |\n1 | Medium |\n2 | High |\n\n Note that we provide two versions of the Community Level. One is called `canCommunityLevel` which is calculated using CAN's data sources and is\navailable for states, counties, and metros. It is updated daily though\ndepends on hospital data which may only update weekly for counties. The\nother is called `cdcCommunityLevel` and is the raw Community Level published\nby the CDC. It is only available for counties and is updated on a weekly\nbasis. \nWhere to access\n\n```\ncommunityLevelsTimeseries.*.canCommunityLevel\n```\n\nand\n * \n\n```\ncommunityLevelsTimeseries.*.cdcCommunityLevel\n```\n\nHealth Service Areas \nA Health Service area (HSA) is a collection of one or more contiguous counties which are relatively self-contained with respect to hospital care. HSAs are used when calculating county-level hospital metrics in order to correct for instances where an individual county does not have any, or has few healthcare facilities within its own borders. For more information see https://seer.cancer.gov/seerstat/variables/countyattribs/hsa.html.\n The source for our county to HSA mappings is `cdc_hsa_mapping.csv` which follows the HSA definitions used by the CDC in their COVID-19 Community Levels. HSA populations are calculated as the sum of the component county populations.\n\nDate: 2020-12-22\nCategories: \nTags: \n\nUpdates to the API will be reflected here.\n\nSunsetting Demographic Vaccine Data \n2023-01-11\n\nUnlike the other data in our API, county-level demographic vaccine data is not actively quality assured, and as such, we cannot guarantee that it is of high quality.\n\nWe will continue to provide this data until 02/15/2023, at which point we will remove it from the API. Please reach out to <EMAIL> with any concerns or questions.\n\nCDC Community Level data now available \nAdded on 2022-04-05\n\nThe CDC Community Level metric as well as the subcomponents of the CDC Community Level metric are now available within the Covid Act Now API.\n\nLearn more about how the CDC Community Level is measured.\n\n: The raw CDC Community Level metric. It serves as an exact mirror of the CDC’s published data, which is available for counties only and typically updates once a week. * \n\n: The Covid Act Now team’s version of CDC Community Level metric. It uses the same methodology as the CDC community level, but it is available for states and metros in addition to counties. It also uses different data sources in some cases (New York Times for cases, HHS for state hospitalization data). It updates daily, though county hospitalization data only updates once a week. * \n\n: The number of new COVID cases per week per 100K population. * \n\n: The number of new COVID hospital admissions per week per 100K population. For counties this is calculated at the Health Service Area level. * \n\n: The ratio of staffed inpatient beds that are occupied by COVID patients. For counties this is calculated at the Health Service Area level. * \n\n```\nactuals.hospitalBeds.weeklyCovidAdmissions\n```\n\n: The number of new COVID hospital admissions per week. * \n\n```\nactuals.hsaHospitalBeds.weeklyCovidAdmissions\n```\n\n: The number of new COVID hospital admissions per week measured at the Health Service Area level. * \n `hsaName` : The name of the Health Service Area. * \n `hsaPopulation` : The population of the Health Service Area. * \n `hsaHospitalBeds` : This is a mirror of the existing hospitalBeds field, but measured at the Health Service Area level. * \n `hsaIcuBeds` : This is a mirror of the existing icuBeds field, but measured at the Health Service Area level. \n\nVaccine Booster data now available \nAdded on 2022-01-13\n\nVaccine booster shot (or additional dose) data is now available within the Covid Act Now API.\n\n: Number of individuals who are fully vaccinated and have received a booster (or additional) dose. * \n\n: Ratio of population that are fully vaccinated and have received a booster (or additional) dose. \n\nICU Headroom and Typical Usage Rate removed \nAdded on 2021-09-16\n The following deprecated fields have been removed from the API: `icuHeadroomRatio` , `icuHeadroomDetails` , and `typicalUsageRate` . Consider using `icuCapacityRatio` instead. \n\nCDC Community Transmission Levels \nAdded on 2021-07-30\n\nWe now expose a CDC Community Transmission Level in the API.\n\nThe CDC community transmission levels are similar to the Covid Act Now risk levels, but have slightly different thresholds. See definitions of CDC community transmission levels for more details.\n We calculate the level using the CDC's thresholds and expose it in the field `cdcTransmissionLevel` in all API responses. \nThe values correspond to the following levels:\n\nAPI value | CDC community transmission level |\n | --- | --- |\n0 | Low |\n1 | Moderate |\n2 | Substantial |\n3 | High |\n4 | Unknown |\n\nNote that the value may differ from what the CDC website reports given we have different data sources. We have also introduced an \"Unknown\" level for when both case data and test positivity data are missing for at least 15 days. The CDC does not have an \"Unknown\" level and instead will designate a location as \"Low\" when case and test positivity data are missing.\n\nAggregated US data \nAdded on 2021-03-31\n\nYou can now query US aggregated data.\n\nVaccine demographic data \nAdded on 2021-03-25\n We are now starting to include vaccine demographic data; currently we are collecting two fields:\n\nand \n\n. While we currently only have county level data in TX and PA (as of 3/25) we are working on adding more regions to provide the most complete vaccine demographic data. \nNote that demographic buckets may differ by jurisdiction as different states may collect and bucket demographic data in different ways. We surface the buckets as collected for now but this may change in the future.\n\nVaccines administered \nAdded on 2021-03-23\n Added\n\nto the API. This represents the total number of doses\nadministered for a region. \n\nNew deaths column \nAdded on 2021-03-08\n Added `actuals.newDeaths` and \n\n```\nactualsTimeseries.*.newDeaths\n```\n\nto the API.\nThe processing is similar to `actuals.newCases` - `newDeaths` represent new deaths\nsince previous report with erratic values removed by outlier detection. \n\nField level annotations \nAdded on 2021-01-19\n The Annotations field has a FieldAnnotations for each field in `Actuals` . You can now access the\ndata source(s) used to produce a field and list of dates where an anomalous observation was removed.\nThe exact structure of the `AnomalyAnnotation` may be modified in the future. \n\nVaccine data now available \nAdded on 2021-01-14\n\nVaccine data is now available within the Covid Act Now API.\n\nCurrently the data is available for states only, but county-level vaccination data is coming soon.\n\n* \n `vaccinesDistributed` : Total number of vaccine doses distributed. * \n\n```\nvaccinationsInitiated\n```\n\n: Total number of people initiating vaccination. For a vaccine with a 2-dose regimen, this represents the first dose. * \n\n```\nvaccinationsCompleted\n```\n\n: Total number of people completing vaccination - currently those completing their second shot. * \n\n```\nvaccinationsInitiatedRatio\n```\n\n: Ratio of population that has initiated vaccination. * \n\n```\nvaccinationsCompletedRatio\n```\n\n: Ratio of population that has completed vaccination. You can access these fields in both the `actuals` field and `actualsTimeseries` fields. \n\nView entire timeseries of risk levels for all regions \nAdded on 2020-12-22\n You can now view the history of a region's overall risk level in all timeseries endpoints under the key `riskLevelsTimeseries` . \n\nOverall risk level now based on 3 key metrics \nAdded on 2020-12-22\n The overall risk level is now based on `caseDensity` , `testPositivityRatio` , and `infectionRate` .\nLearn more about the changes we made. We will be continuing to calculate all metrics and have no plans of removing\n\n```\ncontactTracingCapacityRatio\n```\n\n, `icuCapacityRatio` , or `icuHeadroomRatio` at this time. \n\nLink to Covid Act Now website \nAdded on 2020-12-03\n Each region now includes a field `url` that points to the Covid Act Now location page\nfor that region. \n\nUpcoming risk level update \nAdded on 2020-12-01\n\nWe modified our risk levels to include a 5th level on covidactnow.org for locations experiencing a severe outbreak. On Monday, December 7th we will be updating the risk levels in the API to reflect this.\n\nIf you have any code depending on 4 risk levels, you will need to update it to include the fifth risk level.\n This change directly affects the fields `riskLevels.overall` and \n\n```\nriskLevels.caseDensity\n```\n\n. If you would like to include the new risk level right now to reflect what is currently on covidactnow.org, you can do so by classifying both `overall` and `caseDensity` risk as extreme for any location\nwhere \n\n```\nactuals.casesDensity > 75\n```\n\n. \n\nQuery by CBSA \nAdded on 2020-11-09\n\nWe added core-based statistical area endpoints to the API.\n\nYou can now view results aggregated by CBSA:\n\nRead the CBSA API Documentation to learn more.\n\nIncrease county test positivity coverage \nAdded on 2020-11-04\n\nWe increased our test positivity coverage for counties by adding in data from U.S. Department of Health & Human Services as aggregated by the Centers for Medicare & Medicaid Services. See our data sources for more information.\n\nAdd new cases field with outlier detection \nAdded on 2020-10-29\n In addition to cumulative case counts, we added a `New Cases` field to all `actuals` and `actualsTimeseries` values. The `New Cases` field computes new\ncases and applies outlier detection to remove erratic case values. \n\n `locationId` field#Add \nAdded on 2020-10-27\n\nAdds a generic location ID used to represent regions. Will allow for greater flexibility as we add more aggregation levels (such as country).\n\n `riskLevels` #Add \nAdded on 2020-10-15\n\nAdded risk levels as seen on covidactnow.org to the API.\n\n# Covid Act Now API Overview#\n\nOn March 7th, The Covid Tracking Project (CTP) will be winding down their daily updates. Throughout the pandemic they have provided an amazing service and resource with their daily data collection and in-depth reporting. For those looking for a replacement, the Covid Act Now API can be used to serve many of the same use cases.\n\nThe Covid Act Now API provides access to comprehensive COVID data — both current and historical. The data is available for all US states, counties, and metros and is aggregated from a number of official sources, quality assured, and updated daily.\n\nOur API powers all data available on covidactnow.org including daily updates to cases, hospitalization, testing, and vaccination data. It includes raw data, risk levels, and calculated metrics to help you understand covid spread for a location. In addition to state data, we also provide county and metro data where available.\n\nCovid Act Now API Overview \nIn general, the Covid Act Now API provides much of the same data as The Covid Tracking Project. However there are some differences:\n\nCounty and metro data \nIn addition to state-level data as was provided by Covid Tracking Project, we also provide county and metro data where available. Typically county data is not as complete as state data but coverage is improving. Our county data is collected from a wide variety of sources that include federal, state, and local dashboards.\n\nMetrics and risk levels \nWe calculate metrics and risk levels derived from the raw data. These metrics include daily new cases per 100k, infection rate (R_t), test positivity, percent of population vaccinated, and ICU utilization.\n\nVaccination data \nOur API includes vaccination data. We include doses distributed, vaccinations initiated, and vaccinations completed.\n\nTesting data \nFor testing data, we focus on test positivity via PCR specimens which has become the standard metric tracked by most health departments. We have positive and negative PCR tests for all states and a computed test positivity percentage for all states and most counties.\n\nHospitalization data \nWe currently ingest hospitalization data at the state and county level from HHS. For both ICU and overall hospitalization we include total staffed beds, beds in use by COVID patients, and total beds in use.\n\nMany of the fields in the Covid Tracking API do overlap. Cases, deaths, and hospitalization/ICU data have the largest commonalities.\n\nCTP field name | CAN Field Name |\n | --- | --- |\ndate | date |\nfips | fips |\nstate | state |\ndeath | actuals.deaths |\nhospitalizedCurrently | actuals.hospitalBeds.currentUsageCovid |\ninIcuCurrently | actuals.icuBeds.currentUsageCovid |\nnegativeTestsViral | actuals.negativeTests |\npositiveTestsViral | actuals.positiveTests |\npositive | actuals.cases |\npositiveIncrease | actuals.newCases |\n\nSee data definitions for all included fields.\n\nGetting Started \nTo get started, register to get your API key.\n All requests should be made to\n\n```\nhttps://api.covidactnow.org\n```\n\nand include an API key. So for example, to query a CSV for the current values for all states, the request would be of the form: \nMany of endpoints from The Covid Tracking Project are available in our API. Below is a summary of similar endpoints:\n\nDescription | Covid Tracking endpoint | Covid Act Now endpoint |\n | --- | --- | --- |\nCurrent values for all states | /v1/states/current.{csv,json} | /v2/states.{csv,json} |\nHistorical values for all states | /v1/states/daily.{csv,json} | /v2/states.timeseries.{csv,json} |\nCurrent values for a single state | /v1/states/ca/daily.{csv,json} | /v2/state/CA.timeseries.{csv,json} |\nHistorical values for a single state | /v1/states/ca/current.{csv,json} | /v2/state/CA.{json} |\n\nSkip to main content Getting started Data Definitions API Updates Covid Tracking Migration Guide Contact Us If you have any questions about the API, please contact us at <EMAIL> .\n"}}},{"rowIdx":59474,"cells":{"project":{"kind":"string","value":"github.com/takama/router"},"source":{"kind":"string","value":"go"},"language":{"kind":"string","value":"Go"},"content":{"kind":"string","value":"README\n [¶](#section-readme)\n---\n\n### Go Router\n\n[](https://travis-ci.org/takama/router)\n[](https://godoc.org/github.com/takama/router)\n[](https://github.com/takama/router/issues)\n[](https://goreportcard.com/report/github.com/takama/router)\n[](https://codecov.io/github/takama/router?branch=master)\n\nA simple, compact and fast router package to process HTTP requests.\nIt has some sugar from framework however still lightweight. The router package is useful to prepare a RESTful API for Go services. It has JSON output, which bind automatically for relevant type of data. The router has timer feature to display duration of request handling in the header\n\n##### Examples\n\n* Simplest example (serve static route):\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\nfunc Hello(c *router.Control) {\n\tc.Body(\"Hello world\")\n}\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/hello\", Hello)\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i http://localhost:8888/hello/\n\nHTTP/1.1 200 OK Content-Type: text/plain Date: Sun, 17 Aug 2014 13:25:50 GMT Content-Length: 11\n\nHello world\n```\n* Serve dynamic route with parameter:\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/hello/:name\", func(c *router.Control) {\n\t\tc.Body(\"Hello \" + c.Get(\":name\"))\n\t})\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i http://localhost:8888/hello/John\n\nHTTP/1.1 200 OK Content-Type: text/plain Date: Sun, 17 Aug 2014 13:25:55 GMT Content-Length: 10\n\nHello John\n```\n* Checks JSON Content-Type automatically:\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\n// Data is helper to construct JSON type Data map[string]interface{}\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/api/v1/settings/database/:db\", func(c *router.Control) {\n\t\tdata := Data{\n\t\t\t\"Database settings\": Data{\n\t\t\t\t\"database\": c.Get(\":db\"),\n\t\t\t\t\"host\": \"localhost\",\n\t\t\t\t\"port\": \"3306\",\n\t\t\t},\n\t\t}\n\t\tc.Code(200).Body(data)\n\t})\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i http://localhost:8888/api/v1/settings/database/testdb\n\nHTTP/1.1 200 OK Content-Type: application/json Date: Sun, 17 Aug 2014 13:25:58 GMT Content-Length: 102\n\n{\n \"Database settings\": {\n \"database\": \"testdb\",\n \"host\": \"localhost\",\n \"port\": \"3306\"\n }\n}\n```\n* Use timer to calculate duration of request handling:\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\n// Data is helper to construct JSON type Data map[string]interface{}\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/api/v1/settings/database/:db\", func(c *router.Control) {\n\t\tc.UseTimer()\n\n\t\t// Do something\n\n\t\tdata := Data{\n\t\t\t\"Database settings\": Data{\n\t\t\t\t\"database\": c.Get(\":db\"),\n\t\t\t\t\"host\": \"localhost\",\n\t\t\t\t\"port\": \"3306\",\n\t\t\t},\n\t\t}\n\t\tc.Code(200).Body(data)\n\t})\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i http://localhost:8888/api/v1/settings/database/testdb\n\nHTTP/1.1 200 OK Content-Type: application/json Date: Sun, 17 Aug 2014 13:26:05 GMT Content-Length: 143\n\n{\n \"duration\": 5356123\n \"took\": \"5.356ms\",\n \"data\": {\n \"Database settings\": {\n \"database\": \"testdb\",\n \"host\": \"localhost\",\n \"port\": \"3306\"\n }\n }\n}\n```\n* Custom handler with \"Access-Control-Allow\" options and compact JSON:\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\n// Data is helper to construct JSON type Data map[string]interface{}\n\nfunc baseHandler(handle router.Handle) router.Handle {\n\treturn func(c *router.Control) {\n\t\tc.CompactJSON(true)\n\t\tif origin := c.Request.Header.Get(\"Origin\"); origin != \"\" {\n\t\t\tc.Writer.Header().Set(\"Access-Control-Allow-Origin\", origin)\n\t\t\tc.Writer.Header().Set(\"Access-Control-Allow-Credentials\", \"true\")\n\t\t}\n\t\thandle(c)\n\t}\n}\n\nfunc Info(c *router.Control) {\n\tdata := Data{\n\t\t\"debug\": true,\n\t\t\"error\": false,\n\t}\n\tc.Body(data)\n}\n\nfunc main() {\n\tr := router.New()\n\tr.CustomHandler = baseHandler\n\tr.GET(\"/info\", Info)\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i -H 'Origin: http://foo.com' http://localhost:8888/info/\n\nHTTP/1.1 200 OK Access-Control-Allow-Credentials: true Access-Control-Allow-Origin: http://foo.com Content-Type: text/plain Date: Sun, 17 Aug 2014 13:27:10 GMT Content-Length: 28\n\n{\"debug\":true,\"error\":false}\n```\n* Use google json style `https://google.github.io/styleguide/jsoncstyleguide.xml`:\n```\npackage main\n\nimport (\n\t\"net/http\"\n\n\t\"github.com/takama/router\"\n)\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/api/v1/people/:action/:id\", func(c *router.Control) {\n\n\t\t// Do something\n\n\t\tc.Method(\"people.\" + c.Get(\":action\"))\n\t\tc.SetParams(map[string]string{\"userId\": c.Get(\":id\")})\n\t\tc.SetError(http.StatusNotFound, \"UserId not found\")\n\t\tc.AddError(router.Error{Message: \"Group or User not found\"})\n\t\tc.Code(http.StatusNotFound).Body(nil)\n\t})\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\n* Check it:\n```\ncurl -i http://localhost:8888/api/v1/people/get/@me\n\nHTTP/1.1 404 Not Found Content-Type: application/json Date: Sat, 22 Oct 2016 14:50:00 GMT Content-Length: 220\n\n{\n \"method\": \"people.get\",\n \"params\": {\n \"userId\": \"@me\"\n },\n \"error\": {\n \"code\": 404,\n \"message\": \"UserId not found\",\n \"errors\": [\n {\n \"message\": \"Group or User not found\"\n }\n ]\n }\n}\n```\n#### Contributors (unsorted)\n\n* [<NAME>](https://github.com/takama)\n* [<NAME>](https://github.com/CSharpRU)\n\nAll the contributors are welcome. If you would like to be the contributor please accept some rules.\n\n* The pull requests will be accepted only in \"develop\" branch\n* All modifications or additions should be tested\n* Sorry, I'll not accept code with any dependency, only standard library\n\nThank you for your understanding!\n\n#### License\n\n[BSD License](https://github.com/takama/router/raw/master/LICENSE)\n\nDocumentation\n [¶](#section-documentation)\n---\n\n \n### Overview [¶](#pkg-overview)\n\nPackage router 0.6.5 provides fast HTTP request router.\n\nThe router matches incoming requests by the request method and the path.\nIf a handle is registered for this path and method, the router delegates the request to defined handler.\nThe router package is useful to prepare a RESTful API for Go services.\nIt has JSON output, which bind automatically for relevant type of data.\nThe router has timer feature to display duration of request handling in the header\n\nSimplest example (serve static route):\n```\npackage main\n\nimport (\n\t\"github.com/takama/router\"\n)\n\nfunc Hello(c *router.Control) {\n\tc.Body(\"Hello\")\n}\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/hello\", Hello)\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\nCheck it:\n```\ncurl -i http://localhost:8888/hello\n```\nServe dynamic route with parameter:\n```\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/hello/:name\", func(c *router.Control) {\n\t\tc.Code(200).Body(\"Hello \" + c.Get(\":name\"))\n\t})\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\nChecks JSON Content-Type automatically:\n```\n// Data is helper to construct JSON type Data map[string]interface{}\n\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/settings/database/:db\", func(c *router.Control) {\n\t\tdata := map[string]map[string]string{\n\t\t\t\"Database settings\": {\n\t\t\t\t\"database\": c.Get(\":db\"),\n\t\t\t\t\"host\": \"localhost\",\n\t\t\t\t\"port\": \"3306\",\n\t\t\t},\n\t\t}\n\t\tc.Code(200).Body(data)\n\t})\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\nCustom handler with \"Access-Control-Allow\" options and compact JSON:\n```\n// Data is helper to construct JSON type Data map[string]interface{}\n\nfunc baseHandler(handle router.Handle) router.Handle {\n\treturn func(c *router.Control) {\n\t\tc.CompactJSON(true)\n\t\tif origin := c.Request.Header.Get(\"Origin\"); origin != \"\" {\n\t\t\tc.Writer.Header().Set(\"Access-Control-Allow-Origin\", origin)\n\t\t\tc.Writer.Header().Set(\"Access-Control-Allow-Credentials\", \"true\")\n\t\t}\n\t\thandle(c)\n\t}\n}\n\nfunc Info(c *router.Control) {\n\tdata := Data{\n\t\t\"debug\": true,\n\t\t\"error\": false,\n\t}\n\tc.Body(data)\n}\n\nfunc main() {\n\tr := router.New()\n\tr.CustomHandler = baseHandler\n\tr.GET(\"/info\", Info)\n\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\nUse google json style `<https://google.github.io/styleguide/jsoncstyleguide.xml>`\n```\nfunc main() {\n\tr := router.New()\n\tr.GET(\"/api/v1/people/:action/:id\", func(c *router.Control) {\n\n\t\t// Do something\n\n\t\tc.Method(\"people.\" + c.Get(\":action\"))\n\t\tc.SetParams(map[string]string{\"userId\": c.Get(\":id\")})\n\t\tc.SetError(http.StatusNotFound, \"UserId not found\")\n\t\tc.AddError(router.Error{Message: \"Group or User not found\"})\n\t\tc.Code(http.StatusNotFound).Body(nil)\n\t})\n\t// Listen and serve on 0.0.0.0:8888\n\tr.Listen(\":8888\")\n}\n```\nGo Router\n\n### Index [¶](#pkg-index)\n\n* [Constants](#pkg-constants)\n* [type Control](#Control)\n* + [func (c *Control) APIVersion(version string) *Control](#Control.APIVersion)\n\t+ [func (c *Control) AddError(errors ...Error) *Control](#Control.AddError)\n\t+ [func (c *Control) Body(data interface{})](#Control.Body)\n\t+ [func (c *Control) Code(code int) *Control](#Control.Code)\n\t+ [func (c *Control) CompactJSON(mode bool) *Control](#Control.CompactJSON)\n\t+ [func (c *Control) Get(name string) string](#Control.Get)\n\t+ [func (c *Control) GetCode() int](#Control.GetCode)\n\t+ [func (c *Control) GetTimer() time.Time](#Control.GetTimer)\n\t+ [func (c *Control) HeaderContext(context string) *Control](#Control.HeaderContext)\n\t+ [func (c *Control) ID(id string) *Control](#Control.ID)\n\t+ [func (c *Control) Method(method string) *Control](#Control.Method)\n\t+ [func (c *Control) Set(params ...Param) *Control](#Control.Set)\n\t+ [func (c *Control) SetError(code uint16, message string) *Control](#Control.SetError)\n\t+ [func (c *Control) SetParams(params interface{}) *Control](#Control.SetParams)\n\t+ [func (c *Control) UseMetaData() *Control](#Control.UseMetaData)\n\t+ [func (c *Control) UseTimer()](#Control.UseTimer)\n* [type Error](#Error)\n* [type ErrorHeader](#ErrorHeader)\n* [type Handle](#Handle)\n* [type Header](#Header)\n* [type Param](#Param)\n* [type Route](#Route)\n* [type Router](#Router)\n* + [func New() *Router](#New)\n* + [func (r *Router) AllowedMethods(path string) []string](#Router.AllowedMethods)\n\t+ [func (r *Router) DELETE(path string, h Handle)](#Router.DELETE)\n\t+ [func (r *Router) GET(path string, h Handle)](#Router.GET)\n\t+ [func (r *Router) HEAD(path string, h Handle)](#Router.HEAD)\n\t+ [func (r *Router) Handle(method, path string, h Handle)](#Router.Handle)\n\t+ [func (r *Router) Handler(method, path string, handler http.Handler)](#Router.Handler)\n\t+ [func (r *Router) HandlerFunc(method, path string, handler http.HandlerFunc)](#Router.HandlerFunc)\n\t+ [func (r *Router) Listen(hostPort string)](#Router.Listen)\n\t+ [func (r *Router) Lookup(method, path string) (Handle, []Param, bool)](#Router.Lookup)\n\t+ [func (r *Router) OPTIONS(path string, h Handle)](#Router.OPTIONS)\n\t+ [func (r *Router) PATCH(path string, handle Handle)](#Router.PATCH)\n\t+ [func (r *Router) POST(path string, h Handle)](#Router.POST)\n\t+ [func (r *Router) PUT(path string, h Handle)](#Router.PUT)\n\t+ [func (r *Router) Routes() []Route](#Router.Routes)\n\t+ [func (r *Router) ServeHTTP(w http.ResponseWriter, req *http.Request)](#Router.ServeHTTP)\n\n### Constants [¶](#pkg-constants)\n\n```\nconst (\n // MIMEJSON - \"Content-type\" for JSON\n\tMIMEJSON = \"application/json\"\n // MIMETEXT - \"Content-type\" for TEXT\n\tMIMETEXT = \"text/plain\"\n)\n```\nDefault content types\n\n### Variables [¶](#pkg-variables)\n\nThis section is empty.\n\n### Functions [¶](#pkg-functions)\n\nThis section is empty.\n\n### Types [¶](#pkg-types)\n\n#### \ntype [Control](https://github.com/takama/router/blob/v0.6.5/control.go#L26) [¶](#Control)\n```\ntype Control struct {\n\n // Context embedded\n\t[context](/context).[Context](/context#Context)\n\n // Request is an adapter which allows the usage of a http.Request as standard request\n\tRequest *[http](/net/http).[Request](/net/http#Request)\n\n // Writer is an adapter which allows the usage of a http.ResponseWriter as standard writer\n\tWriter [http](/net/http).[ResponseWriter](/net/http#ResponseWriter)\n\n // User content type\n\tContentType [string](/builtin#string)\n\t// contains filtered or unexported fields\n}\n```\nControl allows us to pass variables between middleware,\nassign Http codes and render a Body.\n\n#### \nfunc (*Control) [APIVersion](https://github.com/takama/router/blob/v0.6.5/control.go#L143) [¶](#Control.APIVersion)\n```\nfunc (c *[Control](#Control)) APIVersion(version [string](/builtin#string)) *[Control](#Control)\n```\nAPIVersion adds API version meta data\n\n#### \nfunc (*Control) [AddError](https://github.com/takama/router/blob/v0.6.5/control.go#L186) [¶](#Control.AddError)\n```\nfunc (c *[Control](#Control)) AddError(errors ...[Error](#Error)) *[Control](#Control)\n```\nAddError adds new error\n\n#### \nfunc (*Control) [Body](https://github.com/takama/router/blob/v0.6.5/control.go#L204) [¶](#Control.Body)\n```\nfunc (c *[Control](#Control)) Body(data interface{})\n```\nBody renders the given data into the response body\n\n#### \nfunc (*Control) [Code](https://github.com/takama/router/blob/v0.6.5/control.go#L118) [¶](#Control.Code)\n```\nfunc (c *[Control](#Control)) Code(code [int](/builtin#int)) *[Control](#Control)\n```\nCode assigns http status code, which returns on http request\n\n#### \nfunc (*Control) [CompactJSON](https://github.com/takama/router/blob/v0.6.5/control.go#L131) [¶](#Control.CompactJSON)\n```\nfunc (c *[Control](#Control)) CompactJSON(mode [bool](/builtin#bool)) *[Control](#Control)\n```\nCompactJSON changes JSON output format (default mode is false)\n\n#### \nfunc (*Control) [Get](https://github.com/takama/router/blob/v0.6.5/control.go#L101) [¶](#Control.Get)\n```\nfunc (c *[Control](#Control)) Get(name [string](/builtin#string)) [string](/builtin#string)\n```\nGet returns the first value associated with the given name.\nIf there are no values associated with the key, an empty string is returned.\n\n#### \nfunc (*Control) [GetCode](https://github.com/takama/router/blob/v0.6.5/control.go#L126) [¶](#Control.GetCode)\n```\nfunc (c *[Control](#Control)) GetCode() [int](/builtin#int)\n```\nGetCode returns status code\n\n#### \nfunc (*Control) [GetTimer](https://github.com/takama/router/blob/v0.6.5/control.go#L199) [¶](#Control.GetTimer)\n```\nfunc (c *[Control](#Control)) GetTimer() [time](/time).[Time](/time#Time)\n```\nGetTimer returns timer state\n\n#### \nfunc (*Control) [HeaderContext](https://github.com/takama/router/blob/v0.6.5/control.go#L150) [¶](#Control.HeaderContext)\n```\nfunc (c *[Control](#Control)) HeaderContext(context [string](/builtin#string)) *[Control](#Control)\n```\nHeaderContext adds context meta data\n\n#### \nfunc (*Control) [ID](https://github.com/takama/router/blob/v0.6.5/control.go#L157) [¶](#Control.ID)\n```\nfunc (c *[Control](#Control)) ID(id [string](/builtin#string)) *[Control](#Control)\n```\nID adds id meta data\n\n#### \nfunc (*Control) [Method](https://github.com/takama/router/blob/v0.6.5/control.go#L164) [¶](#Control.Method)\n```\nfunc (c *[Control](#Control)) Method(method [string](/builtin#string)) *[Control](#Control)\n```\nMethod adds method meta data\n\n#### \nfunc (*Control) [Set](https://github.com/takama/router/blob/v0.6.5/control.go#L112) [¶](#Control.Set)\n```\nfunc (c *[Control](#Control)) Set(params ...[Param](#Param)) *[Control](#Control)\n```\nSet adds new parameters which represents as set of key/value.\n\n#### \nfunc (*Control) [SetError](https://github.com/takama/router/blob/v0.6.5/control.go#L178) [¶](#Control.SetError)\n```\nfunc (c *[Control](#Control)) SetError(code [uint16](/builtin#uint16), message [string](/builtin#string)) *[Control](#Control)\n```\nSetError sets error code and error message\n\n#### \nfunc (*Control) [SetParams](https://github.com/takama/router/blob/v0.6.5/control.go#L171) [¶](#Control.SetParams)\n```\nfunc (c *[Control](#Control)) SetParams(params interface{}) *[Control](#Control)\n```\nSetParams adds params meta data in alternative format\n\n#### \nfunc (*Control) [UseMetaData](https://github.com/takama/router/blob/v0.6.5/control.go#L137) [¶](#Control.UseMetaData)\n```\nfunc (c *[Control](#Control)) UseMetaData() *[Control](#Control)\n```\nUseMetaData shows meta data in JSON Header\n\n#### \nfunc (*Control) [UseTimer](https://github.com/takama/router/blob/v0.6.5/control.go#L193) [¶](#Control.UseTimer)\n```\nfunc (c *[Control](#Control)) UseTimer()\n```\nUseTimer allows caalculate elapsed time of request handling\n\n#### \ntype [Error](https://github.com/takama/router/blob/v0.6.5/control.go#L89) [¶](#Error)\n```\ntype Error struct {\n Domain [string](/builtin#string) `json:\"domain,omitempty\"`\n Reason [string](/builtin#string) `json:\"reason,omitempty\"`\n Message [string](/builtin#string) `json:\"message,omitempty\"`\n Location [string](/builtin#string) `json:\"location,omitempty\"`\n LocationType [string](/builtin#string) `json:\"locationType,omitempty\"`\n ExtendedHelp [string](/builtin#string) `json:\"extendedHelp,omitempty\"`\n SendReport [string](/builtin#string) `json:\"sendReport,omitempty\"`\n}\n```\nError report format\n\n#### \ntype [ErrorHeader](https://github.com/takama/router/blob/v0.6.5/control.go#L82) [¶](#ErrorHeader)\n```\ntype ErrorHeader struct {\n Code [uint16](/builtin#uint16) `json:\"code,omitempty\"`\n Message [string](/builtin#string) `json:\"message,omitempty\"`\n Errors [][Error](#Error) `json:\"errors,omitempty\"`\n}\n```\nErrorHeader contains error code, message and array of specified error reports\n\n#### \ntype [Handle](https://github.com/takama/router/blob/v0.6.5/router.go#L158) [¶](#Handle)\n```\ntype Handle func(*[Control](#Control))\n```\nHandle type is aliased to type of handler function.\n\n#### \ntype [Header](https://github.com/takama/router/blob/v0.6.5/control.go#L69) [¶](#Header)\n```\ntype Header struct {\n Duration [time](/time).[Duration](/time#Duration) `json:\"duration,omitempty\"`\n Took [string](/builtin#string) `json:\"took,omitempty\"`\n APIVersion [string](/builtin#string) `json:\"apiVersion,omitempty\"`\n Context [string](/builtin#string) `json:\"context,omitempty\"`\n ID [string](/builtin#string) `json:\"id,omitempty\"`\n Method [string](/builtin#string) `json:\"method,omitempty\"`\n Params interface{} `json:\"params,omitempty\"`\n Data interface{} `json:\"data,omitempty\"`\n Error interface{} `json:\"error,omitempty\"`\n}\n```\nHeader is used to prepare a JSON header with meta data\n\n#### \ntype [Param](https://github.com/takama/router/blob/v0.6.5/control.go#L63) [¶](#Param)\n```\ntype Param struct {\n Key [string](/builtin#string) `json:\"key,omitempty\"`\n Value [string](/builtin#string) `json:\"value,omitempty\"`\n}\n```\nParam is a URL parameter which represents as key and value.\n\n#### \ntype [Route](https://github.com/takama/router/blob/v0.6.5/router.go#L161) [¶](#Route)\n```\ntype Route struct {\n Method [string](/builtin#string)\n Path [string](/builtin#string)\n}\n```\nRoute type contains information about HTTP method and path\n\n#### \ntype [Router](https://github.com/takama/router/blob/v0.6.5/router.go#L136) [¶](#Router)\n```\ntype Router struct {\n\n // NotFound is called when unknown HTTP method or a handler not found.\n\t// If it is not set, http.NotFound is used.\n\t// Please overwrite this if need your own NotFound handler.\n\tNotFound [Handle](#Handle)\n\n // PanicHandler is called when panic happen.\n\t// The handler prevents your server from crashing and should be used to return\n\t// http status code http.StatusInternalServerError (500)\n\tPanicHandler [Handle](#Handle)\n\n // CustomHandler is called allways if defined\n\tCustomHandler func([Handle](#Handle)) [Handle](#Handle)\n\n // Logger activates logging user function for each requests\n\tLogger [Handle](#Handle)\n\t// contains filtered or unexported fields\n}\n```\nRouter represents a multiplexer for HTTP requests.\n\n#### \nfunc [New](https://github.com/takama/router/blob/v0.6.5/router.go#L167) [¶](#New)\n```\nfunc New() *[Router](#Router)\n```\nNew it returns a new multiplexer (Router).\n\n#### \nfunc (*Router) [AllowedMethods](https://github.com/takama/router/blob/v0.6.5/router.go#L241) [¶](#Router.AllowedMethods)\n```\nfunc (r *[Router](#Router)) AllowedMethods(path [string](/builtin#string)) [][string](/builtin#string)\n```\nAllowedMethods returns list of allowed methods\n\n#### \nfunc (*Router) [DELETE](https://github.com/takama/router/blob/v0.6.5/router.go#L187) [¶](#Router.DELETE)\n```\nfunc (r *[Router](#Router)) DELETE(path [string](/builtin#string), h [Handle](#Handle))\n```\nDELETE is a shortcut for Router Handle(\"DELETE\", path, handle)\n\n#### \nfunc (*Router) [GET](https://github.com/takama/router/blob/v0.6.5/router.go#L172) [¶](#Router.GET)\n```\nfunc (r *[Router](#Router)) GET(path [string](/builtin#string), h [Handle](#Handle))\n```\nGET is a shortcut for Router Handle(\"GET\", path, handle)\n\n#### \nfunc (*Router) [HEAD](https://github.com/takama/router/blob/v0.6.5/router.go#L192) [¶](#Router.HEAD)\n```\nfunc (r *[Router](#Router)) HEAD(path [string](/builtin#string), h [Handle](#Handle))\n```\nHEAD is a shortcut for Router Handle(\"HEAD\", path, handle)\n\n#### \nfunc (*Router) [Handle](https://github.com/takama/router/blob/v0.6.5/router.go#L207) [¶](#Router.Handle)\n```\nfunc (r *[Router](#Router)) Handle(method, path [string](/builtin#string), h [Handle](#Handle))\n```\nHandle registers a new request handle with the given path and method.\n\n#### \nfunc (*Router) [Handler](https://github.com/takama/router/blob/v0.6.5/router.go#L215) [¶](#Router.Handler)\n```\nfunc (r *[Router](#Router)) Handler(method, path [string](/builtin#string), handler [http](/net/http).[Handler](/net/http#Handler))\n```\nHandler allows the usage of an http.Handler as a request handle.\n\n#### \nfunc (*Router) [HandlerFunc](https://github.com/takama/router/blob/v0.6.5/router.go#L224) [¶](#Router.HandlerFunc)\n```\nfunc (r *[Router](#Router)) HandlerFunc(method, path [string](/builtin#string), handler [http](/net/http).[HandlerFunc](/net/http#HandlerFunc))\n```\nHandlerFunc allows the usage of an http.HandlerFunc as a request handle.\n\n#### \nfunc (*Router) [Listen](https://github.com/takama/router/blob/v0.6.5/router.go#L253) [¶](#Router.Listen)\n```\nfunc (r *[Router](#Router)) Listen(hostPort [string](/builtin#string))\n```\nListen and serve on requested host and port.\n\n#### \nfunc (*Router) [Lookup](https://github.com/takama/router/blob/v0.6.5/router.go#L233) [¶](#Router.Lookup)\n```\nfunc (r *[Router](#Router)) Lookup(method, path [string](/builtin#string)) ([Handle](#Handle), [][Param](#Param), [bool](/builtin#bool))\n```\nLookup returns handler and URL parameters that associated with path.\n\n#### \nfunc (*Router) [OPTIONS](https://github.com/takama/router/blob/v0.6.5/router.go#L197) [¶](#Router.OPTIONS)\n```\nfunc (r *[Router](#Router)) OPTIONS(path [string](/builtin#string), h [Handle](#Handle))\n```\nOPTIONS is a shortcut for Router Handle(\"OPTIONS\", path, handle)\n\n#### \nfunc (*Router) [PATCH](https://github.com/takama/router/blob/v0.6.5/router.go#L202) [¶](#Router.PATCH)\n```\nfunc (r *[Router](#Router)) PATCH(path [string](/builtin#string), handle [Handle](#Handle))\n```\nPATCH is a shortcut for router.Handle(\"PATCH\", path, handle)\n\n#### \nfunc (*Router) [POST](https://github.com/takama/router/blob/v0.6.5/router.go#L177) [¶](#Router.POST)\n```\nfunc (r *[Router](#Router)) POST(path [string](/builtin#string), h [Handle](#Handle))\n```\nPOST is a shortcut for Router Handle(\"POST\", path, handle)\n\n#### \nfunc (*Router) [PUT](https://github.com/takama/router/blob/v0.6.5/router.go#L182) [¶](#Router.PUT)\n```\nfunc (r *[Router](#Router)) PUT(path [string](/builtin#string), h [Handle](#Handle))\n```\nPUT is a shortcut for Router Handle(\"PUT\", path, handle)\n\n#### \nfunc (*Router) [Routes](https://github.com/takama/router/blob/v0.6.5/router.go#L306) [¶](#Router.Routes)\n```\nfunc (r *[Router](#Router)) Routes() [][Route](#Route)\n```\nRoutes returns list of registered HTTP methods with path\n\n#### \nfunc (*Router) [ServeHTTP](https://github.com/takama/router/blob/v0.6.5/router.go#L260) [¶](#Router.ServeHTTP)\n```\nfunc (r *[Router](#Router)) ServeHTTP(w [http](/net/http).[ResponseWriter](/net/http#ResponseWriter), req *[http](/net/http).[Request](/net/http#Request))\n```\nServeHTTP implements http.Handler interface."}}},{"rowIdx":59475,"cells":{"project":{"kind":"string","value":"PL94171"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘PL94171’\n October 12, 2022\nType Package\nTitle Tabulate P.L. 94-171 Redistricting Data Summary Files\nVersion 1.1.2\nMaintainer <NAME> <<EMAIL>>\nDescription Tools to process legacy format summary redistricting data files\n produced by the United States Census Bureau pursuant to P.L. 94-171. These\n files are generally available earlier but are difficult to work with as-is.\nDepends R (>= 4.0.0)\nImports cli, stringr, readr, dplyr (>= 1.0.0), tinytiger, sf, withr,\n httr\nSuggests testthat (>= 3.0.0), lifecycle, knitr, rmarkdown, ggplot2\nLicense MIT + file LICENSE\nEncoding UTF-8\nLazyData true\nRoxygenNote 7.2.1\nURL https://corymccartan.com/PL94171/,\n https://github.com/CoryMcCartan/PL94171/\nBugReports https://github.com/CoryMcCartan/PL94171/issues\nConfig/testthat/edition 3\nVignetteBuilder knitr\nLanguage en-US\nNeedsCompilation no\nAuthor <NAME> [aut, cre],\n <NAME> [aut]\nRepository CRAN\nDate/Publication 2022-09-11 22:13:02 UTC\nR topics documented:\npl_crosswal... 2\npl_e... 3\npl_geog_level... 3\npl_get_ba... 4\npl_get_prototyp... 4\npl_get_vt... 6\npl_rea... 6\npl_retall... 7\npl_select_standar... 8\npl_subse... 9\npl_tidy_sh... 10\npl_ur... 10\n pl_crosswalk Download Block Crosswalk Files\nDescription\n Downloads crosswalks from https://www.census.gov/geographies/reference-files/time-series/\n geo/relationship-files.html. Adjusts land overlap area to ensure weights sum to 1.\nUsage\n pl_crosswalk(abbr, from_year = 2010L, to_year = from_year + 10L)\nArguments\n abbr the state to download the crosswalk for.\n from_year the year with the blocks that the data is currently tabulated with respect to.\n to_year the year with the blocks that the data should be tabulated into.\nValue\n A tibble, with two sets of GEOIDs and overlap information.\nExamples\n ## Not run:\n # Takes a bit of time to run\n pl_crosswalk(\"RI\", 2010, 2020)\n ## End(Not run)\n pl_ex PL Example File\nDescription\n This data contains a subset of the 2020 prototype PL data\nUsage\n data(\"pl_ex\")\nFormat\n list of tibbles containing the four PL files.\n 00001 Tables P1 and P2\n 00002 Tables P3, P4, and H1\n 00003 Table P5\n geo geographic header file\nExamples\n data(pl_ex)\n pl_geog_levels List of Summary Levels and Official Descriptions\nDescription\n This dataset is tibble version of the descriptions of (potentially) available summary levels within\n the P.L. 94-171 data, as described in the 2018 Redistricting Data Prototype (Public Law 94-171)\n Summary File documentation.\nUsage\n pl_geog_levels\nFormat\n a tibble with two columns:\n SUMLEV The three character summary level code\n SUMLEV_description The summary level description\n pl_get_baf Download 2020 Block Assignment Files for a State\nDescription\n [Experimental] From the Census: \"The Block Assignment Files (BAFs) are among the geographic\n products that the Census Bureau provides to states and other data users containing the small area\n census data necessary for legislative redistricting. The BAFs contain Census tabulation block codes\n and geographic area codes for a specific geographic entity type.\"\nUsage\n pl_get_baf(abbr, geographies = NULL, cache_to = NULL, refresh = FALSE)\nArguments\n abbr the state abbreviation to get the BAF for\n geographies the geographies to get. Defaults to all available.\n cache_to the file name, if any, to cache the results to (as an RDS). If a file exists and\n refresh=FALSE, will read BAF from this file.\n refresh if TRUE, force a re-download of the BAF data.\nValue\n A list of tibbles, one for each available BAF geography.\nExamples\n pl_get_baf(\"RI\")\n pl_get_baf(\"RI\", \"VTD\")\n pl_get_prototype Download TIGER Prototype shapefiles\nDescription\n [Experimental] These prototype shapefiles correspond to the Rhode Island end-to-end Census test\n and the accompanying prototype P.L. 94-171 data. This function is unlikely to be useful for working\n with any actual decennial Census data. The corresponding tinytiger or tigris functions should\n be used instead.\nUsage\n pl_get_prototype(\n geog,\n year = 2020,\n full_state = TRUE,\n cache_to = NULL,\n clean_names = TRUE,\n refresh = FALSE\n )\nArguments\n geog Geography to download data for. See details for full list.\n year year, either 2010 or 2020\n full_state whether to return the full state (TRUE) or the single county subset (FALSE)\n cache_to the file name, if any, to cache the results to (as an RDS). If a file exists and\n refresh=FALSE, will read from this file.\n clean_names whether to clean and rename columns\n refresh if TRUE, force a re-download of the data.\nDetails\n Current acceptable arguments to geog include:\n • block: block\n • block_group: block group\n • tract: tract\n • county: county\n • state: state\n • sld_low: state legislative district lower house\n • sld_up: state legislative district upper house\n • congressional_district: federal congressional district\n • place: Census place\n • voting_district: voting tabulation district\nValue\n An sf object containing the blocks.\nExamples\n shp <- pl_get_prototype(\"block\")\n pl_get_vtd Download 2020 Voting District Shapefiles\nDescription\n [Experimental] A (likely temporary) function to download TIGER shapefiles for 2020 voting tab-\n ulation districts (VTDs).\nUsage\n pl_get_vtd(abbr, cache_to = NULL, refresh = FALSE)\nArguments\n abbr Geography to download data for. See details for full list.\n cache_to the file name, if any, to cache the results to (as an RDS). If a file exists and\n refresh=FALSE, will read from this file.\n refresh if TRUE, force a re-download of the data.\nValue\n An sf object containing the VTDs.\nExamples\n shp <- pl_get_vtd(\"RI\")\n pl_read Read a set of PL Files\nDescription\n PL files come in one of four types and are pipe-delimited with no header row. This function speedily\n reads in the files and assigns the appropriate column names and types.\nUsage\n pl_read(path, ...)\n read_pl(path, ...)\nArguments\n path a path to a folder containing PL files. Can also be path or a URL for a ZIP file,\n which will be downloaded and unzipped.\n ... passed on to readr::read_delim()\nValue\n A list of data frames containing the four PL files.\nExamples\n pl_ex_path <- system.file('extdata/ri2018_2020Style.pl', package = 'PL94171')\n pl <- pl_read(pl_ex_path)\n # or try `pl_read(pl_url(\"RI\", 2010))`\n pl_retally Approximately re-tally Census data under new block boundaries\nDescription\n Applies a block crosswalk to a table of block data using areal interpolation. That is, the fraction of\n land area in the overlapping region between old and new blocks is used to divide the population of\n the old blocks into the new.\nUsage\n pl_retally(d_from, crosswalk)\nArguments\n d_from The data frame to process. All numeric columns will be re-tallied. Integer\n columns will be re-tallied with rounding. Character columns will be preserved\n if constant across new block geometries.\n crosswalk The crosswalk data frame, from pl_crosswalk()\nDetails\n All numeric columns will be re-tallied. Integer columns will be re-tallied with rounding. Character\n columns will be preserved if constant across new block geometries.\n Blocks from other states will be ignored.\nValue\n A new data frame, like d_from, except with the geometry column dropped, if one exists. New\n geometry should be loaded, perhaps with tinytiger::tt_blocks().\nExamples\n crosswalk = pl_crosswalk(\"RI\", 2010, 2020)\n RI_2010 = pl_tidy_shp(\"RI\", pl_url(\"RI\", 2010), 2010)\n pl_retally(RI_2010, crosswalk)\n pl_select_standard Select the Standard Redistricting Columns\nDescription\n Selects the standard set of basic population groups and VAP groups. Optionally renames them from\n the PXXXYYYY naming convention (where XXX is the table and YYYY is the variable) to more\n human readable names. pop_* is the total population, from tables 1 and 2, while vap_* is the 18+\n population (voting age population).\nUsage\n pl_select_standard(pl, clean_names = TRUE)\nArguments\n pl A list of PL tables, as read in by pl_read()\n clean_names whether to clean names\nDetails\n If clean names=TRUE, then the variables extracted are as follows:\n • \\*_hisp: Hispanic or Latino (of any race)\n • \\*_white: White alone, not Hispanic or Latino\n • \\*_black: Black or African American alone, not Hispanic or Latino\n • \\*_aian: American Indian and Alaska Native alone, not Hispanic or Latino\n • \\*_asian: Asian alone, not Hispanic or Latino\n • \\*_nhpi: Native Hawaiian and Other Pacific Islander alone, not Hispanic or Latino\n • \\*_other: Some Other Race alone, not Hispanic or Latino\n • \\*_two: Population of two or more races, not Hispanic or Latino\n where \\* is pop or vap.\nValue\n A tibble with the selected and optionally renamed columns\nExamples\n pl_ex_path <- system.file('extdata/ri2018_2020Style.pl', package = 'PL94171')\n pl <- pl_read(pl_ex_path)\n pl <- pl_select_standard(pl)\n pl_subset Subset to a Summary Level\nDescription\n This subsets a pl table to a desired summary level. Typical choices include:\n • ’750’: block\n • ’150’: block group\n • ’630’: voting district\n • ’050’: county\nUsage\n pl_subset(pl, sumlev = \"750\")\nArguments\n pl A list of PL tables, as read in by pl_read()\n sumlev the summary level to filter to. A 3 character SUMLEV code. Default is ’750’\n for blocks.\nDetails\n All summary levels are listed in pl_geog_levels.\nValue\n tibble\nExamples\n pl_ex_path <- system.file('extdata/ri2018_2020Style.pl', package = 'PL94171')\n pl <- pl_read(pl_ex_path)\n pl <- pl_subset(pl)\n pl_tidy_shp All-in-one Shapefile Function\nDescription\n Downloads block geography and merges with the cleaned PL 94-171 file.\nUsage\n pl_tidy_shp(abbr, path, year = 2020, type = c(\"blocks\", \"vtds\"), ...)\nArguments\n abbr The state to make the shapefile for\n path The path to the PL files, as in pl_read()\n year The year to download the block geography for. Should match the year of the PL\n files.\n type If \"blocks\", make a Census block shapefile; if \"vtds\" make a VTD shapefile.\n ... passed on to dplyr::filter(); use to subset to a certain county, for example.\nValue\n an sf object with demographic and shapefile information for the state.\nExamples\n pl_ex_path <- system.file(\"extdata/ri2018_2020Style.pl\", package = \"PL94171\")\n pl_tidy_shp(\"RI\", pl_ex_path)\n pl_url Get the URL for PL files for a particular state and year\nDescription\n Get the URL for PL files for a particular state and year\nUsage\n pl_url(abbr, year = 2010)\nArguments\n abbr The state to download the PL files for\n year The year of PL file to download. Supported years: 2000, 2010, 2020 (after\n release). 2000 files are in a different format. Earlier years available on tape or\n CD-ROM only.\nValue\n a character vector containing the URL to a ZIP containing the PL files.\nExamples\n pl_url(\"RI\", 2010)"}}},{"rowIdx":59476,"cells":{"project":{"kind":"string","value":"littler"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘littler’\n March 26, 2023\nType Package\nTitle R at the Command-Line via 'r'\nVersion 0.3.18\nDate 2023-03-25\nAuthor <NAME> and <NAME>\nMaintainer <NAME> <<EMAIL>>\nDescription A scripting and command-line front-end\n is provided by 'r' (aka 'littler') as a lightweight binary wrapper around\n the GNU R language and environment for statistical computing and graphics.\n While R can be used in batch mode, the r binary adds full support for\n both 'shebang'-style scripting (i.e. using a hash-mark-exclamation-path\n expression as the first line in scripts) as well as command-line use in\n standard Unix pipelines. In other words, r provides the R language without\n the environment.\nURL https://github.com/eddelbuettel/littler,\n https://dirk.eddelbuettel.com/code/littler.html,\n https://eddelbuettel.github.io/littler/\nBugReports https://github.com/eddelbuettel/littler/issues\nLicense GPL (>= 2)\nOS_type unix\nSystemRequirements libR\nSuggests simplermarkdown, docopt, rcmdcheck, foghorn\nVignetteBuilder simplermarkdown\nRoxygenNote 5.0.1\nNeedsCompilation yes\nRepository CRAN\nDate/Publication 2023-03-26 10:20:05 UTC\nR topics documented:\nlittle... 2\n... 3\n littler Command-line and scripting front-end for R\nDescription\n The r binary provides a convenient and powerful front-end. By embedding R, it permits four\n distinct ways to leverage the power of R at the shell prompt: scripting, filename execution, piping\n and direct expression evaluation.\nDetails\n The r front-end was written with four distinct usage modes in mind.\n First, it allow to write so-called ‘shebang’ scripts starting with #!/usr/bin/env r. These ‘shebang’\n scripts are perfectly suited for automation and execution via e.g. via cron.\n Second, we can use r somefile.R to quickly execute the name R source file. This is useful as r is\n both easy to type—and quicker to start that either R itself, or its scripting tool Rscript, while still\n loading the methods package.\n Third, r can be used in ‘pipes’ which are very common in Unix. A simple and trivial example\n is echo 'cat(2+2)' | r illustrating that the standard output of one program can be used as the\n standard input of another program.\n Fourth, r can be used as a calculator by supplying expressions after the -e or --eval options.\nValue\n Common with other shell tools and programs, r returns its exit code where a value of zero indicates\n success.\nNote\n On OS X one may have to link the binary to, say, lr instead. As OS X insists that files named R and\n r are the same, we cannot use the latter.\nAuthor(s)\n <NAME> and <NAME> wrote littler from 2006 to today, with contributions from\n several others.\n <NAME> <<EMAIL>> is the maintainer.\nExamples\n ## Not run:\n #!/usr/bin/env r ## for use in scripts\n other input | r ## for use in pipes\n r somefile.R ## for running files\n r -e 'expr' ## for evaluating expressions\n r --help ## to show a quick synopsis\n ## End(Not run)\n r Return Path to r Binary\nDescription\n Return the path of the install r binary.\nUsage\n r(usecat = FALSE)\nArguments\n usecat Optional toggle to request output to stdout (useful in Makefiles)\nDetails\n The test for Windows is of course superfluous as we have no binary for Windows. Maybe one day...\nValue\n The path is returned as character variable. If the usecat option is set the character variable is\n displayed via cat instead.\nAuthor(s)\n <NAME>"}}},{"rowIdx":59477,"cells":{"project":{"kind":"string","value":"daymetr"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘daymetr’\n September 15, 2023\nTitle Interface to the 'Daymet' Web Services\nVersion 1.7.1\nDescription Programmatic interface to the 'Daymet' web services\n (<http://daymet.ornl.gov>). Allows for easy downloads of\n 'Daymet' climate data directly to your R workspace or your computer.\n Routines for both single pixel data downloads and\n gridded (netCDF) data are provided.\nDepends R (>= 3.6)\nImports sf, terra, ncdf4, httr, tidyr, tibble, tools, utils\nLicense AGPL-3\nLazyData true\nByteCompile true\nRoxygenNote 7.2.3\nSuggests ggplot2, dplyr, knitr, markdown, covr, testthat\nVignetteBuilder knitr\nURL https://github.com/bluegreen-labs/daymetr\nBugReports https://github.com/bluegreen-labs/daymetr/issues\nNeedsCompilation no\nAuthor <NAME> [aut, cre] (<https://orcid.org/0000-0002-5070-8109>),\n BlueGreen Labs [cph, fnd]\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-09-15 14:52:05 UTC\nR topics documented:\ncalc_n... 2\ndaymet_grid_ag... 3\ndaymet_grid_offse... 4\ndaymet_grid_tmea... 5\ndownload_dayme... 6\ndownload_daymet_batc... 8\ndownload_daymet_ncs... 9\ndownload_daymet_tile... 11\nnc2ti... 12\nread_dayme... 13\ntile_outline... 14\n calc_nd Count days meeting set criteria\nDescription\n Function to count the number of days in a given time period that meet a given set of criteria. This\n can be used to extract indices such as Growing Degree Days (tmin > 0), or days with precipitation\n (prcp != 0).\nUsage\n calc_nd(\n file,\n start_doy = 1,\n end_doy = 365,\n criteria,\n value,\n internal = FALSE,\n path = tempdir()\n )\nArguments\n file path of a file containing the daily gridded Daymet data\n start_doy numeric day-of-year at which counting should begin. (default = 1)\n end_doy numeric day of year at which counting should end. (default = 365)\n criteria logical expression (\">=\",\">\",\"<=\",\"<\",\"==\", \"!=\") to evaluate\n value the value that the criteria is evaluated against\n internal return to workspace (TRUE) or write to disk (FALSE) (default = FALSE)\n path path to which to write data to disk (default = tempdir())\nValue\n A raster object in the R workspace or a file on disk with summary statistics for every pixel which\n meet the predefined criteria. Output files if written to file will be named nd_YYYY.tif (with YYYY\n the year of the processed tile or ncss netCDF file).\nExamples\n ## Not run:\n # download daily gridded data\n # using default settings (data written to tempdir())\n download_daymet_ncss()\n # read in the Daymet file and report back the number\n # of days in a year with a minimum temperature lower\n # than 15 degrees C\n r <- calc_nd(file.path(tempdir(),\"tmin_daily_1980_ncss.nc\"),\n criteria = \"<\",\n value = 15,\n internal = TRUE)\n # plot the output\n terra::plot(r)\n ## End(Not run)\n daymet_grid_agg Aggregate daily Daymet data\nDescription\n Aggregates daily Daymet data by time interval to create convenient seasonal datasets for data ex-\n ploration or modelling.\nUsage\n daymet_grid_agg(\n file,\n int = \"seasonal\",\n fun = \"mean\",\n internal = FALSE,\n path = tempdir()\n )\nArguments\n file The name of the file to be processed. Use daily gridded Daymet data.\n int Interval to aggregate by. Options are \"monthly\", \"seasonal\" or \"annual\". Sea-\n sons are defined as the astronomical seasons between solstices and equinoxes\n (default = \"seasonal\")\n fun Function to be used to aggregate data. Genertic R functions can be used. \"mean\"\n and \"sum\" are suggested. na.rm = TRUE by default. (default = \"mean\")\n internal logical If FALSE, write the output to a tif file using the Daymet file format\n protocol.\n path path to a directory where output files should be written. Used only if internal =\n FALSE (default = tempdir())\nValue\n aggregated daily Daymet data as a tiff file written to disk or a raster stack when data is returned to\n the workspace.\nExamples\n ## Not run:\n # This code calculates the average minimum temperature by\n # season for a subset region.\n # download default ncss tiled subset for 1980\n # (daily tmin values only), works on tiles as well\n download_daymet_ncss()\n # Finally, run the function\n daymet_grid_agg(\n file = file.path(tempdir(),\"/tmin_daily_1980_ncss.nc\"),\n int = \"seasonal\",\n fun = \"mean\"\n )\n ## End(Not run)\n daymet_grid_offset Returns a time shifted (offset) dataset\nDescription\n Returns an offset dataset with data running from offset DOY in year - 1 to offset DOY in the current\n year. Two years of data (730 data layers) are required for this function to work. The output serves\n as input for further data processing and / or ecosystem modelling efforts.\nUsage\n daymet_grid_offset(data, offset = 264)\nArguments\n data rasterStack or rasterBrick of 730 layers (2 consecutive years)\n offset offset of the time series in DOY (default = 264, sept 21)\nExamples\n ## Not run:\n my_subset <- daymet_gridded_offset(mystack, offset = 264)\n ## End(Not run)\n daymet_grid_tmean Averages tmax and tmin ’Daymet’ gridded products\nDescription\n Combines data into a single mean daily temperature (tmean) gridded output (geotiff) for easy post\n processing and modelling. Optionally a raster object is returned to the current workspace.\nUsage\n daymet_grid_tmean(path = tempdir(), product, year, internal = FALSE)\nArguments\n path full path location of the daymet tiles (default = tempdir())\n product either a tile number or a ncss product name\n year which year to process\n internal TRUE / FALSE (if FALSE, write the output to file) using the Daymet file format\n protocol.\nExamples\n ## Not run:\n # This code calculates the mean temperature\n # for all daymet tiles in a user provided\n # directory. In this example we first\n # download tile 11935 for tmin and tmax\n # download a tile\n download_daymet_tiles(tiles = 11935,\n start = 1980,\n end = 1980,\n param = c(\"tmin\",\"tmax\"),\n path = tempdir())\n # calculate the mean temperature and export\n # the result to the R workspace (internal = TRUE)\n # If internal = FALSE, a file tmean_11935_1980.tif\n # is written into the source path (path_with_daymet_tiles)\n tmean <- daymet_grid_tmean(path = tempdir(),\n tile = 11935,\n year = 1980,\n internal = TRUE)\n ## End(Not run)\n download_daymet Function to download single location ’Daymet’ data\nDescription\n Function to download single location ’Daymet’ data\nUsage\n download_daymet(\n site = \"Daymet\",\n lat = 36.0133,\n lon = -84.2625,\n start = 2000,\n end = as.numeric(format(Sys.time(), \"%Y\")) - 2,\n path = tempdir(),\n internal = TRUE,\n silent = FALSE,\n force = FALSE,\n simplify = FALSE\n )\nArguments\n site the site name.\n lat latitude (decimal degrees)\n lon longitude (decimal degrees)\n start start of the range of years over which to download data\n end end of the range of years over which to download data\n path set path where to save the data if internal = FALSE (default = NULL)\n internal TRUE or FALSE, if TRUE returns a list to the R workspace if FALSE puts the down-\n loaded data into the current working directory (default = FALSE)\n silent TRUE or FALSE (default), to provide verbose output\n force TRUE or FALSE (default), override the conservative end year setting\n simplify output data as a tibble, logical FALSE or TRUE (default = TRUE)\nValue\n Daymet data for a point location, returned to the R workspace or written to disk as a csv file.\ndownload_daymet 7\nExamples\n ## Not run:\n # The following commands download and process Daymet data\n # for 10 years of the >30 year of data available since 1980.\n daymet_data <- download_daymet(\n \"testsite_name\",\n lat = 36.0133,\n lon = -84.2625,\n start = 2000,\n end = 2010,\n internal = TRUE\n )\n # We can now quickly calculate and plot\n # daily mean temperature. Also, take note of\n # the weird format of the header. This format\n # is not altered as to keep compatibility\n # with other ways of acquiring Daymet data\n # through the ORNL DAAC website.\n # The below command lists headers of\n # the downloaded nested list.\n # This data includes information on the site\n # location etc. The true climate data is stored\n # in the \"data\" part of the nested list.\n # In this case it can be accessed through\n # daymet_data$data. Other attributes include\n # for example the tile location (daymet_data$tile),\n # the altitude (daymet_data$altitude), etc.\n str(daymet_data)\n # load the tidyverse (install if necessary)\n if(!require(tidyverse)){install.package(tidyverse)}\n library(tidyverse)\n # Calculate the mean temperature from min\n # max temperatures and convert the year and doy\n # to a proper date format.\n daymet_data$data <- daymet_data$data |>\n mutate(\n tmean = (tmax..deg.c. + tmin..deg.c.)/2,\n date = as.Date(paste(year, yday, sep = \"-\"), \"%Y-%j\")\n )\n # show a simple graph of the mean temperature\n plot(daymet_data$data$date,\n daymet_data$data$tmean,\n xlab = \"Date\",\n ylab = \"mean temperature\")\n # For other practical examples consult the included\n # vignette.\n ## End(Not run)\n download_daymet_batch This function downloads ’Daymet’ data for several single pixel loca-\n tion, as specified by a batch file.\nDescription\n This function downloads ’Daymet’ data for several single pixel location, as specified by a batch file.\nUsage\n download_daymet_batch(\n file_location = NULL,\n start = 1980,\n end = as.numeric(format(Sys.time(), \"%Y\")) - 1,\n internal = TRUE,\n force = FALSE,\n silent = FALSE,\n path = tempdir(),\n simplify = FALSE\n )\nArguments\n file_location file with several site locations and coordinates in a comma delimited format:\n site, latitude, longitude\n start start of the range of years over which to download data\n end end of the range of years over which to download data\n internal assign or FALSE, load data into workspace or save to disc\n force TRUE or FALSE (default), override the conservative end year setting\n silent suppress the verbose output (default = FALSE)\n path set path where to save the data if internal = FALSE (default = tempdir())\n simplify output data to a tibble, logical FALSE or TRUE (default = TRUE)\nValue\n Daymet data for point locations as a nested list or data written to csv files\nExamples\n ## Not run:\n # The download_daymet_batch() routine is a wrapper around\n # the download_daymet() function. It queries a file with\n # coordinates to easily download a large batch of daymet\n # pixel locations. When internal = TRUE, the data is stored\n # in a structured list in an R variable. If FALSE, the data\n # is written to disk.\n # create demo locations (two sites)\n locations <- data.frame(site = c(\"site1\", \"site2\"),\n lat = rep(36.0133, 2),\n lon = rep(-84.2625, 2))\n # write data to csv file\n write.table(locations, paste0(tempdir(),\"/locations.csv\"),\n sep = \",\",\n col.names = TRUE,\n row.names = FALSE,\n quote = FALSE)\n # download data, will return nested list of daymet data\n df_batch <- download_daymet_batch(file_location = paste0(tempdir(),\n \"/locations.csv\"),\n start = 1980,\n end = 1980,\n internal = TRUE,\n silent = TRUE)\n # For other practical examples consult the included\n # vignette.\n ## End(Not run)\n download_daymet_ncss Function to geographically subset ’Daymet’ regions exceeding tile\n limits\nDescription\n Function to geographically subset ’Daymet’ regions exceeding tile limits\nUsage\n download_daymet_ncss(\n location = c(34, -82, 33.75, -81.75),\n start = 1980,\n end = 1980,\n param = \"tmin\",\n frequency = \"daily\",\n mosaic = \"na\",\n path = tempdir(),\n silent = FALSE,\n force = FALSE,\n ssl = TRUE\n )\nArguments\n location location of a bounding box c(lat, lon, lat, lon) defined by a top left and bottom-\n right coordinates\n start start of the range of years over which to download data\n end end of the range of years over which to download data\n param climate variable you want to download vapour pressure (vp), minimum and\n maximum temperature (tmin,tmax), snow water equivalent (swe), solar radia-\n tion (srad), precipitation (prcp) , day length (dayl). The default setting is ALL,\n this will download all the previously mentioned climate variables.\n frequency frequency of the data requested (default = \"daily\", other options are \"monthly\"\n or \"annual\").\n mosaic which tile mosiac to source from (na = Northern America, hi = Hawaii, pr =\n Puerto Rico), defaults to \"na\".\n path directory where to store the downloaded data (default = tempdir())\n silent suppress the verbose output\n force TRUE or FALSE (default), override the conservative end year setting\n ssl TRUE (default) or FALSE, override default SSL settings in case of CA issues\nValue\n netCDF data file of an area circumscribed by the location bounding box\nExamples\n ## Not run:\n # The following call allows you to subset gridded\n # Daymet data using a bounding box location. This\n # is an alternative way to query gridded data. The\n # routine is particularly helpful if you need certain\n # data which stradles boundaries of multiple tiles\n # or a smaller subset of a larger tile. Keep in mind\n # that there is a 6GB upper limit to the output file\n # so querying larger regions will result in an error.\n # To download larger areas use the download_daymet_tiles()\n # function.\n # Download a subset of a / multiple tiles\n # into your current working directory.\n download_daymet_ncss(location = c(34, -82, 33.75, -81.75),\n start = 1980,\n end = 1980,\n param = \"tmin\",\n path = tempdir())\n # For other practical examples consult the included\n # vignette.\n ## End(Not run)\n download_daymet_tiles Function to batch download gridded ’Daymet’ data tiles\nDescription\n Function to batch download gridded ’Daymet’ data tiles\nUsage\n download_daymet_tiles(\n location = c(18.9103, -114.6109),\n tiles,\n start = 1980,\n end = 1980,\n path = tempdir(),\n param = \"ALL\",\n silent = FALSE,\n force = FALSE\n )\nArguments\n location location of a point c(lat, lon) or a bounding box defined by a top left and bottom-\n right coordinates c(lat, lon, lat, lon)\n tiles which tiles to download, overrides geographic constraints\n start start of the range of years over which to download data\n end end of the range of years over which to download data\n path where should the downloaded tiles be stored (default = tempdir())\n param climate variable you want to download vapour pressure (vp), minimum and\n maximum temperature (tmin,tmax), snow water equivalent (swe), solar radia-\n tion (srad), precipitation (prcp) , day length (dayl). The default setting is ALL,\n this will download all the previously mentioned climate variables.\n silent suppress the verbose output\n force TRUE or FALSE (default), override the conservative end year setting\nValue\n downloads netCDF tiles as defined by the Daymet tile grid\nExamples\n ## Not run:\n Download a single tile of minimum temperature\n download_daymet_tiles(location = c(18.9103, -114.6109),\n start = 1980,\n end = 1980,\n param = \"tmin\")\n # For other practical examples consult the included\n # vignette.\n ## End(Not run)\n nc2tif Converts netCDF (nc) files to geotiff\nDescription\n Conversion to .tif to simplify workflows if the data that has been downloaded is to be handled in\n other software (e.g. QGIS).\nUsage\n nc2tif(path = tempdir(), files = NULL, overwrite = FALSE, silent = FALSE)\nArguments\n path a character string showing the path to the directory containing Daymet .nc files\n (default = tempdir())\n files a character vector containing the name of one or more files to be converted\n (optional)\n overwrite a logical controlling whether all files will be written, or whether files will not be\n written in the event that there is already a .tif of that file. (default = NULL)\n silent limit verbose output (default = FALSE)\nValue\n Converted geotiff files of all netCDF data in the provided directory (path).\nExamples\n ## Not run:\n # The below command converts all netCDF data in\n # the provided path to geotiff files. Existing\n # files will be overwritten. If set to FALSE,\n # files will not be overwritten.\n # download the data\n download_daymet_ncss(param = \"tmin\",\n frequency = \"annual\",\n path = tempdir(),\n silent = TRUE)\n # convert files from nc to tif\n nc2tif(path = tempdir(),\n overwrite = TRUE)\n # print converted files\n print(list.files(tempdir(), \"*.tif\"))\n ## End(Not run)\n read_daymet Read Single Pixel Daymet data\nDescription\n Reads Single Pixel Daymet data into a nested list or tibble, preserving header data and critical file\n name information.\nUsage\n read_daymet(file, site, skip_header = FALSE, simplify = TRUE)\nArguments\n file a Daymet Single Pixel data file\n site a sitename (default = NULL)\n skip_header do not ingest header meta-data, logical FALSE or TRUE (default = FALSE)\n simplify output tidy data (tibble), logical FALSE or TRUE (default = TRUE)\nValue\n A nested data structure including site meta-data, the full header and the data as a ‘data.frame()‘.\nExamples\n ## Not run:\n # download the data\n download_daymet(\n site = \"Daymet\",\n start = 1980,\n end = 1980,\n internal = FALSE,\n silent = TRUE\n )\n # read in the Daymet file\n df <- read_daymet(paste0(tempdir(),\"/Daymet_1980_1980.csv\"))\n # print data structure\n print(str(df))\n ## End(Not run)\n tile_outlines tile_outlines\nDescription\n Large simple feature collection containing the outlines of all the Daymet tiles available as well as\n projection information. This data was converted from a shapefile as provided on the Daymet main\n website.\nUsage\n tile_outlines\nFormat\n SpatialPolygonDataFrame\n TileID tile ID number\n XMin minimum longitude\n XMax maximum longitude\n YMin minimum latitude\n YMax maximum latitude"}}},{"rowIdx":59478,"cells":{"project":{"kind":"string","value":"opencv"},"source":{"kind":"string","value":"rust"},"language":{"kind":"string","value":"Rust"},"content":{"kind":"string","value":"Module opencv::alphamat\n===\n\nAlpha Matting\n---\n\nAlpha matting is used to extract a foreground object with soft boundaries from a background image.\n\nThis module is dedicated to computing alpha matte of objects in images from a given input image and a greyscale trimap image that contains information about the foreground, background and unknown pixels. The unknown pixels are assumed to be a combination of foreground and background pixels. The algorithm uses a combination of multiple carefully defined pixels affinities to estimate the opacity of the foreground pixels in the unkown region.\n\nThe implementation is based on aksoy2017designing.\n\nThis module was developed by <NAME> and <NAME> as a project for Google Summer of Code 2019 (GSoC 19).\n\nModules\n---\n\n* prelude\n\nFunctions\n---\n\n* info_flowCompute alpha matte of an object in an image\n\nModule opencv::aruco\n===\n\nAruco markers, module functionality was moved to objdetect module\n---\n\nArUco Marker Detection, module functionality was moved to objdetect module\n\n### See also\n\nArucoDetector, CharucoDetector, Board, GridBoard, CharucoBoard\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* EstimateParametersPose estimation parameters\n\nEnums\n---\n\n* PatternPositionTypervec/tvec define the right handed coordinate system of the marker.\n\nConstants\n---\n\n* ARUCO_CCW_CENTERThe marker coordinate system is centered on the middle of the marker.\n* ARUCO_CW_TOP_LEFT_CORNERThe marker coordinate system is centered on the top-left corner of the marker.\n\nTraits\n---\n\n* EstimateParametersTraitMutable methods for crate::aruco::EstimateParameters\n* EstimateParametersTraitConstConstant methods for crate::aruco::EstimateParameters\n\nFunctions\n---\n\n* calibrate_camera_arucoCalibrate a camera using aruco markers\n* calibrate_camera_aruco_def@overload It’s the same function as calibrate_camera_aruco but without calibration error estimation.\n* calibrate_camera_aruco_extendedCalibrate a camera using aruco markers\n* calibrate_camera_aruco_extended_defCalibrate a camera using aruco markers\n* calibrate_camera_charucoIt’s the same function as calibrate_camera_charuco but without calibration error estimation.\n* calibrate_camera_charuco_defIt’s the same function as calibrate_camera_charuco but without calibration error estimation.\n* calibrate_camera_charuco_extendedCalibrate a camera using Charuco corners\n* calibrate_camera_charuco_extended_defCalibrate a camera using Charuco corners\n* detect_charuco_diamondDeprecatedDetect ChArUco Diamond markers\n* detect_charuco_diamond_defDeprecatedDetect ChArUco Diamond markers\n* detect_markersDeprecateddetect markers\n* detect_markers_defDeprecateddetect markers\n* draw_charuco_diamondDraw a ChArUco Diamond marker\n* draw_charuco_diamond_defDraw a ChArUco Diamond marker\n* draw_planar_boardDeprecateddraw planar board\n* estimate_pose_boardDeprecated**Deprecated**: Use cv::solvePnP\n* estimate_pose_board_defDeprecated**Deprecated**: Use cv::solvePnP\n* estimate_pose_charuco_boardPose estimation for a ChArUco board given some of their corners\n* estimate_pose_charuco_board_defPose estimation for a ChArUco board given some of their corners\n* estimate_pose_single_markersDeprecated**Deprecated**: Use cv::solvePnP\n* estimate_pose_single_markers_defDeprecated**Deprecated**: Use cv::solvePnP\n* get_board_object_and_image_pointsDeprecatedget board object and image points\n* interpolate_corners_charucoDeprecatedInterpolate position of ChArUco board corners\n* interpolate_corners_charuco_defDeprecatedInterpolate position of ChArUco board corners\n* refine_detected_markersDeprecatedrefine detected markers\n* refine_detected_markers_defDeprecatedrefine detected markers\n* test_charuco_corners_collinearDeprecated**Deprecated**: Use CharucoBoard::checkCharucoCornersCollinear\n\nModule opencv::bgsegm\n===\n\nImproved Background-Foreground Segmentation Methods\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BackgroundSubtractorCNTBackground subtraction based on counting.\n* BackgroundSubtractorGMGBackground Subtractor module based on the algorithm given in Gold2012 .\n* BackgroundSubtractorGSOCImplementation of the different yet better algorithm which is called GSOC, as it was implemented during GSOC and was not originated from any paper.\n* BackgroundSubtractorLSBPBackground Subtraction using Local SVD Binary Pattern. More details about the algorithm can be found at LGuo2016\n* BackgroundSubtractorLSBPDescThis is for calculation of the LSBP descriptors.\n* BackgroundSubtractorMOGGaussian Mixture-based Background/Foreground Segmentation Algorithm.\n* SyntheticSequenceGeneratorSynthetic frame sequence generator for testing background subtraction algorithms.\n\nEnums\n---\n\n* LSBPCameraMotionCompensation\n\nConstants\n---\n\n* LSBP_CAMERA_MOTION_COMPENSATION_LK\n* LSBP_CAMERA_MOTION_COMPENSATION_NONE\n\nTraits\n---\n\n* BackgroundSubtractorCNTTraitMutable methods for crate::bgsegm::BackgroundSubtractorCNT\n* BackgroundSubtractorCNTTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorCNT\n* BackgroundSubtractorGMGTraitMutable methods for crate::bgsegm::BackgroundSubtractorGMG\n* BackgroundSubtractorGMGTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorGMG\n* BackgroundSubtractorGSOCTraitMutable methods for crate::bgsegm::BackgroundSubtractorGSOC\n* BackgroundSubtractorGSOCTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorGSOC\n* BackgroundSubtractorLSBPDescTraitMutable methods for crate::bgsegm::BackgroundSubtractorLSBPDesc\n* BackgroundSubtractorLSBPDescTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorLSBPDesc\n* BackgroundSubtractorLSBPTraitMutable methods for crate::bgsegm::BackgroundSubtractorLSBP\n* BackgroundSubtractorLSBPTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorLSBP\n* BackgroundSubtractorMOGTraitMutable methods for crate::bgsegm::BackgroundSubtractorMOG\n* BackgroundSubtractorMOGTraitConstConstant methods for crate::bgsegm::BackgroundSubtractorMOG\n* SyntheticSequenceGeneratorTraitMutable methods for crate::bgsegm::SyntheticSequenceGenerator\n* SyntheticSequenceGeneratorTraitConstConstant methods for crate::bgsegm::SyntheticSequenceGenerator\n\nFunctions\n---\n\n* create_background_subtractor_cntCreates a CNT Background Subtractor\n* create_background_subtractor_cnt_defCreates a CNT Background Subtractor\n* create_background_subtractor_gmgCreates a GMG Background Subtractor\n* create_background_subtractor_gmg_defCreates a GMG Background Subtractor\n* create_background_subtractor_gsocCreates an instance of BackgroundSubtractorGSOC algorithm.\n* create_background_subtractor_gsoc_defCreates an instance of BackgroundSubtractorGSOC algorithm.\n* create_background_subtractor_lsbpCreates an instance of BackgroundSubtractorLSBP algorithm.\n* create_background_subtractor_lsbp_defCreates an instance of BackgroundSubtractorLSBP algorithm.\n* create_background_subtractor_mogCreates mixture-of-gaussian background subtractor\n* create_background_subtractor_mog_defCreates mixture-of-gaussian background subtractor\n* create_synthetic_sequence_generatorCreates an instance of SyntheticSequenceGenerator.\n* create_synthetic_sequence_generator_defCreates an instance of SyntheticSequenceGenerator.\n\nModule opencv::bioinspired\n===\n\nBiologically inspired vision models and derivated tools\n---\n\nThe module provides biological visual systems models (human visual system and others). It also provides derivated objects that take advantage of those bio-inspired models.\n\n[bioinspired_retina]\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* Retinaclass which allows the Gipsa/Listic Labs model to be used with OpenCV.\n* RetinaFastToneMappinga wrapper class which allows the tone mapping algorithm of Meylan&al(2007) to be used with OpenCV.\n* RetinaParametersretina model parameters structure\n* RetinaParameters_IplMagnoParametersInner Plexiform Layer Magnocellular channel (IplMagno)\n* RetinaParameters_OPLandIplParvoParametersOuter Plexiform Layer (OPL) and Inner Plexiform Layer Parvocellular (IplParvo) parameters\n* SegmentationParametersparameter structure that stores the transient events detector setup parameters\n* TransientAreasSegmentationModuleclass which provides a transient/moving areas segmentation module\n\nConstants\n---\n\n* RETINA_COLOR_BAYERstandard bayer sampling\n* RETINA_COLOR_DIAGONALcolor sampling is RGBRGBRGB…, line 2 BRGBRGBRG…, line 3, GBRGBRGBR…\n* RETINA_COLOR_RANDOMeach pixel position is either R, G or B in a random choice\n\nTraits\n---\n\n* RetinaFastToneMappingTraitMutable methods for crate::bioinspired::RetinaFastToneMapping\n* RetinaFastToneMappingTraitConstConstant methods for crate::bioinspired::RetinaFastToneMapping\n* RetinaParametersTraitMutable methods for crate::bioinspired::RetinaParameters\n* RetinaParametersTraitConstConstant methods for crate::bioinspired::RetinaParameters\n* RetinaTraitMutable methods for crate::bioinspired::Retina\n* RetinaTraitConstConstant methods for crate::bioinspired::Retina\n* TransientAreasSegmentationModuleTraitMutable methods for crate::bioinspired::TransientAreasSegmentationModule\n* TransientAreasSegmentationModuleTraitConstConstant methods for crate::bioinspired::TransientAreasSegmentationModule\n\nModule opencv::calib3d\n===\n\nCamera Calibration and 3D Reconstruction\n---\n\nThe functions in this section use a so-called pinhole camera model. The view of a scene is obtained by projecting a scene’s 3D point  into the image plane using a perspective transformation which forms the corresponding pixel . Both \n\nThe distortion-free projective transformation given by a pinhole camera model is shown below.\n\n\n\nwhere  is a 3D point expressed with respect to the world coordinate system,\n is a 2D pixel in the image plane,  is the camera intrinsic matrix,\n and  are the rotation and translation that describe the change of coordinates from world to camera coordinate systems (or camera frame) and  is the projective transformation’s arbitrary scaling and not part of the camera model.\n\nThe camera intrinsic matrix  (notation used as in Zhang2000 and also generally notated as ) projects 3D points given in the camera coordinate system to 2D pixel coordinates, i.e.\n\n\n\nThe camera intrinsic matrix  is composed of the focal lengths  and , which are expressed in pixel units, and the principal point , that is usually close to the image center:\n\n\n\nand thus\n\n\n\nThe matrix of intrinsic parameters does not depend on the scene viewed. So, once estimated, it can be re-used as long as the focal length is fixed (in case of a zoom lens). Thus, if an image from the camera is scaled by a factor, all of these parameters need to be scaled (multiplied/divided,\nrespectively) by the same factor.\n\nThe joint rotation-translation matrix  is the matrix product of a projective transformation and a homogeneous transformation. The 3-by-4 projective transformation maps 3D points represented in camera coordinates to 2D points in the image plane and represented in normalized camera coordinates  and :\n\n\n\nThe homogeneous transformation is encoded by the extrinsic parameters  and  and represents the change of basis from world coordinate system  to the camera coordinate sytem\n. Thus, given the representation of the point  in world coordinates, , we obtain ’s representation in the camera coordinate system, , by\n\n\n\nThis homogeneous transformation is composed out of , a 3-by-3 rotation matrix, and , a 3-by-1 translation vector:\n\n\n\nand therefore\n\n\n\nCombining the projective transformation and the homogeneous transformation, we obtain the projective transformation that maps 3D points in world coordinates into 2D points in the image plane and in normalized camera coordinates:\n\n\n\nwith  and . Putting the equations for instrincs and extrinsics together, we can write out\n as\n\n\n\nIf , the transformation above is equivalent to the following,\n\n\n\nwith\n\n\n\nThe following figure illustrates the pinhole camera model.\n\n\n\nReal lenses usually have some distortion, mostly radial distortion, and slight tangential distortion.\nSo, the above model is extended as:\n\n\n\nwhere\n\n\n\nwith\n\n\n\nand\n\n\n\nif .\n\nThe distortion parameters are the radial coefficients , , , , , and \n, and  are the tangential distortion coefficients, and , , , and ,\nare the thin prism distortion coefficients. Higher-order coefficients are not considered in OpenCV.\n\nThe next figures show two common types of radial distortion: barrel distortion\n( monotonically decreasing)\nand pincushion distortion ( monotonically increasing).\nRadial distortion is always monotonic for real lenses,\nand if the estimator produces a non-monotonic result,\nthis should be considered a calibration failure.\nMore generally, radial distortion must be monotonic and the distortion function must be bijective.\nA failed estimation result may look deceptively good near the image center but will work poorly in e.g. AR/SFM applications.\nThe optimization method used in OpenCV camera calibration does not include these constraints as the framework does not support the required integer programming and polynomial inequalities.\nSee issue #15992 for additional information.\n\n\n\n\nIn some cases, the image sensor may be tilted in order to focus an oblique plane in front of the camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or triangulation with a laser fan. The tilt causes a perspective distortion of  and\n. This distortion can be modeled in the following way, see e.g. Louhichi07.\n\n\n\nwhere\n\n\n\nand the matrix  is defined by two rotations with angular parameter\n and , respectively,\n\n\n\nIn the functions below the coefficients are passed or returned as\n\n\n\nvector. That is, if the vector contains four elements, it means that  . The distortion coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera parameters. And they remain the same regardless of the captured image resolution. If, for example, a camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion coefficients can be used for 640 x 480 images from the same camera while , ,\n, and  need to be scaled appropriately.\n\nThe functions below use the above model to do the following:\n\n* Project 3D points to the image plane given intrinsic and extrinsic parameters.\n* Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their projections.\n* Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (every view is described by several 3D-2D point correspondences).\n* Estimate the relative position and orientation of the stereo camera “heads” and compute the\n*rectification* transformation that makes the camera optical axes parallel.\n\n **Homogeneous Coordinates** \n\nHomogeneous Coordinates are a system of coordinates that are used in projective geometry. Their use allows to represent points at infinity by finite coordinates and simplifies formulas when compared to the cartesian counterparts, e.g. they have the advantage that affine transformations can be expressed as linear homogeneous transformation.\n\nOne obtains the homogeneous vector  by appending a 1 along an n-dimensional cartesian vector  e.g. for a 3D cartesian vector the mapping  is:\n\n\n\nFor the inverse mapping , one divides all elements of the homogeneous vector by its last element, e.g. for a 3D homogeneous vector one gets its 2D cartesian counterpart by:\n\n\n\nif .\n\nDue to this mapping, all multiples , for , of a homogeneous point represent the same point . An intuitive understanding of this property is that under a projective transformation, all multiples of  are mapped to the same point. This is the physical observation one does for pinhole cameras, as all points along a ray through the camera’s pinhole are projected to the same image point, e.g. all points along the red ray in the image of the pinhole camera model above would be mapped to the same image coordinate. This property is also the source for the scale ambiguity s in the equation of the pinhole camera model.\n\nAs mentioned, by using homogeneous coordinates we can express any change of basis parameterized by\n and  as a linear transformation, e.g. for the change of basis from coordinate system 0 to coordinate system 1 becomes:\n\n\n\nNote:\n\n* Many functions in this module take a camera intrinsic matrix as an input parameter. Although all functions assume the same structure of this parameter, they may name it differently. The parameter’s description, however, will be clear in that a camera intrinsic matrix with the structure shown above is required.\n* A calibration sample for 3 cameras in a horizontal position can be found at opencv_source_code/samples/cpp/3calibration.cpp\n* A calibration sample based on a sequence of images can be found at opencv_source_code/samples/cpp/calibration.cpp\n* A calibration sample in order to do 3D reconstruction can be found at opencv_source_code/samples/cpp/build3dmodel.cpp\n* A calibration example on stereo calibration can be found at opencv_source_code/samples/cpp/stereo_calib.cpp\n* A calibration example on stereo matching can be found at opencv_source_code/samples/cpp/stereo_match.cpp\n* (Python) A camera calibration sample can be found at opencv_source_code/samples/python/calibrate.py\n\nFisheye camera model\n---\n\nDefinitions: Let P be a point in 3D of coordinates X in the world reference frame (stored in the matrix X) The coordinate vector of P in the camera reference frame is:\n\n\n\nwhere R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y and z the 3 coordinates of Xc:\n\n\n\nThe pinhole projection coordinates of P is [a; b] where\n\n\n\nFisheye distortion:\n\n\n\nThe distorted point coordinates are [x’; y’] where\n\n\n\nFinally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:\n\n\n\nSummary:\nGeneric camera model Kannala2006 with perspective projection and without distortion correction\n\nC API\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CirclesGridFinderParameters\n* LMSolverLevenberg-Marquardt solver. Starting with the specified vector of parameters it optimizes the target vector criteria “err”\n(finds local minima of each target vector component absolute value).\n* LMSolver_Callback\n* StereoBMClass for computing stereo correspondence using the block matching algorithm, introduced and contributed to OpenCV by <NAME>.\n* StereoMatcherThe base class for stereo correspondence algorithms.\n* StereoSGBMThe class implements the modified H. Hirschmuller algorithm HH08 that differs from the original one as follows:\n* UsacParams\n\nEnums\n---\n\n* CirclesGridFinderParameters_GridType\n* HandEyeCalibrationMethod\n* LocalOptimMethod\n* NeighborSearchMethod\n* PolishingMethod\n* RobotWorldHandEyeCalibrationMethod\n* SamplingMethod\n* ScoreMethod\n* SolvePnPMethod\n* UndistortTypescv::undistort mode\n\nConstants\n---\n\n* CALIB_CB_ACCURACY\n* CALIB_CB_ADAPTIVE_THRESH\n* CALIB_CB_ASYMMETRIC_GRID\n* CALIB_CB_CLUSTERING\n* CALIB_CB_EXHAUSTIVE\n* CALIB_CB_FAST_CHECK\n* CALIB_CB_FILTER_QUADS\n* CALIB_CB_LARGER\n* CALIB_CB_MARKER\n* CALIB_CB_NORMALIZE_IMAGE\n* CALIB_CB_SYMMETRIC_GRID\n* CALIB_FIX_ASPECT_RATIO\n* CALIB_FIX_FOCAL_LENGTH\n* CALIB_FIX_INTRINSIC\n* CALIB_FIX_K1\n* CALIB_FIX_K2\n* CALIB_FIX_K3\n* CALIB_FIX_K4\n* CALIB_FIX_K5\n* CALIB_FIX_K6\n* CALIB_FIX_PRINCIPAL_POINT\n* CALIB_FIX_S1_S2_S3_S4\n* CALIB_FIX_TANGENT_DIST\n* CALIB_FIX_TAUX_TAUY\n* CALIB_HAND_EYE_ANDREFFOn-line Hand-Eye Calibration Andreff99\n* CALIB_HAND_EYE_DANIILIDISHand-Eye Calibration Using Dual Quaternions Daniilidis98\n* CALIB_HAND_EYE_HORAUDHand-eye Calibration Horaud95\n* CALIB_HAND_EYE_PARKRobot Sensor Calibration: Solving AX = XB on the Euclidean Group Park94\n* CALIB_HAND_EYE_TSAIA New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration Tsai89\n* CALIB_NINTRINSIC\n* CALIB_RATIONAL_MODEL\n* CALIB_ROBOT_WORLD_HAND_EYE_LISimultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product Li2010SimultaneousRA\n* CALIB_ROBOT_WORLD_HAND_EYE_SHAHSolving the robot-world/hand-eye calibration problem using the kronecker product Shah2013SolvingTR\n* CALIB_SAME_FOCAL_LENGTH\n* CALIB_THIN_PRISM_MODEL\n* CALIB_TILTED_MODEL\n* CALIB_USE_EXTRINSIC_GUESSfor stereoCalibrate\n* CALIB_USE_INTRINSIC_GUESS\n* CALIB_USE_LUuse LU instead of SVD decomposition for solving. much faster but potentially less precise\n* CALIB_USE_QRuse QR instead of SVD decomposition for solving. Faster but potentially less precise\n* CALIB_ZERO_DISPARITY\n* CALIB_ZERO_TANGENT_DIST\n* COV_POLISHER\n* CirclesGridFinderParameters_ASYMMETRIC_GRID\n* CirclesGridFinderParameters_SYMMETRIC_GRID\n* FM_7POINT7-point algorithm\n* FM_8POINT8-point algorithm\n* FM_LMEDSleast-median algorithm. 7-point algorithm is used.\n* FM_RANSACRANSAC algorithm. It needs at least 15 points. 7-point algorithm is used.\n* Fisheye_CALIB_CHECK_COND\n* Fisheye_CALIB_FIX_FOCAL_LENGTH\n* Fisheye_CALIB_FIX_INTRINSIC\n* Fisheye_CALIB_FIX_K1\n* Fisheye_CALIB_FIX_K2\n* Fisheye_CALIB_FIX_K3\n* Fisheye_CALIB_FIX_K4\n* Fisheye_CALIB_FIX_PRINCIPAL_POINT\n* Fisheye_CALIB_FIX_SKEW\n* Fisheye_CALIB_RECOMPUTE_EXTRINSIC\n* Fisheye_CALIB_USE_INTRINSIC_GUESS\n* Fisheye_CALIB_ZERO_DISPARITY\n* LMEDSleast-median of squares algorithm\n* LOCAL_OPTIM_GC\n* LOCAL_OPTIM_INNER_AND_ITER_LO\n* LOCAL_OPTIM_INNER_LO\n* LOCAL_OPTIM_NULL\n* LOCAL_OPTIM_SIGMA\n* LSQ_POLISHER\n* MAGSAC\n* NEIGH_FLANN_KNN\n* NEIGH_FLANN_RADIUS\n* NEIGH_GRID\n* NONE_POLISHER\n* PROJ_SPHERICAL_EQRECT\n* PROJ_SPHERICAL_ORTHO\n* RANSACRANSAC algorithm\n* RHORHO algorithm\n* SAMPLING_NAPSAC\n* SAMPLING_PROGRESSIVE_NAPSAC\n* SAMPLING_PROSAC\n* SAMPLING_UNIFORM\n* SCORE_METHOD_LMEDS\n* SCORE_METHOD_MAGSAC\n* SCORE_METHOD_MSAC\n* SCORE_METHOD_RANSAC\n* SOLVEPNP_AP3PAn Efficient Algebraic Solution to the Perspective-Three-Point Problem Ke17\n* SOLVEPNP_DLS**Broken implementation. Using this flag will fallback to EPnP.**\n* SOLVEPNP_EPNPEPnP: Efficient Perspective-n-Point Camera Pose Estimation lepetit2009epnp\n* SOLVEPNP_IPPEInfinitesimal Plane-Based Pose Estimation Collins14\n* SOLVEPNP_IPPE_SQUAREInfinitesimal Plane-Based Pose Estimation Collins14\n* SOLVEPNP_ITERATIVEPose refinement using non-linear Levenberg-Marquardt minimization scheme Madsen04 Eade13\n* SOLVEPNP_MAX_COUNTUsed for count\n* SOLVEPNP_P3PComplete Solution Classification for the Perspective-Three-Point Problem gao2003complete\n* SOLVEPNP_SQPNPSQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem Terzakis2020SQPnP\n* SOLVEPNP_UPNP**Broken implementation. Using this flag will fallback to EPnP.**\n* StereoBM_PREFILTER_NORMALIZED_RESPONSE\n* StereoBM_PREFILTER_XSOBEL\n* StereoMatcher_DISP_SCALE\n* StereoMatcher_DISP_SHIFT\n* StereoSGBM_MODE_HH\n* StereoSGBM_MODE_HH4\n* StereoSGBM_MODE_SGBM\n* StereoSGBM_MODE_SGBM_3WAY\n* USAC_ACCURATEUSAC, accurate settings\n* USAC_DEFAULTUSAC algorithm, default settings\n* USAC_FASTUSAC, fast settings\n* USAC_FM_8PTSUSAC, fundamental matrix 8 points\n* USAC_MAGSACUSAC, runs MAGSAC++\n* USAC_PARALLELUSAC, parallel version\n* USAC_PROSACUSAC, sorted points, runs PROSAC\n\nTraits\n---\n\n* LMSolverTraitMutable methods for crate::calib3d::LMSolver\n* LMSolverTraitConstConstant methods for crate::calib3d::LMSolver\n* LMSolver_CallbackTraitMutable methods for crate::calib3d::LMSolver_Callback\n* LMSolver_CallbackTraitConstConstant methods for crate::calib3d::LMSolver_Callback\n* StereoBMTraitMutable methods for crate::calib3d::StereoBM\n* StereoBMTraitConstConstant methods for crate::calib3d::StereoBM\n* StereoMatcherTraitMutable methods for crate::calib3d::StereoMatcher\n* StereoMatcherTraitConstConstant methods for crate::calib3d::StereoMatcher\n* StereoSGBMTraitMutable methods for crate::calib3d::StereoSGBM\n* StereoSGBMTraitConstConstant methods for crate::calib3d::StereoSGBM\n\nFunctions\n---\n\n* calibratePerforms camera calibration\n* calibrate_cameraFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_camera_def@overload\n* calibrate_camera_extendedFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_camera_extended_defFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_camera_roFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_camera_ro_def@overload\n* calibrate_camera_ro_extendedFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_camera_ro_extended_defFinds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.\n* calibrate_defPerforms camera calibration\n* calibrate_hand_eyeComputes Hand-Eye calibration: inline formula\n* calibrate_hand_eye_defComputes Hand-Eye calibration: inline formula\n* calibrate_robot_world_hand_eyeComputes Robot-World/Hand-Eye calibration: inline formula and inline formula\n* calibrate_robot_world_hand_eye_defComputes Robot-World/Hand-Eye calibration: inline formula and inline formula\n* calibration_matrix_valuesComputes useful camera characteristics from the camera intrinsic matrix.\n* check_chessboard\n* compose_rtCombines two rotation-and-shift transformations.\n* compose_rt_defCombines two rotation-and-shift transformations.\n* compute_correspond_epilinesFor points in an image of a stereo pair, computes the corresponding epilines in the other image.\n* convert_points_from_homogeneousConverts points from homogeneous to Euclidean space.\n* convert_points_homogeneousConverts points to/from homogeneous coordinates.\n* convert_points_to_homogeneousConverts points from Euclidean to homogeneous space.\n* correct_matchesRefines coordinates of corresponding points.\n* decompose_essential_matDecompose an essential matrix to possible rotations and translation.\n* decompose_homography_matDecompose a homography matrix to rotation(s), translation(s) and plane normal(s).\n* decompose_projection_matrixDecomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.\n* decompose_projection_matrix_defDecomposes a projection matrix into a rotation matrix and a camera intrinsic matrix.\n* draw_chessboard_cornersRenders the detected chessboard corners.\n* draw_frame_axesDraw axes of the world/object coordinate system from pose estimation. see also: solvePnP\n* draw_frame_axes_defDraw axes of the world/object coordinate system from pose estimation. see also: solvePnP\n* estimate_affine_2dComputes an optimal affine transformation between two 2D point sets.\n* estimate_affine_2d_1\n* estimate_affine_2d_defComputes an optimal affine transformation between two 2D point sets.\n* estimate_affine_3dComputes an optimal affine transformation between two 3D point sets.\n* estimate_affine_3d_1Computes an optimal affine transformation between two 3D point sets.\n* estimate_affine_3d_1_defComputes an optimal affine transformation between two 3D point sets.\n* estimate_affine_3d_defComputes an optimal affine transformation between two 3D point sets.\n* estimate_affine_partial_2dComputes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets.\n* estimate_affine_partial_2d_defComputes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets.\n* estimate_chessboard_sharpnessEstimates the sharpness of a detected chessboard.\n* estimate_chessboard_sharpness_defEstimates the sharpness of a detected chessboard.\n* estimate_new_camera_matrix_for_undistort_rectifyEstimates new camera intrinsic matrix for undistortion or rectification.\n* estimate_new_camera_matrix_for_undistort_rectify_defEstimates new camera intrinsic matrix for undistortion or rectification.\n* estimate_translation_3dComputes an optimal translation between two 3D point sets.\n* estimate_translation_3d_defComputes an optimal translation between two 3D point sets.\n* filter_homography_decomp_by_visible_refpointsFilters homography decompositions based on additional information.\n* filter_homography_decomp_by_visible_refpoints_defFilters homography decompositions based on additional information.\n* filter_specklesFilters off small noise blobs (speckles) in the disparity map\n* filter_speckles_defFilters off small noise blobs (speckles) in the disparity map\n* find4_quad_corner_subpixfinds subpixel-accurate positions of the chessboard corners\n* find_chessboard_cornersFinds the positions of internal corners of the chessboard.\n* find_chessboard_corners_defFinds the positions of internal corners of the chessboard.\n* find_chessboard_corners_sbFinds the positions of internal corners of the chessboard using a sector based approach.\n* find_chessboard_corners_sb_def@overload\n* find_chessboard_corners_sb_with_metaFinds the positions of internal corners of the chessboard using a sector based approach.\n* find_circles_gridFinds centers in the grid of circles.\n* find_circles_grid_1Finds centers in the grid of circles.\n* find_circles_grid_1_def@overload\n* find_essential_matCalculates an essential matrix from the corresponding points in two images.\n* find_essential_mat_1Calculates an essential matrix from the corresponding points in two images.\n* find_essential_mat_1_def@overload\n* find_essential_mat_2Calculates an essential matrix from the corresponding points in two images.\n* find_essential_mat_3Calculates an essential matrix from the corresponding points in two images from potentially two different cameras.\n* find_essential_mat_3_defCalculates an essential matrix from the corresponding points in two images from potentially two different cameras.\n* find_essential_mat_4\n* find_essential_mat_defCalculates an essential matrix from the corresponding points in two images.\n* find_essential_mat_matrixCalculates an essential matrix from the corresponding points in two images.\n* find_fundamental_matCalculates a fundamental matrix from the corresponding points in two images.\n* find_fundamental_mat_1Calculates a fundamental matrix from the corresponding points in two images.\n* find_fundamental_mat_1_def@overload\n* find_fundamental_mat_2\n* find_fundamental_mat_defCalculates a fundamental matrix from the corresponding points in two images.\n* find_fundamental_mat_maskCalculates a fundamental matrix from the corresponding points in two images.\n* find_fundamental_mat_mask_def@overload\n* find_homographyFinds a perspective transformation between two planes.\n* find_homography_1\n* find_homography_def@overload\n* find_homography_extFinds a perspective transformation between two planes.\n* find_homography_ext_defFinds a perspective transformation between two planes.\n* fisheye_distort_pointsDistorts 2D points using fisheye model.\n* fisheye_distort_points_defDistorts 2D points using fisheye model.\n* fisheye_init_undistort_rectify_mapComputes undistortion and rectification maps for image transform by #remap. If D is empty zero distortion is used, if R or P is empty identity matrixes are used.\n* fisheye_project_pointsProjects points using fisheye model\n* fisheye_project_points_defProjects points using fisheye model\n* fisheye_project_points_vecProjects points using fisheye model\n* fisheye_project_points_vec_def@overload\n* fisheye_stereo_calibratePerforms stereo calibration\n* fisheye_stereo_calibrate_def@overload\n* fisheye_stereo_rectifyStereo rectification for fisheye camera model\n* fisheye_stereo_rectify_defStereo rectification for fisheye camera model\n* fisheye_undistort_imageTransforms an image to compensate for fisheye lens distortion.\n* fisheye_undistort_image_defTransforms an image to compensate for fisheye lens distortion.\n* fisheye_undistort_pointsUndistorts 2D points using fisheye model\n* fisheye_undistort_points_defUndistorts 2D points using fisheye model\n* get_default_new_camera_matrixReturns the default new camera matrix.\n* get_default_new_camera_matrix_defReturns the default new camera matrix.\n* get_optimal_new_camera_matrixReturns the new camera intrinsic matrix based on the free scaling parameter.\n* get_optimal_new_camera_matrix_defReturns the new camera intrinsic matrix based on the free scaling parameter.\n* get_valid_disparity_roicomputes valid disparity ROI from the valid ROIs of the rectified images (that are returned by #stereoRectify)\n* init_camera_matrix_2dFinds an initial camera intrinsic matrix from 3D-2D point correspondences.\n* init_camera_matrix_2d_defFinds an initial camera intrinsic matrix from 3D-2D point correspondences.\n* init_inverse_rectification_mapComputes the projection and inverse-rectification transformation map. In essense, this is the inverse of init_undistort_rectify_map to accomodate stereo-rectification of projectors (‘inverse-cameras’) in projector-camera pairs.\n* init_undistort_rectify_mapComputes the undistortion and rectification transformation map.\n* init_wide_angle_proj_mapinitializes maps for [remap] for wide-angle\n* init_wide_angle_proj_map_definitializes maps for [remap] for wide-angle\n* mat_mul_derivComputes partial derivatives of the matrix product for each multiplied matrix.\n* project_pointsProjects 3D points to an image plane.\n* project_points_defProjects 3D points to an image plane.\n* recover_poseRecovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.\n* recover_pose_2_camerasRecovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.\n* recover_pose_2_cameras_defRecovers the relative camera rotation and the translation from corresponding points in two images from two different cameras, using cheirality check. Returns the number of inliers that pass the check.\n* recover_pose_def@overload\n* recover_pose_estimatedRecovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.\n* recover_pose_estimated_defRecovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.\n* recover_pose_triangulatedRecovers the relative camera rotation and the translation from an estimated essential matrix and the corresponding points in two images, using chirality check. Returns the number of inliers that pass the check.\n* recover_pose_triangulated_def@overload\n* rectify3_collinearcomputes the rectification transformations for 3-head camera, where all the heads are on the same line.\n* reproject_image_to_3dReprojects a disparity image to 3D space.\n* reproject_image_to_3d_defReprojects a disparity image to 3D space.\n* rodriguesConverts a rotation matrix to a rotation vector or vice versa.\n* rodrigues_defConverts a rotation matrix to a rotation vector or vice versa.\n* rq_decomp3x3Computes an RQ decomposition of 3x3 matrices.\n* rq_decomp3x3_defComputes an RQ decomposition of 3x3 matrices.\n* sampson_distanceCalculates the Sampson Distance between two points.\n* solve_p3pFinds an object pose from 3 3D-2D point correspondences.\n* solve_pnpFinds an object pose from 3D-2D point correspondences.\n* solve_pnp_defFinds an object pose from 3D-2D point correspondences.\n* solve_pnp_genericFinds an object pose from 3D-2D point correspondences.\n* solve_pnp_generic_defFinds an object pose from 3D-2D point correspondences.\n* solve_pnp_ransacFinds an object pose from 3D-2D point correspondences using the RANSAC scheme.\n* solve_pnp_ransac_1C++ default parameters\n* solve_pnp_ransac_1_defNote\n* solve_pnp_ransac_defFinds an object pose from 3D-2D point correspondences using the RANSAC scheme.\n* solve_pnp_refine_lmRefine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.\n* solve_pnp_refine_lm_defRefine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.\n* solve_pnp_refine_vvsRefine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.\n* solve_pnp_refine_vvs_defRefine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.\n* stereo_calibrateCalibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.\n* stereo_calibrate_1Calibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.\n* stereo_calibrate_1_def@overload\n* stereo_calibrate_2Performs stereo calibration\n* stereo_calibrate_2_defPerforms stereo calibration\n* stereo_calibrate_def@overload\n* stereo_calibrate_extendedCalibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.\n* stereo_calibrate_extended_defCalibrates a stereo camera set up. This function finds the intrinsic parameters for each of the two cameras and the extrinsic parameters between the two cameras.\n* stereo_rectifyComputes rectification transforms for each head of a calibrated stereo camera.\n* stereo_rectify_defComputes rectification transforms for each head of a calibrated stereo camera.\n* stereo_rectify_uncalibratedComputes a rectification transform for an uncalibrated stereo camera.\n* stereo_rectify_uncalibrated_defComputes a rectification transform for an uncalibrated stereo camera.\n* triangulate_pointsThis function reconstructs 3-dimensional points (in homogeneous coordinates) by using their observations with a stereo camera.\n* undistortTransforms an image to compensate for lens distortion.\n* undistort_defTransforms an image to compensate for lens distortion.\n* undistort_image_pointsCompute undistorted image points position\n* undistort_image_points_defCompute undistorted image points position\n* undistort_pointsComputes the ideal point coordinates from the observed point coordinates.\n* undistort_points_defComputes the ideal point coordinates from the observed point coordinates.\n* undistort_points_iterComputes the ideal point coordinates from the observed point coordinates.\n* validate_disparityvalidates disparity using the left-right check. The matrix “cost” should be computed by the stereo correspondence algorithm\n* validate_disparity_defvalidates disparity using the left-right check. The matrix “cost” should be computed by the stereo correspondence algorithm\n\nType Aliases\n---\n\n* CirclesGridFinderParameters2\n\nModule opencv::ccalib\n===\n\nCustom Calibration Pattern for 3D reconstruction\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CustomPattern\n* MultiCameraCalibrationClass for multiple camera calibration that supports pinhole camera and omnidirection camera.\nFor omnidirectional camera model, please refer to omnidir.hpp in ccalib module.\nIt first calibrate each camera individually, then a bundle adjustment like optimization is applied to refine extrinsic parameters. So far, it only support “random” pattern for calibration,\nsee randomPattern.hpp in ccalib module for details.\nImages that are used should be named by “cameraIdx-timestamp.*”, several images with the same timestamp means that they are the same pattern that are photographed. cameraIdx should start from 0.\n* MultiCameraCalibration_edge\n* MultiCameraCalibration_vertex\n* RandomPatternCornerFinderClass for finding features points and corresponding 3D in world coordinate of a “random” pattern, which can be to be used in calibration. It is useful when pattern is partly occluded or only a part of pattern can be observed in multiple cameras calibration.\nThe pattern can be generated by RandomPatternGenerator class described in this file.\n* RandomPatternGenerator\n\nConstants\n---\n\n* CALIB_FIX_CENTER\n* CALIB_FIX_GAMMA\n* CALIB_FIX_K1\n* CALIB_FIX_K2\n* CALIB_FIX_P1\n* CALIB_FIX_P2\n* CALIB_FIX_SKEW\n* CALIB_FIX_XI\n* CALIB_USE_GUESS\n* HEAD\n* INVALID\n* MultiCameraCalibration_OMNIDIRECTIONAL\n* MultiCameraCalibration_PINHOLE\n* RECTIFY_CYLINDRICAL\n* RECTIFY_LONGLATI\n* RECTIFY_PERSPECTIVE\n* RECTIFY_STEREOGRAPHIC\n* XYZ\n* XYZRGB\n\nTraits\n---\n\n* CustomPatternTraitMutable methods for crate::ccalib::CustomPattern\n* CustomPatternTraitConstConstant methods for crate::ccalib::CustomPattern\n* MultiCameraCalibrationTraitMutable methods for crate::ccalib::MultiCameraCalibration\n* MultiCameraCalibrationTraitConstConstant methods for crate::ccalib::MultiCameraCalibration\n* MultiCameraCalibration_edgeTraitMutable methods for crate::ccalib::MultiCameraCalibration_edge\n* MultiCameraCalibration_edgeTraitConstConstant methods for crate::ccalib::MultiCameraCalibration_edge\n* MultiCameraCalibration_vertexTraitMutable methods for crate::ccalib::MultiCameraCalibration_vertex\n* MultiCameraCalibration_vertexTraitConstConstant methods for crate::ccalib::MultiCameraCalibration_vertex\n* RandomPatternCornerFinderTraitMutable methods for crate::ccalib::RandomPatternCornerFinder\n* RandomPatternCornerFinderTraitConstConstant methods for crate::ccalib::RandomPatternCornerFinder\n* RandomPatternGeneratorTraitMutable methods for crate::ccalib::RandomPatternGenerator\n* RandomPatternGeneratorTraitConstConstant methods for crate::ccalib::RandomPatternGenerator\n\nFunctions\n---\n\n* calibratePerform omnidirectional camera calibration, the default depth of outputs is CV_64F.\n* calibrate_defPerform omnidirectional camera calibration, the default depth of outputs is CV_64F.\n* init_undistort_rectify_mapComputes undistortion and rectification maps for omnidirectional camera image transform by a rotation R.\nIt output two maps that are used for cv::remap(). If D is empty then zero distortion is used,\nif R or P is empty then identity matrices are used.\n* project_pointsProjects points for omnidirectional camera using CMei’s model\n* project_points_1Projects points for omnidirectional camera using CMei’s model\n* project_points_1_def@overload\n* project_points_defProjects points for omnidirectional camera using CMei’s model\n* stereo_calibrateStereo calibration for omnidirectional camera model. It computes the intrinsic parameters for two cameras and the extrinsic parameters between two cameras. The default depth of outputs is CV_64F.\n* stereo_calibrate_defStereo calibration for omnidirectional camera model. It computes the intrinsic parameters for two cameras and the extrinsic parameters between two cameras. The default depth of outputs is CV_64F.\n* stereo_reconstructStereo 3D reconstruction from a pair of images\n* stereo_reconstruct_defStereo 3D reconstruction from a pair of images\n* stereo_rectifyStereo rectification for omnidirectional camera model. It computes the rectification rotations for two cameras\n* undistort_imageUndistort omnidirectional images to perspective images\n* undistort_image_defUndistort omnidirectional images to perspective images\n* undistort_pointsUndistort 2D image points for omnidirectional camera using CMei’s model\n\nModule opencv::core\n===\n\nCore functionality\n---\n\nBasic structures\n---\n\nC structures and operations\n---\n\nOperations on arrays\n---\n\nAsynchronous API\n---\n\nXML/YAML Persistence\n---\n\nClustering\n---\n\nUtility and system functions and macros\n---\n\nOpenGL interoperability\n---\n\nIntel IPP Asynchronous C/C++ Converters\n---\n\nOptimization Algorithms\n---\n\nDirectX interoperability\n---\n\nEigen support\n---\n\nOpenCL support\n---\n\nIntel VA-API/OpenCL (CL-VA) interoperability\n---\n\nHardware Acceleration Layer\n---\n\nParallel Processing\n---\n\nRe-exports\n---\n\n* `pub use ptr_extern::PtrExtern;`\n* `pub use ptr_extern::PtrExternCtor;`\n* `pub use vector_extern::VectorExtern;`\n* `pub use vector_extern::VectorExternCopyNonBool;`\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* Affine3docs.opencv.org\n* AlgorithmThis is a base class for all more or less complex algorithms in OpenCV\n* ArraysWrapper for OpenGL Client-Side Vertex arrays.\n* AsyncArrayReturns result of asynchronous operations\n* AsyncPromiseProvides result of asynchronous operations\n* BufferSmart pointer for OpenGL buffer object with reference counting.\n* BufferPoolBufferPool for use with CUDA streams\n* ClassWithKeywordProperties\n* CommandLineParserDesigned for command line parsing\n* ConjGradSolverThis class is used to perform the non-linear non-constrained minimization of a function with known gradient,\n* Context\n* Context_UserContext\n* DMatchClass for matching keypoint descriptors\n* Detail_CheckContext\n* Device\n* DeviceInfoClass providing functionality for querying the specified GPU properties.\n* DownhillSolverThis class is used to perform the non-linear non-constrained minimization of a function,\n* Event\n* Exception! Class passed to an error.\n* FileNodeFile Storage Node class.\n* FileNodeIteratorused to iterate through sequences and mappings.\n* FileStorageXML/YAML/JSON file storage class that encapsulates all the information necessary for writing or reading data to/from a file.\n* Formatted@todo document\n* Formatter@todo document\n* FunctionParams\n* GpuData\n* GpuMatBase storage class for GPU memory with reference counting.\n* GpuMatND\n* GpuMat_Allocator\n* Hamming\n* HostMemClass with reference counting wrapping special memory type allocation functions from CUDA.\n* Image2D\n* Kernel\n* KernelArg\n* KeyPointData structure for salient point detectors.\n* LDALinear Discriminant Analysis\n@todo document this class\n* LogTag\n* Matn-dimensional dense array class \\anchor CVMat_Details\n* MatConstIterator/////////////////////////////// MatConstIterator //////////////////////////////////\n* MatExprMatrix expression representation\n@anchor MatrixExpressions This is a list of implemented matrix operations that can be combined in arbitrary complex expressions (here A, B stand for matrices ( Mat ), s for a scalar ( Scalar ), alpha for a real-valued scalar ( double )):\n* MatIter\n* MatOp////////////////////////////// Matrix Expressions /////////////////////////////////\n* MatSize\n* MatStep\n* Mat_docs.opencv.org\n* Matxdocs.opencv.org\n* Matx_AddOp@cond IGNORED\n* Matx_DivOp\n* Matx_MatMulOp\n* Matx_MulOp\n* Matx_ScaleOp\n* Matx_SubOp\n* Matx_TOp\n* MinProblemSolverBasic interface for all solvers\n* MinProblemSolver_FunctionRepresents function being optimized\n* Momentsstruct returned by cv::moments\n* NodeData\n* OpenCLExecutionContext\n* OriginalClassName\n* OriginalClassName_Params\n* PCAPrincipal Component Analysis\n* ParallelLoopBodyBase class for parallel data processors\n* Platform@deprecated\n* PlatformInfo\n* Point3_docs.opencv.org\n* Point_docs.opencv.org\n* Program\n* ProgramSource\n* PtrThis is similar to Rust `Box`, but handled by the C++. Some OpenCV functions insist on accepting `Ptr` instead of a heap allocated object so we need to satisfy those.\n* Queue\n* RNGRandom Number Generator\n* RNG_MT19937Mersenne Twister random number generator\n* RangeTemplate class specifying a continuous subsequence (slice) of a sequence.\n* Rect_docs.opencv.org\n* RotatedRectThe class represents rotated (i.e. not up-right) rectangles on a plane.\n* SVDSingular Value Decomposition\n* Size_docs.opencv.org\n* SizedArray12\n* SizedArray13\n* SizedArray14\n* SizedArray16\n* SizedArray21\n* SizedArray22\n* SizedArray23\n* SizedArray31\n* SizedArray32\n* SizedArray33\n* SizedArray34\n* SizedArray41\n* SizedArray43\n* SizedArray44\n* SizedArray61\n* SizedArray66\n* SparseMatThe class SparseMat represents multi-dimensional sparse numerical arrays.\n* SparseMatConstIteratorRead-Only Sparse Matrix Iterator.\n* SparseMatIteratorRead-write Sparse Matrix Iterator\n* SparseMat_Hdrthe sparse matrix header\n* SparseMat_Nodesparse matrix node - element of a hash table\n* StreamThis class encapsulates a queue of asynchronous calls.\n* TargetArchsClass providing a set of static methods to check what NVIDIA* card architecture the CUDA module was built for.\n* TermCriteriaThe class defining termination criteria for iterative algorithms.\n* Texture2DSmart pointer for OpenGL 2D texture memory with reference counting.\n* TickMetera Class to measure passing time.\n* Timer\n* TupleWrapper for C++ std::tupe and std::pair\n* UMat@todo document\n* UMatData\n* VecNdocs.opencv.org Named `VecN` to avoid name clash with std’s `Vec`.\n* VectorWrapper for C++ std::vector\n* VectorIterator\n* VectorRefIterator\n* WriteStructContext\n* _InputArrayThis is the proxy class for passing read-only input arrays into OpenCV functions.\n* _InputOutputArray\n* _OutputArrayThis type is very similar to InputArray except that it is used for input/output and output function parameters.\n\nEnums\n---\n\n* AccessFlag\n* BorderTypesVarious border types, image boundaries are denoted with `|`\n* Buffer_Access\n* Buffer_TargetThe target defines how you intend to use the buffer object.\n* CmpTypescomparison types\n* Codeerror codes\n* CovarFlagsCovariation flags\n* CpuFeaturesAvailable CPU features.\n* DecompTypesmatrix decomposition types\n* Detail_TestOp\n* DeviceInfo_ComputeMode\n* DftFlags\n* Event_CreateFlags\n* FLAGS\n* FeatureSetEnumeration providing CUDA computing features.\n* FileStorage_Modefile storage mode\n* FileStorage_State\n* Formatter_FormatType\n* GemmFlagsgeneralized matrix multiplication flags\n* HostMem_AllocType\n* IMPL\n* KmeansFlagsk-Means flags\n* LogLevelSupported logging levels and their semantic\n* MatExprResult\n* NormTypesnorm types\n* OclVectorStrategy\n* PCA_Flags\n* Param\n* ReduceTypes\n* RenderModesrender mode\n* RotateFlags\n* SVD_Flags\n* SolveLPResultreturn codes for cv::solveLP() function\n* SortFlags\n* TYPE\n* TermCriteria_TypeCriteria type, can be one of: COUNT, EPS or COUNT + EPS\n* Texture2D_FormatAn Image Format describes the way that the images in Textures store their data.\n* UMatData_MemoryFlag\n* UMatUsageFlagsUsage flags for allocator\n* _InputArray_KindFlag\n* _OutputArray_DepthMask\n\nConstants\n---\n\n* ACCESS_FAST\n* ACCESS_MASK\n* ACCESS_READ\n* ACCESS_RW\n* ACCESS_WRITE\n* BORDER_CONSTANT`iiiiii|abcdefgh|iiiiiii` with some specified `i`\n* BORDER_DEFAULTsame as BORDER_REFLECT_101\n* BORDER_ISOLATEDdo not look outside of ROI\n* BORDER_REFLECT`fedcba|abcdefgh|hgfedcb`\n* BORDER_REFLECT101same as BORDER_REFLECT_101\n* BORDER_REFLECT_101`gfedcb|abcdefgh|gfedcba`\n* BORDER_REPLICATE`aaaaaa|abcdefgh|hhhhhhh`\n* BORDER_TRANSPARENT`uvwxyz|abcdefgh|ijklmno`\n* BORDER_WRAP`cdefgh|abcdefgh|abcdefg`\n* BadAlignincorrect input align\n* BadAlphaChannel\n* BadCOIinput COI is not supported\n* BadCallBack\n* BadDataPtr\n* BadDepthinput image depth is not supported by the function\n* BadImageSizeimage size is invalid\n* BadModelOrChSeq\n* BadNumChannel1U\n* BadNumChannelsbad number of channels, for example, some functions accept only single channel matrices.\n* BadOffsetoffset is invalid\n* BadOrdernumber of dimensions is out of range\n* BadOriginincorrect input origin\n* BadROISizeincorrect input roi\n* BadStepimage step is wrong, this may happen for a non-continuous matrix.\n* BadTileSize\n* Buffer_ARRAY_BUFFERThe buffer will be used as a source for vertex data\n* Buffer_ELEMENT_ARRAY_BUFFERThe buffer will be used for indices (in glDrawElements, for example)\n* Buffer_PIXEL_PACK_BUFFERThe buffer will be used for reading from OpenGL textures\n* Buffer_PIXEL_UNPACK_BUFFERThe buffer will be used for writing to OpenGL textures\n* Buffer_READ_ONLY\n* Buffer_READ_WRITE\n* Buffer_WRITE_ONLY\n* CMP_EQsrc1 is equal to src2.\n* CMP_GEsrc1 is greater than or equal to src2.\n* CMP_GTsrc1 is greater than src2.\n* CMP_LEsrc1 is less than or equal to src2.\n* CMP_LTsrc1 is less than src2.\n* CMP_NEsrc1 is unequal to src2.\n* COVAR_COLSIf the flag is specified, all the input vectors are stored as columns of the samples matrix. mean should be a single-column vector in this case.\n* COVAR_NORMALThe output covariance matrix is calculated as:\nblock formula covar will be a square matrix of the same size as the total number of elements in each input vector. One and only one of COVAR_SCRAMBLED and COVAR_NORMAL must be specified.\n* COVAR_ROWSIf the flag is specified, all the input vectors are stored as rows of the samples matrix. mean should be a single-row vector in this case.\n* COVAR_SCALEIf the flag is specified, the covariance matrix is scaled. In the\n“normal” mode, scale is 1./nsamples . In the “scrambled” mode, scale is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified), the covariance matrix is not scaled ( scale=1 ).\n* COVAR_SCRAMBLEDThe output covariance matrix is calculated as:\nblock formula The covariance matrix will be nsamples x nsamples. Such an unusual covariance matrix is used for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for face recognition). Eigenvalues of this “scrambled” matrix match the eigenvalues of the true covariance matrix. The “true” eigenvectors can be easily calculated from the eigenvectors of the “scrambled” covariance matrix.\n* COVAR_USE_AVGIf the flag is specified, the function does not calculate mean from the input vectors but, instead, uses the passed mean vector. This is useful if mean has been pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In this case, mean is not a mean vector of the input sub-set of vectors but rather the mean vector of the whole set.\n* CPU_AVX\n* CPU_AVX2\n* CPU_AVX512_CLXCascade Lake with AVX-512F/CD/BW/DQ/VL/VNNI\n* CPU_AVX512_CNLCannon Lake with AVX-512F/CD/BW/DQ/VL/IFMA/VBMI\n* CPU_AVX512_COMMONCommon instructions AVX-512F/CD for all CPUs that support AVX-512\n* CPU_AVX512_ICLIce Lake with AVX-512F/CD/BW/DQ/VL/IFMA/VBMI/VNNI/VBMI2/BITALG/VPOPCNTDQ\n* CPU_AVX512_KNLKnights Landing with AVX-512F/CD/ER/PF\n* CPU_AVX512_KNMKnights Mill with AVX-512F/CD/ER/PF/4FMAPS/4VNNIW/VPOPCNTDQ\n* CPU_AVX512_SKXSkylake-X with AVX-512F/CD/BW/DQ/VL\n* CPU_AVX_512BITALG\n* CPU_AVX_512BW\n* CPU_AVX_512CD\n* CPU_AVX_512DQ\n* CPU_AVX_512ER\n* CPU_AVX_512F\n* CPU_AVX_512IFMA\n* CPU_AVX_512IFMA512\n* CPU_AVX_512PF\n* CPU_AVX_512VBMI\n* CPU_AVX_512VBMI2\n* CPU_AVX_512VL\n* CPU_AVX_512VNNI\n* CPU_AVX_512VPOPCNTDQ\n* CPU_AVX_5124FMAPS\n* CPU_AVX_5124VNNIW\n* CPU_FMA3\n* CPU_FP16\n* CPU_LASX\n* CPU_MAX_FEATURE\n* CPU_MMX\n* CPU_MSA\n* CPU_NEON\n* CPU_NEON_DOTPROD\n* CPU_POPCNT\n* CPU_RISCVV\n* CPU_RVV\n* CPU_SSE\n* CPU_SSE2\n* CPU_SSE3\n* CPU_SSE4_1\n* CPU_SSE4_2\n* CPU_SSSE3\n* CPU_VSX\n* CPU_VSX3\n* CV_2PI\n* CV_8S\n* CV_8SC1\n* CV_8SC2\n* CV_8SC3\n* CV_8SC4\n* CV_8U\n* CV_8UC1\n* CV_8UC2\n* CV_8UC3\n* CV_8UC4\n* CV_16F\n* CV_16FC1\n* CV_16FC2\n* CV_16FC3\n* CV_16FC4\n* CV_16S\n* CV_16SC1\n* CV_16SC2\n* CV_16SC3\n* CV_16SC4\n* CV_16U\n* CV_16UC1\n* CV_16UC2\n* CV_16UC3\n* CV_16UC4\n* CV_32F\n* CV_32FC1\n* CV_32FC2\n* CV_32FC3\n* CV_32FC4\n* CV_32S\n* CV_32SC1\n* CV_32SC2\n* CV_32SC3\n* CV_32SC4\n* CV_64F\n* CV_64FC1\n* CV_64FC2\n* CV_64FC3\n* CV_64FC4\n* CV_AVX\n* CV_AVX2\n* CV_AVX512_CLX\n* CV_AVX512_CNL\n* CV_AVX512_COMMON\n* CV_AVX512_ICL\n* CV_AVX512_KNL\n* CV_AVX512_KNM\n* CV_AVX512_SKX\n* CV_AVX_512BITALG\n* CV_AVX_512BW\n* CV_AVX_512CD\n* CV_AVX_512DQ\n* CV_AVX_512ER\n* CV_AVX_512F\n* CV_AVX_512IFMA\n* CV_AVX_512IFMA512\n* CV_AVX_512PF\n* CV_AVX_512VBMI\n* CV_AVX_512VBMI2\n* CV_AVX_512VL\n* CV_AVX_512VNNI\n* CV_AVX_512VPOPCNTDQ\n* CV_AVX_5124FMAPS\n* CV_AVX_5124VNNIW\n* CV_CN_MAX\n* CV_CN_SHIFT\n* CV_CPU_AVX\n* CV_CPU_AVX2\n* CV_CPU_AVX512_CLX\n* CV_CPU_AVX512_CNL\n* CV_CPU_AVX512_COMMON\n* CV_CPU_AVX512_ICL\n* CV_CPU_AVX512_KNL\n* CV_CPU_AVX512_KNM\n* CV_CPU_AVX512_SKX\n* CV_CPU_AVX_512BITALG\n* CV_CPU_AVX_512BW\n* CV_CPU_AVX_512CD\n* CV_CPU_AVX_512DQ\n* CV_CPU_AVX_512ER\n* CV_CPU_AVX_512F\n* CV_CPU_AVX_512IFMA\n* CV_CPU_AVX_512IFMA512\n* CV_CPU_AVX_512PF\n* CV_CPU_AVX_512VBMI\n* CV_CPU_AVX_512VBMI2\n* CV_CPU_AVX_512VL\n* CV_CPU_AVX_512VNNI\n* CV_CPU_AVX_512VPOPCNTDQ\n* CV_CPU_AVX_5124FMAPS\n* CV_CPU_AVX_5124VNNIW\n* CV_CPU_FMA3\n* CV_CPU_FP16\n* CV_CPU_LASX\n* CV_CPU_MMX\n* CV_CPU_MSA\n* CV_CPU_NEON\n* CV_CPU_NEON_DOTPROD\n* CV_CPU_NONE\n* CV_CPU_POPCNT\n* CV_CPU_RISCVV\n* CV_CPU_RVV\n* CV_CPU_SSE\n* CV_CPU_SSE2\n* CV_CPU_SSE3\n* CV_CPU_SSE4_1\n* CV_CPU_SSE4_2\n* CV_CPU_SSSE3\n* CV_CPU_VSX\n* CV_CPU_VSX3\n* CV_CXX11\n* CV_CXX_MOVE_SEMANTICS\n* CV_CXX_STD_ARRAY\n* CV_DEPTH_MAX\n* CV_ENABLE_UNROLLED\n* CV_FMA3\n* CV_FP16\n* CV_FP16_TYPE\n* CV_HAL_BORDER_CONSTANT\n* CV_HAL_BORDER_ISOLATED\n* CV_HAL_BORDER_REFLECT\n* CV_HAL_BORDER_REFLECT_101\n* CV_HAL_BORDER_REPLICATE\n* CV_HAL_BORDER_TRANSPARENT\n* CV_HAL_BORDER_WRAP\n* CV_HAL_CMP_EQ\n* CV_HAL_CMP_GE\n* CV_HAL_CMP_GT\n* CV_HAL_CMP_LE\n* CV_HAL_CMP_LT\n* CV_HAL_CMP_NE\n* CV_HAL_DFT_COMPLEX_OUTPUT\n* CV_HAL_DFT_INVERSE\n* CV_HAL_DFT_IS_CONTINUOUS\n* CV_HAL_DFT_IS_INPLACE\n* CV_HAL_DFT_REAL_OUTPUT\n* CV_HAL_DFT_ROWS\n* CV_HAL_DFT_SCALE\n* CV_HAL_DFT_STAGE_COLS\n* CV_HAL_DFT_TWO_STAGE\n* CV_HAL_ERROR_NOT_IMPLEMENTED\n* CV_HAL_ERROR_OK\n* CV_HAL_ERROR_UNKNOWN\n* CV_HAL_GEMM_1_T\n* CV_HAL_GEMM_2_T\n* CV_HAL_GEMM_3_T\n* CV_HAL_SVD_FULL_UV\n* CV_HAL_SVD_MODIFY_A\n* CV_HAL_SVD_NO_UV\n* CV_HAL_SVD_SHORT_UV\n* CV_HARDWARE_MAX_FEATURE\n* CV_IMPL_IPP\n* CV_IMPL_MT\n* CV_IMPL_OCL\n* CV_IMPL_PLAIN\n* CV_LASX\n* CV_LOG2\n* CV_LOG_LEVEL_DEBUG\n* CV_LOG_LEVEL_ERROR\n* CV_LOG_LEVEL_FATAL\n* CV_LOG_LEVEL_INFO\n* CV_LOG_LEVEL_SILENT\n* CV_LOG_LEVEL_VERBOSE\n* CV_LOG_LEVEL_WARN\n* CV_LOG_STRIP_LEVEL\n* CV_MAJOR_VERSION\n* CV_MAT_CN_MASK\n* CV_MAT_CONT_FLAG\n* CV_MAT_CONT_FLAG_SHIFT\n* CV_MAT_DEPTH_MASK\n* CV_MAT_TYPE_MASK\n* CV_MINOR_VERSION\n* CV_MMX\n* CV_MSA\n* CV_NEON\n* CV_PI\n* CV_POPCNT\n* CV_RVV\n* CV_RVV071\n* CV_SSE\n* CV_SSE2\n* CV_SSE3\n* CV_SSE4_1\n* CV_SSE4_2\n* CV_SSSE3\n* CV_STRONG_ALIGNMENT\n* CV_SUBMAT_FLAG\n* CV_SUBMAT_FLAG_SHIFT\n* CV_SUBMINOR_VERSION\n* CV_VERSION\n* CV_VERSION_MAJOR\n* CV_VERSION_MINOR\n* CV_VERSION_REVISION\n* CV_VERSION_STATUS\n* CV_VSX\n* CV_VSX3\n* CV_WASM_SIMD\n* CV__EXCEPTION_PTR\n* DCT_INVERSEperforms an inverse 1D or 2D transform instead of the default forward transform.\n* DCT_ROWSperforms a forward or inverse transform of every individual row of the input matrix. This flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transforms and so forth.\n* DECOMP_CHOLESKYCholesky inline formula factorization; the matrix src1 must be symmetrical and positively defined\n* DECOMP_EIGeigenvalue decomposition; the matrix src1 must be symmetrical\n* DECOMP_LUGaussian elimination with the optimal pivot element chosen.\n* DECOMP_NORMALwhile all the previous flags are mutually exclusive, this flag can be used together with any of the previous; it means that the normal equations inline formula are solved instead of the original system inline formula\n* DECOMP_QRQR factorization; the system can be over-defined and/or the matrix src1 can be singular\n* DECOMP_SVDsingular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular\n* DFT_COMPLEX_INPUTspecifies that input is complex input. If this flag is set, the input must have 2 channels.\nOn the other hand, for backwards compatibility reason, if input has 2 channels, input is already considered complex.\n* DFT_COMPLEX_OUTPUTperforms a forward transformation of 1D or 2D real array; the result,\nthough being a complex array, has complex-conjugate symmetry (*CCS*, see the function description below for details), and such an array can be packed into a real array of the same size as input, which is the fastest option and which is what the function does by default;\nhowever, you may wish to get a full complex array (for simpler spectrum analysis, and so on) -\npass the flag to enable the function to produce a full-size complex output array.\n* DFT_INVERSEperforms an inverse 1D or 2D transform instead of the default forward transform.\n* DFT_REAL_OUTPUTperforms an inverse transformation of a 1D or 2D complex array; the result is normally a complex array of the same size, however, if the input array has conjugate-complex symmetry (for example, it is a result of forward transformation with DFT_COMPLEX_OUTPUT flag), the output is a real array; while the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array (note that when the input is packed into a real array and inverse transformation is executed, the function treats the input as a packed complex-conjugate symmetrical array, and the output will also be a real array).\n* DFT_ROWSperforms a forward or inverse transform of every individual row of the input matrix; this flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transformations and so forth.\n* DFT_SCALEscales the result: divide it by the number of array elements. Normally, it is combined with DFT_INVERSE.\n* DYNAMIC_PARALLELISM\n* Detail_CV__LAST_TEST_OP\n* Detail_TEST_CUSTOM\n* Detail_TEST_EQ\n* Detail_TEST_GE\n* Detail_TEST_GT\n* Detail_TEST_LE\n* Detail_TEST_LT\n* Detail_TEST_NE\n* DeviceInfo_ComputeModeDefault< default compute mode (Multiple threads can use cudaSetDevice with this device)\n* DeviceInfo_ComputeModeExclusive< compute-exclusive-thread mode (Only one thread in one process will be able to use cudaSetDevice with this device)\n* DeviceInfo_ComputeModeExclusiveProcess< compute-exclusive-process mode (Many threads in one process will be able to use cudaSetDevice with this device)\n* DeviceInfo_ComputeModeProhibited< compute-prohibited mode (No threads can use cudaSetDevice with this device)\n* Device_EXEC_KERNEL\n* Device_EXEC_NATIVE_KERNEL\n* Device_FP_CORRECTLY_ROUNDED_DIVIDE_SQRT\n* Device_FP_DENORM\n* Device_FP_FMA\n* Device_FP_INF_NAN\n* Device_FP_ROUND_TO_INF\n* Device_FP_ROUND_TO_NEAREST\n* Device_FP_ROUND_TO_ZERO\n* Device_FP_SOFT_FLOAT\n* Device_LOCAL_IS_GLOBAL\n* Device_LOCAL_IS_LOCAL\n* Device_NO_CACHE\n* Device_NO_LOCAL_MEM\n* Device_READ_ONLY_CACHE\n* Device_READ_WRITE_CACHE\n* Device_TYPE_ACCELERATOR\n* Device_TYPE_ALL\n* Device_TYPE_CPU\n* Device_TYPE_DEFAULT\n* Device_TYPE_DGPU\n* Device_TYPE_GPU\n* Device_TYPE_IGPU\n* Device_UNKNOWN_VENDOR\n* Device_VENDOR_AMD\n* Device_VENDOR_INTEL\n* Device_VENDOR_NVIDIA\n* ENUM_LOG_LEVEL_FORCE_INT\n* Event_BLOCKING_SYNC< Event uses blocking synchronization\n* Event_DEFAULT< Default event flag\n* Event_DISABLE_TIMING< Event will not record timing data\n* Event_INTERPROCESS< Event is suitable for interprocess use. DisableTiming must be set\n* FEATURE_SET_COMPUTE_10\n* FEATURE_SET_COMPUTE_11\n* FEATURE_SET_COMPUTE_12\n* FEATURE_SET_COMPUTE_13\n* FEATURE_SET_COMPUTE_20\n* FEATURE_SET_COMPUTE_21\n* FEATURE_SET_COMPUTE_30\n* FEATURE_SET_COMPUTE_32\n* FEATURE_SET_COMPUTE_35\n* FEATURE_SET_COMPUTE_50\n* FLAGS_EXPAND_SAME_NAMES\n* FLAGS_MAPPING\n* FLAGS_NONE\n* FileNode_EMPTYempty structure (sequence or mapping)\n* FileNode_FLOATsynonym or REAL\n* FileNode_FLOWcompact representation of a sequence or mapping. Used only by YAML writer\n* FileNode_INTan integer\n* FileNode_MAPmapping\n* FileNode_NAMEDthe node has a name (i.e. it is element of a mapping).\n* FileNode_NONEempty node\n* FileNode_REALfloating-point number\n* FileNode_SEQsequence\n* FileNode_STRtext string in UTF-8 encoding\n* FileNode_STRINGsynonym for STR\n* FileNode_TYPE_MASK\n* FileNode_UNIFORMif set, means that all the collection elements are numbers of the same type (real’s or int’s).\nUNIFORM is used only when reading FileStorage; FLOW is used only when writing. So they share the same bit\n* FileStorage_APPENDvalue, open the file for appending\n* FileStorage_BASE64flag, write rawdata in Base64 by default. (consider using WRITE_BASE64)\n* FileStorage_FORMAT_AUTOflag, auto format\n* FileStorage_FORMAT_JSONflag, JSON format\n* FileStorage_FORMAT_MASKmask for format flags\n* FileStorage_FORMAT_XMLflag, XML format\n* FileStorage_FORMAT_YAMLflag, YAML format\n* FileStorage_INSIDE_MAP\n* FileStorage_MEMORY< flag, read data from source or write data to the internal buffer (which is returned by FileStorage::release)\n* FileStorage_NAME_EXPECTED\n* FileStorage_READvalue, open the file for reading\n* FileStorage_UNDEFINED\n* FileStorage_VALUE_EXPECTED\n* FileStorage_WRITEvalue, open the file for writing\n* FileStorage_WRITE_BASE64flag, enable both WRITE and BASE64\n* Formatter_FMT_C\n* Formatter_FMT_CSV\n* Formatter_FMT_DEFAULT\n* Formatter_FMT_MATLAB\n* Formatter_FMT_NUMPY\n* Formatter_FMT_PYTHON\n* GEMM_1_Ttransposes src1\n* GEMM_2_Ttransposes src2\n* GEMM_3_Ttransposes src3\n* GLOBAL_ATOMICS\n* GpuApiCallErrorGPU API call error\n* GpuNotSupportedno CUDA support\n* HeaderIsNullimage header is NULL\n* HostMem_PAGE_LOCKED\n* HostMem_SHARED\n* HostMem_WRITE_COMBINED\n* IMPL_IPP\n* IMPL_OPENCL\n* IMPL_PLAIN\n* KMEANS_PP_CENTERSUse kmeans++ center initialization by <NAME> Vassilvitskii [Arthur2007].\n* KMEANS_RANDOM_CENTERSSelect random initial centers in each attempt.\n* KMEANS_USE_INITIAL_LABELSDuring the first (and possibly the only) attempt, use the user-supplied labels instead of computing them from the initial centers. For the second and further attempts, use the random or semi-random centers. Use one of KMEANS_*_CENTERS flag to specify the exact method.\n* KernelArg_CONSTANT\n* KernelArg_LOCAL\n* KernelArg_NO_SIZE\n* KernelArg_PTR_ONLY\n* KernelArg_READ_ONLY\n* KernelArg_READ_WRITE\n* KernelArg_WRITE_ONLY\n* LINES\n* LINE_LOOP\n* LINE_STRIP\n* LOG_LEVEL_DEBUGDebug message. Disabled in the “Release” build.\n* LOG_LEVEL_ERRORError message\n* LOG_LEVEL_FATALFatal (critical) error (unrecoverable internal error)\n* LOG_LEVEL_INFOInfo message\n* LOG_LEVEL_SILENTfor using in setLogVevel() call\n* LOG_LEVEL_VERBOSEVerbose (trace) messages. Requires verbosity level. Disabled in the “Release” build.\n* LOG_LEVEL_WARNINGWarning message\n* MaskIsTiled\n* Mat_AUTO_STEP\n* Mat_CONTINUOUS_FLAG\n* Mat_DEPTH_MASK\n* Mat_MAGIC_MASK\n* Mat_MAGIC_VAL\n* Mat_SUBMATRIX_FLAG\n* Mat_TYPE_MASK\n* NATIVE_DOUBLE\n* NORM_HAMMINGIn the case of one input array, calculates the Hamming distance of the array from zero,\nIn the case of two input arrays, calculates the Hamming distance between the arrays.\n* NORM_HAMMING2Similar to NORM_HAMMING, but in the calculation, each two bits of the input sequence will be added and treated as a single bit to be used in the same calculation as NORM_HAMMING.\n* NORM_INFblock formula\n* NORM_L1block formula\n* NORM_L2block formula\n* NORM_L2SQRblock formula\n* NORM_MINMAXflag\n* NORM_RELATIVEflag\n* NORM_TYPE_MASKbit-mask which can be used to separate norm type from norm flags\n* OCL_VECTOR_DEFAULT\n* OCL_VECTOR_MAX\n* OCL_VECTOR_OWN\n* OPENCV_ABI_COMPATIBILITY\n* OPENCV_USE_FASTMATH_BUILTINS\n* OpenCLApiCallErrorOpenCL API call error\n* OpenCLDoubleNotSupported\n* OpenCLInitErrorOpenCL initialization error\n* OpenCLNoAMDBlasFft\n* OpenGlApiCallErrorOpenGL API call error\n* OpenGlNotSupportedno OpenGL support\n* PCA_DATA_AS_COLindicates that the input samples are stored as matrix columns\n* PCA_DATA_AS_ROWindicates that the input samples are stored as matrix rows\n* PCA_USE_AVG\n* POINTS\n* POLYGON\n* Param_ALGORITHM\n* Param_BOOLEAN\n* Param_FLOAT\n* Param_INT\n* Param_MAT\n* Param_MAT_VECTOR\n* Param_REAL\n* Param_SCALAR\n* Param_STRING\n* Param_UCHAR\n* Param_UINT64\n* Param_UNSIGNED_INT\n* QUADS\n* QUAD_STRIP\n* REDUCE_AVGthe output is the mean vector of all rows/columns of the matrix.\n* REDUCE_MAXthe output is the maximum (column/row-wise) of all rows/columns of the matrix.\n* REDUCE_MINthe output is the minimum (column/row-wise) of all rows/columns of the matrix.\n* REDUCE_SUMthe output is the sum of all rows/columns of the matrix.\n* REDUCE_SUM2the output is the sum of all squared rows/columns of the matrix.\n* RNG_NORMAL\n* RNG_UNIFORM\n* ROTATE_90_CLOCKWISERotate 90 degrees clockwise\n* ROTATE_90_COUNTERCLOCKWISERotate 270 degrees clockwise\n* ROTATE_180Rotate 180 degrees clockwise\n* SHARED_ATOMICS\n* SOLVELP_LOSTproblem is feasible, but solver lost solution due to floating-point arithmetic errors\n* SOLVELP_MULTIthere are multiple maxima for target function - the arbitrary one is returned\n* SOLVELP_SINGLEthere is only one maximum for target function\n* SOLVELP_UNBOUNDEDproblem is unbounded (target function can achieve arbitrary high values)\n* SOLVELP_UNFEASIBLEproblem is unfeasible (there are no points that satisfy all the constraints imposed)\n* SORT_ASCENDINGeach matrix row is sorted in the ascending order.\n* SORT_DESCENDINGeach matrix row is sorted in the descending order; this flag and the previous one are also mutually exclusive.\n* SORT_EVERY_COLUMNeach matrix column is sorted independently; this flag and the previous one are mutually exclusive.\n* SORT_EVERY_ROWeach matrix row is sorted independently\n* SVD_FULL_UVwhen the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is specified, u and vt will be full-size square orthogonal matrices.\n* SVD_MODIFY_Aallow the algorithm to modify the decomposed matrix; it can save space and speed up processing. currently ignored.\n* SVD_NO_UVindicates that only a vector of singular values `w` is to be processed, while u and vt will be set to empty matrices\n* SparseMat_HASH_BIT\n* SparseMat_HASH_SCALE\n* SparseMat_MAGIC_VAL\n* SparseMat_MAX_DIM\n* StsAssertassertion failed\n* StsAutoTracetracing\n* StsBackTracepseudo error for back trace\n* StsBadArgfunction arg/param is bad\n* StsBadFlagflag is wrong or not supported\n* StsBadFuncunsupported function\n* StsBadMaskbad format of mask (neither 8uC1 nor 8sC1)\n* StsBadMemBlockan allocated block has been corrupted\n* StsBadPointbad CvPoint\n* StsBadSizethe input/output structure size is incorrect\n* StsDivByZerodivision by zero\n* StsErrorunknown /unspecified error\n* StsFilterOffsetErrincorrect filter offset value\n* StsFilterStructContentErrincorrect filter structure content\n* StsInplaceNotSupportedin-place operation is not supported\n* StsInternalinternal error (bad state)\n* StsKernelStructContentErrincorrect transform kernel content\n* StsNoConviteration didn’t converge\n* StsNoMeminsufficient memory\n* StsNotImplementedthe requested function/feature is not implemented\n* StsNullPtrnull pointer\n* StsObjectNotFoundrequest can’t be completed\n* StsOkeverything is ok\n* StsOutOfRangesome of parameters are out of range\n* StsParseErrorinvalid syntax/structure of the parsed file\n* StsUnmatchedFormatsformats of input/output arrays differ\n* StsUnmatchedSizessizes of input/output structures do not match\n* StsUnsupportedFormatthe data format/type is not supported by the function\n* StsVecLengthErrincorrect vector length\n* TRIANGLES\n* TRIANGLE_FAN\n* TRIANGLE_STRIP\n* TYPE_FUN\n* TYPE_GENERAL\n* TYPE_MARKER\n* TYPE_WRAPPER\n* TermCriteria_COUNTthe maximum number of iterations or elements to compute\n* TermCriteria_EPSthe desired accuracy or change in parameters at which the iterative algorithm stops\n* TermCriteria_MAX_ITERditto\n* Texture2D_DEPTH_COMPONENTDepth\n* Texture2D_NONE\n* Texture2D_RGBRed, Green, Blue\n* Texture2D_RGBARed, Green, Blue, Alpha\n* UMatData_ASYNC_CLEANUP\n* UMatData_COPY_ON_MAP\n* UMatData_DEVICE_COPY_OBSOLETE\n* UMatData_DEVICE_MEM_MAPPED\n* UMatData_HOST_COPY_OBSOLETE\n* UMatData_TEMP_COPIED_UMAT\n* UMatData_TEMP_UMAT\n* UMatData_USER_ALLOCATED\n* UMat_AUTO_STEP\n* UMat_CONTINUOUS_FLAG\n* UMat_DEPTH_MASK\n* UMat_MAGIC_MASK\n* UMat_MAGIC_VAL\n* UMat_SUBMATRIX_FLAG\n* UMat_TYPE_MASK\n* USAGE_ALLOCATE_DEVICE_MEMORY\n* USAGE_ALLOCATE_HOST_MEMORY\n* USAGE_ALLOCATE_SHARED_MEMORY\n* USAGE_DEFAULT\n* WARP_SHUFFLE_FUNCTIONS\n* _InputArray_CUDA_GPU_MAT\n* _InputArray_CUDA_HOST_MEM\n* _InputArray_EXPRremoved: https://github.com/opencv/opencv/pull/17046\n* _InputArray_FIXED_SIZE\n* _InputArray_FIXED_TYPE\n* _InputArray_KIND_MASK\n* _InputArray_KIND_SHIFT\n* _InputArray_MAT\n* _InputArray_MATX\n* _InputArray_NONE\n* _InputArray_OPENGL_BUFFER\n* _InputArray_STD_ARRAYremoved: https://github.com/opencv/opencv/issues/18897\n* _InputArray_STD_ARRAY_MAT\n* _InputArray_STD_BOOL_VECTOR\n* _InputArray_STD_VECTOR\n* _InputArray_STD_VECTOR_CUDA_GPU_MAT\n* _InputArray_STD_VECTOR_MAT\n* _InputArray_STD_VECTOR_UMAT\n* _InputArray_STD_VECTOR_VECTOR\n* _InputArray_UMAT\n* _OutputArray_DEPTH_MASK_8S\n* _OutputArray_DEPTH_MASK_8U\n* _OutputArray_DEPTH_MASK_16F\n* _OutputArray_DEPTH_MASK_16S\n* _OutputArray_DEPTH_MASK_16U\n* _OutputArray_DEPTH_MASK_32F\n* _OutputArray_DEPTH_MASK_32S\n* _OutputArray_DEPTH_MASK_64F\n* _OutputArray_DEPTH_MASK_ALL\n* _OutputArray_DEPTH_MASK_ALL_16F\n* _OutputArray_DEPTH_MASK_ALL_BUT_8S\n* _OutputArray_DEPTH_MASK_FLT\n* __UMAT_USAGE_FLAGS_32BIT\n\nTraits\n---\n\n* AlgorithmTraitMutable methods for core::Algorithm\n* AlgorithmTraitConstConstant methods for core::Algorithm\n* ArraysTraitMutable methods for core::Arrays\n* ArraysTraitConstConstant methods for core::Arrays\n* AsyncArrayTraitMutable methods for core::AsyncArray\n* AsyncArrayTraitConstConstant methods for core::AsyncArray\n* AsyncPromiseTraitMutable methods for core::AsyncPromise\n* AsyncPromiseTraitConstConstant methods for core::AsyncPromise\n* BufferPoolTraitMutable methods for core::BufferPool\n* BufferPoolTraitConstConstant methods for core::BufferPool\n* BufferTraitMutable methods for core::Buffer\n* BufferTraitConstConstant methods for core::Buffer\n* CommandLineParserTraitMutable methods for core::CommandLineParser\n* CommandLineParserTraitConstConstant methods for core::CommandLineParser\n* ConjGradSolverTraitMutable methods for core::ConjGradSolver\n* ConjGradSolverTraitConstConstant methods for core::ConjGradSolver\n* ContextTraitMutable methods for core::Context\n* ContextTraitConstConstant methods for core::Context\n* Context_UserContextTraitMutable methods for core::Context_UserContext\n* Context_UserContextTraitConstConstant methods for core::Context_UserContext\n* DataTypeImplement this trait types that are valid to use as Mat elements.\n* Detail_CheckContextTraitMutable methods for core::Detail_CheckContext\n* Detail_CheckContextTraitConstConstant methods for core::Detail_CheckContext\n* DeviceInfoTraitMutable methods for core::DeviceInfo\n* DeviceInfoTraitConstConstant methods for core::DeviceInfo\n* DeviceTraitMutable methods for core::Device\n* DeviceTraitConstConstant methods for core::Device\n* DownhillSolverTraitMutable methods for core::DownhillSolver\n* DownhillSolverTraitConstConstant methods for core::DownhillSolver\n* ElemMulelementwise multiplication\n* EventTraitMutable methods for core::Event\n* EventTraitConstConstant methods for core::Event\n* ExceptionTraitMutable methods for core::Exception\n* ExceptionTraitConstConstant methods for core::Exception\n* FileNodeIteratorTraitMutable methods for core::FileNodeIterator\n* FileNodeIteratorTraitConstConstant methods for core::FileNodeIterator\n* FileNodeTraitMutable methods for core::FileNode\n* FileNodeTraitConstConstant methods for core::FileNode\n* FileStorageTraitMutable methods for core::FileStorage\n* FileStorageTraitConstConstant methods for core::FileStorage\n* FormattedTraitMutable methods for core::Formatted\n* FormattedTraitConstConstant methods for core::Formatted\n* FormatterTraitMutable methods for core::Formatter\n* FormatterTraitConstConstant methods for core::Formatter\n* FunctionParamsTraitMutable methods for core::FunctionParams\n* FunctionParamsTraitConstConstant methods for core::FunctionParams\n* GpuDataTraitMutable methods for core::GpuData\n* GpuDataTraitConstConstant methods for core::GpuData\n* GpuMatNDTraitMutable methods for core::GpuMatND\n* GpuMatNDTraitConstConstant methods for core::GpuMatND\n* GpuMatTraitMutable methods for core::GpuMat\n* GpuMatTraitConstConstant methods for core::GpuMat\n* GpuMat_AllocatorTraitMutable methods for core::GpuMat_Allocator\n* GpuMat_AllocatorTraitConstConstant methods for core::GpuMat_Allocator\n* HammingTraitMutable methods for core::Hamming\n* HammingTraitConstConstant methods for core::Hamming\n* HostMemTraitMutable methods for core::HostMem\n* HostMemTraitConstConstant methods for core::HostMem\n* Image2DTraitMutable methods for core::Image2D\n* Image2DTraitConstConstant methods for core::Image2D\n* KernelArgTraitMutable methods for core::KernelArg\n* KernelArgTraitConstConstant methods for core::KernelArg\n* KernelTraitMutable methods for core::Kernel\n* KernelTraitConstConstant methods for core::Kernel\n* KeyPointTraitMutable methods for core::KeyPoint\n* KeyPointTraitConstConstant methods for core::KeyPoint\n* LDATraitMutable methods for core::LDA\n* LDATraitConstConstant methods for core::LDA\n* LogTagTraitMutable methods for core::LogTag\n* LogTagTraitConstConstant methods for core::LogTag\n* MatConstIteratorTraitMutable methods for core::MatConstIterator\n* MatConstIteratorTraitConstConstant methods for core::MatConstIterator\n* MatConstIteratorTraitManual\n* MatExprTraitMutable methods for core::MatExpr\n* MatExprTraitConstConstant methods for core::MatExpr\n* MatOpTraitMutable methods for core::MatOp\n* MatOpTraitConstConstant methods for core::MatOp\n* MatSizeTraitMutable methods for core::MatSize\n* MatSizeTraitConstConstant methods for core::MatSize\n* MatStepTraitMutable methods for core::MatStep\n* MatStepTraitConstConstant methods for core::MatStep\n* MatTraitMutable methods for core::Mat\n* MatTraitConstConstant methods for core::Mat\n* MatTraitConstManual\n* MatTraitManual\n* MatxTrait\n* Matx_AddOpTraitMutable methods for core::Matx_AddOp\n* Matx_AddOpTraitConstConstant methods for core::Matx_AddOp\n* Matx_DivOpTraitMutable methods for core::Matx_DivOp\n* Matx_DivOpTraitConstConstant methods for core::Matx_DivOp\n* Matx_MatMulOpTraitMutable methods for core::Matx_MatMulOp\n* Matx_MatMulOpTraitConstConstant methods for core::Matx_MatMulOp\n* Matx_MulOpTraitMutable methods for core::Matx_MulOp\n* Matx_MulOpTraitConstConstant methods for core::Matx_MulOp\n* Matx_ScaleOpTraitMutable methods for core::Matx_ScaleOp\n* Matx_ScaleOpTraitConstConstant methods for core::Matx_ScaleOp\n* Matx_SubOpTraitMutable methods for core::Matx_SubOp\n* Matx_SubOpTraitConstConstant methods for core::Matx_SubOp\n* Matx_TOpTraitMutable methods for core::Matx_TOp\n* Matx_TOpTraitConstConstant methods for core::Matx_TOp\n* MinProblemSolverTraitMutable methods for core::MinProblemSolver\n* MinProblemSolverTraitConstConstant methods for core::MinProblemSolver\n* MinProblemSolver_FunctionTraitMutable methods for core::MinProblemSolver_Function\n* MinProblemSolver_FunctionTraitConstConstant methods for core::MinProblemSolver_Function\n* NodeDataTraitMutable methods for core::NodeData\n* NodeDataTraitConstConstant methods for core::NodeData\n* OpenCLExecutionContextTraitMutable methods for core::OpenCLExecutionContext\n* OpenCLExecutionContextTraitConstConstant methods for core::OpenCLExecutionContext\n* OriginalClassNameTraitMutable methods for core::OriginalClassName\n* OriginalClassNameTraitConstConstant methods for core::OriginalClassName\n* PCATraitMutable methods for core::PCA\n* PCATraitConstConstant methods for core::PCA\n* ParallelLoopBodyTraitMutable methods for core::ParallelLoopBody\n* ParallelLoopBodyTraitConstConstant methods for core::ParallelLoopBody\n* PlatformInfoTraitMutable methods for core::PlatformInfo\n* PlatformInfoTraitConstConstant methods for core::PlatformInfo\n* PlatformTraitMutable methods for core::Platform\n* PlatformTraitConstConstant methods for core::Platform\n* ProgramSourceTraitMutable methods for core::ProgramSource\n* ProgramSourceTraitConstConstant methods for core::ProgramSource\n* ProgramTraitMutable methods for core::Program\n* ProgramTraitConstConstant methods for core::Program\n* QueueTraitMutable methods for core::Queue\n* QueueTraitConstConstant methods for core::Queue\n* RNGTraitMutable methods for core::RNG\n* RNGTraitConstConstant methods for core::RNG\n* RNG_MT19937TraitMutable methods for core::RNG_MT19937\n* RNG_MT19937TraitConstConstant methods for core::RNG_MT19937\n* RangeTraitMutable methods for core::Range\n* RangeTraitConstConstant methods for core::Range\n* SVDTraitMutable methods for core::SVD\n* SVDTraitConstConstant methods for core::SVD\n* SizedArray\n* SparseMatConstIteratorTraitMutable methods for core::SparseMatConstIterator\n* SparseMatConstIteratorTraitConstConstant methods for core::SparseMatConstIterator\n* SparseMatIteratorTraitMutable methods for core::SparseMatIterator\n* SparseMatIteratorTraitConstConstant methods for core::SparseMatIterator\n* SparseMatTraitMutable methods for core::SparseMat\n* SparseMatTraitConstConstant methods for core::SparseMat\n* SparseMat_HdrTraitMutable methods for core::SparseMat_Hdr\n* SparseMat_HdrTraitConstConstant methods for core::SparseMat_Hdr\n* SparseMat_NodeTraitMutable methods for core::SparseMat_Node\n* SparseMat_NodeTraitConstConstant methods for core::SparseMat_Node\n* StreamTraitMutable methods for core::Stream\n* StreamTraitConstConstant methods for core::Stream\n* TargetArchsTraitMutable methods for core::TargetArchs\n* TargetArchsTraitConstConstant methods for core::TargetArchs\n* Texture2DTraitMutable methods for core::Texture2D\n* Texture2DTraitConstConstant methods for core::Texture2D\n* TickMeterTraitMutable methods for core::TickMeter\n* TickMeterTraitConstConstant methods for core::TickMeter\n* TimerTraitMutable methods for core::Timer\n* TimerTraitConstConstant methods for core::Timer\n* ToInputArrayTrait to serve as a replacement for `InputArray` in C++ OpenCV\n* ToInputOutputArrayTrait to serve as a replacement for `InputOutputArray` in C++ OpenCV\n* ToOutputArrayTrait to serve as a replacement for `OutputArray` in C++ OpenCV\n* TupleExtern\n* UMatDataTraitMutable methods for core::UMatData\n* UMatDataTraitConstConstant methods for core::UMatData\n* UMatTraitMutable methods for core::UMat\n* UMatTraitConstConstant methods for core::UMat\n* VectorElementThis trait is implemented by any type that can be stored inside `Vector`.\n* WriteStructContextTraitMutable methods for core::WriteStructContext\n* WriteStructContextTraitConstConstant methods for core::WriteStructContext\n* _InputArrayTraitMutable methods for core::_InputArray\n* _InputArrayTraitConstConstant methods for core::_InputArray\n* _InputOutputArrayTraitMutable methods for core::_InputOutputArray\n* _InputOutputArrayTraitConstConstant methods for core::_InputOutputArray\n* _OutputArrayTraitMutable methods for core::_OutputArray\n* _OutputArrayTraitConstConstant methods for core::_OutputArray\n\nFunctions\n---\n\n* CV_MAKETYPE\n* CV_MAKE_TYPE\n* CV_MAT_DEPTH\n* absCalculates an absolute value of each matrix element.\n* abs_matexprCalculates an absolute value of each matrix element.\n* absdiffCalculates the per-element absolute difference between two arrays or between an array and a scalar.\n* addCalculates the per-element sum of two arrays or an array and a scalar.\n* add_defCalculates the per-element sum of two arrays or an array and a scalar.\n* add_mat_mat@relates cv::MatExpr\n* add_mat_matexpr\n* add_mat_scalar\n* add_matexpr_mat\n* add_matexpr_matexpr\n* add_matexpr_scalar\n* add_samples_data_search_pathOverride search data path by adding new search location\n* add_samples_data_search_sub_directoryAppend samples search data sub directory\n* add_scalar_mat\n* add_scalar_matexpr\n* add_weightedCalculates the weighted sum of two arrays.\n* add_weighted_defCalculates the weighted sum of two arrays.\n* and_mat_mat\n* and_mat_scalar\n* and_scalar_mat\n* attach_context⚠Attaches OpenCL context to OpenCV\n* batch_distancenaive nearest neighbor finder\n* batch_distance_defnaive nearest neighbor finder\n* bitwise_andcomputes bitwise conjunction of the two arrays (dst = src1 & src2)\nCalculates the per-element bit-wise conjunction of two arrays or an array and a scalar.\n* bitwise_and_defcomputes bitwise conjunction of the two arrays (dst = src1 & src2)\nCalculates the per-element bit-wise conjunction of two arrays or an array and a scalar.\n* bitwise_notInverts every bit of an array.\n* bitwise_not_defInverts every bit of an array.\n* bitwise_orCalculates the per-element bit-wise disjunction of two arrays or an array and a scalar.\n* bitwise_or_defCalculates the per-element bit-wise disjunction of two arrays or an array and a scalar.\n* bitwise_xorCalculates the per-element bit-wise “exclusive or” operation on two arrays or an array and a scalar.\n* bitwise_xor_defCalculates the per-element bit-wise “exclusive or” operation on two arrays or an array and a scalar.\n* border_interpolateComputes the source location of an extrapolated pixel.\n* build_options_add_matrix_description\n* calc_covar_matrixCalculates the covariance matrix of a set of vectors.\n* calc_covar_matrix_def@overload\n* cart_to_polarCalculates the magnitude and angle of 2D vectors.\n* cart_to_polar_defCalculates the magnitude and angle of 2D vectors.\n* check_failed_auto\n* check_failed_auto_1\n* check_failed_auto_2\n* check_failed_auto_3\n* check_failed_auto_4\n* check_failed_auto_5\n* check_failed_auto_6\n* check_failed_auto_7\n* check_failed_auto_8\n* check_failed_auto_9\n* check_failed_auto_10\n* check_failed_auto_11\n* check_failed_false\n* check_failed_mat_channels\n* check_failed_mat_channels_1\n* check_failed_mat_depth\n* check_failed_mat_depth_1\n* check_failed_mat_type\n* check_failed_mat_type_1\n* check_failed_true\n* check_hardware_supportReturns true if the specified feature is supported by the host hardware.\n* check_optimal_vector_widthC++ default parameters\n* check_optimal_vector_width_defNote\n* check_rangeChecks every element of an input array for invalid values.\n* check_range_defChecks every element of an input array for invalid values.\n* choleskyproxy for hal::Cholesky\n* cholesky_f32proxy for hal::Cholesky\n* comparePerforms the per-element comparison of two arrays or an array and scalar value.\n* complete_symmCopies the lower or the upper half of a square matrix to its another half.\n* complete_symm_defCopies the lower or the upper half of a square matrix to its another half.\n* convert_fp16Converts an array to half precision floating number.\n* convert_from_buffer⚠Convert OpenCL buffer to UMat\n* convert_from_gl_texture_2dConverts Texture2D object to OutputArray.\n* convert_from_image⚠Convert OpenCL image2d_t to UMat\n* convert_from_va_surface⚠Converts VASurfaceID object to OutputArray.\n* convert_scale_absScales, calculates absolute values, and converts the result to 8-bit.\n* convert_scale_abs_defScales, calculates absolute values, and converts the result to 8-bit.\n* convert_to_gl_texture_2dConverts InputArray to Texture2D object.\n* convert_to_va_surface⚠Converts InputArray to VASurfaceID object.\n* convert_type_str\n* convert_type_str_1\n* copy_make_borderForms a border around an image.\n* copy_make_border_defForms a border around an image.\n* copy_mat_and_dump_named_argumentsC++ default parameters\n* copy_mat_and_dump_named_arguments_defNote\n* copy_toThis is an overloaded member function, provided for convenience (python)\nCopies the matrix to another one.\nWhen the operation mask is specified, if the Mat::create call shown above reallocates the matrix, the newly allocated matrix is initialized with all zeros before copying the data.\n* count_non_zeroCounts non-zero array elements.\n* create_continuousCreates a continuous matrix.\n* create_gpu_mat_from_cuda_memoryBindings overload to create a GpuMat from existing GPU memory.\n* create_gpu_mat_from_cuda_memory_1Bindings overload to create a GpuMat from existing GPU memory.\n* create_gpu_mat_from_cuda_memory_1_def@overload\n* create_gpu_mat_from_cuda_memory_defBindings overload to create a GpuMat from existing GPU memory.\n* cube_rootComputes the cube root of an argument.\n* dctPerforms a forward or inverse discrete Cosine transform of 1D or 2D array.\n* dct_defPerforms a forward or inverse discrete Cosine transform of 1D or 2D array.\n* depth_to_stringReturns string of cv::Mat depth value: CV_8U -> “CV_8U” or “”\n* determinantReturns the determinant of a square floating-point matrix.\n* device_supportschecks whether current device supports the given feature\n* dftPerforms a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.\n* dft_defPerforms a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.\n* div_f64_mat\n* div_f64_matexpr\n* div_mat_f64\n* div_mat_mat\n* div_mat_matexpr\n* div_matexpr_f64\n* div_matexpr_mat\n* div_matexpr_matexpr\n* dividePerforms per-element division of two arrays or a scalar by an array.\n* divide2Performs per-element division of two arrays or a scalar by an array.\n* divide2_defPerforms per-element division of two arrays or a scalar by an array.\n* divide_def@overload\n* dump_bool\n* dump_c_string\n* dump_double\n* dump_float\n* dump_input_array\n* dump_input_array_of_arrays\n* dump_input_output_array\n* dump_input_output_array_of_arrays\n* dump_int\n* dump_int64\n* dump_range\n* dump_rect\n* dump_rotated_rect\n* dump_size_t\n* dump_string\n* dump_term_criteria\n* dump_vec2iC++ default parameters\n* dump_vec2i_defNote\n* dump_vector_of_double\n* dump_vector_of_int\n* dump_vector_of_rect\n* eigenCalculates eigenvalues and eigenvectors of a symmetric matrix.\n* eigen_defCalculates eigenvalues and eigenvectors of a symmetric matrix.\n* eigen_non_symmetricCalculates eigenvalues and eigenvectors of a non-symmetric matrix (real eigenvalues only).\n* ensure_size_is_enoughEnsures that the size of a matrix is big enough and the matrix has a proper type.\n* equals_f64_mat\n* equals_filenodeiterator_filenodeiterator@relates cv::FileNodeIterator\n* equals_mat_f64\n* equals_mat_mat\n* error! Signals an error and raises the exception.\n* error_1Deprecated! Signals an error and raises the exception.\n* expCalculates the exponent of every array element.\n* extract_channelExtracts a single channel from src (coi is 0-based index)\n* fast_atan2Calculates the angle of a 2D vector in degrees.\n* find_fileTry to find requested data file\n* find_file_defTry to find requested data file\n* find_file_or_keepC++ default parameters\n* find_file_or_keep_defNote\n* find_non_zeroReturns the list of locations of non-zero pixels\n* finish\n* flipFlips a 2D array around vertical, horizontal, or both axes.\n* flip_ndFlips a n-dimensional at given axis\n* gemmPerforms generalized matrix multiplication.\n* gemm_defPerforms generalized matrix multiplication.\n* generate_vector_of_int\n* generate_vector_of_mat\n* generate_vector_of_rect\n* get_build_informationReturns full configuration time cmake output.\n* get_cache_directory_for_downloads\n* get_cpu_features_lineReturns list of CPU features enabled during compilation.\n* get_cpu_tick_countReturns the number of CPU ticks.\n* get_cuda_enabled_device_countReturns the number of installed CUDA-enabled devices.\n* get_deviceReturns the current device index set by cuda::setDevice or initialized by default.\n* get_elem_size\n* get_flags\n* get_global_log_tagGet global log tag\n* get_hardware_feature_nameReturns feature name by ID\n* get_ipp_error_location\n* get_ipp_features\n* get_ipp_status\n* get_ipp_version\n* get_log_levelGet global logging level\n* get_log_level_1\n* get_log_tag_level\n* get_num_threadsReturns the number of threads used by OpenCV for parallel regions.\n* get_number_of_cpusReturns the number of logical CPUs available for the process.\n* get_opencl_error_string\n* get_optimal_dft_sizeReturns the optimal DFT size for a given vector size.\n* get_platfoms_info\n* get_thread_id\n* get_thread_numDeprecatedReturns the index of the currently executed thread within the current parallel region. Always returns 0 if called outside of parallel region.\n* get_tick_countReturns the number of ticks.\n* get_tick_frequencyReturns the number of ticks per second.\n* get_type_from_d3d_formatGet OpenCV type from DirectX type\n* get_type_from_dxgi_formatGet OpenCV type from DirectX type\n* get_version_majorReturns major library version\n* get_version_minorReturns minor library version\n* get_version_revisionReturns revision field of the library version\n* get_version_stringReturns library version string\n* globC++ default parameters\n* glob_defNote\n* greater_than_f64_mat\n* greater_than_mat_f64\n* greater_than_mat_mat\n* greater_than_or_equal_f64_mat\n* greater_than_or_equal_mat_f64\n* greater_than_or_equal_mat_mat\n* has_non_zeroChecks for the presence of at least one non-zero array element.\n* have_amd_blas\n* have_amd_fft\n* have_opencl\n* have_openvxCheck if use of OpenVX is possible\n* have_svm\n* hconcatApplies horizontal concatenation to given matrices.\n* hconcat2Applies horizontal concatenation to given matrices.\n* idctCalculates the inverse Discrete Cosine Transform of a 1D or 2D array.\n* idct_defCalculates the inverse Discrete Cosine Transform of a 1D or 2D array.\n* idftCalculates the inverse Discrete Fourier Transform of a 1D or 2D array.\n* idft_defCalculates the inverse Discrete Fourier Transform of a 1D or 2D array.\n* in_rangeChecks if array elements lie between the elements of two other arrays.\n* initialize_context_from_glCreates OpenCL context from GL.\n* initialize_context_from_va⚠Creates OpenCL context from VA.\n* initialize_context_from_va_def⚠Creates OpenCL context from VA.\n* insert_channelInserts a single channel to dst (coi is 0-based index)\n* invertFinds the inverse or pseudo-inverse of a matrix.\n* invert_defFinds the inverse or pseudo-inverse of a matrix.\n* kernel_to_strC++ default parameters\n* kernel_to_str_defNote\n* kmeansFinds centers of clusters and groups input samples around the clusters.\n* kmeans_defFinds centers of clusters and groups input samples around the clusters.\n* less_than_f64_mat\n* less_than_mat_f64\n* less_than_mat_mat\n* less_than_or_equal_f64_mat\n* less_than_or_equal_mat_f64\n* less_than_or_equal_mat_mat\n* logCalculates the natural logarithm of every array element.\n* luproxy for hal::LU\n* lu_f32proxy for hal::LU\n* lutPerforms a look-up table transform of an array.\n* magnitudeCalculates the magnitude of 2D vectors.\n* mahalanobisCalculates the Mahalanobis distance between two vectors.\n* map_gl_bufferMaps Buffer object to process on CL side (convert to UMat).\n* map_gl_buffer_defMaps Buffer object to process on CL side (convert to UMat).\n* maxCalculates per-element maximum of two arrays or an array and a scalar.\n* max_f64_mat\n* max_mat\n* max_mat_f64\n* max_mat_toCalculates per-element maximum of two arrays or an array and a scalar.\n* max_umat_toCalculates per-element maximum of two arrays or an array and a scalar.\n* meanCalculates an average (mean) of array elements.\n* mean_defCalculates an average (mean) of array elements.\n* mean_std_devCalculates a mean and standard deviation of array elements.\n* mean_std_dev_defCalculates a mean and standard deviation of array elements.\n* memop_type_to_str\n* mergeCreates one multi-channel array out of several single-channel ones.\n* minCalculates per-element minimum of two arrays or an array and a scalar.\n* min_f64_mat\n* min_mat\n* min_mat_f64\n* min_mat_toCalculates per-element minimum of two arrays or an array and a scalar.\n* min_max_idxFinds the global minimum and maximum in an array\n* min_max_idx_defFinds the global minimum and maximum in an array\n* min_max_locFinds the global minimum and maximum in an array.\n* min_max_loc_defFinds the global minimum and maximum in an array.\n* min_max_loc_sparseFinds the global minimum and maximum in an array.\n* min_max_loc_sparse_def@overload\n* min_umat_toCalculates per-element minimum of two arrays or an array and a scalar.\n* mix_channelsCopies specified channels from input arrays to the specified channels of output arrays.\n* mix_channels_vecCopies specified channels from input arrays to the specified channels of output arrays.\n* mul_f64_mat\n* mul_f64_matexpr\n* mul_mat_f64\n* mul_mat_mat\n* mul_mat_matexpr\n* mul_matexpr_f64\n* mul_matexpr_mat\n* mul_matexpr_matexpr\n* mul_spectrumsPerforms the per-element multiplication of two Fourier spectrums.\n* mul_spectrums_defPerforms the per-element multiplication of two Fourier spectrums.\n* mul_transposedCalculates the product of a matrix and its transposition.\n* mul_transposed_defCalculates the product of a matrix and its transposition.\n* multiplyCalculates the per-element scaled product of two arrays.\n* multiply_defCalculates the per-element scaled product of two arrays.\n* negate\n* no_array\n* normCalculates the absolute norm of an array.\n* norm2Calculates an absolute difference norm or a relative difference norm.\n* norm2_defCalculates an absolute difference norm or a relative difference norm.\n* norm_defCalculates the absolute norm of an array.\n* norm_sparseCalculates an absolute difference norm or a relative difference norm.\n* normalizeNormalizes the norm or value range of an array.\n* normalize_defNormalizes the norm or value range of an array.\n* normalize_sparseNormalizes the norm or value range of an array.\n* not_equals_f64_mat\n* not_equals_filenodeiterator_filenodeiterator\n* not_equals_mat_f64\n* not_equals_mat_mat\n* or_mat_mat\n* or_mat_scalar\n* or_scalar_mat\n* parallel_for_Parallel data processor\n* parallel_for__defParallel data processor\n* patch_na_nsconverts NaNs to the given number\n* patch_na_ns_defconverts NaNs to the given number\n* pca_back_projectwrap PCA::backProject\n* pca_computewrap PCA::operator()\n* pca_compute2wrap PCA::operator() and add eigenvalues output parameter\n* pca_compute2_defwrap PCA::operator() and add eigenvalues output parameter\n* pca_compute2_variancewrap PCA::operator() and add eigenvalues output parameter\n* pca_compute_defwrap PCA::operator()\n* pca_compute_variancewrap PCA::operator()\n* pca_projectwrap PCA::project\n* perspective_transformPerforms the perspective matrix transformation of vectors.\n* phaseCalculates the rotation angle of 2D vectors.\n* phase_defCalculates the rotation angle of 2D vectors.\n* polar_to_cartCalculates x and y coordinates of 2D vectors from their magnitude and angle.\n* polar_to_cart_defCalculates x and y coordinates of 2D vectors from their magnitude and angle.\n* powRaises every array element to a power.\n* predict_optimal_vector_widthC++ default parameters\n* predict_optimal_vector_width_defNote\n* predict_optimal_vector_width_maxC++ default parameters\n* predict_optimal_vector_width_max_defNote\n* print_cuda_device_info\n* print_short_cuda_device_info\n* psnrComputes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.\n* psnr_defComputes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.\n* rand_shuffleShuffles the array elements randomly.\n* rand_shuffle_defShuffles the array elements randomly.\n* randnFills the array with normally distributed random numbers.\n* randuGenerates a single uniformly-distributed random number or an array of random numbers.\n* read_dmatch\n* read_dmatch_vec_legacy\n* read_f32\n* read_f64\n* read_i32@relates cv::FileNode\n* read_keypoint\n* read_keypoint_vec_legacy\n* read_matC++ default parameters\n* read_mat_defNote\n* read_sparsematC++ default parameters\n* read_sparsemat_defNote\n* read_str\n* rectangle_intersection_areaFinds out if there is any intersection between two rectangles\n* reduceReduces a matrix to a vector.\n* reduce_arg_maxFinds indices of max elements along provided axis\n* reduce_arg_max_defFinds indices of max elements along provided axis\n* reduce_arg_minFinds indices of min elements along provided axis\n* reduce_arg_min_defFinds indices of min elements along provided axis\n* reduce_defReduces a matrix to a vector.\n* register_log_tag\n* register_page_lockedPage-locks the memory of matrix and maps it for the device(s).\n* renderRender OpenGL texture or primitives.\n* render_1Render OpenGL texture or primitives.\n* render_1_def@overload\n* render_2Render OpenGL texture or primitives.\n* render_2_def@overload\n* render_defRender OpenGL texture or primitives.\n* repeatFills the output array with repeated copies of the input array.\n* repeat_toFills the output array with repeated copies of the input array.\n* reset_deviceExplicitly destroys and cleans up all resources associated with the current device in the current process.\n* reset_trace\n* rotateRotates a 2D array in multiples of 90 degrees.\nThe function cv::rotate rotates the array in one of three different ways:\n* scale_addCalculates the sum of a scaled array and another array.\n* set_break_on_errorSets/resets the break-on-error mode.\n* set_buffer_pool_config\n* set_buffer_pool_usageBufferPool management (must be called before Stream creation)\n* set_deviceSets a device and initializes it for the current thread.\n* set_flags\n* set_gl_deviceSets a CUDA device and initializes it for the current thread with OpenGL interoperability.\n* set_gl_device_defSets a CUDA device and initializes it for the current thread with OpenGL interoperability.\n* set_identityInitializes a scaled identity matrix.\n* set_identity_defInitializes a scaled identity matrix.\n* set_ipp_statusC++ default parameters\n* set_ipp_status_defNote\n* set_log_levelSet global logging level\n* set_log_level_1@cond IGNORED\n* set_log_tag_level\n* set_num_threadsOpenCV will try to set the number of threads for subsequent parallel regions.\n* set_rng_seedSets state of default random number generator.\n* set_use_instrumentation\n* set_use_ipp\n* set_use_ipp_not_exact\n* set_use_opencl\n* set_use_openvxEnable/disable use of OpenVX\n* set_use_optimizedEnables or disables the optimized code.\n* solveSolves one or more linear systems or least-squares problems.\n* solve_cubicFinds the real roots of a cubic equation.\n* solve_defSolves one or more linear systems or least-squares problems.\n* solve_lpSolve given (non-integer) linear programming problem using the Simplex Algorithm (Simplex Method).\n* solve_lp_1Solve given (non-integer) linear programming problem using the Simplex Algorithm (Simplex Method).\n* solve_polyFinds the real or complex roots of a polynomial equation.\n* solve_poly_defFinds the real or complex roots of a polynomial equation.\n* sortSorts each row or each column of a matrix.\n* sort_idxSorts each row or each column of a matrix.\n* splitDivides a multi-channel array into several single-channel arrays.\n* split_sliceDivides a multi-channel array into several single-channel arrays.\n* sqrtCalculates a square root of array elements.\n* sub_mat\n* sub_mat_mat\n* sub_mat_matexpr\n* sub_mat_scalar\n* sub_matexpr\n* sub_matexpr_mat\n* sub_matexpr_matexpr\n* sub_matexpr_scalar\n* sub_scalar_mat\n* sub_scalar_matexpr\n* subtractCalculates the per-element difference between two arrays or array and a scalar.\n* subtract_defCalculates the per-element difference between two arrays or array and a scalar.\n* sum_elemsCalculates the sum of array elements.\n* sv_back_substwrap SVD::backSubst\n* sv_decompwrap SVD::compute\n* sv_decomp_defwrap SVD::compute\n* swapSwaps two matrices\n* swap_umatSwaps two matrices\n* tempfileC++ default parameters\n* tempfile_defNote\n* test_async_array\n* test_async_exception\n* test_echo_boolean_function\n* test_overload_resolutionC++ default parameters\n* test_overload_resolution_1\n* test_overload_resolution_defNote\n* test_overwrite_native_method\n* test_raise_general_exception\n* test_reserved_keyword_conversionC++ default parameters\n* test_reserved_keyword_conversion_defNote\n* test_rotated_rect\n* test_rotated_rect_vector\n* the_rngReturns the default random number generator.\n* traceReturns the trace of a matrix.\n* transformPerforms the matrix transformation of every array element.\n* transposeTransposes a matrix.\n* transpose_ndTranspose for n-dimensional matrices.\n* type_to_str\n* type_to_stringReturns string of cv::Mat depth value: CV_8UC3 -> “CV_8UC3” or “”\n* unmap_gl_bufferUnmaps Buffer object (releases UMat, previously mapped from Buffer).\n* unregister_page_lockedUnmaps the memory of matrix and makes it pageable again.\n* use_instrumentation\n* use_ipp\n* use_ipp_not_exact\n* use_opencl\n* use_openvxCheck if use of OpenVX is enabled\n* use_optimizedReturns the status of optimized code usage.\n* vconcatApplies vertical concatenation to given matrices.\n* vconcat2Applies vertical concatenation to given matrices.\n* vecop_type_to_str\n* wrap_streamBindings overload to create a Stream object from the address stored in an existing CUDA Runtime API stream pointer (cudaStream_t).\n* write_dmatch_vec\n* write_f32\n* write_f64\n* write_i32@relates cv::FileStorage\n* write_keypoint_vec\n* write_log_messageWrite log message\n* write_log_message_exWrite log message\n* write_mat\n* write_scalar_f32\n* write_scalar_f64\n* write_scalar_i32\n* write_scalar_str\n* write_sparsemat\n* write_str\n* xor_mat_mat\n* xor_mat_scalar\n* xor_scalar_mat\n\nType Aliases\n---\n\n* Affine3d\n* Affine3f\n* GpuMatND_IndexArray\n* GpuMatND_SizeArray\n* GpuMatND_StepArray\n* HammingLUT\n* Hamming_result_type\n* Hamming_value_type\n* InputArray\n* InputArrayOfArrays\n* InputOutputArray\n* InputOutputArrayOfArrays\n* Mat1b\n* Mat1d\n* Mat1f\n* Mat1i\n* Mat1s\n* Mat1w\n* Mat2b\n* Mat2d\n* Mat2f\n* Mat2i\n* Mat2s\n* Mat2w\n* Mat3b\n* Mat3d\n* Mat3f\n* Mat3i\n* Mat3s\n* Mat3w\n* Mat4b\n* Mat4d\n* Mat4f\n* Mat4i\n* Mat4s\n* Mat4w\n* MatConstIterator_difference_type\n* MatConstIterator_pointer\n* MatConstIterator_reference\n* MatConstIterator_value_type\n* MatND\n* Matx12\n* Matx12d\n* Matx12f\n* Matx13\n* Matx13d\n* Matx13f\n* Matx14\n* Matx14d\n* Matx14f\n* Matx16\n* Matx16d\n* Matx16f\n* Matx21\n* Matx21d\n* Matx21f\n* Matx22\n* Matx22d\n* Matx22f\n* Matx23\n* Matx23d\n* Matx23f\n* Matx31\n* Matx31d\n* Matx31f\n* Matx32\n* Matx32d\n* Matx32f\n* Matx33\n* Matx33d\n* Matx33f\n* Matx34\n* Matx34d\n* Matx34f\n* Matx41\n* Matx41d\n* Matx41f\n* Matx43\n* Matx43d\n* Matx43f\n* Matx44\n* Matx44d\n* Matx44f\n* Matx61\n* Matx61d\n* Matx61f\n* Matx66\n* Matx66d\n* Matx66f\n* OutputArray\n* OutputArrayOfArrays\n* Point\n* Point2d\n* Point2f\n* Point2i\n* Point2l\n* Point3d\n* Point3f\n* Point3i\n* ProgramSource_hash_t\n* Rect\n* Rect2d\n* Rect2f\n* Rect2i\n* Scalar\n* Scalar_docs.opencv.org\n* Size\n* Size2d\n* Size2f\n* Size2i\n* Size2l\n* SparseMat_const_iterator\n* SparseMat_iterator\n* Stream_StreamCallback\n* Vec2bShorter aliases for the most popular specializations of Vec<T,n>\n* Vec2d\n* Vec2f\n* Vec2i\n* Vec2s\n* Vec2w\n* Vec3b\n* Vec3d\n* Vec3f\n* Vec3i\n* Vec3s\n* Vec3w\n* Vec4b\n* Vec4d\n* Vec4f\n* Vec4i\n* Vec4s\n* Vec4w\n* Vec6d\n* Vec6f\n* Vec6i\n* Vec8i\n* va_display\n* va_surface_id\n\nModule opencv::cudaarithm\n===\n\nOperations on Matrices\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ConvolutionBase class for convolution (or cross-correlation) operator. :\n* DFTBase class for DFT operator as a cv::Algorithm. :\n* LookUpTableBase class for transform using lookup table.\n\nTraits\n---\n\n* ConvolutionTraitMutable methods for crate::cudaarithm::Convolution\n* ConvolutionTraitConstConstant methods for crate::cudaarithm::Convolution\n* DFTTraitMutable methods for crate::cudaarithm::DFT\n* DFTTraitConstConstant methods for crate::cudaarithm::DFT\n* LookUpTableTraitMutable methods for crate::cudaarithm::LookUpTable\n* LookUpTableTraitConstConstant methods for crate::cudaarithm::LookUpTable\n\nFunctions\n---\n\n* absComputes an absolute value of each matrix element.\n* abs_defComputes an absolute value of each matrix element.\n* abs_sumReturns the sum of absolute values for matrix elements.\n* abs_sum_defReturns the sum of absolute values for matrix elements.\n* absdiffComputes per-element absolute difference of two matrices (or of a matrix and scalar).\n* absdiff_defComputes per-element absolute difference of two matrices (or of a matrix and scalar).\n* addComputes a matrix-matrix or matrix-scalar sum.\n* add_defComputes a matrix-matrix or matrix-scalar sum.\n* add_weightedComputes the weighted sum of two arrays.\n* add_weighted_defComputes the weighted sum of two arrays.\n* bitwise_andPerforms a per-element bitwise conjunction of two matrices (or of matrix and scalar).\n* bitwise_and_defPerforms a per-element bitwise conjunction of two matrices (or of matrix and scalar).\n* bitwise_notPerforms a per-element bitwise inversion.\n* bitwise_not_defPerforms a per-element bitwise inversion.\n* bitwise_orPerforms a per-element bitwise disjunction of two matrices (or of matrix and scalar).\n* bitwise_or_defPerforms a per-element bitwise disjunction of two matrices (or of matrix and scalar).\n* bitwise_xorPerforms a per-element bitwise exclusive or operation of two matrices (or of matrix and scalar).\n* bitwise_xor_defPerforms a per-element bitwise exclusive or operation of two matrices (or of matrix and scalar).\n* calc_abs_sumThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* calc_abs_sum_def@overload\n* calc_normThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* calc_norm_def@overload\n* calc_norm_diffThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* calc_norm_diff_def@overload\n* calc_sqr_sumThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* calc_sqr_sum_def@overload\n* calc_sumThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* calc_sum_def@overload\n* cart_to_polarConverts Cartesian coordinates into polar.\n* cart_to_polar_defConverts Cartesian coordinates into polar.\n* compareCompares elements of two matrices (or of a matrix and scalar).\n* compare_defCompares elements of two matrices (or of a matrix and scalar).\n* copy_make_borderForms a border around an image.\n* copy_make_border_defForms a border around an image.\n* count_non_zeroCounts non-zero matrix elements.\n* count_non_zero_1Counts non-zero matrix elements.\n* count_non_zero_1_def@overload\n* create_convolutionCreates implementation for cuda::Convolution .\n* create_convolution_defCreates implementation for cuda::Convolution .\n* create_dftCreates implementation for cuda::DFT.\n* create_look_up_tableCreates implementation for cuda::LookUpTable .\n* dftPerforms a forward or inverse discrete Fourier transform (1D or 2D) of the floating point matrix.\n* dft_defPerforms a forward or inverse discrete Fourier transform (1D or 2D) of the floating point matrix.\n* divideComputes a matrix-matrix or matrix-scalar division.\n* divide_defComputes a matrix-matrix or matrix-scalar division.\n* expComputes an exponent of each matrix element.\n* exp_defComputes an exponent of each matrix element.\n* find_min_maxThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* find_min_max_def@overload\n* find_min_max_locThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* find_min_max_loc_def@overload\n* flipFlips a 2D matrix around vertical, horizontal, or both axes.\n* flip_defFlips a 2D matrix around vertical, horizontal, or both axes.\n* gemmPerforms generalized matrix multiplication.\n* gemm_defPerforms generalized matrix multiplication.\n* in_rangeChecks if array elements lie between two scalars.\n* in_range_defChecks if array elements lie between two scalars.\n* integralComputes an integral image.\n* integral_defComputes an integral image.\n* logComputes a natural logarithm of absolute value of each matrix element.\n* log_defComputes a natural logarithm of absolute value of each matrix element.\n* lshiftPerforms pixel by pixel right left of an image by a constant value.\n* lshift_1C++ default parameters\n* lshift_1_defNote\n* lshift_defPerforms pixel by pixel right left of an image by a constant value.\n* magnitudeComputes magnitudes of complex matrix elements.\n* magnitude_1Computes magnitudes of complex matrix elements.\n* magnitude_1_def@overload computes magnitude of each (x(i), y(i)) vector supports only floating-point source\n* magnitude_defComputes magnitudes of complex matrix elements.\n* magnitude_sqrComputes squared magnitudes of complex matrix elements.\n* magnitude_sqr_1Computes squared magnitudes of complex matrix elements.\n* magnitude_sqr_1_def@overload computes squared magnitude of each (x(i), y(i)) vector supports only floating-point source\n* magnitude_sqr_defComputes squared magnitudes of complex matrix elements.\n* maxComputes the per-element maximum of two matrices (or a matrix and a scalar).\n* max_defComputes the per-element maximum of two matrices (or a matrix and a scalar).\n* mean_std_devComputes a mean value and a standard deviation of matrix elements.\n* mean_std_dev_1Computes a mean value and a standard deviation of matrix elements.\n* mean_std_dev_1_def@overload\n* mean_std_dev_2Computes a mean value and a standard deviation of matrix elements.\n* mean_std_dev_3Computes a mean value and a standard deviation of matrix elements.\n* mean_std_dev_defComputes a mean value and a standard deviation of matrix elements.\n* mergeMakes a multi-channel matrix out of several single-channel matrices.\n* merge_1Makes a multi-channel matrix out of several single-channel matrices.\n* merge_1_def@overload\n* merge_defMakes a multi-channel matrix out of several single-channel matrices.\n* minComputes the per-element minimum of two matrices (or a matrix and a scalar).\n* min_defComputes the per-element minimum of two matrices (or a matrix and a scalar).\n* min_maxFinds global minimum and maximum matrix elements and returns their values.\n* min_max_defFinds global minimum and maximum matrix elements and returns their values.\n* min_max_locFinds global minimum and maximum matrix elements and returns their values with locations.\n* min_max_loc_defFinds global minimum and maximum matrix elements and returns their values with locations.\n* mul_and_scale_spectrumsPerforms a per-element multiplication of two Fourier spectrums and scales the result.\n* mul_and_scale_spectrums_defPerforms a per-element multiplication of two Fourier spectrums and scales the result.\n* mul_spectrumsPerforms a per-element multiplication of two Fourier spectrums.\n* mul_spectrums_defPerforms a per-element multiplication of two Fourier spectrums.\n* multiplyComputes a matrix-matrix or matrix-scalar per-element product.\n* multiply_defComputes a matrix-matrix or matrix-scalar per-element product.\n* normReturns the norm of a matrix (or difference of two matrices).\n* norm_1Returns the difference of two matrices.\n* norm_1_defReturns the difference of two matrices.\n* norm_defReturns the norm of a matrix (or difference of two matrices).\n* normalizeNormalizes the norm or value range of an array.\n* normalize_defNormalizes the norm or value range of an array.\n* phaseComputes polar angles of complex matrix elements.\n* phase_defComputes polar angles of complex matrix elements.\n* polar_to_cartConverts polar coordinates into Cartesian.\n* polar_to_cart_defConverts polar coordinates into Cartesian.\n* powRaises every matrix element to a power.\n* pow_defRaises every matrix element to a power.\n* rect_std_devComputes a standard deviation of integral images.\n* rect_std_dev_defComputes a standard deviation of integral images.\n* reduceReduces a matrix to a vector.\n* reduce_defReduces a matrix to a vector.\n* rshiftPerforms pixel by pixel right shift of an image by a constant value.\n* rshift_1C++ default parameters\n* rshift_1_defNote\n* rshift_defPerforms pixel by pixel right shift of an image by a constant value.\n* splitCopies each plane of a multi-channel matrix into an array.\n* split_1Copies each plane of a multi-channel matrix into an array.\n* split_1_def@overload\n* split_defCopies each plane of a multi-channel matrix into an array.\n* sqrComputes a square value of each matrix element.\n* sqr_defComputes a square value of each matrix element.\n* sqr_integralComputes a squared integral image.\n* sqr_integral_defComputes a squared integral image.\n* sqr_sumReturns the squared sum of matrix elements.\n* sqr_sum_defReturns the squared sum of matrix elements.\n* sqrtComputes a square root of each matrix element.\n* sqrt_defComputes a square root of each matrix element.\n* subtractComputes a matrix-matrix or matrix-scalar difference.\n* subtract_defComputes a matrix-matrix or matrix-scalar difference.\n* sumReturns the sum of matrix elements.\n* sum_defReturns the sum of matrix elements.\n* thresholdApplies a fixed-level threshold to each array element.\n* threshold_defApplies a fixed-level threshold to each array element.\n* transposeTransposes a matrix.\n* transpose_defTransposes a matrix.\n\nModule opencv::cudabgsegm\n===\n\nBackground Segmentation\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_BackgroundSubtractorMOGGaussian Mixture-based Background/Foreground Segmentation Algorithm.\n* CUDA_BackgroundSubtractorMOG2Gaussian Mixture-based Background/Foreground Segmentation Algorithm.\n\nTraits\n---\n\n* CUDA_BackgroundSubtractorMOG2TraitMutable methods for crate::cudabgsegm::CUDA_BackgroundSubtractorMOG2\n* CUDA_BackgroundSubtractorMOG2TraitConstConstant methods for crate::cudabgsegm::CUDA_BackgroundSubtractorMOG2\n* CUDA_BackgroundSubtractorMOGTraitMutable methods for crate::cudabgsegm::CUDA_BackgroundSubtractorMOG\n* CUDA_BackgroundSubtractorMOGTraitConstConstant methods for crate::cudabgsegm::CUDA_BackgroundSubtractorMOG\n\nFunctions\n---\n\n* create_background_subtractor_mogCreates mixture-of-gaussian background subtractor\n* create_background_subtractor_mog2Creates MOG2 Background Subtractor\n* create_background_subtractor_mog2_defCreates MOG2 Background Subtractor\n* create_background_subtractor_mog_defCreates mixture-of-gaussian background subtractor\n\nModule opencv::cudacodec\n===\n\nVideo Encoding/Decoding\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_EncodeQpQuantization Parameter for each type of frame when using ENC_PARAMS_RC_MODE::ENC_PARAMS_RC_CONSTQP.\n* CUDA_EncoderCallbackInterface for encoder callbacks.\n* CUDA_EncoderParamsDifferent parameters for CUDA video encoder.\n* CUDA_FormatInfoStruct providing information about video file format. :\n* CUDA_RawVideoSourceInterface for video demultiplexing. :\n* CUDA_VideoReaderVideo reader interface.\n* CUDA_VideoReaderInitParamsVideoReader initialization parameters\n* CUDA_VideoWriterVideo writer interface.\n\nEnums\n---\n\n* CUDA_ChromaFormatChroma formats supported by cudacodec::VideoReader.\n* CUDA_CodecVideo codecs supported by cudacodec::VideoReader and cudacodec::VideoWriter.\n* CUDA_ColorFormatColorFormat for the frame returned by VideoReader::nextFrame() and VideoReader::retrieve() or used to initialize a VideoWriter.\n* CUDA_DeinterlaceModeDeinterlacing mode used by decoder.\n* CUDA_EncodeMultiPassMulti Pass Encoding.\n* CUDA_EncodeParamsRcModeRate Control Modes.\n* CUDA_EncodePresetNvidia Encoding Presets. Performance degrades and quality improves as we move from P1 to P7.\n* CUDA_EncodeProfileSupported Encoder Profiles.\n* CUDA_EncodeTuningInfoTuning information.\n* CUDA_VideoReaderPropscv::cudacodec::VideoReader generic properties identifier.\n\nConstants\n---\n\n* CUDA_AV1\n* CUDA_Adaptive\n* CUDA_Bob\n* CUDA_ColorFormat_BGROpenCV color format, can be used with both VideoReader and VideoWriter.\n* CUDA_ColorFormat_BGRAOpenCV color format, can be used with both VideoReader and VideoWriter.\n* CUDA_ColorFormat_GRAYOpenCV color format, can be used with both VideoReader and VideoWriter.\n* CUDA_ColorFormat_NV_AYUVNvidia Buffer Format - 8 bit Packed A8Y8U8V8. This is a word-ordered format where a pixel is represented by a 32-bit word with V in the lowest 8 bits, U in the next 8 bits, Y in the 8 bits after that and A in the highest 8 bits, can only be used with VideoWriter.\n* CUDA_ColorFormat_NV_IYUVNvidia Buffer Format - Planar YUV [Y plane followed by U and V planes], use with VideoReader, can only be used with VideoWriter.\n* CUDA_ColorFormat_NV_NV12Nvidia color format - equivalent to YUV - Semi-Planar YUV [Y plane followed by interleaved UV plane], can be used with both VideoReader and VideoWriter.\n* CUDA_ColorFormat_NV_YUV444Nvidia Buffer Format - Planar YUV [Y plane followed by U and V planes], use with VideoReader, can only be used with VideoWriter.\n* CUDA_ColorFormat_NV_YV12Nvidia Buffer Format - Planar YUV [Y plane followed by V and U planes], use with VideoReader, can only be used with VideoWriter.\n* CUDA_ColorFormat_PROP_NOT_SUPPORTED\n* CUDA_ColorFormat_RGBOpenCV color format, can only be used with VideoWriter.\n* CUDA_ColorFormat_RGBAOpenCV color format, can only be used with VideoWriter.\n* CUDA_ColorFormat_UNDEFINED\n* CUDA_ENC_CODEC_PROFILE_AUTOSELECT\n* CUDA_ENC_H264_PROFILE_BASELINE\n* CUDA_ENC_H264_PROFILE_CONSTRAINED_HIGH\n* CUDA_ENC_H264_PROFILE_HIGH\n* CUDA_ENC_H264_PROFILE_HIGH_444\n* CUDA_ENC_H264_PROFILE_MAIN\n* CUDA_ENC_H264_PROFILE_PROGRESSIVE_HIGH\n* CUDA_ENC_H264_PROFILE_STEREO\n* CUDA_ENC_HEVC_PROFILE_FREXT\n* CUDA_ENC_HEVC_PROFILE_MAIN\n* CUDA_ENC_HEVC_PROFILE_MAIN10\n* CUDA_ENC_MULTI_PASS_DISABLEDSingle Pass.\n* CUDA_ENC_PARAMS_RC_CBRConstant bitrate mode.\n* CUDA_ENC_PARAMS_RC_CONSTQPConstant QP mode.\n* CUDA_ENC_PARAMS_RC_VBRVariable bitrate mode.\n* CUDA_ENC_PRESET_P1\n* CUDA_ENC_PRESET_P2\n* CUDA_ENC_PRESET_P3\n* CUDA_ENC_PRESET_P4\n* CUDA_ENC_PRESET_P5\n* CUDA_ENC_PRESET_P6\n* CUDA_ENC_PRESET_P7\n* CUDA_ENC_TUNING_INFO_COUNT\n* CUDA_ENC_TUNING_INFO_HIGH_QUALITYTune presets for latency tolerant encoding.\n* CUDA_ENC_TUNING_INFO_LOSSLESSTune presets for lossless encoding.\n* CUDA_ENC_TUNING_INFO_LOW_LATENCYTune presets for low latency streaming.\n* CUDA_ENC_TUNING_INFO_ULTRA_LOW_LATENCYTune presets for ultra low latency streaming.\n* CUDA_ENC_TUNING_INFO_UNDEFINEDUndefined tuningInfo. Invalid value for encoding.\n* CUDA_ENC_TWO_PASS_FULL_RESOLUTIONTwo Pass encoding is enabled where first Pass is full resolution.\n* CUDA_ENC_TWO_PASS_QUARTER_RESOLUTIONTwo Pass encoding is enabled where first Pass is quarter resolution.\n* CUDA_H264\n* CUDA_H264_MVC\n* CUDA_H264_SVC\n* CUDA_HEVC\n* CUDA_JPEG\n* CUDA_MPEG1\n* CUDA_MPEG2\n* CUDA_MPEG4\n* CUDA_Monochrome\n* CUDA_NumCodecs\n* CUDA_NumFormats\n* CUDA_Uncompressed_NV12Y,UV (4:2:0)\n* CUDA_Uncompressed_UYVYUYVY (4:2:2)\n* CUDA_Uncompressed_YUV420Y,U,V (4:2:0)\n* CUDA_Uncompressed_YUYVYUYV/YUY2 (4:2:2)\n* CUDA_Uncompressed_YV12Y,V,U (4:2:0)\n* CUDA_VC1\n* CUDA_VP8\n* CUDA_VP9\n* CUDA_VideoReaderProps_PROP_ALLOW_FRAME_DROPStatus of VideoReaderInitParams::allowFrameDrop initialization.\n* CUDA_VideoReaderProps_PROP_COLOR_FORMATSet the ColorFormat of the decoded frame. This can be changed before every call to nextFrame() and retrieve().\n* CUDA_VideoReaderProps_PROP_DECODED_FRAME_IDXIndex for retrieving the decoded frame using retrieve().\n* CUDA_VideoReaderProps_PROP_EXTRA_DATA_INDEXIndex for retrieving the extra data associated with a video source using retrieve().\n* CUDA_VideoReaderProps_PROP_LRF_HAS_KEY_FRAMEFFmpeg source only - Indicates whether the Last Raw Frame (LRF), output from VideoReader::retrieve() when VideoReader is initialized in raw mode, contains encoded data for a key frame.\n* CUDA_VideoReaderProps_PROP_NOT_SUPPORTED\n* CUDA_VideoReaderProps_PROP_NUMBER_OF_RAW_PACKAGES_SINCE_LAST_GRABNumber of raw packages recieved since the last call to grab().\n* CUDA_VideoReaderProps_PROP_RAW_MODEStatus of raw mode.\n* CUDA_VideoReaderProps_PROP_RAW_PACKAGES_BASE_INDEXBase index for retrieving raw encoded data using retrieve().\n* CUDA_VideoReaderProps_PROP_UDP_SOURCEStatus of VideoReaderInitParams::udpSource initialization.\n* CUDA_Weave\n* CUDA_YUV420\n* CUDA_YUV422\n* CUDA_YUV444\n\nTraits\n---\n\n* CUDA_EncoderCallbackTraitMutable methods for crate::cudacodec::CUDA_EncoderCallback\n* CUDA_EncoderCallbackTraitConstConstant methods for crate::cudacodec::CUDA_EncoderCallback\n* CUDA_RawVideoSourceTraitMutable methods for crate::cudacodec::CUDA_RawVideoSource\n* CUDA_RawVideoSourceTraitConstConstant methods for crate::cudacodec::CUDA_RawVideoSource\n* CUDA_VideoReaderTraitMutable methods for crate::cudacodec::CUDA_VideoReader\n* CUDA_VideoReaderTraitConstConstant methods for crate::cudacodec::CUDA_VideoReader\n* CUDA_VideoWriterTraitMutable methods for crate::cudacodec::CUDA_VideoWriter\n* CUDA_VideoWriterTraitConstConstant methods for crate::cudacodec::CUDA_VideoWriter\n\nFunctions\n---\n\n* create_video_readerCreates video reader.\n* create_video_reader_1Creates video reader.\n* create_video_reader_1_def@overload\n* create_video_reader_defCreates video reader.\n* create_video_writerCreates video writer.\n* create_video_writer_1Creates video writer.\n* create_video_writer_1_defCreates video writer.\n* create_video_writer_defCreates video writer.\n* equals_cuda_encoderparams_cuda_encoderparams\n\nModule opencv::cudafeatures2d\n===\n\nFeature Detection and Description\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_DescriptorMatcherAbstract base class for matching keypoint descriptors.\n* CUDA_FastFeatureDetectorWrapping class for feature detection using the FAST method.\n* CUDA_Feature2DAsyncAbstract base class for CUDA asynchronous 2D image feature detectors and descriptor extractors.\n* CUDA_ORBClass implementing the ORB (*oriented BRIEF*) keypoint detector and descriptor extractor\n\nTraits\n---\n\n* CUDA_DescriptorMatcherTraitMutable methods for crate::cudafeatures2d::CUDA_DescriptorMatcher\n* CUDA_DescriptorMatcherTraitConstConstant methods for crate::cudafeatures2d::CUDA_DescriptorMatcher\n* CUDA_FastFeatureDetectorTraitMutable methods for crate::cudafeatures2d::CUDA_FastFeatureDetector\n* CUDA_FastFeatureDetectorTraitConstConstant methods for crate::cudafeatures2d::CUDA_FastFeatureDetector\n* CUDA_Feature2DAsyncTraitMutable methods for crate::cudafeatures2d::CUDA_Feature2DAsync\n* CUDA_Feature2DAsyncTraitConstConstant methods for crate::cudafeatures2d::CUDA_Feature2DAsync\n* CUDA_ORBTraitMutable methods for crate::cudafeatures2d::CUDA_ORB\n* CUDA_ORBTraitConstConstant methods for crate::cudafeatures2d::CUDA_ORB\n\nModule opencv::cudafilters\n===\n\nImage Filtering\n---\n\nFunctions and classes described in this section are used to perform various linear or non-linear filtering operations on 2D images.\n\nNote:\n\n* An example containing all basic morphology operators like erode and dilate can be found at opencv_source_code/samples/gpu/morphology.cpp\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* FilterCommon interface for all CUDA filters :\n\nTraits\n---\n\n* FilterTraitMutable methods for crate::cudafilters::Filter\n* FilterTraitConstConstant methods for crate::cudafilters::Filter\n\nFunctions\n---\n\n* create_box_filterCreates a normalized 2D box filter.\n* create_box_filter_defCreates a normalized 2D box filter.\n* create_box_max_filterCreates the maximum filter.\n* create_box_max_filter_defCreates the maximum filter.\n* create_box_min_filterCreates the minimum filter.\n* create_box_min_filter_defCreates the minimum filter.\n* create_column_sum_filterCreates a vertical 1D box filter.\n* create_column_sum_filter_defCreates a vertical 1D box filter.\n* create_deriv_filterCreates a generalized Deriv operator.\n* create_deriv_filter_defCreates a generalized Deriv operator.\n* create_gaussian_filterCreates a Gaussian filter.\n* create_gaussian_filter_defCreates a Gaussian filter.\n* create_laplacian_filterCreates a Laplacian operator.\n* create_laplacian_filter_defCreates a Laplacian operator.\n* create_linear_filterCreates a non-separable linear 2D filter.\n* create_linear_filter_defCreates a non-separable linear 2D filter.\n* create_median_filterPerforms median filtering for each point of the source image.\n* create_median_filter_defPerforms median filtering for each point of the source image.\n* create_morphology_filterCreates a 2D morphological filter.\n* create_morphology_filter_defCreates a 2D morphological filter.\n* create_row_sum_filterCreates a horizontal 1D box filter.\n* create_row_sum_filter_defCreates a horizontal 1D box filter.\n* create_scharr_filterCreates a vertical or horizontal Scharr operator.\n* create_scharr_filter_defCreates a vertical or horizontal Scharr operator.\n* create_separable_linear_filterCreates a separable linear filter.\n* create_separable_linear_filter_defCreates a separable linear filter.\n* create_sobel_filterCreates a Sobel operator.\n* create_sobel_filter_defCreates a Sobel operator.\n\nModule opencv::cudaimgproc\n===\n\nImage Processing\n---\n\nColor space processing\n---\n\nHistogram Calculation\n---\n\nHough Transform\n---\n\nFeature Detection\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_CLAHEBase class for Contrast Limited Adaptive Histogram Equalization. :\n* CUDA_CannyEdgeDetectorBase class for Canny Edge Detector. :\n* CUDA_CornernessCriteriaBase class for Cornerness Criteria computation. :\n* CUDA_CornersDetectorBase class for Corners Detector. :\n* CUDA_HoughCirclesDetectorBase class for circles detector algorithm. :\n* CUDA_HoughLinesDetectorBase class for lines detector algorithm. :\n* CUDA_HoughSegmentDetectorBase class for line segments detector algorithm. :\n* CUDA_TemplateMatchingBase class for Template Matching. :\n\nEnums\n---\n\n* CUDA_AlphaCompTypes\n* CUDA_ConnectedComponentsAlgorithmsTypesConnected Components Algorithm\n* CUDA_DemosaicTypes\n\nConstants\n---\n\n* CUDA_ALPHA_ATOP\n* CUDA_ALPHA_ATOP_PREMUL\n* CUDA_ALPHA_IN\n* CUDA_ALPHA_IN_PREMUL\n* CUDA_ALPHA_OUT\n* CUDA_ALPHA_OUT_PREMUL\n* CUDA_ALPHA_OVER\n* CUDA_ALPHA_OVER_PREMUL\n* CUDA_ALPHA_PLUS\n* CUDA_ALPHA_PLUS_PREMUL\n* CUDA_ALPHA_PREMUL\n* CUDA_ALPHA_XOR\n* CUDA_ALPHA_XOR_PREMUL\n* CUDA_CCL_BKEBKE Allegretti2019 algorithm for 8-way connectivity.\n* CUDA_CCL_DEFAULTBKE Allegretti2019 algorithm for 8-way connectivity.\n* CUDA_COLOR_BayerBG2BGR_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerBG2GRAY_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerBG2RGB_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGB2BGR_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGB2GRAY_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGB2RGB_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGR2BGR_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGR2GRAY_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerGR2RGB_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerRG2BGR_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerRG2GRAY_MHTBayer Demosaicing (Malvar, He, and Cutler)\n* CUDA_COLOR_BayerRG2RGB_MHTBayer Demosaicing (Malvar, He, and Cutler)\n\nTraits\n---\n\n* CUDA_CLAHETraitMutable methods for crate::cudaimgproc::CUDA_CLAHE\n* CUDA_CLAHETraitConstConstant methods for crate::cudaimgproc::CUDA_CLAHE\n* CUDA_CannyEdgeDetectorTraitMutable methods for crate::cudaimgproc::CUDA_CannyEdgeDetector\n* CUDA_CannyEdgeDetectorTraitConstConstant methods for crate::cudaimgproc::CUDA_CannyEdgeDetector\n* CUDA_CornernessCriteriaTraitMutable methods for crate::cudaimgproc::CUDA_CornernessCriteria\n* CUDA_CornernessCriteriaTraitConstConstant methods for crate::cudaimgproc::CUDA_CornernessCriteria\n* CUDA_CornersDetectorTraitMutable methods for crate::cudaimgproc::CUDA_CornersDetector\n* CUDA_CornersDetectorTraitConstConstant methods for crate::cudaimgproc::CUDA_CornersDetector\n* CUDA_HoughCirclesDetectorTraitMutable methods for crate::cudaimgproc::CUDA_HoughCirclesDetector\n* CUDA_HoughCirclesDetectorTraitConstConstant methods for crate::cudaimgproc::CUDA_HoughCirclesDetector\n* CUDA_HoughLinesDetectorTraitMutable methods for crate::cudaimgproc::CUDA_HoughLinesDetector\n* CUDA_HoughLinesDetectorTraitConstConstant methods for crate::cudaimgproc::CUDA_HoughLinesDetector\n* CUDA_HoughSegmentDetectorTraitMutable methods for crate::cudaimgproc::CUDA_HoughSegmentDetector\n* CUDA_HoughSegmentDetectorTraitConstConstant methods for crate::cudaimgproc::CUDA_HoughSegmentDetector\n* CUDA_TemplateMatchingTraitMutable methods for crate::cudaimgproc::CUDA_TemplateMatching\n* CUDA_TemplateMatchingTraitConstConstant methods for crate::cudaimgproc::CUDA_TemplateMatching\n\nFunctions\n---\n\n* alpha_compComposites two images using alpha opacity values contained in each image.\n* alpha_comp_defComposites two images using alpha opacity values contained in each image.\n* bilateral_filterPerforms bilateral filtering of passed image\n* bilateral_filter_defPerforms bilateral filtering of passed image\n* blend_linearPerforms linear blending of two images.\n* blend_linear_defPerforms linear blending of two images.\n* calc_histCalculates histogram for one channel 8-bit image.\n* calc_hist_1Calculates histogram for one channel 8-bit image confined in given mask.\n* calc_hist_1_defCalculates histogram for one channel 8-bit image confined in given mask.\n* calc_hist_defCalculates histogram for one channel 8-bit image.\n* connected_componentsComputes the Connected Components Labeled image of a binary image.\n* connected_components_def@overload\n* connected_components_with_algorithmComputes the Connected Components Labeled image of a binary image.\n* create_canny_edge_detectorCreates implementation for cuda::CannyEdgeDetector .\n* create_canny_edge_detector_defCreates implementation for cuda::CannyEdgeDetector .\n* create_claheCreates implementation for cuda::CLAHE .\n* create_clahe_defCreates implementation for cuda::CLAHE .\n* create_generalized_hough_ballardCreates implementation for generalized hough transform from Ballard1981 .\n* create_generalized_hough_guilCreates implementation for generalized hough transform from Guil1999 .\n* create_good_features_to_track_detectorCreates implementation for cuda::CornersDetector .\n* create_good_features_to_track_detector_defCreates implementation for cuda::CornersDetector .\n* create_harris_cornerCreates implementation for Harris cornerness criteria.\n* create_harris_corner_defCreates implementation for Harris cornerness criteria.\n* create_hough_circles_detectorCreates implementation for cuda::HoughCirclesDetector .\n* create_hough_circles_detector_defCreates implementation for cuda::HoughCirclesDetector .\n* create_hough_lines_detectorCreates implementation for cuda::HoughLinesDetector .\n* create_hough_lines_detector_defCreates implementation for cuda::HoughLinesDetector .\n* create_hough_segment_detectorCreates implementation for cuda::HoughSegmentDetector .\n* create_hough_segment_detector_defCreates implementation for cuda::HoughSegmentDetector .\n* create_min_eigen_val_cornerCreates implementation for the minimum eigen value of a 2x2 derivative covariation matrix (the cornerness criteria).\n* create_min_eigen_val_corner_defCreates implementation for the minimum eigen value of a 2x2 derivative covariation matrix (the cornerness criteria).\n* create_template_matchingCreates implementation for cuda::TemplateMatching .\n* create_template_matching_defCreates implementation for cuda::TemplateMatching .\n* cvt_colorConverts an image from one color space to another.\n* cvt_color_defConverts an image from one color space to another.\n* demosaicingConverts an image from Bayer pattern to RGB or grayscale.\n* demosaicing_defConverts an image from Bayer pattern to RGB or grayscale.\n* equalize_histEqualizes the histogram of a grayscale image.\n* equalize_hist_defEqualizes the histogram of a grayscale image.\n* even_levelsComputes levels with even distribution.\n* even_levels_defComputes levels with even distribution.\n* gamma_correctionRoutines for correcting image color gamma.\n* gamma_correction_defRoutines for correcting image color gamma.\n* hist_evenCalculates a histogram with evenly distributed bins.\n* hist_even_defCalculates a histogram with evenly distributed bins.\n* hist_rangeCalculates a histogram with bins determined by the levels array.\n* hist_range_defCalculates a histogram with bins determined by the levels array.\n* mean_shift_filteringPerforms mean-shift filtering for each point of the source image.\n* mean_shift_filtering_defPerforms mean-shift filtering for each point of the source image.\n* mean_shift_procPerforms a mean-shift procedure and stores information about processed points (their colors and positions) in two images.\n* mean_shift_proc_defPerforms a mean-shift procedure and stores information about processed points (their colors and positions) in two images.\n* mean_shift_segmentationPerforms a mean-shift segmentation of the source image and eliminates small segments.\n* mean_shift_segmentation_defPerforms a mean-shift segmentation of the source image and eliminates small segments.\n* swap_channelsExchanges the color channels of an image in-place.\n* swap_channels_defExchanges the color channels of an image in-place.\n\nModule opencv::cudaobjdetect\n===\n\nObject Detection\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_CascadeClassifierCascade classifier class used for object detection. Supports HAAR and LBP cascades. :\n* CUDA_HOGThe class implements Histogram of Oriented Gradients (Dalal2005) object detector.\n\nTraits\n---\n\n* CUDA_CascadeClassifierTraitMutable methods for crate::cudaobjdetect::CUDA_CascadeClassifier\n* CUDA_CascadeClassifierTraitConstConstant methods for crate::cudaobjdetect::CUDA_CascadeClassifier\n* CUDA_HOGTraitMutable methods for crate::cudaobjdetect::CUDA_HOG\n* CUDA_HOGTraitConstConstant methods for crate::cudaobjdetect::CUDA_HOG\n\nModule opencv::cudaoptflow\n===\n\nOptical Flow\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_BroxOpticalFlowClass computing the optical flow for two images using Brox et al Optical Flow algorithm (Brox2004).\n* CUDA_DenseOpticalFlowBase interface for dense optical flow algorithms.\n* CUDA_DensePyrLKOpticalFlowClass used for calculating a dense optical flow.\n* CUDA_FarnebackOpticalFlowClass computing a dense optical flow using the Gunnar Farneback’s algorithm.\n* CUDA_NvidiaHWOpticalFlowBase Interface for optical flow algorithms using NVIDIA Optical Flow SDK.\n* CUDA_NvidiaOpticalFlow_1_0Class for computing the optical flow vectors between two images using NVIDIA Optical Flow hardware and Optical Flow SDK 1.0.\n* CUDA_NvidiaOpticalFlow_2_0Class for computing the optical flow vectors between two images using NVIDIA Optical Flow hardware and Optical Flow SDK 2.0.\n* CUDA_OpticalFlowDual_TVL1Implementation of the Zach, Pock and Bischof Dual TV-L1 Optical Flow method.\n* CUDA_SparseOpticalFlowBase interface for sparse optical flow algorithms.\n* CUDA_SparsePyrLKOpticalFlowClass used for calculating a sparse optical flow.\n\nEnums\n---\n\n* CUDA_NvidiaOpticalFlow_1_0_NVIDIA_OF_PERF_LEVELSupported optical flow performance levels.\n* CUDA_NvidiaOpticalFlow_2_0_NVIDIA_OF_HINT_VECTOR_GRID_SIZESupported grid size for hint buffer.\n* CUDA_NvidiaOpticalFlow_2_0_NVIDIA_OF_OUTPUT_VECTOR_GRID_SIZESupported grid size for output buffer.\n* CUDA_NvidiaOpticalFlow_2_0_NVIDIA_OF_PERF_LEVELSupported optical flow performance levels.\n\nConstants\n---\n\n* CUDA_NvidiaOpticalFlow_1_0_NV_OF_PERF_LEVEL_FAST< Fast perf level results in high performance and low quality\n* CUDA_NvidiaOpticalFlow_1_0_NV_OF_PERF_LEVEL_MAX\n* CUDA_NvidiaOpticalFlow_1_0_NV_OF_PERF_LEVEL_MEDIUM< Medium perf level results in low performance and medium quality\n* CUDA_NvidiaOpticalFlow_1_0_NV_OF_PERF_LEVEL_SLOW< Slow perf level results in lowest performance and best quality\n* CUDA_NvidiaOpticalFlow_1_0_NV_OF_PERF_LEVEL_UNDEFINED\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_1< Hint buffer grid size is 1x1.\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_2< Hint buffer grid size is 2x2.\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_4< Hint buffer grid size is 4x4.\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_8< Hint buffer grid size is 8x8.\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_MAX\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_HINT_VECTOR_GRID_SIZE_UNDEFINED\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_OUTPUT_VECTOR_GRID_SIZE_1< Output buffer grid size is 1x1\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_OUTPUT_VECTOR_GRID_SIZE_2< Output buffer grid size is 2x2\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_OUTPUT_VECTOR_GRID_SIZE_4< Output buffer grid size is 4x4\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_OUTPUT_VECTOR_GRID_SIZE_MAX\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_OUTPUT_VECTOR_GRID_SIZE_UNDEFINED\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_PERF_LEVEL_FAST< Fast perf level results in high performance and low quality\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_PERF_LEVEL_MAX\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_PERF_LEVEL_MEDIUM< Medium perf level results in low performance and medium quality\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_PERF_LEVEL_SLOW< Slow perf level results in lowest performance and best quality\n* CUDA_NvidiaOpticalFlow_2_0_NV_OF_PERF_LEVEL_UNDEFINED\n\nTraits\n---\n\n* CUDA_BroxOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_BroxOpticalFlow\n* CUDA_BroxOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_BroxOpticalFlow\n* CUDA_DenseOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_DenseOpticalFlow\n* CUDA_DenseOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_DenseOpticalFlow\n* CUDA_DensePyrLKOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_DensePyrLKOpticalFlow\n* CUDA_DensePyrLKOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_DensePyrLKOpticalFlow\n* CUDA_FarnebackOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_FarnebackOpticalFlow\n* CUDA_FarnebackOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_FarnebackOpticalFlow\n* CUDA_NvidiaHWOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_NvidiaHWOpticalFlow\n* CUDA_NvidiaHWOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_NvidiaHWOpticalFlow\n* CUDA_NvidiaOpticalFlow_1_0TraitMutable methods for crate::cudaoptflow::CUDA_NvidiaOpticalFlow_1_0\n* CUDA_NvidiaOpticalFlow_1_0TraitConstConstant methods for crate::cudaoptflow::CUDA_NvidiaOpticalFlow_1_0\n* CUDA_NvidiaOpticalFlow_2_0TraitMutable methods for crate::cudaoptflow::CUDA_NvidiaOpticalFlow_2_0\n* CUDA_NvidiaOpticalFlow_2_0TraitConstConstant methods for crate::cudaoptflow::CUDA_NvidiaOpticalFlow_2_0\n* CUDA_OpticalFlowDual_TVL1TraitMutable methods for crate::cudaoptflow::CUDA_OpticalFlowDual_TVL1\n* CUDA_OpticalFlowDual_TVL1TraitConstConstant methods for crate::cudaoptflow::CUDA_OpticalFlowDual_TVL1\n* CUDA_SparseOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_SparseOpticalFlow\n* CUDA_SparseOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_SparseOpticalFlow\n* CUDA_SparsePyrLKOpticalFlowTraitMutable methods for crate::cudaoptflow::CUDA_SparsePyrLKOpticalFlow\n* CUDA_SparsePyrLKOpticalFlowTraitConstConstant methods for crate::cudaoptflow::CUDA_SparsePyrLKOpticalFlow\n\nModule opencv::cudastereo\n===\n\nStereo Correspondence\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CUDA_DisparityBilateralFilterClass refining a disparity map using joint bilateral filtering. :\n* CUDA_StereoBMClass computing stereo correspondence (disparity map) using the block matching algorithm. :\n* CUDA_StereoBeliefPropagationClass computing stereo correspondence using the belief propagation algorithm. :\n* CUDA_StereoConstantSpaceBPClass computing stereo correspondence using the constant space belief propagation algorithm. :\n* CUDA_StereoSGMThe class implements the modified H. Hirschmuller algorithm HH08.\nLimitation and difference are as follows:\n\nTraits\n---\n\n* CUDA_DisparityBilateralFilterTraitMutable methods for crate::cudastereo::CUDA_DisparityBilateralFilter\n* CUDA_DisparityBilateralFilterTraitConstConstant methods for crate::cudastereo::CUDA_DisparityBilateralFilter\n* CUDA_StereoBMTraitMutable methods for crate::cudastereo::CUDA_StereoBM\n* CUDA_StereoBMTraitConstConstant methods for crate::cudastereo::CUDA_StereoBM\n* CUDA_StereoBeliefPropagationTraitMutable methods for crate::cudastereo::CUDA_StereoBeliefPropagation\n* CUDA_StereoBeliefPropagationTraitConstConstant methods for crate::cudastereo::CUDA_StereoBeliefPropagation\n* CUDA_StereoConstantSpaceBPTraitMutable methods for crate::cudastereo::CUDA_StereoConstantSpaceBP\n* CUDA_StereoConstantSpaceBPTraitConstConstant methods for crate::cudastereo::CUDA_StereoConstantSpaceBP\n* CUDA_StereoSGMTraitMutable methods for crate::cudastereo::CUDA_StereoSGM\n* CUDA_StereoSGMTraitConstConstant methods for crate::cudastereo::CUDA_StereoSGM\n\nFunctions\n---\n\n* create_disparity_bilateral_filterCreates DisparityBilateralFilter object.\n* create_disparity_bilateral_filter_defCreates DisparityBilateralFilter object.\n* create_stereo_belief_propagationCreates StereoBeliefPropagation object.\n* create_stereo_belief_propagation_defCreates StereoBeliefPropagation object.\n* create_stereo_bmCreates StereoBM object.\n* create_stereo_bm_defCreates StereoBM object.\n* create_stereo_constant_space_bpCreates StereoConstantSpaceBP object.\n* create_stereo_constant_space_bp_defCreates StereoConstantSpaceBP object.\n* create_stereo_sgmCreates StereoSGM object.\n* create_stereo_sgm_defCreates StereoSGM object.\n* draw_color_dispColors a disparity image.\n* draw_color_disp_defColors a disparity image.\n* reproject_image_to_3dReprojects a disparity image to 3D space.\n* reproject_image_to_3d_1C++ default parameters\n* reproject_image_to_3d_1_defNote\n* reproject_image_to_3d_defReprojects a disparity image to 3D space.\n\nModule opencv::cudawarping\n===\n\nImage Warping\n---\n\nModules\n---\n\n* prelude\n\nFunctions\n---\n\n* build_warp_affine_mapsBuilds transformation maps for affine transformation.\n* build_warp_affine_maps_1C++ default parameters\n* build_warp_affine_maps_1_defNote\n* build_warp_affine_maps_2C++ default parameters\n* build_warp_affine_maps_2_defNote\n* build_warp_affine_maps_defBuilds transformation maps for affine transformation.\n* build_warp_perspective_mapsBuilds transformation maps for perspective transformation.\n* build_warp_perspective_maps_1C++ default parameters\n* build_warp_perspective_maps_1_defNote\n* build_warp_perspective_maps_2C++ default parameters\n* build_warp_perspective_maps_2_defNote\n* build_warp_perspective_maps_defBuilds transformation maps for perspective transformation.\n* pyr_downSmoothes an image and downsamples it.\n* pyr_down_defSmoothes an image and downsamples it.\n* pyr_upUpsamples an image and then smoothes it.\n* pyr_up_defUpsamples an image and then smoothes it.\n* remapApplies a generic geometrical transformation to an image.\n* remap_defApplies a generic geometrical transformation to an image.\n* resizeResizes an image.\n* resize_defResizes an image.\n* rotateRotates an image around the origin (0,0) and then shifts it.\n* rotate_defRotates an image around the origin (0,0) and then shifts it.\n* warp_affineApplies an affine transformation to an image.\n* warp_affine_1C++ default parameters\n* warp_affine_1_defNote\n* warp_affine_2C++ default parameters\n* warp_affine_2_defNote\n* warp_affine_defApplies an affine transformation to an image.\n* warp_perspectiveApplies a perspective transformation to an image.\n* warp_perspective_1C++ default parameters\n* warp_perspective_1_defNote\n* warp_perspective_2C++ default parameters\n* warp_perspective_2_defNote\n* warp_perspective_defApplies a perspective transformation to an image.\n\nModule opencv::cvv\n===\n\nGUI for Interactive Visual Debugging of Computer Vision Programs\n---\n\nNamespace for all functions is **cvv**, i.e. *cvv::showImage()*.\n\nCompilation:\n\n* For development, i.e. for cvv GUI to show up, compile your code using cvv with\n*g++ -DCVVISUAL_DEBUGMODE*.\n* For release, i.e. cvv calls doing nothing, compile your code without above flag.\n\nSee cvv tutorial for a commented example application using cvv.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CallMetaDataOptional information about a location in Code.\n\nTraits\n---\n\n* CallMetaDataTraitMutable methods for crate::cvv::CallMetaData\n* CallMetaDataTraitConstConstant methods for crate::cvv::CallMetaData\n\nFunctions\n---\n\n* debug_d_match\n* debug_filter\n* final_show\n* show_image\n\nModule opencv::dnn\n===\n\nDeep Neural Network module\n---\n\nThis module contains:\n- API for new layers creation, layers are building bricks of neural networks;\n- set of built-in most-useful Layers;\n- API to construct and modify comprehensive neural networks from layers;\n- functionality for loading serialized networks models from different frameworks.\n\nFunctionality of this module is designed only for forward pass computations (i.e. network testing).\nA network training is in principle not supported.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AbsLayer\n* AccumLayer\n* AcosLayer\n* AcoshLayer\n* ActivationLayer\n* ActivationLayerInt8\n* ArgLayerArgMax/ArgMin layer\n* AsinLayer\n* AsinhLayer\n* AtanLayer\n* AtanhLayer\n* BNLLLayer\n* BackendNodeDerivatives of this class encapsulates functions of certain backends.\n* BackendWrapperDerivatives of this class wraps cv::Mat for different backends and targets.\n* BaseConvolutionLayer\n* BatchNormLayer\n* BatchNormLayerInt8\n* BlankLayerPartial List of Implemented Layers\n* CeilLayer\n* CeluLayer\n* ChannelsPReLULayer\n* ClassificationModelThis class represents high-level API for classification models.\n* CompareLayer\n* ConcatLayer\n* ConstLayerConstant layer produces the same data blob at an every forward pass.\n* ConvolutionLayer\n* ConvolutionLayerInt8\n* CorrelationLayer\n* CosLayer\n* CoshLayer\n* CropAndResizeLayer\n* CropLayer\n* CumSumLayer\n* DataAugmentationLayer\n* DeconvolutionLayer\n* DequantizeLayer\n* DetectionModelThis class represents high-level API for object detection networks.\n* DetectionOutputLayerDetection output layer.\n* DictThis class implements name-value dictionary, values are instances of DictValue.\n* DictValueThis struct stores the scalar value (or array) of one of the following type: double, cv::String or int64.\n@todo Maybe int64 is useless because double type exactly stores at least 2^52 integers.\n* ELULayer\n* EltwiseLayerElement wise operation on inputs\n* EltwiseLayerInt8\n* ErfLayer\n* ExpLayer\n* FlattenLayer\n* FloorLayer\n* FlowWarpLayer\n* GRULayerGRU recurrent one-layer\n* GatherLayerGather layer\n* GeluApproximationLayer\n* GeluLayer\n* HardSigmoidLayer\n* HardSwishLayer\n* Image2BlobParamsProcessing params of image to blob.\n* InnerProductLayer`InnerProduct`, `MatMul` and `Gemm` operations are all implemented by Fully Connected Layer.\nParameter `is_matmul` is used to distinguish `MatMul` and `Gemm` from `InnerProduct`.\n* InnerProductLayerInt8\n* InterpLayerBilinear resize layer from https://github.com/cdmh/deeplab-public-ver2\n* KeypointsModelThis class represents high-level API for keypoints models\n* LRNLayer\n* LSTMLayerLSTM recurrent layer\n* LayerThis interface class allows to build new Layers - are building blocks of networks.\n* LayerFactory%Layer factory allows to create instances of registered layers.\n* LayerNormLayer\n* LayerParamsThis class provides all data needed to initialize layer.\n* LogLayer\n* MVNLayer\n* MaxUnpoolLayer\n* MishLayer\n* ModelThis class is presented high-level API for neural networks.\n* NaryEltwiseLayer\n* NetThis class allows to create and manipulate comprehensive artificial neural networks.\n* NormalizeBBoxLayerinline formula - normalization layer.\n* NotLayer\n* PaddingLayerAdds extra values for specific axes.\n* PermuteLayer\n* PoolingLayer\n* PoolingLayerInt8\n* PowerLayer\n* PriorBoxLayer\n* ProposalLayer\n* QuantizeLayer\n* RNNLayerClassical recurrent layer\n* ReLU6Layer\n* ReLULayer\n* ReciprocalLayer\n* ReduceLayer\n* RegionLayer\n* ReorgLayer\n* RequantizeLayer\n* ReshapeLayer\n* ResizeLayerResize input 4-dimensional blob by nearest neighbor or bilinear strategy.\n* RoundLayer\n* ScaleLayer\n* ScaleLayerInt8\n* ScatterLayer\n* ScatterNDLayer\n* SegmentationModelThis class represents high-level API for segmentation models\n* SeluLayer\n* ShiftLayer\n* ShiftLayerInt8\n* ShrinkLayer\n* ShuffleChannelLayerPermute channels of 4-dimensional input blob.\n* SigmoidLayer\n* SignLayer\n* SinLayer\n* SinhLayer\n* SliceLayerSlice layer has several modes:\n* SoftmaxLayer\n* SoftmaxLayerInt8\n* SoftplusLayer\n* SoftsignLayer\n* SplitLayer\n* SqrtLayer\n* SwishLayer\n* TanHLayer\n* TanLayer\n* TextDetectionModelBase class for text detection networks\n* TextDetectionModel_DBThis class represents high-level API for text detection DL networks compatible with DB model.\n* TextDetectionModel_EASTThis class represents high-level API for text detection DL networks compatible with EAST model.\n* TextRecognitionModelThis class represents high-level API for text recognition networks.\n* ThresholdedReluLayer\n* TileLayer\n* _Range\n\nEnums\n---\n\n* BackendEnum of computation backends supported by layers.\n* DataLayoutEnum of data layout for model inference.\n* ImagePaddingModeEnum of image processing mode.\nTo facilitate the specialization pre-processing requirements of the dnn model.\nFor example, the `letter box` often used in the Yolo series of models.\n* SoftNMSMethodEnum of Soft NMS methods.\n* TargetEnum of target devices for computations.\n\nConstants\n---\n\n* CV_DNN_BACKEND_INFERENCE_ENGINE_NGRAPH\n* CV_DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_API\n* CV_DNN_INFERENCE_ENGINE_CPU_TYPE_ARM_COMPUTE\n* CV_DNN_INFERENCE_ENGINE_CPU_TYPE_X86\n* CV_DNN_INFERENCE_ENGINE_VPU_TYPE_MYRIAD_2\n* CV_DNN_INFERENCE_ENGINE_VPU_TYPE_MYRIAD_X\n* CV_DNN_INFERENCE_ENGINE_VPU_TYPE_UNSPECIFIED\n* DNN_BACKEND_CANN\n* DNN_BACKEND_CUDA\n* DNN_BACKEND_DEFAULTDNN_BACKEND_DEFAULT equals to DNN_BACKEND_INFERENCE_ENGINE if OpenCV is built with Intel OpenVINO or DNN_BACKEND_OPENCV otherwise.\n* DNN_BACKEND_HALIDEDNN_BACKEND_DEFAULT equals to DNN_BACKEND_INFERENCE_ENGINE if OpenCV is built with Intel OpenVINO or DNN_BACKEND_OPENCV otherwise.\n* DNN_BACKEND_INFERENCE_ENGINEIntel OpenVINO computational backend\n* DNN_BACKEND_OPENCV\n* DNN_BACKEND_TIMVX\n* DNN_BACKEND_VKCOM\n* DNN_BACKEND_WEBNN\n* DNN_LAYOUT_NCDHWOpenCV data layout for 5D data.\n* DNN_LAYOUT_NCHWOpenCV data layout for 4D data.\n* DNN_LAYOUT_NDOpenCV data layout for 2D data.\n* DNN_LAYOUT_NDHWCTensorflow-like data layout for 5D data.\n* DNN_LAYOUT_NHWCTensorflow-like data layout for 4D data.\n* DNN_LAYOUT_PLANARTensorflow-like data layout, it should only be used at tf or tflite model parsing.\n* DNN_LAYOUT_UNKNOWN\n* DNN_PMODE_CROP_CENTER\n* DNN_PMODE_LETTERBOX\n* DNN_PMODE_NULL\n* DNN_TARGET_CPU\n* DNN_TARGET_CPU_FP16\n* DNN_TARGET_CUDA\n* DNN_TARGET_CUDA_FP16\n* DNN_TARGET_FPGAFPGA device with CPU fallbacks using Inference Engine’s Heterogeneous plugin.\n* DNN_TARGET_HDDL\n* DNN_TARGET_MYRIAD\n* DNN_TARGET_NPU\n* DNN_TARGET_OPENCL\n* DNN_TARGET_OPENCL_FP16\n* DNN_TARGET_VULKAN\n* OPENCV_DNN_API_VERSION\n* SoftNMSMethod_SOFTNMS_GAUSSIAN\n* SoftNMSMethod_SOFTNMS_LINEAR\n\nTraits\n---\n\n* AbsLayerTraitMutable methods for crate::dnn::AbsLayer\n* AbsLayerTraitConstConstant methods for crate::dnn::AbsLayer\n* AccumLayerTraitMutable methods for crate::dnn::AccumLayer\n* AccumLayerTraitConstConstant methods for crate::dnn::AccumLayer\n* AcosLayerTraitMutable methods for crate::dnn::AcosLayer\n* AcosLayerTraitConstConstant methods for crate::dnn::AcosLayer\n* AcoshLayerTraitMutable methods for crate::dnn::AcoshLayer\n* AcoshLayerTraitConstConstant methods for crate::dnn::AcoshLayer\n* ActivationLayerInt8TraitMutable methods for crate::dnn::ActivationLayerInt8\n* ActivationLayerInt8TraitConstConstant methods for crate::dnn::ActivationLayerInt8\n* ActivationLayerTraitMutable methods for crate::dnn::ActivationLayer\n* ActivationLayerTraitConstConstant methods for crate::dnn::ActivationLayer\n* ArgLayerTraitMutable methods for crate::dnn::ArgLayer\n* ArgLayerTraitConstConstant methods for crate::dnn::ArgLayer\n* AsinLayerTraitMutable methods for crate::dnn::AsinLayer\n* AsinLayerTraitConstConstant methods for crate::dnn::AsinLayer\n* AsinhLayerTraitMutable methods for crate::dnn::AsinhLayer\n* AsinhLayerTraitConstConstant methods for crate::dnn::AsinhLayer\n* AtanLayerTraitMutable methods for crate::dnn::AtanLayer\n* AtanLayerTraitConstConstant methods for crate::dnn::AtanLayer\n* AtanhLayerTraitMutable methods for crate::dnn::AtanhLayer\n* AtanhLayerTraitConstConstant methods for crate::dnn::AtanhLayer\n* BNLLLayerTraitMutable methods for crate::dnn::BNLLLayer\n* BNLLLayerTraitConstConstant methods for crate::dnn::BNLLLayer\n* BackendNodeTraitMutable methods for crate::dnn::BackendNode\n* BackendNodeTraitConstConstant methods for crate::dnn::BackendNode\n* BackendWrapperTraitMutable methods for crate::dnn::BackendWrapper\n* BackendWrapperTraitConstConstant methods for crate::dnn::BackendWrapper\n* BaseConvolutionLayerTraitMutable methods for crate::dnn::BaseConvolutionLayer\n* BaseConvolutionLayerTraitConstConstant methods for crate::dnn::BaseConvolutionLayer\n* BatchNormLayerInt8TraitMutable methods for crate::dnn::BatchNormLayerInt8\n* BatchNormLayerInt8TraitConstConstant methods for crate::dnn::BatchNormLayerInt8\n* BatchNormLayerTraitMutable methods for crate::dnn::BatchNormLayer\n* BatchNormLayerTraitConstConstant methods for crate::dnn::BatchNormLayer\n* BlankLayerTraitMutable methods for crate::dnn::BlankLayer\n* BlankLayerTraitConstConstant methods for crate::dnn::BlankLayer\n* CeilLayerTraitMutable methods for crate::dnn::CeilLayer\n* CeilLayerTraitConstConstant methods for crate::dnn::CeilLayer\n* CeluLayerTraitMutable methods for crate::dnn::CeluLayer\n* CeluLayerTraitConstConstant methods for crate::dnn::CeluLayer\n* ChannelsPReLULayerTraitMutable methods for crate::dnn::ChannelsPReLULayer\n* ChannelsPReLULayerTraitConstConstant methods for crate::dnn::ChannelsPReLULayer\n* ClassificationModelTraitMutable methods for crate::dnn::ClassificationModel\n* ClassificationModelTraitConstConstant methods for crate::dnn::ClassificationModel\n* CompareLayerTraitMutable methods for crate::dnn::CompareLayer\n* CompareLayerTraitConstConstant methods for crate::dnn::CompareLayer\n* ConcatLayerTraitMutable methods for crate::dnn::ConcatLayer\n* ConcatLayerTraitConstConstant methods for crate::dnn::ConcatLayer\n* ConstLayerTraitMutable methods for crate::dnn::ConstLayer\n* ConstLayerTraitConstConstant methods for crate::dnn::ConstLayer\n* ConvolutionLayerInt8TraitMutable methods for crate::dnn::ConvolutionLayerInt8\n* ConvolutionLayerInt8TraitConstConstant methods for crate::dnn::ConvolutionLayerInt8\n* ConvolutionLayerTraitMutable methods for crate::dnn::ConvolutionLayer\n* ConvolutionLayerTraitConstConstant methods for crate::dnn::ConvolutionLayer\n* CorrelationLayerTraitMutable methods for crate::dnn::CorrelationLayer\n* CorrelationLayerTraitConstConstant methods for crate::dnn::CorrelationLayer\n* CosLayerTraitMutable methods for crate::dnn::CosLayer\n* CosLayerTraitConstConstant methods for crate::dnn::CosLayer\n* CoshLayerTraitMutable methods for crate::dnn::CoshLayer\n* CoshLayerTraitConstConstant methods for crate::dnn::CoshLayer\n* CropAndResizeLayerTraitMutable methods for crate::dnn::CropAndResizeLayer\n* CropAndResizeLayerTraitConstConstant methods for crate::dnn::CropAndResizeLayer\n* CropLayerTraitMutable methods for crate::dnn::CropLayer\n* CropLayerTraitConstConstant methods for crate::dnn::CropLayer\n* CumSumLayerTraitMutable methods for crate::dnn::CumSumLayer\n* CumSumLayerTraitConstConstant methods for crate::dnn::CumSumLayer\n* DataAugmentationLayerTraitMutable methods for crate::dnn::DataAugmentationLayer\n* DataAugmentationLayerTraitConstConstant methods for crate::dnn::DataAugmentationLayer\n* DeconvolutionLayerTraitMutable methods for crate::dnn::DeconvolutionLayer\n* DeconvolutionLayerTraitConstConstant methods for crate::dnn::DeconvolutionLayer\n* DequantizeLayerTraitMutable methods for crate::dnn::DequantizeLayer\n* DequantizeLayerTraitConstConstant methods for crate::dnn::DequantizeLayer\n* DetectionModelTraitMutable methods for crate::dnn::DetectionModel\n* DetectionModelTraitConstConstant methods for crate::dnn::DetectionModel\n* DetectionOutputLayerTraitMutable methods for crate::dnn::DetectionOutputLayer\n* DetectionOutputLayerTraitConstConstant methods for crate::dnn::DetectionOutputLayer\n* DictTraitMutable methods for crate::dnn::Dict\n* DictTraitConstConstant methods for crate::dnn::Dict\n* DictValueTraitMutable methods for crate::dnn::DictValue\n* DictValueTraitConstConstant methods for crate::dnn::DictValue\n* ELULayerTraitMutable methods for crate::dnn::ELULayer\n* ELULayerTraitConstConstant methods for crate::dnn::ELULayer\n* EltwiseLayerInt8TraitMutable methods for crate::dnn::EltwiseLayerInt8\n* EltwiseLayerInt8TraitConstConstant methods for crate::dnn::EltwiseLayerInt8\n* EltwiseLayerTraitMutable methods for crate::dnn::EltwiseLayer\n* EltwiseLayerTraitConstConstant methods for crate::dnn::EltwiseLayer\n* ErfLayerTraitMutable methods for crate::dnn::ErfLayer\n* ErfLayerTraitConstConstant methods for crate::dnn::ErfLayer\n* ExpLayerTraitMutable methods for crate::dnn::ExpLayer\n* ExpLayerTraitConstConstant methods for crate::dnn::ExpLayer\n* FlattenLayerTraitMutable methods for crate::dnn::FlattenLayer\n* FlattenLayerTraitConstConstant methods for crate::dnn::FlattenLayer\n* FloorLayerTraitMutable methods for crate::dnn::FloorLayer\n* FloorLayerTraitConstConstant methods for crate::dnn::FloorLayer\n* FlowWarpLayerTraitMutable methods for crate::dnn::FlowWarpLayer\n* FlowWarpLayerTraitConstConstant methods for crate::dnn::FlowWarpLayer\n* GRULayerTraitMutable methods for crate::dnn::GRULayer\n* GRULayerTraitConstConstant methods for crate::dnn::GRULayer\n* GatherLayerTraitMutable methods for crate::dnn::GatherLayer\n* GatherLayerTraitConstConstant methods for crate::dnn::GatherLayer\n* GeluApproximationLayerTraitMutable methods for crate::dnn::GeluApproximationLayer\n* GeluApproximationLayerTraitConstConstant methods for crate::dnn::GeluApproximationLayer\n* GeluLayerTraitMutable methods for crate::dnn::GeluLayer\n* GeluLayerTraitConstConstant methods for crate::dnn::GeluLayer\n* HardSigmoidLayerTraitMutable methods for crate::dnn::HardSigmoidLayer\n* HardSigmoidLayerTraitConstConstant methods for crate::dnn::HardSigmoidLayer\n* HardSwishLayerTraitMutable methods for crate::dnn::HardSwishLayer\n* HardSwishLayerTraitConstConstant methods for crate::dnn::HardSwishLayer\n* InnerProductLayerInt8TraitMutable methods for crate::dnn::InnerProductLayerInt8\n* InnerProductLayerInt8TraitConstConstant methods for crate::dnn::InnerProductLayerInt8\n* InnerProductLayerTraitMutable methods for crate::dnn::InnerProductLayer\n* InnerProductLayerTraitConstConstant methods for crate::dnn::InnerProductLayer\n* InterpLayerTraitMutable methods for crate::dnn::InterpLayer\n* InterpLayerTraitConstConstant methods for crate::dnn::InterpLayer\n* KeypointsModelTraitMutable methods for crate::dnn::KeypointsModel\n* KeypointsModelTraitConstConstant methods for crate::dnn::KeypointsModel\n* LRNLayerTraitMutable methods for crate::dnn::LRNLayer\n* LRNLayerTraitConstConstant methods for crate::dnn::LRNLayer\n* LSTMLayerTraitMutable methods for crate::dnn::LSTMLayer\n* LSTMLayerTraitConstConstant methods for crate::dnn::LSTMLayer\n* LayerFactoryTraitMutable methods for crate::dnn::LayerFactory\n* LayerFactoryTraitConstConstant methods for crate::dnn::LayerFactory\n* LayerNormLayerTraitMutable methods for crate::dnn::LayerNormLayer\n* LayerNormLayerTraitConstConstant methods for crate::dnn::LayerNormLayer\n* LayerParamsTraitMutable methods for crate::dnn::LayerParams\n* LayerParamsTraitConstConstant methods for crate::dnn::LayerParams\n* LayerTraitMutable methods for crate::dnn::Layer\n* LayerTraitConstConstant methods for crate::dnn::Layer\n* LogLayerTraitMutable methods for crate::dnn::LogLayer\n* LogLayerTraitConstConstant methods for crate::dnn::LogLayer\n* MVNLayerTraitMutable methods for crate::dnn::MVNLayer\n* MVNLayerTraitConstConstant methods for crate::dnn::MVNLayer\n* MaxUnpoolLayerTraitMutable methods for crate::dnn::MaxUnpoolLayer\n* MaxUnpoolLayerTraitConstConstant methods for crate::dnn::MaxUnpoolLayer\n* MishLayerTraitMutable methods for crate::dnn::MishLayer\n* MishLayerTraitConstConstant methods for crate::dnn::MishLayer\n* ModelTraitMutable methods for crate::dnn::Model\n* ModelTraitConstConstant methods for crate::dnn::Model\n* NaryEltwiseLayerTraitMutable methods for crate::dnn::NaryEltwiseLayer\n* NaryEltwiseLayerTraitConstConstant methods for crate::dnn::NaryEltwiseLayer\n* NetTraitMutable methods for crate::dnn::Net\n* NetTraitConstConstant methods for crate::dnn::Net\n* NormalizeBBoxLayerTraitMutable methods for crate::dnn::NormalizeBBoxLayer\n* NormalizeBBoxLayerTraitConstConstant methods for crate::dnn::NormalizeBBoxLayer\n* NotLayerTraitMutable methods for crate::dnn::NotLayer\n* NotLayerTraitConstConstant methods for crate::dnn::NotLayer\n* PaddingLayerTraitMutable methods for crate::dnn::PaddingLayer\n* PaddingLayerTraitConstConstant methods for crate::dnn::PaddingLayer\n* PermuteLayerTraitMutable methods for crate::dnn::PermuteLayer\n* PermuteLayerTraitConstConstant methods for crate::dnn::PermuteLayer\n* PoolingLayerInt8TraitMutable methods for crate::dnn::PoolingLayerInt8\n* PoolingLayerInt8TraitConstConstant methods for crate::dnn::PoolingLayerInt8\n* PoolingLayerTraitMutable methods for crate::dnn::PoolingLayer\n* PoolingLayerTraitConstConstant methods for crate::dnn::PoolingLayer\n* PowerLayerTraitMutable methods for crate::dnn::PowerLayer\n* PowerLayerTraitConstConstant methods for crate::dnn::PowerLayer\n* PriorBoxLayerTraitMutable methods for crate::dnn::PriorBoxLayer\n* PriorBoxLayerTraitConstConstant methods for crate::dnn::PriorBoxLayer\n* ProposalLayerTraitMutable methods for crate::dnn::ProposalLayer\n* ProposalLayerTraitConstConstant methods for crate::dnn::ProposalLayer\n* QuantizeLayerTraitMutable methods for crate::dnn::QuantizeLayer\n* QuantizeLayerTraitConstConstant methods for crate::dnn::QuantizeLayer\n* RNNLayerTraitMutable methods for crate::dnn::RNNLayer\n* RNNLayerTraitConstConstant methods for crate::dnn::RNNLayer\n* ReLU6LayerTraitMutable methods for crate::dnn::ReLU6Layer\n* ReLU6LayerTraitConstConstant methods for crate::dnn::ReLU6Layer\n* ReLULayerTraitMutable methods for crate::dnn::ReLULayer\n* ReLULayerTraitConstConstant methods for crate::dnn::ReLULayer\n* ReciprocalLayerTraitMutable methods for crate::dnn::ReciprocalLayer\n* ReciprocalLayerTraitConstConstant methods for crate::dnn::ReciprocalLayer\n* ReduceLayerTraitMutable methods for crate::dnn::ReduceLayer\n* ReduceLayerTraitConstConstant methods for crate::dnn::ReduceLayer\n* RegionLayerTraitMutable methods for crate::dnn::RegionLayer\n* RegionLayerTraitConstConstant methods for crate::dnn::RegionLayer\n* ReorgLayerTraitMutable methods for crate::dnn::ReorgLayer\n* ReorgLayerTraitConstConstant methods for crate::dnn::ReorgLayer\n* RequantizeLayerTraitMutable methods for crate::dnn::RequantizeLayer\n* RequantizeLayerTraitConstConstant methods for crate::dnn::RequantizeLayer\n* ReshapeLayerTraitMutable methods for crate::dnn::ReshapeLayer\n* ReshapeLayerTraitConstConstant methods for crate::dnn::ReshapeLayer\n* ResizeLayerTraitMutable methods for crate::dnn::ResizeLayer\n* ResizeLayerTraitConstConstant methods for crate::dnn::ResizeLayer\n* RoundLayerTraitMutable methods for crate::dnn::RoundLayer\n* RoundLayerTraitConstConstant methods for crate::dnn::RoundLayer\n* ScaleLayerInt8TraitMutable methods for crate::dnn::ScaleLayerInt8\n* ScaleLayerInt8TraitConstConstant methods for crate::dnn::ScaleLayerInt8\n* ScaleLayerTraitMutable methods for crate::dnn::ScaleLayer\n* ScaleLayerTraitConstConstant methods for crate::dnn::ScaleLayer\n* ScatterLayerTraitMutable methods for crate::dnn::ScatterLayer\n* ScatterLayerTraitConstConstant methods for crate::dnn::ScatterLayer\n* ScatterNDLayerTraitMutable methods for crate::dnn::ScatterNDLayer\n* ScatterNDLayerTraitConstConstant methods for crate::dnn::ScatterNDLayer\n* SegmentationModelTraitMutable methods for crate::dnn::SegmentationModel\n* SegmentationModelTraitConstConstant methods for crate::dnn::SegmentationModel\n* SeluLayerTraitMutable methods for crate::dnn::SeluLayer\n* SeluLayerTraitConstConstant methods for crate::dnn::SeluLayer\n* ShiftLayerInt8TraitMutable methods for crate::dnn::ShiftLayerInt8\n* ShiftLayerInt8TraitConstConstant methods for crate::dnn::ShiftLayerInt8\n* ShiftLayerTraitMutable methods for crate::dnn::ShiftLayer\n* ShiftLayerTraitConstConstant methods for crate::dnn::ShiftLayer\n* ShrinkLayerTraitMutable methods for crate::dnn::ShrinkLayer\n* ShrinkLayerTraitConstConstant methods for crate::dnn::ShrinkLayer\n* ShuffleChannelLayerTraitMutable methods for crate::dnn::ShuffleChannelLayer\n* ShuffleChannelLayerTraitConstConstant methods for crate::dnn::ShuffleChannelLayer\n* SigmoidLayerTraitMutable methods for crate::dnn::SigmoidLayer\n* SigmoidLayerTraitConstConstant methods for crate::dnn::SigmoidLayer\n* SignLayerTraitMutable methods for crate::dnn::SignLayer\n* SignLayerTraitConstConstant methods for crate::dnn::SignLayer\n* SinLayerTraitMutable methods for crate::dnn::SinLayer\n* SinLayerTraitConstConstant methods for crate::dnn::SinLayer\n* SinhLayerTraitMutable methods for crate::dnn::SinhLayer\n* SinhLayerTraitConstConstant methods for crate::dnn::SinhLayer\n* SliceLayerTraitMutable methods for crate::dnn::SliceLayer\n* SliceLayerTraitConstConstant methods for crate::dnn::SliceLayer\n* SoftmaxLayerInt8TraitMutable methods for crate::dnn::SoftmaxLayerInt8\n* SoftmaxLayerInt8TraitConstConstant methods for crate::dnn::SoftmaxLayerInt8\n* SoftmaxLayerTraitMutable methods for crate::dnn::SoftmaxLayer\n* SoftmaxLayerTraitConstConstant methods for crate::dnn::SoftmaxLayer\n* SoftplusLayerTraitMutable methods for crate::dnn::SoftplusLayer\n* SoftplusLayerTraitConstConstant methods for crate::dnn::SoftplusLayer\n* SoftsignLayerTraitMutable methods for crate::dnn::SoftsignLayer\n* SoftsignLayerTraitConstConstant methods for crate::dnn::SoftsignLayer\n* SplitLayerTraitMutable methods for crate::dnn::SplitLayer\n* SplitLayerTraitConstConstant methods for crate::dnn::SplitLayer\n* SqrtLayerTraitMutable methods for crate::dnn::SqrtLayer\n* SqrtLayerTraitConstConstant methods for crate::dnn::SqrtLayer\n* SwishLayerTraitMutable methods for crate::dnn::SwishLayer\n* SwishLayerTraitConstConstant methods for crate::dnn::SwishLayer\n* TanHLayerTraitMutable methods for crate::dnn::TanHLayer\n* TanHLayerTraitConstConstant methods for crate::dnn::TanHLayer\n* TanLayerTraitMutable methods for crate::dnn::TanLayer\n* TanLayerTraitConstConstant methods for crate::dnn::TanLayer\n* TextDetectionModelTraitMutable methods for crate::dnn::TextDetectionModel\n* TextDetectionModelTraitConstConstant methods for crate::dnn::TextDetectionModel\n* TextDetectionModel_DBTraitMutable methods for crate::dnn::TextDetectionModel_DB\n* TextDetectionModel_DBTraitConstConstant methods for crate::dnn::TextDetectionModel_DB\n* TextDetectionModel_EASTTraitMutable methods for crate::dnn::TextDetectionModel_EAST\n* TextDetectionModel_EASTTraitConstConstant methods for crate::dnn::TextDetectionModel_EAST\n* TextRecognitionModelTraitMutable methods for crate::dnn::TextRecognitionModel\n* TextRecognitionModelTraitConstConstant methods for crate::dnn::TextRecognitionModel\n* ThresholdedReluLayerTraitMutable methods for crate::dnn::ThresholdedReluLayer\n* ThresholdedReluLayerTraitConstConstant methods for crate::dnn::ThresholdedReluLayer\n* TileLayerTraitMutable methods for crate::dnn::TileLayer\n* TileLayerTraitConstConstant methods for crate::dnn::TileLayer\n* _RangeTraitMutable methods for crate::dnn::_Range\n* _RangeTraitConstConstant methods for crate::dnn::_Range\n\nFunctions\n---\n\n* blob_from_imageCreates 4-dimensional blob from image. Optionally resizes and crops @p image from center,\nsubtract @p mean values, scales values by @p scalefactor, swap Blue and Red channels.\n* blob_from_image_defCreates 4-dimensional blob from image. Optionally resizes and crops @p image from center,\nsubtract @p mean values, scales values by @p scalefactor, swap Blue and Red channels.\n* blob_from_image_toCreates 4-dimensional blob from image.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* blob_from_image_to_defCreates 4-dimensional blob from image.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* blob_from_image_with_paramsCreates 4-dimensional blob from image with given params.\n* blob_from_image_with_params_1Creates 4-dimensional blob from image with given params.\n* blob_from_image_with_params_1_def@overload\n* blob_from_image_with_params_defCreates 4-dimensional blob from image with given params.\n* blob_from_imagesCreates 4-dimensional blob from series of images. Optionally resizes and crops @p images from center, subtract @p mean values, scales values by @p scalefactor,\nswap Blue and Red channels.\n* blob_from_images_defCreates 4-dimensional blob from series of images. Optionally resizes and crops @p images from center, subtract @p mean values, scales values by @p scalefactor,\nswap Blue and Red channels.\n* blob_from_images_toCreates 4-dimensional blob from series of images.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* blob_from_images_to_defCreates 4-dimensional blob from series of images.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* blob_from_images_with_paramsCreates 4-dimensional blob from series of images with given params.\n* blob_from_images_with_params_1Creates 4-dimensional blob from series of images with given params.\n* blob_from_images_with_params_1_def@overload\n* blob_from_images_with_params_defCreates 4-dimensional blob from series of images with given params.\n* concat\n* enable_model_diagnosticsEnables detailed logging of the DNN model loading with CV DNN API.\n* get_available_backends\n* get_available_targets\n* get_inference_engine_backend_typeReturns Inference Engine internal backend API.\n* get_inference_engine_cpu_typeReturns Inference Engine CPU type.\n* get_inference_engine_vpu_typeReturns Inference Engine VPU type.\n* get_plane\n* images_from_blobParse a 4D blob and output the images it contains as 2D arrays through a simpler data structure\n(std::vectorcv::Mat).\n* nms_boxesPerforms non maximum suppression given boxes and corresponding scores.\n* nms_boxes_batchedPerforms batched non maximum suppression on given boxes and corresponding scores across different classes.\n* nms_boxes_batched_1C++ default parameters\n* nms_boxes_batched_1_defNote\n* nms_boxes_batched_defPerforms batched non maximum suppression on given boxes and corresponding scores across different classes.\n* nms_boxes_defPerforms non maximum suppression given boxes and corresponding scores.\n* nms_boxes_f64C++ default parameters\n* nms_boxes_f64_defNote\n* nms_boxes_rotatedC++ default parameters\n* nms_boxes_rotated_defNote\n* read_netRead deep learning network represented in one of the supported formats.\n* read_net_1Read deep learning network represented in one of the supported formats.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_1_defRead deep learning network represented in one of the supported formats.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_defRead deep learning network represented in one of the supported formats.\n* read_net_from_caffeReads a network model stored in Caffe framework’s format.\n* read_net_from_caffe_bufferReads a network model stored in Caffe model in memory.\n* read_net_from_caffe_buffer_defReads a network model stored in Caffe model in memory.\n* read_net_from_caffe_defReads a network model stored in Caffe framework’s format.\n* read_net_from_caffe_strReads a network model stored in Caffe model in memory.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_from_caffe_str_defReads a network model stored in Caffe model in memory.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_from_darknetReads a network model stored in Darknet model files.\n* read_net_from_darknet_bufferReads a network model stored in Darknet model files.\n* read_net_from_darknet_buffer_defReads a network model stored in Darknet model files.\n* read_net_from_darknet_defReads a network model stored in Darknet model files.\n* read_net_from_darknet_strReads a network model stored in Darknet model files.\n* read_net_from_darknet_str_defReads a network model stored in Darknet model files.\n* read_net_from_model_optimizerLoad a network from Intel’s Model Optimizer intermediate representation.\n* read_net_from_model_optimizer_1Load a network from Intel’s Model Optimizer intermediate representation.\n* read_net_from_model_optimizer_2Load a network from Intel’s Model Optimizer intermediate representation.\n* read_net_from_onnxReads a network model ONNX.\n* read_net_from_onnx_bufferReads a network model from ONNX in-memory buffer.\n* read_net_from_onnx_strReads a network model from ONNX in-memory buffer.\n* read_net_from_tensorflowReads a network model stored in TensorFlow framework’s format.\n* read_net_from_tensorflow_bufferReads a network model stored in TensorFlow framework’s format.\n* read_net_from_tensorflow_buffer_defReads a network model stored in TensorFlow framework’s format.\n* read_net_from_tensorflow_defReads a network model stored in TensorFlow framework’s format.\n* read_net_from_tensorflow_strReads a network model stored in TensorFlow framework’s format.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_from_tensorflow_str_defReads a network model stored in TensorFlow framework’s format.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_from_tf_liteReads a network model stored in TFLite framework’s format.\n* read_net_from_tf_lite_1Reads a network model stored in TFLite framework’s format.\n* read_net_from_tf_lite_2Reads a network model stored in TFLite framework’s format.\n@details This is an overloaded member function, provided for convenience.\nIt differs from the above function only in what argument(s) it accepts.\n* read_net_from_torchReads a network model stored in Torch7 framework’s format.\n* read_net_from_torch_defReads a network model stored in Torch7 framework’s format.\n* read_tensor_from_onnxCreates blob from .pb file.\n* read_torch_blobLoads blob which was serialized as torch.Tensor object of Torch7 framework.\n@warning This function has the same limitations as readNetFromTorch().\n* read_torch_blob_defLoads blob which was serialized as torch.Tensor object of Torch7 framework.\n@warning This function has the same limitations as readNetFromTorch().\n* release_hddl_pluginRelease a HDDL plugin.\n* reset_myriad_deviceRelease a Myriad device (binded by OpenCV).\n* set_inference_engine_backend_typeSpecify Inference Engine internal backend API.\n* shape\n* shape_1\n* shape_2\n* shape_3\n* shape_4C++ default parameters\n* shape_4_defNote\n* shrink_caffe_modelConvert all weights of Caffe network to half precision floating point.\n* shrink_caffe_model_defConvert all weights of Caffe network to half precision floating point.\n* slice\n* slice_1\n* slice_2\n* slice_3\n* soft_nms_boxesPerforms soft non maximum suppression given boxes and corresponding scores.\nReference: https://arxiv.org/abs/1704.04503\n* soft_nms_boxes_defPerforms soft non maximum suppression given boxes and corresponding scores.\nReference: https://arxiv.org/abs/1704.04503\n* totalC++ default parameters\n* total_1C++ default parameters\n* total_1_defNote\n* total_defNote\n* write_text_graphCreate a text representation for a binary network stored in protocol buffer format.\n\nType Aliases\n---\n\n* LayerFactory_ConstructorEach Layer class must provide this function to the factory\n* MatShape\n* Net_LayerIdDeprecatedContainer for strings and integers.\n\nModule opencv::dnn_superres\n===\n\nDNN used for super resolution\n---\n\nThis module contains functionality for upscaling an image via convolutional neural networks.\nThe following four models are implemented:\n\n* EDSR https://arxiv.org/abs/1707.02921\n* ESPCN https://arxiv.org/abs/1609.05158\n* FSRCNN https://arxiv.org/abs/1608.00367\n* LapSRN https://arxiv.org/abs/1710.01992\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* DnnSuperResImplA class to upscale images via convolutional neural networks.\nThe following four models are implemented:\n\nTraits\n---\n\n* DnnSuperResImplTraitMutable methods for crate::dnn_superres::DnnSuperResImpl\n* DnnSuperResImplTraitConstConstant methods for crate::dnn_superres::DnnSuperResImpl\n\nModule opencv::dpm\n===\n\nDeformable Part-based Models\n---\n\n### Discriminatively Trained Part Based Models for Object Detection\n\nThe object detector described below has been initially proposed by <NAME> in Felzenszwalb2010a . It is based on a Dalal-Triggs detector that uses a single filter on histogram of oriented gradients (HOG) features to represent an object category. This detector uses a sliding window approach, where a filter is applied at all positions and scales of an image. The first innovation is enriching the Dalal-Triggs model using a star-structured part-based model defined by a\n“root” filter (analogous to the Dalal-Triggs filter) plus a set of parts filters and associated deformation models. The score of one of star models at a particular position and scale within an image is the score of the root filter at the given location plus the sum over parts of the maximum,\nover placements of that part, of the part filter score on its location minus a deformation cost easuring the deviation of the part from its ideal location relative to the root. Both root and part filter scores are defined by the dot product between a filter (a set of weights) and a subwindow of a feature pyramid computed from the input image. Another improvement is a representation of the class of models by a mixture of star models. The score of a mixture model at a particular position and scale is the maximum over components, of the score of that component model at the given location.\n\nThe detector was dramatically speeded-up with cascade algorithm proposed by <NAME> in Felzenszwalb2010b . The algorithm prunes partial hypotheses using thresholds on their scores.The basic idea of the algorithm is to use a hierarchy of models defined by an ordering of the original model’s parts. For a model with (n+1) parts, including the root, a sequence of (n+1) models is obtained. The i-th model in this sequence is defined by the first i parts from the original model.\nUsing this hierarchy, low scoring hypotheses can be pruned after looking at the best configuration of a subset of the parts. Hypotheses that score high under a weak model are evaluated further using a richer model.\n\nIn OpenCV there is an C++ implementation of DPM cascade detector.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* DPMDetectorThis is a C++ abstract class, it provides external user API to work with DPM.\n* DPMDetector_ObjectDetection\n\nTraits\n---\n\n* DPMDetectorTraitMutable methods for crate::dpm::DPMDetector\n* DPMDetectorTraitConstConstant methods for crate::dpm::DPMDetector\n* DPMDetector_ObjectDetectionTraitMutable methods for crate::dpm::DPMDetector_ObjectDetection\n* DPMDetector_ObjectDetectionTraitConstConstant methods for crate::dpm::DPMDetector_ObjectDetection\n\nModule opencv::face\n===\n\nFace Analysis\n---\n\n* [face_changelog]\n* [tutorial_face_main]\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BIFImplementation of bio-inspired features (BIF) from the paper:\n<NAME>, et al. “Human age estimation using bio-inspired features.”\nComputer Vision and Pattern Recognition, 2009. CVPR 2009.\n* BasicFaceRecognizer\n* CParams\n* EigenFaceRecognizer\n* FaceRecognizerAbstract base class for all face recognition models\n* FacemarkAbstract base class for all facemark models\n* FacemarkAAM\n* FacemarkAAM_Config\\brief Optional parameter for fitting process.\n* FacemarkAAM_Data\\brief Data container for the facemark::getData function\n* FacemarkAAM_Model\\brief The model of AAM Algorithm\n* FacemarkAAM_Model_Texture\n* FacemarkAAM_Params\n* FacemarkKazemi\n* FacemarkKazemi_Params\n* FacemarkLBF\n* FacemarkLBF_Params\n* FacemarkTrainAbstract base class for trainable facemark models\n* FisherFaceRecognizer\n* LBPHFaceRecognizer\n* MACEMinimum Average Correlation Energy Filter useful for authentication with (cancellable) biometrical features.\n(does not need many positives to train (10-50), and no negatives at all, also robust to noise/salting)\n* PredictCollectorAbstract base class for all strategies of prediction result handling\n* StandardCollectorDefault predict collector\n* StandardCollector_PredictResult\n\nTraits\n---\n\n* BIFTraitMutable methods for crate::face::BIF\n* BIFTraitConstConstant methods for crate::face::BIF\n* BasicFaceRecognizerTraitMutable methods for crate::face::BasicFaceRecognizer\n* BasicFaceRecognizerTraitConstConstant methods for crate::face::BasicFaceRecognizer\n* CParamsTraitMutable methods for crate::face::CParams\n* CParamsTraitConstConstant methods for crate::face::CParams\n* EigenFaceRecognizerTraitMutable methods for crate::face::EigenFaceRecognizer\n* EigenFaceRecognizerTraitConstConstant methods for crate::face::EigenFaceRecognizer\n* FaceRecognizerTraitMutable methods for crate::face::FaceRecognizer\n* FaceRecognizerTraitConstConstant methods for crate::face::FaceRecognizer\n* FacemarkAAMTraitMutable methods for crate::face::FacemarkAAM\n* FacemarkAAMTraitConstConstant methods for crate::face::FacemarkAAM\n* FacemarkAAM_ConfigTraitMutable methods for crate::face::FacemarkAAM_Config\n* FacemarkAAM_ConfigTraitConstConstant methods for crate::face::FacemarkAAM_Config\n* FacemarkAAM_DataTraitMutable methods for crate::face::FacemarkAAM_Data\n* FacemarkAAM_DataTraitConstConstant methods for crate::face::FacemarkAAM_Data\n* FacemarkAAM_ModelTraitMutable methods for crate::face::FacemarkAAM_Model\n* FacemarkAAM_ModelTraitConstConstant methods for crate::face::FacemarkAAM_Model\n* FacemarkAAM_Model_TextureTraitMutable methods for crate::face::FacemarkAAM_Model_Texture\n* FacemarkAAM_Model_TextureTraitConstConstant methods for crate::face::FacemarkAAM_Model_Texture\n* FacemarkAAM_ParamsTraitMutable methods for crate::face::FacemarkAAM_Params\n* FacemarkAAM_ParamsTraitConstConstant methods for crate::face::FacemarkAAM_Params\n* FacemarkKazemiTraitMutable methods for crate::face::FacemarkKazemi\n* FacemarkKazemiTraitConstConstant methods for crate::face::FacemarkKazemi\n* FacemarkKazemi_ParamsTraitMutable methods for crate::face::FacemarkKazemi_Params\n* FacemarkKazemi_ParamsTraitConstConstant methods for crate::face::FacemarkKazemi_Params\n* FacemarkLBFTraitMutable methods for crate::face::FacemarkLBF\n* FacemarkLBFTraitConstConstant methods for crate::face::FacemarkLBF\n* FacemarkLBF_ParamsTraitMutable methods for crate::face::FacemarkLBF_Params\n* FacemarkLBF_ParamsTraitConstConstant methods for crate::face::FacemarkLBF_Params\n* FacemarkTrainTraitMutable methods for crate::face::FacemarkTrain\n* FacemarkTrainTraitConstConstant methods for crate::face::FacemarkTrain\n* FacemarkTraitMutable methods for crate::face::Facemark\n* FacemarkTraitConstConstant methods for crate::face::Facemark\n* FisherFaceRecognizerTraitMutable methods for crate::face::FisherFaceRecognizer\n* FisherFaceRecognizerTraitConstConstant methods for crate::face::FisherFaceRecognizer\n* LBPHFaceRecognizerTraitMutable methods for crate::face::LBPHFaceRecognizer\n* LBPHFaceRecognizerTraitConstConstant methods for crate::face::LBPHFaceRecognizer\n* MACETraitMutable methods for crate::face::MACE\n* MACETraitConstConstant methods for crate::face::MACE\n* PredictCollectorTraitMutable methods for crate::face::PredictCollector\n* PredictCollectorTraitConstConstant methods for crate::face::PredictCollector\n* StandardCollectorTraitMutable methods for crate::face::StandardCollector\n* StandardCollectorTraitConstConstant methods for crate::face::StandardCollector\n\nFunctions\n---\n\n* create_facemark_aamconstruct an AAM facemark detector\n* create_facemark_kazemiconstruct a Kazemi facemark detector\n* create_facemark_lbfconstruct an LBF facemark detector\n* draw_facemarksUtility to draw the detected facial landmark points\n* draw_facemarks_defUtility to draw the detected facial landmark points\n* get_facesDefault face detector This function is mainly utilized by the implementation of a Facemark Algorithm.\nEnd users are advised to use function Facemark::getFaces which can be manually defined and circumvented to the algorithm by Facemark::setFaceDetector.\n* get_faces_haar\n* load_dataset_listA utility to load list of paths to training image and annotation file.\n* load_face_pointsA utility to load facial landmark information from a given file.\n* load_face_points_defA utility to load facial landmark information from a given file.\n* load_training_dataA utility to load facial landmark dataset from a single file.\n* load_training_data_1A utility to load facial landmark information from the dataset.\n* load_training_data_1_defA utility to load facial landmark information from the dataset.\n* load_training_data_2This function extracts the data for training from .txt files which contains the corresponding image name and landmarks.\nThe first file in each file should give the path of the image whose landmarks are being described in the file. Then in the subsequent lines there should be coordinates of the landmarks in the image i.e each line should be of the form x,y where x represents the x coordinate of the landmark and y represents the y coordinate of the landmark.\n* load_training_data_defA utility to load facial landmark dataset from a single file.\n\nType Aliases\n---\n\n* FN_FaceDetector\n\nModule opencv::features2d\n===\n\n2D Features Framework\n---\n\nFeature Detection and Description\n---\n\nDescriptor Matchers\n---\n\nMatchers of keypoint descriptors in OpenCV have wrappers with a common interface that enables you to easily switch between different algorithms solving the same problem. This section is devoted to matching descriptors that are represented as vectors in a multidimensional space. All objects that implement vector descriptor matchers inherit the DescriptorMatcher interface.\n\nDrawing Function of Keypoints and Matches\n---\n\nObject Categorization\n---\n\nThis section describes approaches based on local 2D features and used to categorize objects.\n\nHardware Acceleration Layer\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AKAZEClass implementing the AKAZE keypoint detector and descriptor extractor, described in ANB13.\n* AffineFeatureClass for implementing the wrapper which makes detectors and extractors to be affine invariant,\ndescribed as ASIFT in YM11 .\n* AgastFeatureDetectorWrapping class for feature detection using the AGAST method. :\n* BFMatcherBrute-force descriptor matcher.\n* BOWImgDescriptorExtractorClass to compute an image descriptor using the *bag of visual words*.\n* BOWKMeansTrainerkmeans -based class to train visual vocabulary using the *bag of visual words* approach. :\n* BOWTrainerAbstract base class for training the *bag of visual words* vocabulary from a set of descriptors.\n* BRISKClass implementing the BRISK keypoint detector and descriptor extractor, described in LCS11 .\n* DescriptorMatcherAbstract base class for matching keypoint descriptors.\n* FastFeatureDetectorWrapping class for feature detection using the FAST method. :\n* Feature2D\n* FlannBasedMatcherFlann-based descriptor matcher.\n* GFTTDetectorWrapping class for feature detection using the goodFeaturesToTrack function. :\n* KAZEClass implementing the KAZE keypoint detector and descriptor extractor, described in ABD12 .\n* KeyPointsFilterA class filters a vector of keypoints.\n* MSERMaximally stable extremal region extractor\n* ORBClass implementing the ORB (*oriented BRIEF*) keypoint detector and descriptor extractor\n* SIFTClass for extracting keypoints and computing descriptors using the Scale Invariant Feature Transform\n(SIFT) algorithm by <NAME> .\n* SimpleBlobDetectorClass for extracting blobs from an image. :\n* SimpleBlobDetector_Params\n\nEnums\n---\n\n* AKAZE_DescriptorType\n* AgastFeatureDetector_DetectorType\n* DescriptorMatcher_MatcherType\n* DrawMatchesFlags\n* FastFeatureDetector_DetectorType\n* KAZE_DiffusivityType\n* ORB_ScoreType\n\nConstants\n---\n\n* AKAZE_DESCRIPTOR_KAZE\n* AKAZE_DESCRIPTOR_KAZE_UPRIGHTUpright descriptors, not invariant to rotation\n* AKAZE_DESCRIPTOR_MLDB\n* AKAZE_DESCRIPTOR_MLDB_UPRIGHTUpright descriptors, not invariant to rotation\n* AgastFeatureDetector_AGAST_5_8\n* AgastFeatureDetector_AGAST_7_12d\n* AgastFeatureDetector_AGAST_7_12s\n* AgastFeatureDetector_NONMAX_SUPPRESSION\n* AgastFeatureDetector_OAST_9_16\n* AgastFeatureDetector_THRESHOLD\n* DescriptorMatcher_BRUTEFORCE\n* DescriptorMatcher_BRUTEFORCE_HAMMING\n* DescriptorMatcher_BRUTEFORCE_HAMMINGLUT\n* DescriptorMatcher_BRUTEFORCE_L1\n* DescriptorMatcher_BRUTEFORCE_SL2\n* DescriptorMatcher_FLANNBASED\n* DrawMatchesFlags_DEFAULTOutput image matrix will be created (Mat::create),\ni.e. existing memory of output image may be reused.\nTwo source image, matches and single keypoints will be drawn.\nFor each keypoint only the center point will be drawn (without the circle around keypoint with keypoint size and orientation).\n* DrawMatchesFlags_DRAW_OVER_OUTIMGOutput image matrix will not be created (Mat::create).\nMatches will be drawn on existing content of output image.\n* DrawMatchesFlags_DRAW_RICH_KEYPOINTSFor each keypoint the circle around keypoint with keypoint size and orientation will be drawn.\n* DrawMatchesFlags_NOT_DRAW_SINGLE_POINTSSingle keypoints will not be drawn.\n* FastFeatureDetector_FAST_N\n* FastFeatureDetector_NONMAX_SUPPRESSION\n* FastFeatureDetector_THRESHOLD\n* FastFeatureDetector_TYPE_5_8\n* FastFeatureDetector_TYPE_7_12\n* FastFeatureDetector_TYPE_9_16\n* KAZE_DIFF_CHARBONNIER\n* KAZE_DIFF_PM_G1\n* KAZE_DIFF_PM_G2\n* KAZE_DIFF_WEICKERT\n* ORB_FAST_SCORE\n* ORB_HARRIS_SCORE\n\nTraits\n---\n\n* AKAZETraitMutable methods for crate::features2d::AKAZE\n* AKAZETraitConstConstant methods for crate::features2d::AKAZE\n* AffineFeatureTraitMutable methods for crate::features2d::AffineFeature\n* AffineFeatureTraitConstConstant methods for crate::features2d::AffineFeature\n* AgastFeatureDetectorTraitMutable methods for crate::features2d::AgastFeatureDetector\n* AgastFeatureDetectorTraitConstConstant methods for crate::features2d::AgastFeatureDetector\n* BFMatcherTraitMutable methods for crate::features2d::BFMatcher\n* BFMatcherTraitConstConstant methods for crate::features2d::BFMatcher\n* BOWImgDescriptorExtractorTraitMutable methods for crate::features2d::BOWImgDescriptorExtractor\n* BOWImgDescriptorExtractorTraitConstConstant methods for crate::features2d::BOWImgDescriptorExtractor\n* BOWKMeansTrainerTraitMutable methods for crate::features2d::BOWKMeansTrainer\n* BOWKMeansTrainerTraitConstConstant methods for crate::features2d::BOWKMeansTrainer\n* BOWTrainerTraitMutable methods for crate::features2d::BOWTrainer\n* BOWTrainerTraitConstConstant methods for crate::features2d::BOWTrainer\n* BRISKTraitMutable methods for crate::features2d::BRISK\n* BRISKTraitConstConstant methods for crate::features2d::BRISK\n* DescriptorMatcherTraitMutable methods for crate::features2d::DescriptorMatcher\n* DescriptorMatcherTraitConstConstant methods for crate::features2d::DescriptorMatcher\n* FastFeatureDetectorTraitMutable methods for crate::features2d::FastFeatureDetector\n* FastFeatureDetectorTraitConstConstant methods for crate::features2d::FastFeatureDetector\n* Feature2DTraitMutable methods for crate::features2d::Feature2D\n* Feature2DTraitConstConstant methods for crate::features2d::Feature2D\n* FlannBasedMatcherTraitMutable methods for crate::features2d::FlannBasedMatcher\n* FlannBasedMatcherTraitConstConstant methods for crate::features2d::FlannBasedMatcher\n* GFTTDetectorTraitMutable methods for crate::features2d::GFTTDetector\n* GFTTDetectorTraitConstConstant methods for crate::features2d::GFTTDetector\n* KAZETraitMutable methods for crate::features2d::KAZE\n* KAZETraitConstConstant methods for crate::features2d::KAZE\n* KeyPointsFilterTraitMutable methods for crate::features2d::KeyPointsFilter\n* KeyPointsFilterTraitConstConstant methods for crate::features2d::KeyPointsFilter\n* MSERTraitMutable methods for crate::features2d::MSER\n* MSERTraitConstConstant methods for crate::features2d::MSER\n* ORBTraitMutable methods for crate::features2d::ORB\n* ORBTraitConstConstant methods for crate::features2d::ORB\n* SIFTTraitMutable methods for crate::features2d::SIFT\n* SIFTTraitConstConstant methods for crate::features2d::SIFT\n* SimpleBlobDetectorTraitMutable methods for crate::features2d::SimpleBlobDetector\n* SimpleBlobDetectorTraitConstConstant methods for crate::features2d::SimpleBlobDetector\n\nFunctions\n---\n\n* agastDetects corners using the AGAST algorithm\n* agast_def@overload\n* agast_with_typeDetects corners using the AGAST algorithm\n* compute_recall_precision_curve\n* draw_keypointsDraws keypoints.\n* draw_keypoints_defDraws keypoints.\n* draw_matchesDraws the found matches of keypoints from two images.\n* draw_matches_1Draws the found matches of keypoints from two images.\n* draw_matches_1_def@overload\n* draw_matches_defDraws the found matches of keypoints from two images.\n* draw_matches_knnC++ default parameters\n* draw_matches_knn_defNote\n* evaluate_feature_detector *************************************************************************************Functions to evaluate the feature detectors and [generic] descriptor extractors *\n***************************************************************************************\n* evaluate_feature_detector_def *************************************************************************************Functions to evaluate the feature detectors and [generic] descriptor extractors *\n***************************************************************************************\n* fastDetects corners using the FAST algorithm\n* fast_def@overload\n* fast_with_typeDetects corners using the FAST algorithm\n* get_nearest_point\n* get_recall\n\nType Aliases\n---\n\n* AffineDescriptorExtractor\n* AffineFeatureDetector\n* DescriptorExtractorExtractors of keypoint descriptors in OpenCV have wrappers with a common interface that enables you to easily switch between different algorithms solving the same problem. This section is devoted to computing descriptors represented as vectors in a multidimensional space. All objects that implement the vector descriptor extractors inherit the DescriptorExtractor interface.\n* FeatureDetectorFeature detectors in OpenCV have wrappers with a common interface that enables you to easily switch between different algorithms solving the same problem. All objects that implement keypoint detectors inherit the FeatureDetector interface.\n* SiftDescriptorExtractor\n* SiftFeatureDetector\n\nModule opencv::flann\n===\n\nClustering and Search in Multi-Dimensional Spaces\n---\n\nThis section documents OpenCV’s interface to the FLANN library. FLANN (Fast Library for Approximate Nearest Neighbors) is a library that contains a collection of algorithms optimized for fast nearest neighbor search in large datasets and for high dimensional features. More information about FLANN can be found in Muja2009 .\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AutotunedIndexParams\n* CompositeIndexParams\n* HierarchicalClusteringIndexParams\n* Index\n* IndexParams\n* KDTreeIndexParams\n* KMeansIndexParams\n* LinearIndexParams\n* LshIndexParams\n* SavedIndexParams\n* SearchParams\n\nEnums\n---\n\n* FlannIndexType\n* flann_algorithm_t\n* flann_centers_init_t\n* flann_datatype_t\n* flann_distance_t\n* flann_log_level_t\n\nConstants\n---\n\n* AUTOTUNED\n* BITS_PER_BASE\n* BITS_PER_CHAR\n* BLOCKSIZE\n* CENTERS_GONZALES\n* CENTERS_KMEANSPP\n* CENTERS_RANDOM\n* COMPOSITE\n* CS\n* EUCLIDEAN\n* FLANN_CENTERS_GONZALES\n* FLANN_CENTERS_GROUPWISE\n* FLANN_CENTERS_KMEANSPP\n* FLANN_CENTERS_RANDOM\n* FLANN_CHECKS_AUTOTUNED\n* FLANN_CHECKS_UNLIMITED\n* FLANN_DIST_CHI_SQUARE\n* FLANN_DIST_CS\n* FLANN_DIST_DNAMMING\n* FLANN_DIST_EUCLIDEAN\n* FLANN_DIST_HAMMING\n* FLANN_DIST_HELLINGER\n* FLANN_DIST_HIST_INTERSECT\n* FLANN_DIST_KL\n* FLANN_DIST_KULLBACK_LEIBLER\n* FLANN_DIST_L1\n* FLANN_DIST_L2\n* FLANN_DIST_MANHATTAN\n* FLANN_DIST_MAX\n* FLANN_DIST_MINKOWSKI\n* FLANN_FLOAT32\n* FLANN_FLOAT64\n* FLANN_INDEX_AUTOTUNED\n* FLANN_INDEX_COMPOSITE\n* FLANN_INDEX_HIERARCHICAL\n* FLANN_INDEX_KDTREE\n* FLANN_INDEX_KDTREE_SINGLE\n* FLANN_INDEX_KMEANS\n* FLANN_INDEX_LINEAR\n* FLANN_INDEX_LSH\n* FLANN_INDEX_SAVED\n* FLANN_INDEX_TYPE_8S\n* FLANN_INDEX_TYPE_8U\n* FLANN_INDEX_TYPE_16S\n* FLANN_INDEX_TYPE_16U\n* FLANN_INDEX_TYPE_32F\n* FLANN_INDEX_TYPE_32S\n* FLANN_INDEX_TYPE_64F\n* FLANN_INDEX_TYPE_ALGORITHM\n* FLANN_INDEX_TYPE_BOOL\n* FLANN_INDEX_TYPE_STRING\n* FLANN_INT8\n* FLANN_INT16\n* FLANN_INT32\n* FLANN_INT64\n* FLANN_LOG_ERROR\n* FLANN_LOG_FATAL\n* FLANN_LOG_INFO\n* FLANN_LOG_NONE\n* FLANN_LOG_WARN\n* FLANN_SIGNATURE_\n* FLANN_UINT8\n* FLANN_UINT16\n* FLANN_UINT32\n* FLANN_UINT64\n* FLANN_USE_BOOST\n* FLANN_VERSION_\n* HELLINGER\n* HIST_INTERSECT\n* KDTREE\n* KDTREE_SINGLE\n* KL\n* KMEANS\n* KULLBACK_LEIBLER\n* LAST_VALUE_FLANN_INDEX_TYPE\n* LINEAR\n* MANHATTAN\n* MAX_DIST\n* MINKOWSKI\n* SAVED\n* USE_UNORDERED_MAP\n* WORDSIZEPooled storage allocator\n\nTraits\n---\n\n* AutotunedIndexParamsTraitMutable methods for crate::flann::AutotunedIndexParams\n* AutotunedIndexParamsTraitConstConstant methods for crate::flann::AutotunedIndexParams\n* CompositeIndexParamsTraitMutable methods for crate::flann::CompositeIndexParams\n* CompositeIndexParamsTraitConstConstant methods for crate::flann::CompositeIndexParams\n* HierarchicalClusteringIndexParamsTraitMutable methods for crate::flann::HierarchicalClusteringIndexParams\n* HierarchicalClusteringIndexParamsTraitConstConstant methods for crate::flann::HierarchicalClusteringIndexParams\n* IndexParamsTraitMutable methods for crate::flann::IndexParams\n* IndexParamsTraitConstConstant methods for crate::flann::IndexParams\n* IndexTraitMutable methods for crate::flann::Index\n* IndexTraitConstConstant methods for crate::flann::Index\n* KDTreeIndexParamsTraitMutable methods for crate::flann::KDTreeIndexParams\n* KDTreeIndexParamsTraitConstConstant methods for crate::flann::KDTreeIndexParams\n* KMeansIndexParamsTraitMutable methods for crate::flann::KMeansIndexParams\n* KMeansIndexParamsTraitConstConstant methods for crate::flann::KMeansIndexParams\n* LinearIndexParamsTraitMutable methods for crate::flann::LinearIndexParams\n* LinearIndexParamsTraitConstConstant methods for crate::flann::LinearIndexParams\n* LshIndexParamsTraitMutable methods for crate::flann::LshIndexParams\n* LshIndexParamsTraitConstConstant methods for crate::flann::LshIndexParams\n* SavedIndexParamsTraitMutable methods for crate::flann::SavedIndexParams\n* SavedIndexParamsTraitConstConstant methods for crate::flann::SavedIndexParams\n* SearchParamsTraitMutable methods for crate::flann::SearchParams\n* SearchParamsTraitConstConstant methods for crate::flann::SearchParams\n\nFunctions\n---\n\n* flann_distance_type\n* set_distance_type\n\nType Aliases\n---\n\n* BucketA bucket in an LSH table\n* bucket_keyThe id from which we can get a bucket back in an LSH table\n* feature_indexWhat is stored in an LSH bucket\n\nModule opencv::freetype\n===\n\nDrawing UTF-8 strings with freetype/harfbuzz\n---\n\nThis modules is to draw UTF-8 strings with freetype/harfbuzz.\n\n1. Install freetype2 and harfbuzz in your system.\n2. Create FreeType2 instance with createFreeType2() function.\n3. Load font file with loadFontData() function.\n4. Draw text with putText() function.\n\n* If thickness parameter is negative, drawing glyph is filled.\n* If thickness parameter is positive, drawing glyph is outlined with thickness.\n* If line_type parameter is 16(or CV_AA), drawing glyph is smooth.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* FreeType2\n\nTraits\n---\n\n* FreeType2TraitMutable methods for crate::freetype::FreeType2\n* FreeType2TraitConstConstant methods for crate::freetype::FreeType2\n\nFunctions\n---\n\n* create_free_type2Create FreeType2 Instance\n\nModule opencv::fuzzy\n===\n\nImage processing based on fuzzy mathematics\n---\n\nNamespace for all functions is `ft`. The module brings implementation of the last image processing algorithms based on fuzzy mathematics. Method are named based on the pattern `FT`_degree_dimension`_`method.\n\nMath with F0-transform support\n---\n\nFuzzy transform (-transform) of the 0th degree transforms whole image to a matrix of its components. These components are used in latter computation where each of them represents average color of certain subarea.\n\nMath with F1-transform support\n---\n\nFuzzy transform (-transform) of the 1th degree transforms whole image to a matrix of its components. Each component is polynomial of the 1th degree carrying information about average color and average gradient of certain subarea.\n\nFuzzy image processing\n---\n\nImage proceesing based on fuzzy mathematics namely F-transform.\n\nModules\n---\n\n* prelude\n\nConstants\n---\n\n* ITERATIVEprocessing in several iterations\n* LINEARlinear (triangular) shape\n* MULTI_STEPprocessing in multiple step\n* ONE_STEPprocessing in one step\n* SINUSsinusoidal shape\n\nFunctions\n---\n\n* create_kernelCreates kernel from general functions.\n* create_kernel1Creates kernel from basic functions.\n* filterImage filtering\n* ft0_2d_componentsComputes components of the array using direct inline formula-transform.\n* ft0_2d_components_defComputes components of the array using direct inline formula-transform.\n* ft0_2d_fl_processSligtly less accurate version of inline formula-transfrom computation optimized for higher speed. The methods counts with linear basic function.\n* ft0_2d_fl_process_floatSligtly less accurate version of inline formula-transfrom computation optimized for higher speed. The methods counts with linear basic function.\n* ft0_2d_inverse_ftComputes inverse inline formula-transfrom.\n* ft0_2d_iterationComputes inline formula-transfrom and inverse inline formula-transfrom at once and return state.\n* ft0_2d_processComputes inline formula-transfrom and inverse inline formula-transfrom at once.\n* ft0_2d_process_defComputes inline formula-transfrom and inverse inline formula-transfrom at once.\n* ft1_2d_componentsComputes components of the array using direct inline formula-transform.\n* ft1_2d_create_polynom_matrix_horizontalCreates horizontal matrix for inline formula-transform computation.\n* ft1_2d_create_polynom_matrix_verticalCreates vertical matrix for inline formula-transform computation.\n* ft1_2d_inverse_ftComputes inverse inline formula-transfrom.\n* ft1_2d_polynomialComputes elements of inline formula-transform components.\n* ft1_2d_polynomial_defComputes elements of inline formula-transform components.\n* ft1_2d_processComputes inline formula-transfrom and inverse inline formula-transfrom at once.\n* ft1_2d_process_defComputes inline formula-transfrom and inverse inline formula-transfrom at once.\n* inpaintImage inpainting\n\nModule opencv::gapi\n===\n\n\\defgroup gapi G-API framework\n\nG-API Main Classes\n---\n\nG-API Data Types\n---\n\nG-API Standard Backends\n---\n\nG-API Graph Compilation Arguments\n---\n\nG-API Serialization functionality\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CircleThis structure represents a circle to draw.\n* DataThis aggregate type represents all types which G-API can handle (via variant).\n* Detail_ExtractArgsCallback\n* Detail_ExtractMetaCallback\n* Detail_GArrayU\n* Detail_GOpaqueU\n* GArg\n* GArrayDesc\\addtogroup gapi_meta_args\n* GBackend@private\n* GCall\n* GCompileArgRepresents an arbitrary compilation argument.\n* GCompiled\\addtogroup gapi_main_classes\n/\n* GComputation\\addtogroup gapi_main_classes\n* GFrame\\addtogroup gapi_data_objects\n/\n* GFrameDesc\\addtogroup gapi_meta_args\n* GFunctor@private\n* GKernel\n* GKernelImpl\n* GKernelPackageA container class for heterogeneous kernel implementation collections and graph transformations.\n* GMat\\addtogroup gapi_data_objects\n* GMatDesc\\addtogroup gapi_meta_args\n* GMatP\n* GOpaqueDesc\\addtogroup gapi_meta_args\n* GRunArg\n* GScalar\\addtogroup gapi_data_objects\n/\n* GScalarDesc\\addtogroup gapi_meta_args\n* GStreamingCompiled\\addtogroup gapi_main_classes\n/\n* GTransform\n* GTypeInfo\n* ImageThis structure represents an image to draw.\n* LineThis structure represents a line to draw.\n* MediaFrame\\addtogroup gapi_data_structures\n* MediaFrame_IAdapterAn interface class for MediaFrame data adapters.\n* MediaFrame_ViewProvides access to the MediaFrame’s underlying data.\n* MosaicThis structure represents a mosaicing operation.\n* PolyThis structure represents a polygon to draw.\n* RMat\\addtogroup gapi_data_structures\n* RMat_IAdapter\n* RMat_View\n* RectThis structure represents a rectangle to draw.\n* Scalar\n* TextThis structure represents a text string to draw.Parameters match cv::putText().\n* any\n* queue_capacitySpecify queue capacity for streaming execution.\n* use_only\\addtogroup gapi_compile_args\n/\n\nEnums\n---\n\n* Detail_ArgKind\n* Detail_OpaqueKind\n* GShape\n* MediaFormat\n* MediaFrame_AccessThis enum defines different types of cv::MediaFrame provided access to the underlying data. Note that different flags can’t be combined in this version.\n* RMat_Access\n\nConstants\n---\n\n* Detail_ArgKind_GARRAY\n* Detail_ArgKind_GFRAME\n* Detail_ArgKind_GMAT\n* Detail_ArgKind_GMATP\n* Detail_ArgKind_GOBJREF\n* Detail_ArgKind_GOPAQUE\n* Detail_ArgKind_GSCALAR\n* Detail_ArgKind_OPAQUE\n* Detail_ArgKind_OPAQUE_VAL\n* Detail_OpaqueKind_CV_BOOL\n* Detail_OpaqueKind_CV_DOUBLE\n* Detail_OpaqueKind_CV_DRAW_PRIM\n* Detail_OpaqueKind_CV_FLOAT\n* Detail_OpaqueKind_CV_INT\n* Detail_OpaqueKind_CV_INT64\n* Detail_OpaqueKind_CV_MAT\n* Detail_OpaqueKind_CV_POINT\n* Detail_OpaqueKind_CV_POINT2F\n* Detail_OpaqueKind_CV_POINT3F\n* Detail_OpaqueKind_CV_RECT\n* Detail_OpaqueKind_CV_SCALAR\n* Detail_OpaqueKind_CV_SIZE\n* Detail_OpaqueKind_CV_STRING\n* Detail_OpaqueKind_CV_UINT64\n* Detail_OpaqueKind_CV_UNKNOWN\n* GShape_GARRAY\n* GShape_GFRAME\n* GShape_GMAT\n* GShape_GOPAQUE\n* GShape_GSCALAR\n* MediaFormat_BGR\n* MediaFormat_GRAY\n* MediaFormat_NV12\n* MediaFrame_Access_RAccess data for reading\n* MediaFrame_Access_WAccess data for writing\n* RMat_Access_R\n* RMat_Access_W\n\nTraits\n---\n\n* DataTraitMutable methods for crate::gapi::Data\n* DataTraitConstConstant methods for crate::gapi::Data\n* Detail_ExtractArgsCallbackTraitMutable methods for crate::gapi::Detail_ExtractArgsCallback\n* Detail_ExtractArgsCallbackTraitConstConstant methods for crate::gapi::Detail_ExtractArgsCallback\n* Detail_ExtractMetaCallbackTraitMutable methods for crate::gapi::Detail_ExtractMetaCallback\n* Detail_ExtractMetaCallbackTraitConstConstant methods for crate::gapi::Detail_ExtractMetaCallback\n* Detail_GArrayUTraitMutable methods for crate::gapi::Detail_GArrayU\n* Detail_GArrayUTraitConstConstant methods for crate::gapi::Detail_GArrayU\n* Detail_GOpaqueUTraitMutable methods for crate::gapi::Detail_GOpaqueU\n* Detail_GOpaqueUTraitConstConstant methods for crate::gapi::Detail_GOpaqueU\n* GArgTraitMutable methods for crate::gapi::GArg\n* GArgTraitConstConstant methods for crate::gapi::GArg\n* GArrayDescTraitMutable methods for crate::gapi::GArrayDesc\n* GArrayDescTraitConstConstant methods for crate::gapi::GArrayDesc\n* GBackendTraitMutable methods for crate::gapi::GBackend\n* GBackendTraitConstConstant methods for crate::gapi::GBackend\n* GCallTraitMutable methods for crate::gapi::GCall\n* GCallTraitConstConstant methods for crate::gapi::GCall\n* GCompileArgTraitMutable methods for crate::gapi::GCompileArg\n* GCompileArgTraitConstConstant methods for crate::gapi::GCompileArg\n* GCompiledTraitMutable methods for crate::gapi::GCompiled\n* GCompiledTraitConstConstant methods for crate::gapi::GCompiled\n* GComputationTraitMutable methods for crate::gapi::GComputation\n* GComputationTraitConstConstant methods for crate::gapi::GComputation\n* GFrameDescTraitMutable methods for crate::gapi::GFrameDesc\n* GFrameDescTraitConstConstant methods for crate::gapi::GFrameDesc\n* GFrameTraitMutable methods for crate::gapi::GFrame\n* GFrameTraitConstConstant methods for crate::gapi::GFrame\n* GFunctorTraitMutable methods for crate::gapi::GFunctor\n* GFunctorTraitConstConstant methods for crate::gapi::GFunctor\n* GKernelImplTraitMutable methods for crate::gapi::GKernelImpl\n* GKernelImplTraitConstConstant methods for crate::gapi::GKernelImpl\n* GKernelPackageTraitMutable methods for crate::gapi::GKernelPackage\n* GKernelPackageTraitConstConstant methods for crate::gapi::GKernelPackage\n* GKernelTraitMutable methods for crate::gapi::GKernel\n* GKernelTraitConstConstant methods for crate::gapi::GKernel\n* GMatDescTraitMutable methods for crate::gapi::GMatDesc\n* GMatDescTraitConstConstant methods for crate::gapi::GMatDesc\n* GMatPTraitMutable methods for crate::gapi::GMatP\n* GMatPTraitConstConstant methods for crate::gapi::GMatP\n* GMatTraitMutable methods for crate::gapi::GMat\n* GMatTraitConstConstant methods for crate::gapi::GMat\n* GOpaqueDescTraitMutable methods for crate::gapi::GOpaqueDesc\n* GOpaqueDescTraitConstConstant methods for crate::gapi::GOpaqueDesc\n* GRunArgTraitMutable methods for crate::gapi::GRunArg\n* GRunArgTraitConstConstant methods for crate::gapi::GRunArg\n* GScalarDescTraitMutable methods for crate::gapi::GScalarDesc\n* GScalarDescTraitConstConstant methods for crate::gapi::GScalarDesc\n* GScalarTraitMutable methods for crate::gapi::GScalar\n* GScalarTraitConstConstant methods for crate::gapi::GScalar\n* GStreamingCompiledTraitMutable methods for crate::gapi::GStreamingCompiled\n* GStreamingCompiledTraitConstConstant methods for crate::gapi::GStreamingCompiled\n* GTransformTraitMutable methods for crate::gapi::GTransform\n* GTransformTraitConstConstant methods for crate::gapi::GTransform\n* GTypeInfoTraitMutable methods for crate::gapi::GTypeInfo\n* GTypeInfoTraitConstConstant methods for crate::gapi::GTypeInfo\n* ImageTraitMutable methods for crate::gapi::Image\n* ImageTraitConstConstant methods for crate::gapi::Image\n* MediaFrameTraitMutable methods for crate::gapi::MediaFrame\n* MediaFrameTraitConstConstant methods for crate::gapi::MediaFrame\n* MediaFrame_IAdapterTraitMutable methods for crate::gapi::MediaFrame_IAdapter\n* MediaFrame_IAdapterTraitConstConstant methods for crate::gapi::MediaFrame_IAdapter\n* MediaFrame_ViewTraitMutable methods for crate::gapi::MediaFrame_View\n* MediaFrame_ViewTraitConstConstant methods for crate::gapi::MediaFrame_View\n* PolyTraitMutable methods for crate::gapi::Poly\n* PolyTraitConstConstant methods for crate::gapi::Poly\n* RMatTraitMutable methods for crate::gapi::RMat\n* RMatTraitConstConstant methods for crate::gapi::RMat\n* RMat_IAdapterTraitMutable methods for crate::gapi::RMat_IAdapter\n* RMat_IAdapterTraitConstConstant methods for crate::gapi::RMat_IAdapter\n* RMat_ViewTraitMutable methods for crate::gapi::RMat_View\n* RMat_ViewTraitConstConstant methods for crate::gapi::RMat_View\n* ScalarTraitMutable methods for crate::gapi::Scalar\n* ScalarTraitConstConstant methods for crate::gapi::Scalar\n* TextTraitMutable methods for crate::gapi::Text\n* TextTraitConstConstant methods for crate::gapi::Text\n* anyTraitMutable methods for crate::gapi::any\n* anyTraitConstConstant methods for crate::gapi::any\n* use_onlyTraitMutable methods for crate::gapi::use_only\n* use_onlyTraitConstConstant methods for crate::gapi::use_only\n\nFunctions\n---\n\n* abs_diffCalculates the per-element absolute difference between two matrices.\n* abs_diff_cCalculates absolute value of matrix elements.\n* addCalculates the per-element sum of two matrices.\n* add_cCalculates the per-element sum of matrix and given scalar.\n* add_c_1Calculates the per-element sum of matrix and given scalar.\n* add_c_1_def@overload\n* add_c_defCalculates the per-element sum of matrix and given scalar.\n* add_defCalculates the per-element sum of two matrices.\n* add_gmat_gmat\n* add_gmat_gscalar\n* add_gscalar_gmat\n* add_weightedCalculates the weighted sum of two matrices.\n* add_weighted_defCalculates the weighted sum of two matrices.\n* and_gmat_gmat\n* and_gmat_gscalar\n* and_gscalar_gmat\n* bayer_gr2_rgbConverts an image from BayerGR color space to RGB.\nThe function converts an input image from BayerGR color space to RGB.\nThe conventional ranges for G, R, and B channel values are 0 to 255.\n* bgrGets bgr plane from input frame\n* bgr2_grayConverts an image from BGR color space to gray-scaled.\n* bgr2_i420Converts an image from BGR color space to I420 color space.\n* bgr2_luvConverts an image from BGR color space to LUV color space.\n* bgr2_rgbConverts an image from BGR color space to RGB color space.\n* bgr2_yuvConverts an image from BGR color space to YUV color space.\n* bilateral_filterApplies the bilateral filter to an image.\n* bilateral_filter_defApplies the bilateral filter to an image.\n* bitwise_andcomputes bitwise conjunction of the two matrixes (src1 & src2)\nCalculates the per-element bit-wise logical conjunction of two matrices of the same size.\n* bitwise_and_1computes bitwise conjunction of the two matrixes (src1 & src2)\nCalculates the per-element bit-wise logical conjunction of two matrices of the same size.\n* bitwise_notInverts every bit of an array.\n* bitwise_orcomputes bitwise disjunction of the two matrixes (src1 | src2)\nCalculates the per-element bit-wise logical disjunction of two matrices of the same size.\n* bitwise_or_1computes bitwise disjunction of the two matrixes (src1 | src2)\nCalculates the per-element bit-wise logical disjunction of two matrices of the same size.\n* bitwise_xorcomputes bitwise logical “exclusive or” of the two matrixes (src1 ^ src2)\nCalculates the per-element bit-wise logical “exclusive or” of two matrices of the same size.\n* bitwise_xor_1computes bitwise logical “exclusive or” of the two matrixes (src1 ^ src2)\nCalculates the per-element bit-wise logical “exclusive or” of two matrices of the same size.\n* blurBlurs an image using the normalized box filter.\n* blur_defBlurs an image using the normalized box filter.\n* box_filterBlurs an image using the box filter.\n* box_filter_defBlurs an image using the box filter.\n* cannyFinds edges in an image using the Canny algorithm.\n* canny_defFinds edges in an image using the Canny algorithm.\n* cart_to_polarCalculates the magnitude and angle of 2D vectors.\n* cart_to_polar_defCalculates the magnitude and angle of 2D vectors.\n* cmp_eqPerforms the per-element comparison of two matrices checking if elements from first matrix are equal to elements in second.\n* cmp_eq_1Performs the per-element comparison of two matrices checking if elements from first matrix are equal to elements in second.\n* cmp_gePerforms the per-element comparison of two matrices checking if elements from first matrix are greater or equal compare to elements in second.\n* cmp_ge_1Performs the per-element comparison of two matrices checking if elements from first matrix are greater or equal compare to elements in second.\n* cmp_gtPerforms the per-element comparison of two matrices checking if elements from first matrix are greater compare to elements in second.\n* cmp_gt_1Performs the per-element comparison of two matrices checking if elements from first matrix are greater compare to elements in second.\n* cmp_lePerforms the per-element comparison of two matrices checking if elements from first matrix are less or equal compare to elements in second.\n* cmp_le_1Performs the per-element comparison of two matrices checking if elements from first matrix are less or equal compare to elements in second.\n* cmp_ltPerforms the per-element comparison of two matrices checking if elements from first matrix are less than elements in second.\n* cmp_lt_1Performs the per-element comparison of two matrices checking if elements from first matrix are less than elements in second.\n* cmp_nePerforms the per-element comparison of two matrices checking if elements from first matrix are not equal to elements in second.\n* cmp_ne_1Performs the per-element comparison of two matrices checking if elements from first matrix are not equal to elements in second.\n* combineCreate a new package based on `lhs` and `rhs`.\n* concat_horApplies horizontal concatenation to given matrices.\n* concat_hor_1Applies horizontal concatenation to given matrices.\n* concat_vertApplies vertical concatenation to given matrices.\n* concat_vert_1Applies vertical concatenation to given matrices.\n* convert_toConverts a matrix to another data depth with optional scaling.\n* convert_to_defConverts a matrix to another data depth with optional scaling.\n* copyMakes a copy of the input image. Note that this copy may be not real\n(no actual data copied). Use this function to maintain graph contracts,\ne.g when graph’s input needs to be passed directly to output, like in Streaming mode.\n* copy_1Makes a copy of the input frame. Note that this copy may be not real\n(no actual data copied). Use this function to maintain graph contracts,\ne.g when graph’s input needs to be passed directly to output, like in Streaming mode.\n* cropCrops a 2D matrix.\n* descr_of\n* descr_of_1\n* descr_of_2\n* descr_of_3\n* descr_of_4\n* desyncStarts a desynchronized branch in the graph.\n* desync_1\n* dilateDilates an image by using a specific structuring element.\n* dilate3x3Dilates an image by using 3 by 3 rectangular structuring element.\n* dilate3x3_defDilates an image by using 3 by 3 rectangular structuring element.\n* dilate_defDilates an image by using a specific structuring element.\n* divPerforms per-element division of two matrices.\n* div_cDivides matrix by scalar.\n* div_c_defDivides matrix by scalar.\n* div_defPerforms per-element division of two matrices.\n* div_gmat_gmat\n* div_gmat_gscalar\n* div_gscalar_gmat\n* div_rcDivides scalar by matrix.\n* div_rc_defDivides scalar by matrix.\n* empty_array_desc\n* empty_gopaque_desc\n* empty_scalar_desc\n* equalize_histEqualizes the histogram of a grayscale image.\n* equals_gmat_gmat\n* equals_gmat_gscalar\n* equals_gscalar_gmat\n* erodeErodes an image by using a specific structuring element.\n* erode3x3Erodes an image by using 3 by 3 rectangular structuring element.\n* erode3x3_defErodes an image by using 3 by 3 rectangular structuring element.\n* erode_defErodes an image by using a specific structuring element.\n* filter_2dConvolves an image with the kernel.\n* filter_2d_defConvolves an image with the kernel.\n* flipFlips a 2D matrix around vertical, horizontal, or both axes.\n* gaussian_blurBlurs an image using a Gaussian filter.\n* gaussian_blur_defBlurs an image using a Gaussian filter.\n* greater_than_gmat_gmat\n* greater_than_gmat_gscalar\n* greater_than_gscalar_gmat\n* greater_than_or_equal_gmat_gmat\n* greater_than_or_equal_gmat_gscalar\n* greater_than_or_equal_gscalar_gmat\n* i4202_bgrConverts an image from I420 color space to BGR color space.\n* i4202_rgbConverts an image from I420 color space to BGR color space.\n* in_rangeApplies a range-level threshold to each matrix element.\n* integralCalculates the integral of an image.\n* integral_defCalculates the integral of an image.\n* kernels\n* laplacianCalculates the Laplacian of an image.\n* laplacian_defCalculates the Laplacian of an image.\n* less_than_gmat_gmat\n* less_than_gmat_gscalar\n* less_than_gscalar_gmat\n* less_than_or_equal_gmat_gmat\n* less_than_or_equal_gmat_gscalar\n* less_than_or_equal_gscalar_gmat\n* lutPerforms a look-up table transform of a matrix.\n* luv2_bgrConverts an image from LUV color space to BGR color space.\n* maskApplies a mask to a matrix.\n* maxCalculates per-element maximum of two matrices.\n* meanCalculates an average (mean) of matrix elements.\n* median_blurBlurs an image using the median filter.\n* merge3Creates one 3-channel matrix out of 3 single-channel ones.\n* merge4Creates one 4-channel matrix out of 4 single-channel ones.\n* minCalculates per-element minimum of two matrices.\n* morphology_exPerforms advanced morphological transformations.\n* morphology_ex_defPerforms advanced morphological transformations.\n* mulCalculates the per-element scaled product of two matrices.\n* mul_cMultiplies matrix by scalar.\n* mul_c_1Multiplies matrix by scalar.\n* mul_c_1_def@overload\n* mul_c_2Multiplies matrix by scalar.\n* mul_c_2_def@overload\n* mul_c_defMultiplies matrix by scalar.\n* mul_defCalculates the per-element scaled product of two matrices.\n* mul_f32_gmat\n* mul_gmat_f32\n* mul_gmat_gscalar\n* mul_gscalar_gmat\n* negate\n* norm_infCalculates the absolute infinite norm of a matrix.\n* norm_l1Calculates the absolute L1 norm of a matrix.\n* norm_l2Calculates the absolute L2 norm of a matrix.\n* normalizeNormalizes the norm or value range of an array.\n* normalize_defNormalizes the norm or value range of an array.\n* not_equals_gmat_gmat\n* not_equals_gmat_gscalar\n* not_equals_gscalar_gmat\n* nv12to_bg_rpConverts an image from NV12 (YUV420p) color space to BGR.\nThe function converts an input image from NV12 color space to BGR.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n* nv12to_bgrConverts an image from NV12 (YUV420p) color space to BGR.\nThe function converts an input image from NV12 color space to RGB.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n* nv12to_grayConverts an image from NV12 (YUV420p) color space to gray-scaled.\nThe function converts an input image from NV12 color space to gray-scaled.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n* nv12to_rg_bpConverts an image from NV12 (YUV420p) color space to RGB.\nThe function converts an input image from NV12 color space to RGB.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n* nv12to_rgbConverts an image from NV12 (YUV420p) color space to RGB.\nThe function converts an input image from NV12 color space to RGB.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n* or_gmat_gmat\n* or_gmat_gscalar\n* or_gscalar_gmat\n* phaseCalculates the rotation angle of 2D vectors.\n* phase_defCalculates the rotation angle of 2D vectors.\n* polar_to_cartCalculates x and y coordinates of 2D vectors from their magnitude and angle.\n* polar_to_cart_defCalculates x and y coordinates of 2D vectors from their magnitude and angle.\n* remapApplies a generic geometrical transformation to an image.\n* remap_defApplies a generic geometrical transformation to an image.\n* resizeResizes an image.\n* resize_defResizes an image.\n* resize_pResizes a planar image.\n* resize_p_defResizes a planar image.\n* rgb2_grayConverts an image from RGB color space to gray-scaled.\n* rgb2_gray_1Converts an image from RGB color space to gray-scaled.\n* rgb2_hsvConverts an image from RGB color space to HSV.\nThe function converts an input image from RGB color space to HSV.\nThe conventional ranges for R, G, and B channel values are 0 to 255.\n* rgb2_i420Converts an image from RGB color space to I420 color space.\n* rgb2_labConverts an image from RGB color space to Lab color space.\n* rgb2_yuvConverts an image from RGB color space to YUV color space.\n* rgb2_yuv422Converts an image from RGB color space to YUV422.\nThe function converts an input image from RGB color space to YUV422.\nThe conventional ranges for R, G, and B channel values are 0 to 255.\n* selectSelect values from either first or second of input matrices by given mask.\nThe function set to the output matrix either the value from the first input matrix if corresponding value of mask matrix is 255,\nor value from the second input matrix (if value of mask matrix set to 0).\n* sep_filterApplies a separable linear filter to a matrix(image).\n* sep_filter_defApplies a separable linear filter to a matrix(image).\n* sobelCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* sobel_defCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* sobel_xyCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* sobel_xy_defCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* split3Divides a 3-channel matrix into 3 single-channel matrices.\n* split4Divides a 4-channel matrix into 4 single-channel matrices.\n* sqrtCalculates a square root of array elements.\n* subCalculates the per-element difference between two matrices.\n* sub_cCalculates the per-element difference between matrix and given scalar.\n* sub_c_defCalculates the per-element difference between matrix and given scalar.\n* sub_defCalculates the per-element difference between two matrices.\n* sub_gmat_gmat\n* sub_gmat_gscalar\n* sub_gscalar_gmat\n* sub_rcCalculates the per-element difference between given scalar and the matrix.\n* sub_rc_defCalculates the per-element difference between given scalar and the matrix.\n* sumCalculates sum of all matrix elements.\n* thresholdApplies a fixed-level threshold to each matrix element.\n* threshold_1Applies a fixed-level threshold to each matrix element.\n* transposeTransposes a matrix.\n* uvExtracts UV plane from media frame.\n* validate_input_arg\n* validate_input_args\n* warp_affineApplies an affine transformation to an image.\n* warp_affine_defApplies an affine transformation to an image.\n* warp_perspectiveApplies a perspective transformation to an image.\n* warp_perspective_defApplies a perspective transformation to an image.\n* xor_gmat_gmat\n* xor_gmat_gscalar\n* xor_gscalar_gmat\n* yExtracts Y plane from media frame.\n* yuv2_bgrConverts an image from YUV color space to BGR color space.\n* yuv2_rgbConverts an image from YUV color space to RGB.\nThe function converts an input image from YUV color space to RGB.\nThe conventional ranges for Y, U, and V channel values are 0 to 255.\n\nType Aliases\n---\n\n* GArgs\n* GCompileArgs\n* GKinds\n* GMat2\n* GMat3\n* GMat4\n* GMatScalar\n* GRunArgs\n* GShapes\n* GTypesInfo\n* ImgProc_GMat2\n* ImgProc_GMat3\n* ImgProc_cont_method\n* ImgProc_retr_mode\n* RMat_Adapter\n* RMat_View_stepsT\n\nModule opencv::hdf\n===\n\nHierarchical Data Format I/O routines\n---\n\nThis module provides storage routines for Hierarchical Data Format objects.\n\nHierarchical Data Format version 5\n---\n\n### Hierarchical Data Format version 5\n\nIn order to use it, the hdf5 library has to be installed, which means cmake should find it using `find_package(HDF5)` .\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* HDF5Hierarchical Data Format version 5 interface.\n\nConstants\n---\n\n* HDF5_H5_GETCHUNKDIMSGet the chunk sizes of a dataset. see also: dsgetsize()\n* HDF5_H5_GETDIMSGet the dimension information of a dataset. see also: dsgetsize()\n* HDF5_H5_GETMAXDIMSGet the maximum dimension information of a dataset. see also: dsgetsize()\n* HDF5_H5_NONENo compression, see also: dscreate()\n* HDF5_H5_UNLIMITEDThe dimension size is unlimited, see also: dscreate()\n\nTraits\n---\n\n* HDF5TraitMutable methods for crate::hdf::HDF5\n* HDF5TraitConstConstant methods for crate::hdf::HDF5\n\nFunctions\n---\n\n* openOpen or create hdf5 file\n\nModule opencv::hfs\n===\n\nHierarchical Feature Selection for Efficient Image Segmentation\n---\n\nThe opencv hfs module contains an efficient algorithm to segment an image.\nThis module is implemented based on the paper Hierarchical Feature Selection for Efficient Image Segmentation, ECCV 2016. The original project was developed by <NAME>(https://github.com/yun-liu/hfs).\n\n### Introduction to Hierarchical Feature Selection\n\nThis algorithm is executed in 3 stages:\n\nIn the first stage, the algorithm uses SLIC (simple linear iterative clustering) algorithm to obtain the superpixel of the input image.\n\nIn the second stage, the algorithm view each superpixel as a node in the graph.\nIt will calculate a feature vector for each edge of the graph. It then calculates a weight for each edge based on the feature vector and trained SVM parameters. After obtaining weight for each edge, it will exploit EGB (Efficient Graph-based Image Segmentation)\nalgorithm to merge some nodes in the graph thus obtaining a coarser segmentation After these operations, a post process will be executed to merge regions that are smaller then a specific number of pixels into their nearby region.\n\nIn the third stage, the algorithm exploits the similar mechanism to further merge the small regions obtained in the second stage into even coarser segmentation.\n\nAfter these three stages, we can obtain the final segmentation of the image.\nFor further details about the algorithm, please refer to the original paper:\nHierarchical Feature Selection for Efficient Image Segmentation, ECCV 2016\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* HfsSegment\n\nTraits\n---\n\n* HfsSegmentTraitMutable methods for crate::hfs::HfsSegment\n* HfsSegmentTraitConstConstant methods for crate::hfs::HfsSegment\n\nModule opencv::highgui\n===\n\nHigh-level GUI\n---\n\nWhile OpenCV was designed for use in full-scale applications and can be used within functionally rich UI frameworks (such as Qt*, WinForms*, or Cocoa*) or without any UI at all, sometimes there it is required to try functionality quickly and visualize the results. This is what the HighGUI module has been designed for.\n\nIt provides easy interface to:\n\n* Create and manipulate windows that can display images and “remember” their content (no need to handle repaint events from OS).\n* Add trackbars to the windows, handle simple mouse events as well as keyboard commands.\n\nFlags related creating and manipulating HighGUI windows and mouse events\n---\n\nOpenGL support\n---\n\nQt New Functions\n---\n\n\n\nThis figure explains new functionality implemented with Qt* GUI. The new GUI provides a statusbar,\na toolbar, and a control panel. The control panel can have trackbars and buttonbars attached to it.\nIf you cannot see the control panel, press Ctrl+P or right-click any Qt window and select **Display properties window**.\n\n* To attach a trackbar, the window name parameter must be NULL.\n* To attach a buttonbar, a button must be created. If the last bar attached to the control panel is a buttonbar, the new button is added to the right of the last button. If the last bar attached to the control panel is a trackbar, or the control panel is empty, a new buttonbar is created. Then, a new button is attached to it.\n\nSee below the example used to generate the figure:\n```\n int main(int argc, char *argv[])\n {\n\n int value = 50;\n int value2 = 0;\n\n namedWindow(\"main1\",WINDOW_NORMAL);\n namedWindow(\"main2\",WINDOW_AUTOSIZE | WINDOW_GUI_NORMAL);\n createTrackbar( \"track1\", \"main1\", &value, 255, NULL);\n\n String nameb1 = \"button1\";\n String nameb2 = \"button2\";\n\n createButton(nameb1,callbackButton,&nameb1,QT_CHECKBOX,1);\n createButton(nameb2,callbackButton,NULL,QT_CHECKBOX,0);\n createTrackbar( \"track2\", NULL, &value2, 255, NULL);\n createButton(\"button5\",callbackButton1,NULL,QT_RADIOBOX,0);\n createButton(\"button6\",callbackButton2,NULL,QT_RADIOBOX,1);\n\n setMouseCallback( \"main2\",on_mouse,NULL );\n\n Mat img1 = imread(\"files/flower.jpg\");\n VideoCapture video;\n video.open(\"files/hockey.avi\");\n\n Mat img2,img3;\n\n while( waitKey(33) != 27 )\n {\n img1.convertTo(img2,-1,1,value);\n video >> img3;\n\n imshow(\"main1\",img2);\n imshow(\"main2\",img3);\n }\n\n destroyAllWindows();\n\n return 0;\n }\n```\nWinRT support\n---\n\nThis figure explains new functionality implemented with WinRT GUI. The new GUI provides an Image control,\nand a slider panel. Slider panel holds trackbars attached to it.\n\nSliders are attached below the image control. Every new slider is added below the previous one.\n\nSee below the example used to generate the figure:\n```\n void sample_app::MainPage::ShowWindow()\n {\n static cv::String windowName(\"sample\");\n cv::winrt_initContainer(this->cvContainer);\n cv::namedWindow(windowName); // not required\n\n cv::Mat image = cv::imread(\"Assets/sample.jpg\");\n cv::Mat converted = cv::Mat(image.rows, image.cols, CV_8UC4);\n cv::cvtColor(image, converted, COLOR_BGR2BGRA);\n cv::imshow(windowName, converted); // this will create window if it hasn't been created before\n\n int state = 42;\n cv::TrackbarCallback callback = [](int pos, void* userdata)\n {\n if (pos == 0) {\n cv::destroyWindow(windowName);\n }\n };\n cv::TrackbarCallback callbackTwin = [](int pos, void* userdata)\n {\n if (pos >= 70) {\n cv::destroyAllWindows();\n }\n };\n cv::createTrackbar(\"Sample trackbar\", windowName, &state, 100, callback);\n cv::createTrackbar(\"Twin brother\", windowName, &state, 100, callbackTwin);\n }\n```\nC API\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* QtFontQtFont available only for Qt. See cv::fontQt\n\nEnums\n---\n\n* MouseEventFlagsMouse Event Flags see cv::MouseCallback\n* MouseEventTypesMouse Events see cv::MouseCallback\n* QtButtonTypesQt “button” type\n* QtFontStylesQt font style\n* QtFontWeightsQt font weight\n* WindowFlagsFlags for cv::namedWindow\n* WindowPropertyFlagsFlags for cv::setWindowProperty / cv::getWindowProperty\n\nConstants\n---\n\n* EVENT_FLAG_ALTKEYindicates that ALT Key is pressed.\n* EVENT_FLAG_CTRLKEYindicates that CTRL Key is pressed.\n* EVENT_FLAG_LBUTTONindicates that the left mouse button is down.\n* EVENT_FLAG_MBUTTONindicates that the middle mouse button is down.\n* EVENT_FLAG_RBUTTONindicates that the right mouse button is down.\n* EVENT_FLAG_SHIFTKEYindicates that SHIFT Key is pressed.\n* EVENT_LBUTTONDBLCLKindicates that left mouse button is double clicked.\n* EVENT_LBUTTONDOWNindicates that the left mouse button is pressed.\n* EVENT_LBUTTONUPindicates that left mouse button is released.\n* EVENT_MBUTTONDBLCLKindicates that middle mouse button is double clicked.\n* EVENT_MBUTTONDOWNindicates that the middle mouse button is pressed.\n* EVENT_MBUTTONUPindicates that middle mouse button is released.\n* EVENT_MOUSEHWHEELpositive and negative values mean right and left scrolling, respectively.\n* EVENT_MOUSEMOVEindicates that the mouse pointer has moved over the window.\n* EVENT_MOUSEWHEELpositive and negative values mean forward and backward scrolling, respectively.\n* EVENT_RBUTTONDBLCLKindicates that right mouse button is double clicked.\n* EVENT_RBUTTONDOWNindicates that the right mouse button is pressed.\n* EVENT_RBUTTONUPindicates that right mouse button is released.\n* QT_CHECKBOXCheckbox button.\n* QT_FONT_BLACKWeight of 87\n* QT_FONT_BOLDWeight of 75\n* QT_FONT_DEMIBOLDWeight of 63\n* QT_FONT_LIGHTWeight of 25\n* QT_FONT_NORMALWeight of 50\n* QT_NEW_BUTTONBARButton should create a new buttonbar\n* QT_PUSH_BUTTONPush button.\n* QT_RADIOBOXRadiobox button.\n* QT_STYLE_ITALICItalic font.\n* QT_STYLE_NORMALNormal font.\n* QT_STYLE_OBLIQUEOblique font.\n* WINDOW_AUTOSIZEthe user cannot resize the window, the size is constrainted by the image displayed.\n* WINDOW_FREERATIOthe image expends as much as it can (no ratio constraint).\n* WINDOW_FULLSCREENchange the window to fullscreen.\n* WINDOW_GUI_EXPANDEDstatus bar and tool bar\n* WINDOW_GUI_NORMALold fashious way\n* WINDOW_KEEPRATIOthe ratio of the image is respected.\n* WINDOW_NORMALthe user can resize the window (no constraint) / also use to switch a fullscreen window to a normal size.\n* WINDOW_OPENGLwindow with opengl support.\n* WND_PROP_ASPECT_RATIOwindow’s aspect ration (can be set to WINDOW_FREERATIO or WINDOW_KEEPRATIO).\n* WND_PROP_AUTOSIZEautosize property (can be WINDOW_NORMAL or WINDOW_AUTOSIZE).\n* WND_PROP_FULLSCREENfullscreen property (can be WINDOW_NORMAL or WINDOW_FULLSCREEN).\n* WND_PROP_OPENGLopengl support.\n* WND_PROP_TOPMOSTproperty to toggle normal window being topmost or not\n* WND_PROP_VISIBLEchecks whether the window exists and is visible\n* WND_PROP_VSYNCenable or disable VSYNC (in OpenGL mode)\n\nTraits\n---\n\n* QtFontTraitMutable methods for crate::highgui::QtFont\n* QtFontTraitConstConstant methods for crate::highgui::QtFont\n\nFunctions\n---\n\n* add_textDraws a text on the image.\n* add_text_with_fontDraws a text on the image.\n* add_text_with_font_defDraws a text on the image.\n* create_buttonAttaches a button to the control panel.\n* create_button_defAttaches a button to the control panel.\n* create_trackbarCreates a trackbar and attaches it to the specified window.\n* destroy_all_windowsDestroys all of the HighGUI windows.\n* destroy_windowDestroys the specified window.\n* display_overlayDisplays a text on a window image as an overlay for a specified duration.\n* display_overlay_defDisplays a text on a window image as an overlay for a specified duration.\n* display_status_barDisplays a text on the window statusbar during the specified period of time.\n* display_status_bar_defDisplays a text on the window statusbar during the specified period of time.\n* font_qtCreates the font to draw a text on an image.\n* font_qt_defCreates the font to draw a text on an image.\n* get_mouse_wheel_deltaGets the mouse-wheel motion delta, when handling mouse-wheel events cv::EVENT_MOUSEWHEEL and cv::EVENT_MOUSEHWHEEL.\n* get_trackbar_posReturns the trackbar position.\n* get_window_image_rectProvides rectangle of image in the window.\n* get_window_propertyProvides parameters of a window.\n* imshowDisplays an image in the specified window.\n* load_window_parametersLoads parameters of the specified window.\n* move_windowMoves the window to the specified position\n* named_windowCreates a window.\n* named_window_defCreates a window.\n* poll_keyPolls for a pressed key.\n* resize_windowResizes the window to the specified size\n* resize_window_sizeResizes the window to the specified size\n* save_window_parametersSaves parameters of the specified window.\n* select_ro_isAllows users to select multiple ROIs on the given image.\n* select_ro_is_defAllows users to select multiple ROIs on the given image.\n* select_roiAllows users to select a ROI on the given image.\n* select_roi_1Allows users to select a ROI on the given image.\n* select_roi_1_def@overload\n* select_roi_defAllows users to select a ROI on the given image.\n* set_mouse_callback@example samples/cpp/create_mask.cpp This program demonstrates using mouse events and how to make and use a mask image (black and white) .\n* set_opengl_contextSets the specified window as current OpenGL context.\n* set_opengl_draw_callbackSets a callback function to be called to draw on top of displayed image.\n* set_trackbar_maxSets the trackbar maximum position.\n* set_trackbar_minSets the trackbar minimum position.\n* set_trackbar_posSets the trackbar position.\n* set_window_propertyChanges parameters of a window dynamically.\n* set_window_titleUpdates window title\n* start_loop\n* start_window_thread\n* stop_loop\n* update_windowForce window to redraw its context and call draw callback ( See cv::setOpenGlDrawCallback ).\n* wait_keyWaits for a pressed key.\n* wait_key_defWaits for a pressed key.\n* wait_key_exSimilar to #waitKey, but returns full key code.\n* wait_key_ex_defSimilar to #waitKey, but returns full key code.\n\nType Aliases\n---\n\n* ButtonCallbackCallback function for a button created by cv::createButton\n* MouseCallbackCallback function for mouse events. see cv::setMouseCallback\n* OpenGlDrawCallbackCallback function defined to be called every frame. See cv::setOpenGlDrawCallback\n* TrackbarCallbackCallback function for Trackbar see cv::createTrackbar\n\nModule opencv::img_hash\n===\n\nThe module brings implementations of different image hashing algorithms.\n---\n\nProvide algorithms to extract the hash of images and fast way to figure out most similar images in huge data set.\n\nNamespace for all functions is cv::img_hash.\n\n#### Supported Algorithms\n\n* Average hash (also called Different hash)\n* PHash (also called Perceptual hash)\n* Marr Hildreth Hash\n* Radial Variance Hash\n* Block Mean Hash (modes 0 and 1)\n* Color Moment Hash (this is the one and only hash algorithm resist to rotation attack(-90~90 degree))\n\nYou can study more about image hashing from following paper and websites:\n\n* “Implementation and benchmarking of perceptual image hash functions” zauner2010implementation\n* “Looks Like It” lookslikeit\n\n#### Code Example\n\n@include samples/hash_samples.cpp\n\n#### Performance under different attacks\n\n\n\n#### Speed comparison with PHash library (100 images from ukbench)\n\n\n\n\nAs you can see, hash computation speed of img_hash module outperform PHash library a lot.\n\nPS : I do not list out the comparison of Average hash, PHash and Color Moment hash, because I cannot find them in PHash.\n\n#### Motivation\n\nCollects useful image hash algorithms into opencv, so we do not need to rewrite them by ourselves again and again or rely on another 3rd party library(ex : PHash library). BOVW or correlation matching are good and robust, but they are very slow compare with image hash, if you need to deal with large scale CBIR(content based image retrieval) problem, image hash is a more reasonable solution.\n\n#### More info\n\nYou can learn more about img_hash modules from following links, these links show you how to find similar image from ukbench dataset, provide thorough benchmark of different attacks(contrast, blur,\nnoise(gaussion,pepper and salt), jpeg compression, watermark, resize).\n\n* Introduction to image hash module of opencv\n* Speed up image hashing of opencv(img_hash) and introduce color moment hash\n\n#### Contributors\n\n<NAME>, <EMAIL>\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AverageHashComputes average hash value of the input image\n* BlockMeanHashImage hash based on block mean.\n* ColorMomentHashImage hash based on color moments.\n* ImgHashBaseThe base class for image hash algorithms\n* MarrHildrethHashMarr-Hildreth Operator Based Hash, slowest but more discriminative.\n* PHashpHash\n* RadialVarianceHashImage hash based on Radon transform.\n\nEnums\n---\n\n* BlockMeanHashMode\n\nConstants\n---\n\n* BLOCK_MEAN_HASH_MODE_0use fewer block and generate 16*16/8 uchar hash value\n* BLOCK_MEAN_HASH_MODE_1use block blocks(step sizes/2), generate 31*31/8 + 1 uchar hash value\n\nTraits\n---\n\n* AverageHashTraitMutable methods for crate::img_hash::AverageHash\n* AverageHashTraitConstConstant methods for crate::img_hash::AverageHash\n* BlockMeanHashTraitMutable methods for crate::img_hash::BlockMeanHash\n* BlockMeanHashTraitConstConstant methods for crate::img_hash::BlockMeanHash\n* ColorMomentHashTraitMutable methods for crate::img_hash::ColorMomentHash\n* ColorMomentHashTraitConstConstant methods for crate::img_hash::ColorMomentHash\n* ImgHashBaseTraitMutable methods for crate::img_hash::ImgHashBase\n* ImgHashBaseTraitConstConstant methods for crate::img_hash::ImgHashBase\n* MarrHildrethHashTraitMutable methods for crate::img_hash::MarrHildrethHash\n* MarrHildrethHashTraitConstConstant methods for crate::img_hash::MarrHildrethHash\n* PHashTraitMutable methods for crate::img_hash::PHash\n* PHashTraitConstConstant methods for crate::img_hash::PHash\n* RadialVarianceHashTraitMutable methods for crate::img_hash::RadialVarianceHash\n* RadialVarianceHashTraitConstConstant methods for crate::img_hash::RadialVarianceHash\n\nFunctions\n---\n\n* average_hashCalculates img_hash::AverageHash in one call\n* block_mean_hashComputes block mean hash of the input image\n* block_mean_hash_defComputes block mean hash of the input image\n* color_moment_hashComputes color moment hash of the input, the algorithm is come from the paper “Perceptual Hashing for Color Images Using Invariant Moments”\n* marr_hildreth_hashComputes average hash value of the input image\n* marr_hildreth_hash_defComputes average hash value of the input image\n* p_hashComputes pHash value of the input image\n* radial_variance_hashComputes radial variance hash of the input image\n* radial_variance_hash_defComputes radial variance hash of the input image\n\nModule opencv::imgcodecs\n===\n\nImage file reading and writing\n---\n\nC API\n---\n\nFlags used for image file reading and writing\n---\n\niOS glue\n---\n\nMacOS(OSX) glue\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ImageCollectionTo read Multi Page images on demand\n* ImageCollection_iterator\n\nEnums\n---\n\n* ImreadModesImread flags\n* ImwriteEXRCompressionFlags\n* ImwriteEXRTypeFlags\n* ImwriteFlagsImwrite flags\n* ImwriteHDRCompressionFlagsImwrite HDR specific values for IMWRITE_HDR_COMPRESSION parameter key\n* ImwriteJPEGSamplingFactorParams\n* ImwritePAMFlagsImwrite PAM specific tupletype flags used to define the ‘TUPLETYPE’ field of a PAM file.\n* ImwritePNGFlagsImwrite PNG specific flags used to tune the compression algorithm.\nThese flags will be modify the way of PNG image compression and will be passed to the underlying zlib processing stage.\n\nConstants\n---\n\n* IMREAD_ANYCOLORIf set, the image is read in any possible color format.\n* IMREAD_ANYDEPTHIf set, return 16-bit/32-bit image when the input has the corresponding depth, otherwise convert it to 8-bit.\n* IMREAD_COLORIf set, always convert image to the 3 channel BGR color image.\n* IMREAD_GRAYSCALEIf set, always convert image to the single channel grayscale image (codec internal conversion).\n* IMREAD_IGNORE_ORIENTATIONIf set, do not rotate the image according to EXIF’s orientation flag.\n* IMREAD_LOAD_GDALIf set, use the gdal driver for loading the image.\n* IMREAD_REDUCED_COLOR_2If set, always convert image to the 3 channel BGR color image and the image size reduced 1/2.\n* IMREAD_REDUCED_COLOR_4If set, always convert image to the 3 channel BGR color image and the image size reduced 1/4.\n* IMREAD_REDUCED_COLOR_8If set, always convert image to the 3 channel BGR color image and the image size reduced 1/8.\n* IMREAD_REDUCED_GRAYSCALE_2If set, always convert image to the single channel grayscale image and the image size reduced 1/2.\n* IMREAD_REDUCED_GRAYSCALE_4If set, always convert image to the single channel grayscale image and the image size reduced 1/4.\n* IMREAD_REDUCED_GRAYSCALE_8If set, always convert image to the single channel grayscale image and the image size reduced 1/8.\n* IMREAD_UNCHANGEDIf set, return the loaded image as is (with alpha channel, otherwise it gets cropped). Ignore EXIF orientation.\n* IMWRITE_AVIF_DEPTHFor AVIF, it can be 8, 10 or 12. If >8, it is stored/read as CV_32F. Default is 8.\n* IMWRITE_AVIF_QUALITYFor AVIF, it can be a quality between 0 and 100 (the higher the better). Default is 95.\n* IMWRITE_AVIF_SPEEDFor AVIF, it is between 0 (slowest) and (fastest). Default is 9.\n* IMWRITE_EXR_COMPRESSIONoverride EXR compression type (ZIP_COMPRESSION = 3 is default)\n* IMWRITE_EXR_COMPRESSION_B44lossy 4-by-4 pixel block compression, fixed compression rate\n* IMWRITE_EXR_COMPRESSION_B44Alossy 4-by-4 pixel block compression, flat fields are compressed more\n* IMWRITE_EXR_COMPRESSION_DWAAlossy DCT based compression, in blocks of 32 scanlines. More efficient for partial buffer access. Supported since OpenEXR 2.2.0.\n* IMWRITE_EXR_COMPRESSION_DWABlossy DCT based compression, in blocks of 256 scanlines. More efficient space wise and faster to decode full frames than DWAA_COMPRESSION. Supported since OpenEXR 2.2.0.\n* IMWRITE_EXR_COMPRESSION_NOno compression\n* IMWRITE_EXR_COMPRESSION_PIZpiz-based wavelet compression\n* IMWRITE_EXR_COMPRESSION_PXR24lossy 24-bit float compression\n* IMWRITE_EXR_COMPRESSION_RLErun length encoding\n* IMWRITE_EXR_COMPRESSION_ZIPzlib compression, in blocks of 16 scan lines\n* IMWRITE_EXR_COMPRESSION_ZIPSzlib compression, one scan line at a time\n* IMWRITE_EXR_DWA_COMPRESSION_LEVELoverride EXR DWA compression level (45 is default)\n* IMWRITE_EXR_TYPEoverride EXR storage type (FLOAT (FP32) is default)\n* IMWRITE_EXR_TYPE_FLOATstore as FP32 (default)\n* IMWRITE_EXR_TYPE_HALFstore as HALF (FP16)\n* IMWRITE_HDR_COMPRESSIONspecify HDR compression\n* IMWRITE_HDR_COMPRESSION_NONE\n* IMWRITE_HDR_COMPRESSION_RLE\n* IMWRITE_JPEG2000_COMPRESSION_X1000For JPEG2000, use to specify the target compression rate (multiplied by 1000). The value can be from 0 to 1000. Default is 1000.\n* IMWRITE_JPEG_CHROMA_QUALITYSeparate chroma quality level, 0 - 100, default is -1 - don’t use.\n* IMWRITE_JPEG_LUMA_QUALITYSeparate luma quality level, 0 - 100, default is -1 - don’t use.\n* IMWRITE_JPEG_OPTIMIZEEnable JPEG features, 0 or 1, default is False.\n* IMWRITE_JPEG_PROGRESSIVEEnable JPEG features, 0 or 1, default is False.\n* IMWRITE_JPEG_QUALITYFor JPEG, it can be a quality from 0 to 100 (the higher is the better). Default value is 95.\n* IMWRITE_JPEG_RST_INTERVALJPEG restart interval, 0 - 65535, default is 0 - no restart.\n* IMWRITE_JPEG_SAMPLING_FACTORFor JPEG, set sampling factor. See cv::ImwriteJPEGSamplingFactorParams.\n* IMWRITE_JPEG_SAMPLING_FACTOR_4114x1,1x1,1x1\n* IMWRITE_JPEG_SAMPLING_FACTOR_4202x2,1x1,1x1(Default)\n* IMWRITE_JPEG_SAMPLING_FACTOR_4222x1,1x1,1x1\n* IMWRITE_JPEG_SAMPLING_FACTOR_4401x2,1x1,1x1\n* IMWRITE_JPEG_SAMPLING_FACTOR_4441x1,1x1,1x1(No subsampling)\n* IMWRITE_PAM_FORMAT_BLACKANDWHITE\n* IMWRITE_PAM_FORMAT_GRAYSCALE\n* IMWRITE_PAM_FORMAT_GRAYSCALE_ALPHA\n* IMWRITE_PAM_FORMAT_NULL\n* IMWRITE_PAM_FORMAT_RGB\n* IMWRITE_PAM_FORMAT_RGB_ALPHA\n* IMWRITE_PAM_TUPLETYPEFor PAM, sets the TUPLETYPE field to the corresponding string value that is defined for the format\n* IMWRITE_PNG_BILEVELBinary level PNG, 0 or 1, default is 0.\n* IMWRITE_PNG_COMPRESSIONFor PNG, it can be the compression level from 0 to 9. A higher value means a smaller size and longer compression time. If specified, strategy is changed to IMWRITE_PNG_STRATEGY_DEFAULT (Z_DEFAULT_STRATEGY). Default value is 1 (best speed setting).\n* IMWRITE_PNG_STRATEGYOne of cv::ImwritePNGFlags, default is IMWRITE_PNG_STRATEGY_RLE.\n* IMWRITE_PNG_STRATEGY_DEFAULTUse this value for normal data.\n* IMWRITE_PNG_STRATEGY_FILTEREDUse this value for data produced by a filter (or predictor).Filtered data consists mostly of small values with a somewhat random distribution. In this case, the compression algorithm is tuned to compress them better.\n* IMWRITE_PNG_STRATEGY_FIXEDUsing this value prevents the use of dynamic Huffman codes, allowing for a simpler decoder for special applications.\n* IMWRITE_PNG_STRATEGY_HUFFMAN_ONLYUse this value to force Huffman encoding only (no string match).\n* IMWRITE_PNG_STRATEGY_RLEUse this value to limit match distances to one (run-length encoding).\n* IMWRITE_PXM_BINARYFor PPM, PGM, or PBM, it can be a binary format flag, 0 or 1. Default value is 1.\n* IMWRITE_TIFF_COMPRESSIONFor TIFF, use to specify the image compression scheme. See libtiff for integer constants corresponding to compression formats. Note, for images whose depth is CV_32F, only libtiff’s SGILOG compression scheme is used. For other supported depths, the compression scheme can be specified by this flag; LZW compression is the default.\n* IMWRITE_TIFF_RESUNITFor TIFF, use to specify which DPI resolution unit to set; see libtiff documentation for valid values\n* IMWRITE_TIFF_XDPIFor TIFF, use to specify the X direction DPI\n* IMWRITE_TIFF_YDPIFor TIFF, use to specify the Y direction DPI\n* IMWRITE_WEBP_QUALITYFor WEBP, it can be a quality from 1 to 100 (the higher is the better). By default (without any parameter) and for quality above 100 the lossless compression is used.\n\nTraits\n---\n\n* ImageCollectionTraitMutable methods for crate::imgcodecs::ImageCollection\n* ImageCollectionTraitConstConstant methods for crate::imgcodecs::ImageCollection\n* ImageCollection_iteratorTraitMutable methods for crate::imgcodecs::ImageCollection_iterator\n* ImageCollection_iteratorTraitConstConstant methods for crate::imgcodecs::ImageCollection_iterator\n\nFunctions\n---\n\n* have_image_readerReturns true if the specified image can be decoded by OpenCV\n* have_image_writerReturns true if an image with the specified filename can be encoded by OpenCV\n* imcountReturns the number of images inside the give file\n* imcount_defReturns the number of images inside the give file\n* imdecodeReads an image from a buffer in memory.\n* imdecode_toReads an image from a buffer in memory.\n* imdecodemultiReads a multi-page image from a buffer in memory.\n* imencodeEncodes an image into a memory buffer.\n* imencode_defEncodes an image into a memory buffer.\n* imreadLoads an image from a file.\n* imread_defLoads an image from a file.\n* imreadmultiLoads a multi-page image from a file.\n* imreadmulti_defLoads a multi-page image from a file.\n* imreadmulti_rangeLoads a of images of a multi-page image from a file.\n* imreadmulti_range_defLoads a of images of a multi-page image from a file.\n* imwriteSaves an image to a specified file.\n* imwrite_defSaves an image to a specified file.\n* imwritemultiThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. multi-image overload for bindings\n* imwritemulti_def@overload multi-image overload for bindings\n\nModule opencv::imgproc\n===\n\nImage Processing\n---\n\nThis module includes image-processing functions.\n\nImage Filtering\n---\n\nFunctions and classes described in this section are used to perform various linear or non-linear filtering operations on 2D images (represented as Mat’s). It means that for each pixel location\n in the source image (normally, rectangular), its neighborhood is considered and used to compute the response. In case of a linear filter, it is a weighted sum of pixel values. In case of morphological operations, it is the minimum or maximum values, and so on. The computed response is stored in the destination image at the same location . It means that the output image will be of the same size as the input image. Normally, the functions support multi-channel arrays,\nin which case every channel is processed independently. Therefore, the output image will also have the same number of channels as the input one.\n\nAnother common feature of the functions and classes described in this section is that, unlike simple arithmetic functions, they need to extrapolate values of some non-existing pixels. For example, if you want to smooth an image using a Gaussian  filter, then, when processing the left-most pixels in each row, you need pixels to the left of them, that is, outside of the image. You can let these pixels be the same as the left-most image pixels (“replicated border” extrapolation method), or assume that all the non-existing pixels are zeros (“constant border” extrapolation method), and so on. OpenCV enables you to specify the extrapolation method.\nFor details, see [border_types]\n\n@anchor filter_depths\n\n#### Depth combinations\n\n| Input depth (src.depth()) | Output depth (ddepth) |\n| --- | --- |\n| CV_8U | -1/CV_16S/CV_32F/CV_64F |\n| CV_16U/CV_16S | -1/CV_32F/CV_64F |\n| CV_32F | -1/CV_32F |\n| CV_64F | -1/CV_64F |\n\nNote: when ddepth=-1, the output image will have the same depth as the source.\n\nNote: if you need double floating-point accuracy and using single floating-point input data\n(CV_32F input and CV_64F output depth combination), you can use [Mat].convertTo to convert the input data to the desired precision.\n\nGeometric Image Transformations\n---\n\nThe functions in this section perform various geometrical transformations of 2D images. They do not change the image content but deform the pixel grid and map this deformed grid to the destination image. In fact, to avoid sampling artifacts, the mapping is done in the reverse order, from destination to the source. That is, for each pixel  of the destination image, the functions compute coordinates of the corresponding “donor” pixel in the source image and copy the pixel value:\n\n\n\nIn case when you specify the forward mapping , the OpenCV functions first compute the corresponding inverse mapping\n and then use the above formula.\n\nThe actual implementations of the geometrical transformations, from the most generic remap and to the simplest and the fastest resize, need to solve two main problems with the above formula:\n\n* Extrapolation of non-existing pixels. Similarly to the filtering functions described in the previous section, for some , either one of , or , or both of them may fall outside of the image. In this case, an extrapolation method needs to be used.\nOpenCV provides the same selection of extrapolation methods as in the filtering functions. In addition, it provides the method #BORDER_TRANSPARENT. This means that the corresponding pixels in the destination image will not be modified at all.\n* Interpolation of pixel values. Usually  and  are floating-point numbers. This means that  can be either an affine or perspective transformation, or radial lens distortion correction, and so on. So, a pixel value at fractional coordinates needs to be retrieved. In the simplest case, the coordinates can be just rounded to the nearest integer coordinates and the corresponding pixel can be used. This is called a nearest-neighbor interpolation. However, a better result can be achieved by using more sophisticated interpolation methods ,\nwhere a polynomial function is fit into some neighborhood of the computed pixel , and then the value of the polynomial at  is taken as the interpolated pixel value. In OpenCV, you can choose between several interpolation methods. See resize for details.\n\nNote: The geometrical transformations do not work with `CV_8S` or `CV_32S` images.\n\nMiscellaneous Image Transformations\n---\n\nDrawing Functions\n---\n\nDrawing functions work with matrices/images of arbitrary depth. The boundaries of the shapes can be rendered with antialiasing (implemented only for 8-bit images for now). All the functions include the parameter color that uses an RGB value (that may be constructed with the Scalar constructor )\nfor color images and brightness for grayscale images. For color images, the channel ordering is normally *Blue, Green, Red*. This is what imshow, imread, and imwrite expect. So, if you form a color using the Scalar constructor, it should look like:\n\n\n\nIf you are using your own image rendering and I/O functions, you can use any channel ordering. The drawing functions process each channel independently and do not depend on the channel order or even on the used color space. The whole image can be converted from BGR to RGB or to a different color space using cvtColor .\n\nIf a drawn figure is partially or completely outside the image, the drawing functions clip it. Also,\nmany drawing functions can handle pixel coordinates specified with sub-pixel accuracy. This means that the coordinates can be passed as fixed-point numbers encoded as integers. The number of fractional bits is specified by the shift parameter and the real point coordinates are calculated as\n . This feature is especially effective when rendering antialiased shapes.\n\nNote: The functions do not support alpha-transparency when the target image is 4-channel. In this case, the color[3] is simply copied to the repainted pixels. Thus, if you want to paint semi-transparent shapes, you can paint them in a separate buffer and then blend it with the main image.\n\nColor Space Conversions\n---\n\nColorMaps in OpenCV\n---\n\nThe human perception isn’t built for observing fine changes in grayscale images. Human eyes are more sensitive to observing changes between colors, so you often need to recolor your grayscale images to get a clue about them. OpenCV now comes with various colormaps to enhance the visualization in your computer vision application.\n\nIn OpenCV you only need applyColorMap to apply a colormap on a given image. The following sample code reads the path to an image from command line, applies a Jet colormap on it and shows the result:\n\n@include snippets/imgproc_applyColorMap.cpp\n\n### See also\n\n[colormap_types]\n\nPlanar Subdivision\n---\n\nThe Subdiv2D class described in this section is used to perform various planar subdivision on a set of 2D points (represented as vector of Point2f). OpenCV subdivides a plane into triangles using the Delaunay’s algorithm, which corresponds to the dual graph of the Voronoi diagram.\nIn the figure below, the Delaunay’s triangulation is marked with black lines and the Voronoi diagram with red lines.\n\n\n\nThe subdivisions can be used for the 3D piece-wise transformation of a plane, morphing, fast location of points on the plane, building special graphs (such as NNG,RNG), and so forth.\n\nHistograms\n---\n\nStructural Analysis and Shape Descriptors\n---\n\nMotion Analysis and Object Tracking\n---\n\nFeature Detection\n---\n\nObject Detection\n---\n\nImage Segmentation\n---\n\nC API\n---\n\nHardware Acceleration Layer\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CLAHEBase class for Contrast Limited Adaptive Histogram Equalization.\n* GeneralizedHoughfinds arbitrary template in the grayscale image using Generalized Hough Transform\n* GeneralizedHoughBallardfinds arbitrary template in the grayscale image using Generalized Hough Transform\n* GeneralizedHoughGuilfinds arbitrary template in the grayscale image using Generalized Hough Transform\n* IntelligentScissorsMBIntelligent Scissors image segmentation\n* LineIteratorClass for iterating over all pixels on a raster line segment.\n* LineSegmentDetectorLine segment detector class\n* Subdiv2D\n\nEnums\n---\n\n* AdaptiveThresholdTypesadaptive threshold algorithm\n* ColorConversionCodesthe color conversion codes\n* ColormapTypesGNU Octave/MATLAB equivalent colormaps\n* ConnectedComponentsAlgorithmsTypesconnected components algorithm\n* ConnectedComponentsTypesconnected components statistics\n* ContourApproximationModesthe contour approximation algorithm\n* DistanceTransformLabelTypesdistanceTransform algorithm flags\n* DistanceTransformMasksMask size for distance transform\n* DistanceTypesDistance types for Distance Transform and M-estimators\n* FloodFillFlagsfloodfill algorithm flags\n* GrabCutClassesclass of the pixel in GrabCut algorithm\n* GrabCutModesGrabCut algorithm flags\n* HersheyFontsOnly a subset of Hershey fonts https://en.wikipedia.org/wiki/Hershey_fonts are supported\n@ingroup imgproc_draw\n* HistCompMethodsHistogram comparison methods\n@ingroup imgproc_hist\n* HoughModesVariants of a Hough transform\n* InterpolationFlagsinterpolation algorithm\n* InterpolationMasks\n* LineSegmentDetectorModesVariants of Line Segment %Detector\n* LineTypestypes of line\n@ingroup imgproc_draw\n* MarkerTypesPossible set of marker types used for the cv::drawMarker function\n@ingroup imgproc_draw\n* MorphShapesshape of the structuring element\n* MorphTypestype of morphological operation\n* RectanglesIntersectTypestypes of intersection between rectangles\n* RetrievalModesmode of the contour retrieval algorithm\n* ShapeMatchModesShape matching methods\n* SpecialFilter\n* TemplateMatchModestype of the template matching operation\n* ThresholdTypestype of the threshold operation threshold types\n* WarpPolarMode\\brief Specify the polar mapping mode\n\nConstants\n---\n\n* ADAPTIVE_THRESH_GAUSSIAN_Cthe threshold value inline formula is a weighted sum (cross-correlation with a Gaussian window) of the inline formula neighborhood of inline formula minus C . The default sigma (standard deviation) is used for the specified blockSize . See\n#getGaussianKernel\n* ADAPTIVE_THRESH_MEAN_Cthe threshold value inline formula is a mean of the inline formula neighborhood of inline formula minus C\n* CCL_BBDTSame as CCL_GRANA. It is preferable to use the flag with the name of the algorithm (CCL_BBDT) rather than the one with the name of the first author (CCL_GRANA).\n* CCL_BOLELLISpaghetti Bolelli2019 algorithm for 8-way connectivity, Spaghetti4C Bolelli2021 algorithm for 4-way connectivity. The parallel implementation described in Bolelli2017 is available for both Spaghetti and Spaghetti4C.\n* CCL_DEFAULTSpaghetti Bolelli2019 algorithm for 8-way connectivity, Spaghetti4C Bolelli2021 algorithm for 4-way connectivity.\n* CCL_GRANABBDT Grana2010 algorithm for 8-way connectivity, SAUF algorithm for 4-way connectivity. The parallel implementation described in Bolelli2017 is available for both BBDT and SAUF.\n* CCL_SAUFSame as CCL_WU. It is preferable to use the flag with the name of the algorithm (CCL_SAUF) rather than the one with the name of the first author (CCL_WU).\n* CCL_SPAGHETTISame as CCL_BOLELLI. It is preferable to use the flag with the name of the algorithm (CCL_SPAGHETTI) rather than the one with the name of the first author (CCL_BOLELLI).\n* CCL_WUSAUF Wu2009 algorithm for 8-way connectivity, SAUF algorithm for 4-way connectivity. The parallel implementation described in Bolelli2017 is available for SAUF.\n* CC_STAT_AREAThe total area (in pixels) of the connected component\n* CC_STAT_HEIGHTThe vertical size of the bounding box\n* CC_STAT_LEFTThe leftmost (x) coordinate which is the inclusive start of the bounding box in the horizontal direction.\n* CC_STAT_MAXMax enumeration value. Used internally only for memory allocation\n* CC_STAT_TOPThe topmost (y) coordinate which is the inclusive start of the bounding box in the vertical direction.\n* CC_STAT_WIDTHThe horizontal size of the bounding box\n* CHAIN_APPROX_NONEstores absolutely all the contour points. That is, any 2 subsequent points (x1,y1) and\n(x2,y2) of the contour will be either horizontal, vertical or diagonal neighbors, that is,\nmax(abs(x1-x2),abs(y2-y1))==1.\n* CHAIN_APPROX_SIMPLEcompresses horizontal, vertical, and diagonal segments and leaves only their end points.\nFor example, an up-right rectangular contour is encoded with 4 points.\n* CHAIN_APPROX_TC89_KCOSapplies one of the flavors of the Teh-Chin chain approximation algorithm TehChin89\n* CHAIN_APPROX_TC89_L1applies one of the flavors of the Teh-Chin chain approximation algorithm TehChin89\n* COLORMAP_AUTUMNautumn\n* COLORMAP_BONEbone\n* COLORMAP_CIVIDIScividis\n* COLORMAP_COOLcool\n* COLORMAP_DEEPGREENdeepgreen\n* COLORMAP_HOThot\n* COLORMAP_HSVHSV\n* COLORMAP_INFERNOinferno\n* COLORMAP_JETjet\n* COLORMAP_MAGMAmagma\n* COLORMAP_OCEANocean\n* COLORMAP_PARULAparula\n* COLORMAP_PINKpink\n* COLORMAP_PLASMAplasma\n* COLORMAP_RAINBOWrainbow\n* COLORMAP_SPRINGspring\n* COLORMAP_SUMMERsummer\n* COLORMAP_TURBOturbo\n* COLORMAP_TWILIGHTtwilight\n* COLORMAP_TWILIGHT_SHIFTEDtwilight shifted\n* COLORMAP_VIRIDISviridis\n* COLORMAP_WINTERwinter\n* COLOR_BGR2BGR555convert between RGB/BGR and BGR555 (16-bit images)\n* COLOR_BGR2BGR565convert between RGB/BGR and BGR565 (16-bit images)\n* COLOR_BGR2BGRAadd alpha channel to RGB or BGR image\n* COLOR_BGR2GRAYconvert between RGB/BGR and grayscale, [color_convert_rgb_gray] “color conversions”\n* COLOR_BGR2HLSconvert RGB/BGR to HLS (hue lightness saturation) with H range 0..180 if 8 bit image, [color_convert_rgb_hls] “color conversions”\n* COLOR_BGR2HLS_FULLconvert RGB/BGR to HLS (hue lightness saturation) with H range 0..255 if 8 bit image, [color_convert_rgb_hls] “color conversions”\n* COLOR_BGR2HSVconvert RGB/BGR to HSV (hue saturation value) with H range 0..180 if 8 bit image, [color_convert_rgb_hsv] “color conversions”\n* COLOR_BGR2HSV_FULLconvert RGB/BGR to HSV (hue saturation value) with H range 0..255 if 8 bit image, [color_convert_rgb_hsv] “color conversions”\n* COLOR_BGR2Labconvert RGB/BGR to CIE Lab, [color_convert_rgb_lab] “color conversions”\n* COLOR_BGR2Luvconvert RGB/BGR to CIE Luv, [color_convert_rgb_luv] “color conversions”\n* COLOR_BGR2RGB\n* COLOR_BGR2RGBAconvert between RGB and BGR color spaces (with or without alpha channel)\n* COLOR_BGR2XYZconvert RGB/BGR to CIE XYZ, [color_convert_rgb_xyz] “color conversions”\n* COLOR_BGR2YCrCbconvert RGB/BGR to luma-chroma (aka YCC), [color_convert_rgb_ycrcb] “color conversions”\n* COLOR_BGR2YUVconvert between RGB/BGR and YUV\n* COLOR_BGR2YUV_I420RGB to YUV 4:2:0 family\n* COLOR_BGR2YUV_IYUVRGB to YUV 4:2:0 family\n* COLOR_BGR2YUV_YV12RGB to YUV 4:2:0 family\n* COLOR_BGR5552BGR\n* COLOR_BGR5552BGRA\n* COLOR_BGR5552GRAY\n* COLOR_BGR5552RGB\n* COLOR_BGR5552RGBA\n* COLOR_BGR5652BGR\n* COLOR_BGR5652BGRA\n* COLOR_BGR5652GRAY\n* COLOR_BGR5652RGB\n* COLOR_BGR5652RGBA\n* COLOR_BGRA2BGRremove alpha channel from RGB or BGR image\n* COLOR_BGRA2BGR555\n* COLOR_BGRA2BGR565\n* COLOR_BGRA2GRAY\n* COLOR_BGRA2RGB\n* COLOR_BGRA2RGBA\n* COLOR_BGRA2YUV_I420RGB to YUV 4:2:0 family\n* COLOR_BGRA2YUV_IYUVRGB to YUV 4:2:0 family\n* COLOR_BGRA2YUV_YV12RGB to YUV 4:2:0 family\n* COLOR_BayerBG2BGRequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2BGRAequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2BGR_EAequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2BGR_VNGequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2GRAYequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2RGBequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2RGBAequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2RGB_EAequivalent to RGGB Bayer pattern\n* COLOR_BayerBG2RGB_VNGequivalent to RGGB Bayer pattern\n* COLOR_BayerBGGR2BGR\n* COLOR_BayerBGGR2BGRA\n* COLOR_BayerBGGR2BGR_EA\n* COLOR_BayerBGGR2BGR_VNG\n* COLOR_BayerBGGR2GRAY\n* COLOR_BayerBGGR2RGB\n* COLOR_BayerBGGR2RGBA\n* COLOR_BayerBGGR2RGB_EA\n* COLOR_BayerBGGR2RGB_VNG\n* COLOR_BayerGB2BGRequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2BGRAequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2BGR_EAequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2BGR_VNGequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2GRAYequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2RGBequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2RGBAequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2RGB_EAequivalent to GRBG Bayer pattern\n* COLOR_BayerGB2RGB_VNGequivalent to GRBG Bayer pattern\n* COLOR_BayerGBRG2BGR\n* COLOR_BayerGBRG2BGRA\n* COLOR_BayerGBRG2BGR_EA\n* COLOR_BayerGBRG2BGR_VNG\n* COLOR_BayerGBRG2GRAY\n* COLOR_BayerGBRG2RGB\n* COLOR_BayerGBRG2RGBA\n* COLOR_BayerGBRG2RGB_EA\n* COLOR_BayerGBRG2RGB_VNG\n* COLOR_BayerGR2BGRequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2BGRAequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2BGR_EAequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2BGR_VNGequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2GRAYequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2RGBequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2RGBAequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2RGB_EAequivalent to GBRG Bayer pattern\n* COLOR_BayerGR2RGB_VNGequivalent to GBRG Bayer pattern\n* COLOR_BayerGRBG2BGR\n* COLOR_BayerGRBG2BGRA\n* COLOR_BayerGRBG2BGR_EA\n* COLOR_BayerGRBG2BGR_VNG\n* COLOR_BayerGRBG2GRAY\n* COLOR_BayerGRBG2RGB\n* COLOR_BayerGRBG2RGBA\n* COLOR_BayerGRBG2RGB_EA\n* COLOR_BayerGRBG2RGB_VNG\n* COLOR_BayerRG2BGRequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2BGRAequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2BGR_EAequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2BGR_VNGequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2GRAYequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2RGBequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2RGBAequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2RGB_EAequivalent to BGGR Bayer pattern\n* COLOR_BayerRG2RGB_VNGequivalent to BGGR Bayer pattern\n* COLOR_BayerRGGB2BGR\n* COLOR_BayerRGGB2BGRA\n* COLOR_BayerRGGB2BGR_EA\n* COLOR_BayerRGGB2BGR_VNG\n* COLOR_BayerRGGB2GRAY\n* COLOR_BayerRGGB2RGB\n* COLOR_BayerRGGB2RGBA\n* COLOR_BayerRGGB2RGB_EA\n* COLOR_BayerRGGB2RGB_VNG\n* COLOR_COLORCVT_MAX\n* COLOR_GRAY2BGR\n* COLOR_GRAY2BGR555convert between grayscale and BGR555 (16-bit images)\n* COLOR_GRAY2BGR565convert between grayscale to BGR565 (16-bit images)\n* COLOR_GRAY2BGRA\n* COLOR_GRAY2RGB\n* COLOR_GRAY2RGBA\n* COLOR_HLS2BGRbackward conversions HLS to RGB/BGR with H range 0..180 if 8 bit image\n* COLOR_HLS2BGR_FULLbackward conversions HLS to RGB/BGR with H range 0..255 if 8 bit image\n* COLOR_HLS2RGB\n* COLOR_HLS2RGB_FULL\n* COLOR_HSV2BGRbackward conversions HSV to RGB/BGR with H range 0..180 if 8 bit image\n* COLOR_HSV2BGR_FULLbackward conversions HSV to RGB/BGR with H range 0..255 if 8 bit image\n* COLOR_HSV2RGB\n* COLOR_HSV2RGB_FULL\n* COLOR_LBGR2Lab\n* COLOR_LBGR2Luv\n* COLOR_LRGB2Lab\n* COLOR_LRGB2Luv\n* COLOR_Lab2BGR\n* COLOR_Lab2LBGR\n* COLOR_Lab2LRGB\n* COLOR_Lab2RGB\n* COLOR_Luv2BGR\n* COLOR_Luv2LBGR\n* COLOR_Luv2LRGB\n* COLOR_Luv2RGB\n* COLOR_RGB2BGR\n* COLOR_RGB2BGR555\n* COLOR_RGB2BGR565\n* COLOR_RGB2BGRA\n* COLOR_RGB2GRAY\n* COLOR_RGB2HLS\n* COLOR_RGB2HLS_FULL\n* COLOR_RGB2HSV\n* COLOR_RGB2HSV_FULL\n* COLOR_RGB2Lab\n* COLOR_RGB2Luv\n* COLOR_RGB2RGBA\n* COLOR_RGB2XYZ\n* COLOR_RGB2YCrCb\n* COLOR_RGB2YUV\n* COLOR_RGB2YUV_I420RGB to YUV 4:2:0 family\n* COLOR_RGB2YUV_IYUVRGB to YUV 4:2:0 family\n* COLOR_RGB2YUV_YV12RGB to YUV 4:2:0 family\n* COLOR_RGBA2BGR\n* COLOR_RGBA2BGR555\n* COLOR_RGBA2BGR565\n* COLOR_RGBA2BGRA\n* COLOR_RGBA2GRAY\n* COLOR_RGBA2RGB\n* COLOR_RGBA2YUV_I420RGB to YUV 4:2:0 family\n* COLOR_RGBA2YUV_IYUVRGB to YUV 4:2:0 family\n* COLOR_RGBA2YUV_YV12RGB to YUV 4:2:0 family\n* COLOR_RGBA2mRGBAalpha premultiplication\n* COLOR_XYZ2BGR\n* COLOR_XYZ2RGB\n* COLOR_YCrCb2BGR\n* COLOR_YCrCb2RGB\n* COLOR_YUV2BGR\n* COLOR_YUV2BGRA_I420YUV 4:2:0 family to RGB\n* COLOR_YUV2BGRA_IYUVYUV 4:2:0 family to RGB\n* COLOR_YUV2BGRA_NV12YUV 4:2:0 family to RGB\n* COLOR_YUV2BGRA_NV21YUV 4:2:0 family to RGB\n* COLOR_YUV2BGRA_UYNVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_UYVYYUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_Y422YUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_YUNVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_YUY2YUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_YUYVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGRA_YV12YUV 4:2:0 family to RGB\n* COLOR_YUV2BGRA_YVYUYUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_I420YUV 4:2:0 family to RGB\n* COLOR_YUV2BGR_IYUVYUV 4:2:0 family to RGB\n* COLOR_YUV2BGR_NV12YUV 4:2:0 family to RGB\n* COLOR_YUV2BGR_NV21YUV 4:2:0 family to RGB\n* COLOR_YUV2BGR_UYNVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_UYVYYUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_Y422YUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_YUNVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_YUY2YUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_YUYVYUV 4:2:2 family to RGB\n* COLOR_YUV2BGR_YV12YUV 4:2:0 family to RGB\n* COLOR_YUV2BGR_YVYUYUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_420YUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_I420YUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_IYUVYUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_NV12YUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_NV21YUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_UYNVYUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_UYVYYUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_Y422YUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_YUNVYUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_YUY2YUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_YUYVYUV 4:2:2 family to RGB\n* COLOR_YUV2GRAY_YV12YUV 4:2:0 family to RGB\n* COLOR_YUV2GRAY_YVYUYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB\n* COLOR_YUV2RGBA_I420YUV 4:2:0 family to RGB\n* COLOR_YUV2RGBA_IYUVYUV 4:2:0 family to RGB\n* COLOR_YUV2RGBA_NV12YUV 4:2:0 family to RGB\n* COLOR_YUV2RGBA_NV21YUV 4:2:0 family to RGB\n* COLOR_YUV2RGBA_UYNVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_UYVYYUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_Y422YUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_YUNVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_YUY2YUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_YUYVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGBA_YV12YUV 4:2:0 family to RGB\n* COLOR_YUV2RGBA_YVYUYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_I420YUV 4:2:0 family to RGB\n* COLOR_YUV2RGB_IYUVYUV 4:2:0 family to RGB\n* COLOR_YUV2RGB_NV12YUV 4:2:0 family to RGB\n* COLOR_YUV2RGB_NV21YUV 4:2:0 family to RGB\n* COLOR_YUV2RGB_UYNVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_UYVYYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_Y422YUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_YUNVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_YUY2YUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_YUYVYUV 4:2:2 family to RGB\n* COLOR_YUV2RGB_YV12YUV 4:2:0 family to RGB\n* COLOR_YUV2RGB_YVYUYUV 4:2:2 family to RGB\n* COLOR_YUV420p2BGRYUV 4:2:0 family to RGB\n* COLOR_YUV420p2BGRAYUV 4:2:0 family to RGB\n* COLOR_YUV420p2GRAYYUV 4:2:0 family to RGB\n* COLOR_YUV420p2RGBYUV 4:2:0 family to RGB\n* COLOR_YUV420p2RGBAYUV 4:2:0 family to RGB\n* COLOR_YUV420sp2BGRYUV 4:2:0 family to RGB\n* COLOR_YUV420sp2BGRAYUV 4:2:0 family to RGB\n* COLOR_YUV420sp2GRAYYUV 4:2:0 family to RGB\n* COLOR_YUV420sp2RGBYUV 4:2:0 family to RGB\n* COLOR_YUV420sp2RGBAYUV 4:2:0 family to RGB\n* COLOR_mRGBA2RGBAalpha premultiplication\n* CONTOURS_MATCH_I1block formula\n* CONTOURS_MATCH_I2block formula\n* CONTOURS_MATCH_I3block formula\n* DIST_Cdistance = max(|x1-x2|,|y1-y2|)\n* DIST_FAIRdistance = c^2(|x|/c-log(1+|x|/c)), c = 1.3998\n* DIST_HUBERdistance = |x|<c ? x^2/2 : c(|x|-c/2), c=1.345\n* DIST_L1distance = |x1-x2| + |y1-y2|\n* DIST_L2the simple euclidean distance\n* DIST_L12L1-L2 metric: distance = 2(sqrt(1+x*x/2) - 1))\n* DIST_LABEL_CCOMPeach connected component of zeros in src (as well as all the non-zero pixels closest to the connected component) will be assigned the same label\n* DIST_LABEL_PIXELeach zero pixel (and all the non-zero pixels closest to it) gets its own label.\n* DIST_MASK_3mask=3\n* DIST_MASK_5mask=5\n* DIST_MASK_PRECISE\n* DIST_USERUser defined distance\n* DIST_WELSCHdistance = c^2/2(1-exp(-(x/c)^2)), c = 2.9846\n* FILLED\n* FILTER_SCHARR\n* FLOODFILL_FIXED_RANGEIf set, the difference between the current pixel and seed pixel is considered. Otherwise,\nthe difference between neighbor pixels is considered (that is, the range is floating).\n* FLOODFILL_MASK_ONLYIf set, the function does not change the image ( newVal is ignored), and only fills the mask with the value specified in bits 8-16 of flags as described above. This option only make sense in function variants that have the mask parameter.\n* FONT_HERSHEY_COMPLEXnormal size serif font\n* FONT_HERSHEY_COMPLEX_SMALLsmaller version of FONT_HERSHEY_COMPLEX\n* FONT_HERSHEY_DUPLEXnormal size sans-serif font (more complex than FONT_HERSHEY_SIMPLEX)\n* FONT_HERSHEY_PLAINsmall size sans-serif font\n* FONT_HERSHEY_SCRIPT_COMPLEXmore complex variant of FONT_HERSHEY_SCRIPT_SIMPLEX\n* FONT_HERSHEY_SCRIPT_SIMPLEXhand-writing style font\n* FONT_HERSHEY_SIMPLEXnormal size sans-serif font\n* FONT_HERSHEY_TRIPLEXnormal size serif font (more complex than FONT_HERSHEY_COMPLEX)\n* FONT_ITALICflag for italic font\n* GC_BGDan obvious background pixels\n* GC_EVALThe value means that the algorithm should just resume.\n* GC_EVAL_FREEZE_MODELThe value means that the algorithm should just run the grabCut algorithm (a single iteration) with the fixed model\n* GC_FGDan obvious foreground (object) pixel\n* GC_INIT_WITH_MASKThe function initializes the state using the provided mask. Note that GC_INIT_WITH_RECT and GC_INIT_WITH_MASK can be combined. Then, all the pixels outside of the ROI are automatically initialized with GC_BGD .\n* GC_INIT_WITH_RECTThe function initializes the state and the mask using the provided rectangle. After that it runs iterCount iterations of the algorithm.\n* GC_PR_BGDa possible background pixel\n* GC_PR_FGDa possible foreground pixel\n* HISTCMP_BHATTACHARYYABhattacharyya distance\n(In fact, OpenCV computes Hellinger distance, which is related to Bhattacharyya coefficient.)\nblock formula\n* HISTCMP_CHISQRChi-Square block formula\n* HISTCMP_CHISQR_ALTAlternative Chi-Square block formula This alternative formula is regularly used for texture comparison. See e.g. Puzicha1997\n* HISTCMP_CORRELCorrelation block formula where\nblock formula and inline formula is a total number of histogram bins.\n* HISTCMP_HELLINGERSynonym for HISTCMP_BHATTACHARYYA\n* HISTCMP_INTERSECTIntersection block formula\n* HISTCMP_KL_DIVKullback-Leibler divergence block formula\n* HOUGH_GRADIENTbasically *21HT*, described in Yuen90\n* HOUGH_GRADIENT_ALTvariation of HOUGH_GRADIENT to get better accuracy\n* HOUGH_MULTI_SCALEmulti-scale variant of the classical Hough transform. The lines are encoded the same way as HOUGH_STANDARD.\n* HOUGH_PROBABILISTICprobabilistic Hough transform (more efficient in case if the picture contains a few long linear segments). It returns line segments rather than the whole line. Each segment is represented by starting and ending points, and the matrix must be (the created sequence will be) of the CV_32SC4 type.\n* HOUGH_STANDARDclassical or standard Hough transform. Every line is represented by two floating-point numbers inline formula , where inline formula is a distance between (0,0) point and the line,\nand inline formula is the angle between x-axis and the normal to the line. Thus, the matrix must be (the created sequence will be) of CV_32FC2 type\n* INTERSECT_FULLOne of the rectangle is fully enclosed in the other\n* INTERSECT_NONENo intersection\n* INTERSECT_PARTIALThere is a partial intersection\n* INTER_AREAresampling using pixel area relation. It may be a preferred method for image decimation, as it gives moire’-free results. But when the image is zoomed, it is similar to the INTER_NEAREST method.\n* INTER_BITS\n* INTER_BITS2\n* INTER_CUBICbicubic interpolation\n* INTER_LANCZOS4Lanczos interpolation over 8x8 neighborhood\n* INTER_LINEARbilinear interpolation\n* INTER_LINEAR_EXACTBit exact bilinear interpolation\n* INTER_MAXmask for interpolation codes\n* INTER_NEARESTnearest neighbor interpolation\n* INTER_NEAREST_EXACTBit exact nearest neighbor interpolation. This will produce same results as the nearest neighbor method in PIL, scikit-image or Matlab.\n* INTER_TAB_SIZE\n* INTER_TAB_SIZE2\n* LINE_44-connected line\n* LINE_88-connected line\n* LINE_AAantialiased line\n* LSD_REFINE_ADVAdvanced refinement. Number of false alarms is calculated, lines are refined through increase of precision, decrement in size, etc.\n* LSD_REFINE_NONENo refinement applied\n* LSD_REFINE_STDStandard refinement is applied. E.g. breaking arches into smaller straighter line approximations.\n* MARKER_CROSSA crosshair marker shape\n* MARKER_DIAMONDA diamond marker shape\n* MARKER_SQUAREA square marker shape\n* MARKER_STARA star marker shape, combination of cross and tilted cross\n* MARKER_TILTED_CROSSA 45 degree tilted crosshair marker shape\n* MARKER_TRIANGLE_DOWNA downwards pointing triangle marker shape\n* MARKER_TRIANGLE_UPAn upwards pointing triangle marker shape\n* MORPH_BLACKHAT“black hat”\nblock formula\n* MORPH_CLOSEa closing operation block formula\n* MORPH_CROSSa cross-shaped structuring element:\nblock formula\n* MORPH_DILATEsee #dilate\n* MORPH_ELLIPSEan elliptic structuring element, that is, a filled ellipse inscribed into the rectangle Rect(0, 0, esize.width, 0.esize.height)\n* MORPH_ERODEsee #erode\n* MORPH_GRADIENTa morphological gradient block formula\n* MORPH_HITMISS“hit or miss”\n.- Only supported for CV_8UC1 binary images. A tutorial can be found in the documentation\n* MORPH_OPENan opening operation block formula\n* MORPH_RECTa rectangular structuring element: block formula\n* MORPH_TOPHAT“top hat”\nblock formula\n* RETR_CCOMPretrieves all of the contours and organizes them into a two-level hierarchy. At the top level, there are external boundaries of the components. At the second level, there are boundaries of the holes. If there is another contour inside a hole of a connected component, it is still put at the top level.\n* RETR_EXTERNALretrieves only the extreme outer contours. It sets `hierarchy[i][2]=hierarchy[i][3]=-1` for all the contours.\n* RETR_FLOODFILL\n* RETR_LISTretrieves all of the contours without establishing any hierarchical relationships.\n* RETR_TREEretrieves all of the contours and reconstructs a full hierarchy of nested contours.\n* Subdiv2D_NEXT_AROUND_DST\n* Subdiv2D_NEXT_AROUND_LEFT\n* Subdiv2D_NEXT_AROUND_ORG\n* Subdiv2D_NEXT_AROUND_RIGHT\n* Subdiv2D_PREV_AROUND_DST\n* Subdiv2D_PREV_AROUND_LEFT\n* Subdiv2D_PREV_AROUND_ORG\n* Subdiv2D_PREV_AROUND_RIGHT\n* Subdiv2D_PTLOC_ERRORPoint location error\n* Subdiv2D_PTLOC_INSIDEPoint inside some facet\n* Subdiv2D_PTLOC_ON_EDGEPoint on some edge\n* Subdiv2D_PTLOC_OUTSIDE_RECTPoint outside the subdivision bounding rect\n* Subdiv2D_PTLOC_VERTEXPoint coincides with one of the subdivision vertices\n* THRESH_BINARYblock formula\n* THRESH_BINARY_INVblock formula\n* THRESH_MASK\n* THRESH_OTSUflag, use Otsu algorithm to choose the optimal threshold value\n* THRESH_TOZEROblock formula\n* THRESH_TOZERO_INVblock formula\n* THRESH_TRIANGLEflag, use Triangle algorithm to choose the optimal threshold value\n* THRESH_TRUNCblock formula\n* TM_CCOEFF!< block formula where\nblock formula with mask:\nblock formula\n* TM_CCOEFF_NORMED!< block formula\n* TM_CCORR!< block formula with mask:\nblock formula\n* TM_CCORR_NORMED!< block formula with mask:\nblock formula\n* TM_SQDIFF!< block formula with mask:\nblock formula\n* TM_SQDIFF_NORMED!< block formula with mask:\nblock formula\n* WARP_FILL_OUTLIERSflag, fills all of the destination image pixels. If some of them correspond to outliers in the source image, they are set to zero\n* WARP_INVERSE_MAPflag, inverse transformation\n* WARP_POLAR_LINEARRemaps an image to/from polar space.\n* WARP_POLAR_LOGRemaps an image to/from semilog-polar space.\n\nTraits\n---\n\n* CLAHETraitMutable methods for crate::imgproc::CLAHE\n* CLAHETraitConstConstant methods for crate::imgproc::CLAHE\n* GeneralizedHoughBallardTraitMutable methods for crate::imgproc::GeneralizedHoughBallard\n* GeneralizedHoughBallardTraitConstConstant methods for crate::imgproc::GeneralizedHoughBallard\n* GeneralizedHoughGuilTraitMutable methods for crate::imgproc::GeneralizedHoughGuil\n* GeneralizedHoughGuilTraitConstConstant methods for crate::imgproc::GeneralizedHoughGuil\n* GeneralizedHoughTraitMutable methods for crate::imgproc::GeneralizedHough\n* GeneralizedHoughTraitConstConstant methods for crate::imgproc::GeneralizedHough\n* IntelligentScissorsMBTraitMutable methods for crate::imgproc::IntelligentScissorsMB\n* IntelligentScissorsMBTraitConstConstant methods for crate::imgproc::IntelligentScissorsMB\n* LineIteratorTraitMutable methods for crate::imgproc::LineIterator\n* LineIteratorTraitConstConstant methods for crate::imgproc::LineIterator\n* LineSegmentDetectorTraitMutable methods for crate::imgproc::LineSegmentDetector\n* LineSegmentDetectorTraitConstConstant methods for crate::imgproc::LineSegmentDetector\n* Subdiv2DTraitMutable methods for crate::imgproc::Subdiv2D\n* Subdiv2DTraitConstConstant methods for crate::imgproc::Subdiv2D\n\nFunctions\n---\n\n* accumulateAdds an image to the accumulator image.\n* accumulate_defAdds an image to the accumulator image.\n* accumulate_productAdds the per-element product of two input images to the accumulator image.\n* accumulate_product_defAdds the per-element product of two input images to the accumulator image.\n* accumulate_squareAdds the square of a source image to the accumulator image.\n* accumulate_square_defAdds the square of a source image to the accumulator image.\n* accumulate_weightedUpdates a running average.\n* accumulate_weighted_defUpdates a running average.\n* adaptive_thresholdApplies an adaptive threshold to an array.\n* apply_color_mapApplies a GNU Octave/MATLAB equivalent colormap on a given image.\n* apply_color_map_userApplies a user colormap on a given image.\n* approx_poly_dpApproximates a polygonal curve(s) with the specified precision.\n* arc_lengthCalculates a contour perimeter or a curve length.\n* arrowed_lineDraws an arrow segment pointing from the first point to the second one.\n* arrowed_line_defDraws an arrow segment pointing from the first point to the second one.\n* bilateral_filterApplies the bilateral filter to an image.\n* bilateral_filter_defApplies the bilateral filter to an image.\n* blend_linearPerforms linear blending of two images:\nblock formula\n* blurBlurs an image using the normalized box filter.\n* blur_defBlurs an image using the normalized box filter.\n* bounding_rectCalculates the up-right bounding rectangle of a point set or non-zero pixels of gray-scale image.\n* box_filterBlurs an image using the box filter.\n* box_filter_defBlurs an image using the box filter.\n* box_pointsFinds the four vertices of a rotated rect. Useful to draw the rotated rectangle.\n* build_pyramidConstructs the Gaussian pyramid for an image.\n* build_pyramid_defConstructs the Gaussian pyramid for an image.\n* calc_back_projectCalculates the back projection of a histogram.\n* calc_histCalculates a histogram of a set of arrays.\n* calc_hist_def@overload\n* cannyFinds edges in an image using the Canny algorithm Canny86 .\n* canny_defFinds edges in an image using the Canny algorithm Canny86 .\n* canny_derivative\\overload\n* canny_derivative_def\\overload\n* circleDraws a circle.\n* circle_defDraws a circle.\n* clip_lineClips the line against the image rectangle.\n* clip_line_sizeClips the line against the image rectangle.\n* clip_line_size_i64Clips the line against the image rectangle.\n* compare_histCompares two histograms.\n* compare_hist_1Compares two histograms.\n* connected_componentscomputes the connected components labeled image of boolean image\n* connected_components_def@overload\n* connected_components_with_algorithmcomputes the connected components labeled image of boolean image\n* connected_components_with_statscomputes the connected components labeled image of boolean image and also produces a statistics output for each label\n* connected_components_with_stats_def@overload\n* connected_components_with_stats_with_algorithmcomputes the connected components labeled image of boolean image and also produces a statistics output for each label\n* contour_areaCalculates a contour area.\n* contour_area_defCalculates a contour area.\n* convert_mapsConverts image transformation maps from one representation to another.\n* convert_maps_defConverts image transformation maps from one representation to another.\n* convex_hullFinds the convex hull of a point set.\n* convex_hull_defFinds the convex hull of a point set.\n* convexity_defectsFinds the convexity defects of a contour.\n* corner_eigen_vals_and_vecsCalculates eigenvalues and eigenvectors of image blocks for corner detection.\n* corner_eigen_vals_and_vecs_defCalculates eigenvalues and eigenvectors of image blocks for corner detection.\n* corner_harrisHarris corner detector.\n* corner_harris_defHarris corner detector.\n* corner_min_eigen_valCalculates the minimal eigenvalue of gradient matrices for corner detection.\n* corner_min_eigen_val_defCalculates the minimal eigenvalue of gradient matrices for corner detection.\n* corner_sub_pixRefines the corner locations.\n* create_claheCreates a smart pointer to a cv::CLAHE class and initializes it.\n* create_clahe_defCreates a smart pointer to a cv::CLAHE class and initializes it.\n* create_generalized_hough_ballardCreates a smart pointer to a cv::GeneralizedHoughBallard class and initializes it.\n* create_generalized_hough_guilCreates a smart pointer to a cv::GeneralizedHoughGuil class and initializes it.\n* create_hanning_windowThis function computes a Hanning window coefficients in two dimensions.\n* create_line_segment_detectorCreates a smart pointer to a LineSegmentDetector object and initializes it.\n* create_line_segment_detector_defCreates a smart pointer to a LineSegmentDetector object and initializes it.\n* cvt_colorConverts an image from one color space to another.\n* cvt_color_defConverts an image from one color space to another.\n* cvt_color_two_planeConverts an image from one color space to another where the source image is stored in two planes.\n* demosaicingmain function for all demosaicing processes\n* demosaicing_defmain function for all demosaicing processes\n* dilateDilates an image by using a specific structuring element.\n* dilate_defDilates an image by using a specific structuring element.\n* distance_transformCalculates the distance to the closest zero pixel for each pixel of the source image.\n* distance_transform_def@overload\n* distance_transform_with_labelsCalculates the distance to the closest zero pixel for each pixel of the source image.\n* distance_transform_with_labels_defCalculates the distance to the closest zero pixel for each pixel of the source image.\n* div_spectrumsPerforms the per-element division of the first Fourier spectrum by the second Fourier spectrum.\n* div_spectrums_defPerforms the per-element division of the first Fourier spectrum by the second Fourier spectrum.\n* draw_contoursDraws contours outlines or filled contours.\n* draw_contours_defDraws contours outlines or filled contours.\n* draw_markerDraws a marker on a predefined position in an image.\n* draw_marker_defDraws a marker on a predefined position in an image.\n* ellipseDraws a simple or thick elliptic arc or fills an ellipse sector.\n* ellipse_2_polyApproximates an elliptic arc with a polyline.\n* ellipse_2_poly_f64Approximates an elliptic arc with a polyline.\n* ellipse_defDraws a simple or thick elliptic arc or fills an ellipse sector.\n* ellipse_rotated_rectDraws a simple or thick elliptic arc or fills an ellipse sector.\n* ellipse_rotated_rect_def@overload\n* emdComputes the “minimal work” distance between two weighted point configurations.\n* emd_1C++ default parameters\n* emd_1_defNote\n* emd_defComputes the “minimal work” distance between two weighted point configurations.\n* equalize_histEqualizes the histogram of a grayscale image.\n* erodeErodes an image by using a specific structuring element.\n* erode_defErodes an image by using a specific structuring element.\n* fill_convex_polyFills a convex polygon.\n* fill_convex_poly_defFills a convex polygon.\n* fill_polyFills the area bounded by one or more polygons.\n* fill_poly_defFills the area bounded by one or more polygons.\n* filter_2dConvolves an image with the kernel.\n* filter_2d_defConvolves an image with the kernel.\n* find_contoursFinds contours in a binary image.\n* find_contours_def@overload\n* find_contours_with_hierarchyFinds contours in a binary image.\n* find_contours_with_hierarchy_defFinds contours in a binary image.\n* fit_ellipseFits an ellipse around a set of 2D points.\n* fit_ellipse_amsFits an ellipse around a set of 2D points.\n* fit_ellipse_directFits an ellipse around a set of 2D points.\n* fit_lineFits a line to a 2D or 3D point set.\n* flood_fillFills a connected component with the given color.\n* flood_fill_def@overload\n* flood_fill_maskFills a connected component with the given color.\n* flood_fill_mask_defFills a connected component with the given color.\n* gaussian_blurBlurs an image using a Gaussian filter.\n* gaussian_blur_defBlurs an image using a Gaussian filter.\n* get_affine_transform\n* get_affine_transform_sliceCalculates an affine transform from three pairs of the corresponding points.\n* get_deriv_kernelsReturns filter coefficients for computing spatial image derivatives.\n* get_deriv_kernels_defReturns filter coefficients for computing spatial image derivatives.\n* get_font_scale_from_heightCalculates the font-specific size to use to achieve a given height in pixels.\n* get_font_scale_from_height_defCalculates the font-specific size to use to achieve a given height in pixels.\n* get_gabor_kernelReturns Gabor filter coefficients.\n* get_gabor_kernel_defReturns Gabor filter coefficients.\n* get_gaussian_kernelReturns Gaussian filter coefficients.\n* get_gaussian_kernel_defReturns Gaussian filter coefficients.\n* get_perspective_transformCalculates a perspective transform from four pairs of the corresponding points.\n* get_perspective_transform_defCalculates a perspective transform from four pairs of the corresponding points.\n* get_perspective_transform_sliceCalculates a perspective transform from four pairs of the corresponding points.\n* get_perspective_transform_slice_def@overload\n* get_rect_sub_pixRetrieves a pixel rectangle from an image with sub-pixel accuracy.\n* get_rect_sub_pix_defRetrieves a pixel rectangle from an image with sub-pixel accuracy.\n* get_rotation_matrix_2dCalculates an affine matrix of 2D rotation.\n* get_rotation_matrix_2d_matxSee also\n* get_structuring_elementReturns a structuring element of the specified size and shape for morphological operations.\n* get_structuring_element_defReturns a structuring element of the specified size and shape for morphological operations.\n* get_text_sizeCalculates the width and height of a text string.\n* good_features_to_trackDetermines strong corners on an image.\n* good_features_to_track_defDetermines strong corners on an image.\n* good_features_to_track_with_gradientC++ default parameters\n* good_features_to_track_with_gradient_defNote\n* good_features_to_track_with_qualitySame as above, but returns also quality measure of the detected corners.\n* good_features_to_track_with_quality_defSame as above, but returns also quality measure of the detected corners.\n* grab_cutRuns the GrabCut algorithm.\n* grab_cut_defRuns the GrabCut algorithm.\n* hough_circlesFinds circles in a grayscale image using the Hough transform.\n* hough_circles_defFinds circles in a grayscale image using the Hough transform.\n* hough_linesFinds lines in a binary image using the standard Hough transform.\n* hough_lines_defFinds lines in a binary image using the standard Hough transform.\n* hough_lines_pFinds line segments in a binary image using the probabilistic Hough transform.\n* hough_lines_p_defFinds line segments in a binary image using the probabilistic Hough transform.\n* hough_lines_point_setFinds lines in a set of points using the standard Hough transform.\n* hu_momentsCalculates seven Hu invariants.\n* hu_moments_1Calculates seven Hu invariants.\n* integralCalculates the integral of an image.\n* integral2Calculates the integral of an image.\n* integral2_def@overload\n* integral3Calculates the integral of an image.\n* integral3_defCalculates the integral of an image.\n* integral_def@overload\n* intersect_convex_convexFinds intersection of two convex polygons\n* intersect_convex_convex_defFinds intersection of two convex polygons\n* invert_affine_transformInverts an affine transformation.\n* is_contour_convexTests a contour convexity.\n* laplacianCalculates the Laplacian of an image.\n* laplacian_defCalculates the Laplacian of an image.\n* lineDraws a line segment connecting two points.\n* line_defDraws a line segment connecting two points.\n* linear_polarDeprecatedRemaps an image to polar coordinates space.\n* log_polarDeprecatedRemaps an image to semilog-polar coordinates space.\n* match_shapesCompares two shapes.\n* match_templateCompares a template against overlapped image regions.\n* match_template_defCompares a template against overlapped image regions.\n* median_blurBlurs an image using the median filter.\n* min_area_rectFinds a rotated rectangle of the minimum area enclosing the input 2D point set.\n* min_enclosing_circleFinds a circle of the minimum area enclosing a 2D point set.\n* min_enclosing_triangleFinds a triangle of minimum area enclosing a 2D point set and returns its area.\n* momentsCalculates all of the moments up to the third order of a polygon or rasterized shape.\n* moments_defCalculates all of the moments up to the third order of a polygon or rasterized shape.\n* morphology_default_border_valuereturns “magic” border value for erosion and dilation. It is automatically transformed to Scalar::all(-DBL_MAX) for dilation.\n* morphology_exPerforms advanced morphological transformations.\n* morphology_ex_defPerforms advanced morphological transformations.\n* phase_correlateThe function is used to detect translational shifts that occur between two images.\n* phase_correlate_defThe function is used to detect translational shifts that occur between two images.\n* point_polygon_testPerforms a point-in-contour test.\n* polylinesDraws several polygonal curves.\n* polylines_defDraws several polygonal curves.\n* pre_corner_detectCalculates a feature map for corner detection.\n* pre_corner_detect_defCalculates a feature map for corner detection.\n* put_textDraws a text string.\n* put_text_defDraws a text string.\n* pyr_downBlurs an image and downsamples it.\n* pyr_down_defBlurs an image and downsamples it.\n* pyr_mean_shift_filteringPerforms initial step of meanshift segmentation of an image.\n* pyr_mean_shift_filtering_defPerforms initial step of meanshift segmentation of an image.\n* pyr_upUpsamples an image and then blurs it.\n* pyr_up_defUpsamples an image and then blurs it.\n* rectangleDraws a simple, thick, or filled up-right rectangle.\n* rectangle_def@overload\n* rectangle_pointsDraws a simple, thick, or filled up-right rectangle.\n* rectangle_points_defDraws a simple, thick, or filled up-right rectangle.\n* remapApplies a generic geometrical transformation to an image.\n* remap_defApplies a generic geometrical transformation to an image.\n* resizeResizes an image.\n* resize_defResizes an image.\n* rotated_rectangle_intersectionFinds out if there is any intersection between two rotated rectangles.\n* scharrCalculates the first x- or y- image derivative using Scharr operator.\n* scharr_defCalculates the first x- or y- image derivative using Scharr operator.\n* sep_filter_2dApplies a separable linear filter to an image.\n* sep_filter_2d_defApplies a separable linear filter to an image.\n* sobelCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* sobel_defCalculates the first, second, third, or mixed image derivatives using an extended Sobel operator.\n* spatial_gradientCalculates the first order image derivative in both x and y using a Sobel operator\n* spatial_gradient_defCalculates the first order image derivative in both x and y using a Sobel operator\n* sqr_box_filterCalculates the normalized sum of squares of the pixel values overlapping the filter.\n* sqr_box_filter_defCalculates the normalized sum of squares of the pixel values overlapping the filter.\n* stack_blurBlurs an image using the stackBlur.\n* thresholdApplies a fixed-level threshold to each array element.\n* warp_affineApplies an affine transformation to an image.\n* warp_affine_defApplies an affine transformation to an image.\n* warp_perspectiveApplies a perspective transformation to an image.\n* warp_perspective_defApplies a perspective transformation to an image.\n* warp_polar\\brief Remaps an image to polar or semilog-polar coordinates space\n* watershedPerforms a marker-based image segmentation using the watershed algorithm.\n\nModule opencv::intensity_transform\n===\n\nThe module brings implementations of intensity transformation algorithms to adjust image contrast.\n---\n\nNamespace for all functions is `cv::intensity_transform`.\n\n#### Supported Algorithms\n\n* Autoscaling\n* Log Transformations\n* Power-Law (Gamma) Transformations\n* Contrast Stretching\n* BIMEF, A Bio-Inspired Multi-Exposure Fusion Framework for Low-light Image Enhancement ying2017bio ying2017new\n\nReferences from following book and websites:\n\n* Digital Image Processing 4th Edition Chapter 3 [<NAME>, <NAME>] Gonzalez2018\n* http://www.cs.uregina.ca/Links/class-info/425/Lab3/ lcs435lab\n* https://theailearner.com/2019/01/30/contrast-stretching/ theailearner\n\nModules\n---\n\n* prelude\n\nFunctions\n---\n\n* autoscalingGiven an input bgr or grayscale image, apply autoscaling on domain [0, 255] to increase the contrast of the input image and return the resulting image.\n* bimefGiven an input color image, enhance low-light images using the BIMEF method (ying2017bio ying2017new).\n* bimef2Given an input color image, enhance low-light images using the BIMEF method (ying2017bio ying2017new).\n* bimef_defGiven an input color image, enhance low-light images using the BIMEF method (ying2017bio ying2017new).\n* contrast_stretchingGiven an input bgr or grayscale image, apply linear contrast stretching on domain [0, 255]\nand return the resulting image.\n* gamma_correctionGiven an input bgr or grayscale image and constant gamma, apply power-law transformation,\na.k.a. gamma correction to the image on domain [0, 255] and return the resulting image.\n* log_transformGiven an input bgr or grayscale image and constant c, apply log transformation to the image on domain [0, 255] and return the resulting image.\n\nModule opencv::line_descriptor\n===\n\nBinary descriptors for lines extracted from an image\n---\n\n### Introduction\n\nOne of the most challenging activities in computer vision is the extraction of useful information from a given image. Such information, usually comes in the form of points that preserve some kind of property (for instance, they are scale-invariant) and are actually representative of input image.\n\nThe goal of this module is seeking a new kind of representative information inside an image and providing the functionalities for its extraction and representation. In particular, differently from previous methods for detection of relevant elements inside an image, lines are extracted in place of points; a new class is defined ad hoc to summarize a line’s properties, for reuse and plotting purposes.\n\n### Computation of binary descriptors\n\nTo obtatin a binary descriptor representing a certain line detected from a certain octave of an image, we first compute a non-binary descriptor as described in LBD . Such algorithm works on lines extracted using EDLine detector, as explained in EDL . Given a line, we consider a rectangular region centered at it and called *line support region (LSR)*. Such region is divided into a set of bands , whose length equals the one of line.\n\nIf we indicate with  the direction of line, the orthogonal and clockwise direction to line\n\n\nLater on, a Gaussian function is applied to all LSR’s pixels along  direction; first,\nwe assign a global weighting coefficient  to\n*i*-th row in LSR, where  is the distance of *i*-th row from the center row in LSR,\n and  is the width of bands (the same for every band). Secondly,\nconsidering a band  and its neighbor bands , we assign a local weighting\n, where  is the distance of *k*-th row from the center row in  and . Using the global and local weights, we obtain,\nat the same time, the reduction of role played by gradients far from line and of boundary effect,\nrespectively.\n\nEach band  in LSR has an associated *band descriptor(BD)* which is computed considering previous and next band (top and bottom bands are ignored when computing descriptor for first and last band). Once each band has been assignen its BD, the LBD descriptor of line is simply given by\n\n\n\nTo compute a band descriptor , each *k*-th row in it is considered and the gradients in such row are accumulated:\n\n\n\nwith .\n\nBy stacking previous results, we obtain the *band description matrix (BDM)*\n\n\n\nwith  the number of rows in band :\n\n\n\nEach  can be obtained using the standard deviation vector  and mean vector  of\n. Thus, finally:\n\n\n\nOnce the LBD has been obtained, it must be converted into a binary form. For such purpose, we consider 32 possible pairs of BD inside it; each couple of BD is compared bit by bit and comparison generates an 8 bit string. Concatenating 32 comparison strings, we get the 256-bit final binary representation of a single LBD.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BinaryDescriptorClass implements both functionalities for detection of lines and computation of their binary descriptor.\n* BinaryDescriptorMatcherfurnishes all functionalities for querying a dataset provided by user or internal to class (that user must, anyway, populate) on the model of [features2d_match]\n* BinaryDescriptor_ParamsList of BinaryDescriptor parameters:\n* KeyLineA class to represent a line\n* LSDDetector\n* LSDParamLines extraction methodology\n\nEnums\n---\n\n* DrawLinesMatchesFlags\n\nConstants\n---\n\n* DrawLinesMatchesFlags_DEFAULTOutput image matrix will be created (Mat::create),\ni.e. existing memory of output image may be reused.\nTwo source images, matches, and single keylines will be drawn.\n* DrawLinesMatchesFlags_DRAW_OVER_OUTIMGOutput image matrix will not be created (using Mat::create). Matches will be drawn on existing content of output image.\n* DrawLinesMatchesFlags_NOT_DRAW_SINGLE_LINESSingle keylines will not be drawn.\n* MLN10\n* RELATIVE_ERROR_FACTOR\n\nTraits\n---\n\n* BinaryDescriptorMatcherTraitMutable methods for crate::line_descriptor::BinaryDescriptorMatcher\n* BinaryDescriptorMatcherTraitConstConstant methods for crate::line_descriptor::BinaryDescriptorMatcher\n* BinaryDescriptorTraitMutable methods for crate::line_descriptor::BinaryDescriptor\n* BinaryDescriptorTraitConstConstant methods for crate::line_descriptor::BinaryDescriptor\n* BinaryDescriptor_ParamsTraitMutable methods for crate::line_descriptor::BinaryDescriptor_Params\n* BinaryDescriptor_ParamsTraitConstConstant methods for crate::line_descriptor::BinaryDescriptor_Params\n* LSDDetectorTraitMutable methods for crate::line_descriptor::LSDDetector\n* LSDDetectorTraitConstConstant methods for crate::line_descriptor::LSDDetector\n\nFunctions\n---\n\n* draw_keylinesDraws keylines.\n* draw_keylines_defDraws keylines.\n* draw_line_matchesDraws the found matches of keylines from two images.\n* draw_line_matches_defDraws the found matches of keylines from two images.\n\nType Aliases\n---\n\n* uint8\n* uint16\n* uint32\n* uint64\n\nModule opencv::mcc\n===\n\nMacbeth Chart module\n---\n\nColor Correction Model\n---\n\n### Introduction\n\nColorCharts are a tool for calibrating the color profile of camera, which not only depends on the intrinsic and extrinsic parameters of camera but also on the lighting conditions. This is done by taking the image of a chart, such that the value of its colors present in it known, in the image the color values changes depeding on many variables, this gives us the colors initially present and the colors that are present in the image, based on this information we can apply any suitable algorithm to find the actual color of all the objects present in the image.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ColorCorrectionModelCore class of ccm model\n* MCC_CCheckerCChecker\n* MCC_CCheckerDetectorA class to find the positions of the ColorCharts in the image.\n* MCC_CCheckerDraw\\brief checker draw\n* MCC_DetectorParametersParameters for the detectMarker process:\n\nEnums\n---\n\n* CCM_TYPEEnum of the possible types of ccm.\n* COLOR_SPACE\n* CONST_COLORMacbeth and Vinyl ColorChecker with 2deg D50\n* DISTANCE_TYPEEnum of possible functions to calculate the distance between colors.\n* INITIAL_METHOD_TYPEEnum of the possible types of initial method.\n* LINEAR_TYPELinearization transformation type\n* MCC_TYPECHARTTYPECHART\n\nConstants\n---\n\n* CCM_3x3The CCM with the shape inline formula performs linear transformation on color values.\n* CCM_4x3The CCM with the shape inline formula performs affine transformation.\n* COLORCHECKER_DigitalSGDigitalSG ColorChecker with 140 squares\n* COLORCHECKER_MacbethMacbeth ColorChecker\n* COLORCHECKER_VinylDKK ColorChecker\n* COLOR_SPACE_AdobeRGBhttps://en.wikipedia.org/wiki/Adobe_RGB_color_space , RGB color space\n* COLOR_SPACE_AdobeRGBLhttps://en.wikipedia.org/wiki/Adobe_RGB_color_space , linear RGB color space\n* COLOR_SPACE_AppleRGBhttps://en.wikipedia.org/wiki/RGB_color_space , RGB color space\n* COLOR_SPACE_AppleRGBLhttps://en.wikipedia.org/wiki/RGB_color_space , linear RGB color space\n* COLOR_SPACE_DCI_P3_RGBhttps://en.wikipedia.org/wiki/DCI-P3 , RGB color space\n* COLOR_SPACE_DCI_P3_RGBLhttps://en.wikipedia.org/wiki/DCI-P3 , linear RGB color space\n* COLOR_SPACE_Lab_A_2non-RGB color space\n* COLOR_SPACE_Lab_A_10non-RGB color space\n* COLOR_SPACE_Lab_D50_2non-RGB color space\n* COLOR_SPACE_Lab_D50_10non-RGB color space\n* COLOR_SPACE_Lab_D55_2non-RGB color space\n* COLOR_SPACE_Lab_D55_10non-RGB color space\n* COLOR_SPACE_Lab_D65_2https://en.wikipedia.org/wiki/CIELAB_color_space , non-RGB color space\n* COLOR_SPACE_Lab_D65_10non-RGB color space\n* COLOR_SPACE_Lab_D75_2non-RGB color space\n* COLOR_SPACE_Lab_D75_10non-RGB color space\n* COLOR_SPACE_Lab_E_2non-RGB color space\n* COLOR_SPACE_Lab_E_10non-RGB color space\n* COLOR_SPACE_ProPhotoRGBhttps://en.wikipedia.org/wiki/ProPhoto_RGB_color_space , RGB color space\n* COLOR_SPACE_ProPhotoRGBLhttps://en.wikipedia.org/wiki/ProPhoto_RGB_color_space , linear RGB color space\n* COLOR_SPACE_REC_709_RGBhttps://en.wikipedia.org/wiki/Rec._709 , RGB color space\n* COLOR_SPACE_REC_709_RGBLhttps://en.wikipedia.org/wiki/Rec._709 , linear RGB color space\n* COLOR_SPACE_REC_2020_RGBhttps://en.wikipedia.org/wiki/Rec._2020 , RGB color space\n* COLOR_SPACE_REC_2020_RGBLhttps://en.wikipedia.org/wiki/Rec._2020 , linear RGB color space\n* COLOR_SPACE_WideGamutRGBhttps://en.wikipedia.org/wiki/Wide-gamut_RGB_color_space , RGB color space\n* COLOR_SPACE_WideGamutRGBLhttps://en.wikipedia.org/wiki/Wide-gamut_RGB_color_space , linear RGB color space\n* COLOR_SPACE_XYZ_A_2non-RGB color space\n* COLOR_SPACE_XYZ_A_10non-RGB color space\n* COLOR_SPACE_XYZ_D50_2non-RGB color space\n* COLOR_SPACE_XYZ_D50_10non-RGB color space\n* COLOR_SPACE_XYZ_D55_2non-RGB color space\n* COLOR_SPACE_XYZ_D55_10non-RGB color space\n* COLOR_SPACE_XYZ_D65_2https://en.wikipedia.org/wiki/CIE_1931_color_space , non-RGB color space\n* COLOR_SPACE_XYZ_D65_10non-RGB color space\n* COLOR_SPACE_XYZ_D75_2non-RGB color space\n* COLOR_SPACE_XYZ_D75_10non-RGB color space\n* COLOR_SPACE_XYZ_E_2non-RGB color space\n* COLOR_SPACE_XYZ_E_10non-RGB color space\n* COLOR_SPACE_sRGBhttps://en.wikipedia.org/wiki/SRGB , RGB color space\n* COLOR_SPACE_sRGBLhttps://en.wikipedia.org/wiki/SRGB , linear RGB color space\n* DISTANCE_CIE76The 1976 formula is the first formula that related a measured color difference to a known set of CIELAB coordinates.\n* DISTANCE_CIE94_GRAPHIC_ARTSThe 1976 definition was extended to address perceptual non-uniformities.\n* DISTANCE_CIE94_TEXTILES\n* DISTANCE_CIE2000\n* DISTANCE_CMC_1TO1In 1984, the Colour Measurement Committee of the Society of Dyers and Colourists defined a difference measure, also based on the L*C*h color model.\n* DISTANCE_CMC_2TO1\n* DISTANCE_RGBEuclidean distance of rgb color space\n* DISTANCE_RGBLEuclidean distance of rgbl color space\n* INITIAL_METHOD_LEAST_SQUAREthe least square method is an optimal solution under the linear RGB distance function\n* INITIAL_METHOD_WHITE_BALANCEThe white balance method. The initial value is:\n* LINEARIZATION_COLORLOGPOLYFITlogarithmic polynomial fitting channels respectively; Need assign a value to deg simultaneously\n* LINEARIZATION_COLORPOLYFITpolynomial fitting channels respectively; Need assign a value to deg simultaneously\n* LINEARIZATION_GAMMAgamma correction; Need assign a value to gamma simultaneously\n* LINEARIZATION_GRAYLOGPOLYFITgrayscale Logarithmic polynomial fitting; Need assign a value to deg and dst_whites simultaneously\n* LINEARIZATION_GRAYPOLYFITgrayscale polynomial fitting; Need assign a value to deg and dst_whites simultaneously\n* LINEARIZATION_IDENTITYno change is made\n* MCC_MCC24Standard Macbeth Chart with 24 squares\n* MCC_SG140DigitalSG with 140 squares\n* MCC_VINYL18DKK color chart with 12 squares and 6 rectangle\n\nTraits\n---\n\n* ColorCorrectionModelTraitMutable methods for crate::mcc::ColorCorrectionModel\n* ColorCorrectionModelTraitConstConstant methods for crate::mcc::ColorCorrectionModel\n* MCC_CCheckerDetectorTraitMutable methods for crate::mcc::MCC_CCheckerDetector\n* MCC_CCheckerDetectorTraitConstConstant methods for crate::mcc::MCC_CCheckerDetector\n* MCC_CCheckerDrawTraitMutable methods for crate::mcc::MCC_CCheckerDraw\n* MCC_CCheckerDrawTraitConstConstant methods for crate::mcc::MCC_CCheckerDraw\n* MCC_CCheckerTraitMutable methods for crate::mcc::MCC_CChecker\n* MCC_CCheckerTraitConstConstant methods for crate::mcc::MCC_CChecker\n* MCC_DetectorParametersTraitMutable methods for crate::mcc::MCC_DetectorParameters\n* MCC_DetectorParametersTraitConstConstant methods for crate::mcc::MCC_DetectorParameters\n\nModule opencv::ml\n===\n\nMachine Learning\n---\n\nThe Machine Learning Library (MLL) is a set of classes and functions for statistical classification, regression, and clustering of data.\n\nMost of the classification and regression algorithms are implemented as C++ classes. As the algorithms have different sets of features (like an ability to handle missing measurements or categorical input variables), there is a little common ground between the classes. This common ground is defined by the class cv::ml::StatModel that all the other ML classes are derived from.\n\nSee detailed overview here: [ml_intro].\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ANN_MLPArtificial Neural Networks - Multi-Layer Perceptrons.\n* BoostBoosted tree classifier derived from DTrees\n* DTreesThe class represents a single decision tree or a collection of decision trees.\n* DTrees_NodeThe class represents a decision tree node.\n* DTrees_SplitThe class represents split in a decision tree.\n* EMThe class implements the Expectation Maximization algorithm.\n* KNearestThe class implements K-Nearest Neighbors model\n* LogisticRegressionImplements Logistic Regression classifier.\n* NormalBayesClassifierBayes classifier for normally distributed data.\n* ParamGridThe structure represents the logarithmic grid range of statmodel parameters.\n* RTreesThe class implements the random forest predictor.\n* SVMSupport Vector Machines.\n* SVMSGD!\nStochastic Gradient Descent SVM classifier\n* SVM_Kernel\n* StatModelBase class for statistical models in OpenCV ML.\n* TrainDataClass encapsulating training data.\n\nEnums\n---\n\n* ANN_MLP_ActivationFunctionspossible activation functions\n* ANN_MLP_TrainFlagsTrain options\n* ANN_MLP_TrainingMethodsAvailable training methods\n* Boost_TypesBoosting type.\nGentle AdaBoost and Real AdaBoost are often the preferable choices.\n* DTrees_FlagsPredict options\n* EM_TypesType of covariation matrices\n* ErrorTypes%Error types\n* KNearest_TypesImplementations of KNearest algorithm\n* LogisticRegression_MethodsTraining methods\n* LogisticRegression_RegKindsRegularization kinds\n* SVMSGD_MarginTypeMargin type.\n* SVMSGD_SvmsgdTypeSVMSGD type.\nASGD is often the preferable choice.\n* SVM_KernelTypes%SVM kernel type\n* SVM_ParamTypes%SVM params type\n* SVM_Types%SVM type\n* SampleTypesSample types\n* StatModel_FlagsPredict options\n* VariableTypesVariable types\n\nConstants\n---\n\n* ANN_MLP_ANNEALThe simulated annealing algorithm. See Kirkpatrick83 for details.\n* ANN_MLP_BACKPROPThe back-propagation algorithm.\n* ANN_MLP_GAUSSIANGaussian function: inline formula\n* ANN_MLP_IDENTITYIdentity function: inline formula\n* ANN_MLP_LEAKYRELULeaky ReLU function: for x>0 inline formula and x<=0 inline formula\n* ANN_MLP_NO_INPUT_SCALEDo not normalize the input vectors. If this flag is not set, the training algorithm normalizes each input feature independently, shifting its mean value to 0 and making the standard deviation equal to 1. If the network is assumed to be updated frequently, the new training data could be much different from original one. In this case, you should take care of proper normalization.\n* ANN_MLP_NO_OUTPUT_SCALEDo not normalize the output vectors. If the flag is not set, the training algorithm normalizes each output feature independently, by transforming it to the certain range depending on the used activation function.\n* ANN_MLP_RELUReLU function: inline formula\n* ANN_MLP_RPROPThe RPROP algorithm. See RPROP93 for details.\n* ANN_MLP_SIGMOID_SYMSymmetrical sigmoid: inline formula\n* ANN_MLP_UPDATE_WEIGHTSUpdate the network weights, rather than compute them from scratch. In the latter case the weights are initialized using the Nguyen-Widrow algorithm.\n* Boost_DISCRETEDiscrete AdaBoost.\n* Boost_GENTLEGentle AdaBoost. It puts less weight on outlier data points and for that reason is often good with regression data.\n* Boost_LOGITLogitBoost. It can produce good regression fits.\n* Boost_REALReal AdaBoost. It is a technique that utilizes confidence-rated predictions and works well with categorical data.\n* COL_SAMPLEeach training sample occupies a column of samples\n* DTrees_PREDICT_AUTO\n* DTrees_PREDICT_MASK\n* DTrees_PREDICT_MAX_VOTE\n* DTrees_PREDICT_SUM\n* EM_COV_MAT_DEFAULTA symmetric positively defined matrix. The number of free parameters in each matrix is about inline formula. It is not recommended to use this option, unless there is pretty accurate initial estimation of the parameters and/or a huge number of training samples.\n* EM_COV_MAT_DIAGONALA diagonal matrix with positive diagonal elements. The number of free parameters is d for each matrix. This is most commonly used option yielding good estimation results.\n* EM_COV_MAT_GENERICA symmetric positively defined matrix. The number of free parameters in each matrix is about inline formula. It is not recommended to use this option, unless there is pretty accurate initial estimation of the parameters and/or a huge number of training samples.\n* EM_COV_MAT_SPHERICALA scaled identity matrix inline formula. There is the only parameter inline formula to be estimated for each matrix. The option may be used in special cases,\nwhen the constraint is relevant, or as a first step in the optimization (for example in case when the data is preprocessed with PCA). The results of such preliminary estimation may be passed again to the optimization procedure, this time with covMatType=EM::COV_MAT_DIAGONAL.\n* EM_DEFAULT_MAX_ITERS\n* EM_DEFAULT_NCLUSTERS\n* EM_START_AUTO_STEP\n* EM_START_E_STEP\n* EM_START_M_STEP\n* KNearest_BRUTE_FORCE\n* KNearest_KDTREE\n* LogisticRegression_BATCH\n* LogisticRegression_MINI_BATCHSet MiniBatchSize to a positive integer when using this method.\n* LogisticRegression_REG_DISABLERegularization disabled\n* LogisticRegression_REG_L1%L1 norm\n* LogisticRegression_REG_L2%L2 norm\n* ROW_SAMPLEeach training sample is a row of samples\n* SVMSGD_ASGDAverage Stochastic Gradient Descent\n* SVMSGD_HARD_MARGINMore accurate for the case of linearly separable sets.\n* SVMSGD_SGDStochastic Gradient Descent\n* SVMSGD_SOFT_MARGINGeneral case, suits to the case of non-linearly separable sets, allows outliers.\n* SVM_C\n* SVM_CHI2Exponential Chi2 kernel, similar to the RBF kernel:\ninline formula.\n* SVM_COEF\n* SVM_CUSTOMReturned by SVM::getKernelType in case when custom kernel has been set\n* SVM_C_SVCC-Support Vector Classification. n-class classification (n inline formula 2), allows imperfect separation of classes with penalty multiplier C for outliers.\n* SVM_DEGREE\n* SVM_EPS_SVRinline formula-Support Vector Regression. The distance between feature vectors from the training set and the fitting hyper-plane must be less than p. For outliers the penalty multiplier C is used.\n* SVM_GAMMA\n* SVM_INTERHistogram intersection kernel. A fast kernel. inline formula.\n* SVM_LINEARLinear kernel. No mapping is done, linear discrimination (or regression) is done in the original feature space. It is the fastest option. inline formula.\n* SVM_NU\n* SVM_NU_SVCinline formula-Support Vector Classification. n-class classification with possible imperfect separation. Parameter inline formula (in the range 0..1, the larger the value, the smoother the decision boundary) is used instead of C.\n* SVM_NU_SVRinline formula-Support Vector Regression. inline formula is used instead of p.\nSee LibSVM for details.\n* SVM_ONE_CLASSDistribution Estimation (One-class %SVM). All the training data are from the same class, %SVM builds a boundary that separates the class from the rest of the feature space.\n* SVM_P\n* SVM_POLYPolynomial kernel:\ninline formula.\n* SVM_RBFRadial basis function (RBF), a good choice in most cases.\ninline formula.\n* SVM_SIGMOIDSigmoid kernel: inline formula.\n* StatModel_COMPRESSED_INPUT\n* StatModel_PREPROCESSED_INPUT\n* StatModel_RAW_OUTPUTmakes the method return the raw results (the sum), not the class label\n* StatModel_UPDATE_MODEL\n* TEST_ERROR\n* TRAIN_ERROR\n* VAR_CATEGORICALcategorical variables\n* VAR_NUMERICALsame as VAR_ORDERED\n* VAR_ORDEREDordered variables\n\nTraits\n---\n\n* ANN_MLPTraitMutable methods for crate::ml::ANN_MLP\n* ANN_MLPTraitConstConstant methods for crate::ml::ANN_MLP\n* BoostTraitMutable methods for crate::ml::Boost\n* BoostTraitConstConstant methods for crate::ml::Boost\n* DTreesTraitMutable methods for crate::ml::DTrees\n* DTreesTraitConstConstant methods for crate::ml::DTrees\n* DTrees_NodeTraitMutable methods for crate::ml::DTrees_Node\n* DTrees_NodeTraitConstConstant methods for crate::ml::DTrees_Node\n* DTrees_SplitTraitMutable methods for crate::ml::DTrees_Split\n* DTrees_SplitTraitConstConstant methods for crate::ml::DTrees_Split\n* EMTraitMutable methods for crate::ml::EM\n* EMTraitConstConstant methods for crate::ml::EM\n* KNearestTraitMutable methods for crate::ml::KNearest\n* KNearestTraitConstConstant methods for crate::ml::KNearest\n* LogisticRegressionTraitMutable methods for crate::ml::LogisticRegression\n* LogisticRegressionTraitConstConstant methods for crate::ml::LogisticRegression\n* NormalBayesClassifierTraitMutable methods for crate::ml::NormalBayesClassifier\n* NormalBayesClassifierTraitConstConstant methods for crate::ml::NormalBayesClassifier\n* ParamGridTraitMutable methods for crate::ml::ParamGrid\n* ParamGridTraitConstConstant methods for crate::ml::ParamGrid\n* RTreesTraitMutable methods for crate::ml::RTrees\n* RTreesTraitConstConstant methods for crate::ml::RTrees\n* SVMSGDTraitMutable methods for crate::ml::SVMSGD\n* SVMSGDTraitConstConstant methods for crate::ml::SVMSGD\n* SVMTraitMutable methods for crate::ml::SVM\n* SVMTraitConstConstant methods for crate::ml::SVM\n* SVM_KernelTraitMutable methods for crate::ml::SVM_Kernel\n* SVM_KernelTraitConstConstant methods for crate::ml::SVM_Kernel\n* StatModelTraitMutable methods for crate::ml::StatModel\n* StatModelTraitConstConstant methods for crate::ml::StatModel\n* TrainDataTraitMutable methods for crate::ml::TrainData\n* TrainDataTraitConstConstant methods for crate::ml::TrainData\n\nFunctions\n---\n\n* create_concentric_spheres_test_setCreates test set\n* rand_mv_normalGenerates *sample* from multivariate normal distribution\n\nType Aliases\n---\n\n* ANN_MLP_ANNEAL\n\nModule opencv::objdetect\n===\n\nObject Detection\n---\n\nCascade Classifier for Object Detection\n---\n\nThe object detector described below has been initially proposed by Paul Viola Viola01 and improved by <NAME> .\n\nFirst, a classifier (namely a *cascade of boosted classifiers working with haar-like features*) is trained with a few hundred sample views of a particular object (i.e., a face or a car), called positive examples, that are scaled to the same size (say, 20x20), and negative examples - arbitrary images of the same size.\n\nAfter a classifier is trained, it can be applied to a region of interest (of the same size as used during the training) in an input image. The classifier outputs a “1” if the region is likely to show the object (i.e., face/car), and “0” otherwise. To search for the object in the whole image one can move the search window across the image and check every location using the classifier. The classifier is designed so that it can be easily “resized” in order to be able to find the objects of interest at different sizes, which is more efficient than resizing the image itself. So, to find an object of an unknown size in the image the scan procedure should be done several times at different scales.\n\nThe word “cascade” in the classifier name means that the resultant classifier consists of several simpler classifiers (*stages*) that are applied subsequently to a region of interest until at some stage the candidate is rejected or all the stages are passed. The word “boosted” means that the classifiers at every stage of the cascade are complex themselves and they are built out of basic classifiers using one of four different boosting techniques (weighted voting). Currently Discrete Adaboost, Real Adaboost, Gentle Adaboost and Logitboost are supported. The basic classifiers are decision-tree classifiers with at least 2 leaves. Haar-like features are the input to the basic classifiers, and are calculated as described below. The current algorithm uses the following Haar-like features:\n\n\n\nThe feature used in a particular classifier is specified by its shape (1a, 2b etc.), position within the region of interest and the scale (this scale is not the same as the scale used at the detection stage, though these two scales are multiplied). For example, in the case of the third line feature\n(2c) the response is calculated as the difference between the sum of image pixels under the rectangle covering the whole feature (including the two white stripes and the black stripe in the middle) and the sum of the image pixels under the black stripe multiplied by 3 in order to compensate for the differences in the size of areas. The sums of pixel values over a rectangular regions are calculated rapidly using integral images (see below and the integral description).\n\nCheck [tutorial_cascade_classifier] “the corresponding tutorial” for more details.\n\nThe following reference is for the detection part only. There is a separate application called opencv_traincascade that can train a cascade of boosted classifiers from a set of samples.\n\nNote: In the new C++ interface it is also possible to use LBP (local binary pattern) features in addition to Haar-like features. .. [Viola01] <NAME> and <NAME>. Rapid Object Detection using a Boosted Cascade of Simple Features. IEEE CVPR, 2001. The paper is available online at https://github.com/SvHey/thesis/blob/master/Literature/ObjectDetection/violaJones_CVPR2001.pdf\n\nHOG (Histogram of Oriented Gradients) descriptor and object detector\n---\n\nBarcode detection and decoding\n---\n\nQRCode detection and encoding\n---\n\nDNN-based face detection and recognition\n---\n\nCheck [tutorial_dnn_face] “the corresponding tutorial” for more details.\n\nCommon functions and classes\n---\n\nArUco markers and boards detection for robust camera pose estimation\n---\n```\n ArUco Marker Detection\n Square fiducial markers (also known as Augmented Reality Markers) are useful for easy,\n fast and robust camera pose estimation.\n\n The main functionality of ArucoDetector class is detection of markers in an image. If the markers are grouped\n as a board, then you can try to recover the missing markers with ArucoDetector::refineDetectedMarkers().\n ArUco markers can also be used for advanced chessboard corner finding. To do this, group the markers in the\n CharucoBoard and find the corners of the chessboard with the CharucoDetector::detectBoard().\n\n The implementation is based on the ArUco Library by <NAME> and <NAME> [Aruco2014](https://docs.opencv.org/4.8.1/d0/de3/citelist.html#CITEREF_Aruco2014).\n\n Markers can also be detected based on the AprilTag 2 [wang2016iros](https://docs.opencv.org/4.8.1/d0/de3/citelist.html#CITEREF_wang2016iros) fiducial detection method.\n```\n### See also\n\nAruco2014 This code has been originally developed by <NAME> as a project for Google Summer of Code 2015 (GSoC 15).\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ArucoDetectorThe main functionality of ArucoDetector class is detection of markers in an image with detectMarkers() method.\n* BarcodeDetector\n* BaseCascadeClassifier\n* BaseCascadeClassifier_MaskGenerator\n* BoardBoard of ArUco markers\n* CascadeClassifier@example samples/cpp/facedetect.cpp This program demonstrates usage of the Cascade classifier class\n\\image html Cascade_Classifier_Tutorial_Result_Haar.jpg “Sample screenshot” width=321 height=254\n* CharucoBoardChArUco board is a planar chessboard where the markers are placed inside the white squares of a chessboard.\n* CharucoDetector\n* CharucoParameters\n* DetectionBasedTracker\n* DetectionBasedTracker_ExtObject\n* DetectionBasedTracker_IDetector\n* DetectionBasedTracker_Parameters\n* DetectionROIstruct for detection region of interest (ROI)\n* DetectorParametersstruct DetectorParameters is used by ArucoDetector\n* DictionaryDictionary/Set of markers, it contains the inner codification\n* FaceDetectorYNDNN-based face detector\n* FaceRecognizerSFDNN-based face recognizer\n* GraphicalCodeDetector\n* GridBoardPlanar board with grid arrangement of markers\n* HOGDescriptorImplementation of HOG (Histogram of Oriented Gradients) descriptor and object detector.\n* QRCodeDetector\n* QRCodeDetectorAruco\n* QRCodeDetectorAruco_Params\n* QRCodeEncoder\n* QRCodeEncoder_ParamsQR code encoder parameters.\n* RefineParametersstruct RefineParameters is used by ArucoDetector\n* SimilarRectsThis class is used for grouping object candidates detected by Cascade Classifier, HOG etc.\n\nEnums\n---\n\n* CornerRefineMethod\n* DetectionBasedTracker_ObjectStatus\n* FaceRecognizerSF_DisTypeDefinition of distance used for calculating the distance between two face features\n* HOGDescriptor_DescriptorStorageFormat\n* HOGDescriptor_HistogramNormType\n* PredefinedDictionaryTypePredefined markers dictionaries/sets\n* QRCodeEncoder_CorrectionLevel\n* QRCodeEncoder_ECIEncodings\n* QRCodeEncoder_EncodeMode\n\nConstants\n---\n\n* CASCADE_DO_CANNY_PRUNING\n* CASCADE_DO_ROUGH_SEARCH\n* CASCADE_FIND_BIGGEST_OBJECT\n* CASCADE_SCALE_IMAGE\n* CORNER_REFINE_APRILTAGTag and corners detection based on the AprilTag 2 approach wang2016iros\n* CORNER_REFINE_CONTOURArUco approach and refine the corners locations using the contour-points line fitting\n* CORNER_REFINE_NONETag and corners detection based on the ArUco approach\n* CORNER_REFINE_SUBPIXArUco approach and refine the corners locations using corner subpixel accuracy\n* DICT_4X4_504x4 bits, minimum hamming distance between any two codes = 4, 50 codes\n* DICT_4X4_1004x4 bits, minimum hamming distance between any two codes = 3, 100 codes\n* DICT_4X4_2504x4 bits, minimum hamming distance between any two codes = 3, 250 codes\n* DICT_4X4_10004x4 bits, minimum hamming distance between any two codes = 2, 1000 codes\n* DICT_5X5_505x5 bits, minimum hamming distance between any two codes = 8, 50 codes\n* DICT_5X5_1005x5 bits, minimum hamming distance between any two codes = 7, 100 codes\n* DICT_5X5_2505x5 bits, minimum hamming distance between any two codes = 6, 250 codes\n* DICT_5X5_10005x5 bits, minimum hamming distance between any two codes = 5, 1000 codes\n* DICT_6X6_506x6 bits, minimum hamming distance between any two codes = 13, 50 codes\n* DICT_6X6_1006x6 bits, minimum hamming distance between any two codes = 12, 100 codes\n* DICT_6X6_2506x6 bits, minimum hamming distance between any two codes = 11, 250 codes\n* DICT_6X6_10006x6 bits, minimum hamming distance between any two codes = 9, 1000 codes\n* DICT_7X7_507x7 bits, minimum hamming distance between any two codes = 19, 50 codes\n* DICT_7X7_1007x7 bits, minimum hamming distance between any two codes = 18, 100 codes\n* DICT_7X7_2507x7 bits, minimum hamming distance between any two codes = 17, 250 codes\n* DICT_7X7_10007x7 bits, minimum hamming distance between any two codes = 14, 1000 codes\n* DICT_APRILTAG_16h54x4 bits, minimum hamming distance between any two codes = 5, 30 codes\n* DICT_APRILTAG_25h95x5 bits, minimum hamming distance between any two codes = 9, 35 codes\n* DICT_APRILTAG_36h106x6 bits, minimum hamming distance between any two codes = 10, 2320 codes\n* DICT_APRILTAG_36h116x6 bits, minimum hamming distance between any two codes = 11, 587 codes\n* DICT_ARUCO_MIP_36h126x6 bits, minimum hamming distance between any two codes = 12, 250 codes\n* DICT_ARUCO_ORIGINAL6x6 bits, minimum hamming distance between any two codes = 3, 1024 codes\n* DetectionBasedTracker_DETECTED\n* DetectionBasedTracker_DETECTED_NOT_SHOWN_YET\n* DetectionBasedTracker_DETECTED_TEMPORARY_LOST\n* DetectionBasedTracker_WRONG_OBJECT\n* FaceRecognizerSF_FR_COSINE\n* FaceRecognizerSF_FR_NORM_L2\n* HOGDescriptor_DEFAULT_NLEVELSDefault nlevels value.\n* HOGDescriptor_DESCR_FORMAT_COL_BY_COL\n* HOGDescriptor_DESCR_FORMAT_ROW_BY_ROW\n* HOGDescriptor_L2HysDefault histogramNormType\n* QRCodeEncoder_CORRECT_LEVEL_H\n* QRCodeEncoder_CORRECT_LEVEL_L\n* QRCodeEncoder_CORRECT_LEVEL_M\n* QRCodeEncoder_CORRECT_LEVEL_Q\n* QRCodeEncoder_ECI_UTF8\n* QRCodeEncoder_MODE_ALPHANUMERIC\n* QRCodeEncoder_MODE_AUTO\n* QRCodeEncoder_MODE_BYTE\n* QRCodeEncoder_MODE_ECI\n* QRCodeEncoder_MODE_KANJI\n* QRCodeEncoder_MODE_NUMERIC\n* QRCodeEncoder_MODE_STRUCTURED_APPEND\n\nTraits\n---\n\n* ArucoDetectorTraitMutable methods for crate::objdetect::ArucoDetector\n* ArucoDetectorTraitConstConstant methods for crate::objdetect::ArucoDetector\n* BarcodeDetectorTraitMutable methods for crate::objdetect::BarcodeDetector\n* BarcodeDetectorTraitConstConstant methods for crate::objdetect::BarcodeDetector\n* BaseCascadeClassifierTraitMutable methods for crate::objdetect::BaseCascadeClassifier\n* BaseCascadeClassifierTraitConstConstant methods for crate::objdetect::BaseCascadeClassifier\n* BaseCascadeClassifier_MaskGeneratorTraitMutable methods for crate::objdetect::BaseCascadeClassifier_MaskGenerator\n* BaseCascadeClassifier_MaskGeneratorTraitConstConstant methods for crate::objdetect::BaseCascadeClassifier_MaskGenerator\n* BoardTraitMutable methods for crate::objdetect::Board\n* BoardTraitConstConstant methods for crate::objdetect::Board\n* CascadeClassifierTraitMutable methods for crate::objdetect::CascadeClassifier\n* CascadeClassifierTraitConstConstant methods for crate::objdetect::CascadeClassifier\n* CharucoBoardTraitMutable methods for crate::objdetect::CharucoBoard\n* CharucoBoardTraitConstConstant methods for crate::objdetect::CharucoBoard\n* CharucoDetectorTraitMutable methods for crate::objdetect::CharucoDetector\n* CharucoDetectorTraitConstConstant methods for crate::objdetect::CharucoDetector\n* CharucoParametersTraitMutable methods for crate::objdetect::CharucoParameters\n* CharucoParametersTraitConstConstant methods for crate::objdetect::CharucoParameters\n* DetectionBasedTrackerTraitMutable methods for crate::objdetect::DetectionBasedTracker\n* DetectionBasedTrackerTraitConstConstant methods for crate::objdetect::DetectionBasedTracker\n* DetectionBasedTracker_ExtObjectTraitMutable methods for crate::objdetect::DetectionBasedTracker_ExtObject\n* DetectionBasedTracker_ExtObjectTraitConstConstant methods for crate::objdetect::DetectionBasedTracker_ExtObject\n* DetectionBasedTracker_IDetectorTraitMutable methods for crate::objdetect::DetectionBasedTracker_IDetector\n* DetectionBasedTracker_IDetectorTraitConstConstant methods for crate::objdetect::DetectionBasedTracker_IDetector\n* DetectionBasedTracker_ParametersTraitMutable methods for crate::objdetect::DetectionBasedTracker_Parameters\n* DetectionBasedTracker_ParametersTraitConstConstant methods for crate::objdetect::DetectionBasedTracker_Parameters\n* DetectionROITraitMutable methods for crate::objdetect::DetectionROI\n* DetectionROITraitConstConstant methods for crate::objdetect::DetectionROI\n* DetectorParametersTraitMutable methods for crate::objdetect::DetectorParameters\n* DetectorParametersTraitConstConstant methods for crate::objdetect::DetectorParameters\n* DictionaryTraitMutable methods for crate::objdetect::Dictionary\n* DictionaryTraitConstConstant methods for crate::objdetect::Dictionary\n* FaceDetectorYNTraitMutable methods for crate::objdetect::FaceDetectorYN\n* FaceDetectorYNTraitConstConstant methods for crate::objdetect::FaceDetectorYN\n* FaceRecognizerSFTraitMutable methods for crate::objdetect::FaceRecognizerSF\n* FaceRecognizerSFTraitConstConstant methods for crate::objdetect::FaceRecognizerSF\n* GraphicalCodeDetectorTraitMutable methods for crate::objdetect::GraphicalCodeDetector\n* GraphicalCodeDetectorTraitConstConstant methods for crate::objdetect::GraphicalCodeDetector\n* GridBoardTraitMutable methods for crate::objdetect::GridBoard\n* GridBoardTraitConstConstant methods for crate::objdetect::GridBoard\n* HOGDescriptorTraitMutable methods for crate::objdetect::HOGDescriptor\n* HOGDescriptorTraitConstConstant methods for crate::objdetect::HOGDescriptor\n* QRCodeDetectorArucoTraitMutable methods for crate::objdetect::QRCodeDetectorAruco\n* QRCodeDetectorArucoTraitConstConstant methods for crate::objdetect::QRCodeDetectorAruco\n* QRCodeDetectorTraitMutable methods for crate::objdetect::QRCodeDetector\n* QRCodeDetectorTraitConstConstant methods for crate::objdetect::QRCodeDetector\n* QRCodeEncoderTraitMutable methods for crate::objdetect::QRCodeEncoder\n* QRCodeEncoderTraitConstConstant methods for crate::objdetect::QRCodeEncoder\n* SimilarRectsTraitMutable methods for crate::objdetect::SimilarRects\n* SimilarRectsTraitConstConstant methods for crate::objdetect::SimilarRects\n\nFunctions\n---\n\n* create_face_detection_mask_generator\n* draw_detected_corners_charucoDraws a set of Charuco corners\n* draw_detected_corners_charuco_defDraws a set of Charuco corners\n* draw_detected_diamondsDraw a set of detected ChArUco Diamond markers\n* draw_detected_diamonds_defDraw a set of detected ChArUco Diamond markers\n* draw_detected_markersDraw detected markers in image\n* draw_detected_markers_defDraw detected markers in image\n* extend_dictionaryExtend base dictionary by new nMarkers\n* extend_dictionary_defExtend base dictionary by new nMarkers\n* generate_image_markerGenerate a canonical marker image\n* generate_image_marker_defGenerate a canonical marker image\n* get_predefined_dictionaryReturns one of the predefined dictionaries defined in PredefinedDictionaryType\n* get_predefined_dictionary_i32Returns one of the predefined dictionaries referenced by DICT_*.\n* group_rectanglesGroups the object candidate rectangles.\n* group_rectangles_defGroups the object candidate rectangles.\n* group_rectangles_levelsGroups the object candidate rectangles.\n* group_rectangles_levels_def@overload\n* group_rectangles_levelweightsGroups the object candidate rectangles.\n* group_rectangles_meanshiftThis is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.\n* group_rectangles_meanshift_def@overload\n* group_rectangles_weightsGroups the object candidate rectangles.\n* group_rectangles_weights_def@overload\n\nType Aliases\n---\n\n* DetectionBasedTracker_Object\n\nModule opencv::optflow\n===\n\nOptical Flow Algorithms\n---\n\nDense optical flow algorithms compute motion for each point:\n\n* cv::optflow::calcOpticalFlowSF\n* cv::optflow::createOptFlow_DeepFlow\n\nMotion templates is alternative technique for detecting motion and computing its direction.\nSee samples/motempl.py.\n\n* cv::motempl::updateMotionHistory\n* cv::motempl::calcMotionGradient\n* cv::motempl::calcGlobalOrientation\n* cv::motempl::segmentMotion\n\nFunctions reading and writing .flo files in “Middlebury” format, see: http://vision.middlebury.edu/flow/code/flow-code/README.txt\n\n* cv::optflow::readOpticalFlow\n* cv::optflow::writeOpticalFlow\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* DenseRLOFOpticalFlowFast dense optical flow computation based on robust local optical flow (RLOF) algorithms and sparse-to-dense interpolation scheme.\n* DualTVL1OpticalFlow“Dual TV L1” Optical Flow Algorithm.\n* GPCDetails\n* GPCMatchingParamsClass encapsulating matching parameters.\n* GPCPatchDescriptor\n* GPCPatchSample\n* GPCTrainingParamsClass encapsulating training parameters.\n* GPCTrainingSamplesClass encapsulating training samples.\n* GPCTreeClass for individual tree.\n* GPCTree_Node\n* OpticalFlowPCAFlowPCAFlow algorithm.\n* PCAPriorThis class can be used for imposing a learned prior on the resulting optical flow.\nSolution will be regularized according to this prior.\nYou need to generate appropriate prior file with “learn_prior.py” script beforehand.\n* RLOFOpticalFlowParameterThis is used store and set up the parameters of the robust local optical flow (RLOF) algoritm.\n* SparseRLOFOpticalFlowClass used for calculation sparse optical flow and feature tracking with robust local optical flow (RLOF) algorithms.\n\nEnums\n---\n\n* GPCDescTypeDescriptor types for the Global Patch Collider.\n* InterpolationType\n* SolverType\n* SupportRegionType\n\nConstants\n---\n\n* GPC_DESCRIPTOR_DCTBetter quality but slow\n* GPC_DESCRIPTOR_WHTWorse quality but much faster\n* INTERP_EPIC< Edge-preserving interpolation using ximgproc::EdgeAwareInterpolator, see Revaud2015,Geistert2016.\n* INTERP_GEO< Fast geodesic interpolation, see Geistert2016\n* INTERP_RIC< SLIC based robust interpolation using ximgproc::RICInterpolator, see Hu2017.\n* SR_CROSS< Apply a adaptive support region obtained by cross-based segmentation as described in Senst2014\n* SR_FIXED< Apply a constant support region\n* ST_BILINEAR< Apply optimized iterative refinement based bilinear equation solutions as described in Senst2013\n* ST_STANDART< Apply standard iterative refinement\n\nTraits\n---\n\n* DenseRLOFOpticalFlowTraitMutable methods for crate::optflow::DenseRLOFOpticalFlow\n* DenseRLOFOpticalFlowTraitConstConstant methods for crate::optflow::DenseRLOFOpticalFlow\n* DualTVL1OpticalFlowTraitMutable methods for crate::optflow::DualTVL1OpticalFlow\n* DualTVL1OpticalFlowTraitConstConstant methods for crate::optflow::DualTVL1OpticalFlow\n* GPCDetailsTraitMutable methods for crate::optflow::GPCDetails\n* GPCDetailsTraitConstConstant methods for crate::optflow::GPCDetails\n* GPCPatchDescriptorTraitMutable methods for crate::optflow::GPCPatchDescriptor\n* GPCPatchDescriptorTraitConstConstant methods for crate::optflow::GPCPatchDescriptor\n* GPCPatchSampleTraitMutable methods for crate::optflow::GPCPatchSample\n* GPCPatchSampleTraitConstConstant methods for crate::optflow::GPCPatchSample\n* GPCTrainingSamplesTraitMutable methods for crate::optflow::GPCTrainingSamples\n* GPCTrainingSamplesTraitConstConstant methods for crate::optflow::GPCTrainingSamples\n* GPCTreeTraitMutable methods for crate::optflow::GPCTree\n* GPCTreeTraitConstConstant methods for crate::optflow::GPCTree\n* OpticalFlowPCAFlowTraitMutable methods for crate::optflow::OpticalFlowPCAFlow\n* OpticalFlowPCAFlowTraitConstConstant methods for crate::optflow::OpticalFlowPCAFlow\n* PCAPriorTraitMutable methods for crate::optflow::PCAPrior\n* PCAPriorTraitConstConstant methods for crate::optflow::PCAPrior\n* RLOFOpticalFlowParameterTraitMutable methods for crate::optflow::RLOFOpticalFlowParameter\n* RLOFOpticalFlowParameterTraitConstConstant methods for crate::optflow::RLOFOpticalFlowParameter\n* SparseRLOFOpticalFlowTraitMutable methods for crate::optflow::SparseRLOFOpticalFlow\n* SparseRLOFOpticalFlowTraitConstConstant methods for crate::optflow::SparseRLOFOpticalFlow\n\nFunctions\n---\n\n* calc_global_orientationCalculates a global motion orientation in a selected region.\n* calc_motion_gradientCalculates a gradient orientation of a motion history image.\n* calc_motion_gradient_defCalculates a gradient orientation of a motion history image.\n* calc_optical_flow_dense_rlofFast dense optical flow computation based on robust local optical flow (RLOF) algorithms and sparse-to-dense interpolation scheme.\n* calc_optical_flow_dense_rlof_defFast dense optical flow computation based on robust local optical flow (RLOF) algorithms and sparse-to-dense interpolation scheme.\n* calc_optical_flow_sfCalculate an optical flow using “SimpleFlow” algorithm.\n* calc_optical_flow_sf_1Calculate an optical flow using “SimpleFlow” algorithm.\n* calc_optical_flow_sparse_rlofCalculates fast optical flow for a sparse feature set using the robust local optical flow (RLOF) similar to optflow::calcOpticalFlowPyrLK().\n* calc_optical_flow_sparse_rlof_defCalculates fast optical flow for a sparse feature set using the robust local optical flow (RLOF) similar to optflow::calcOpticalFlowPyrLK().\n* calc_optical_flow_sparse_to_denseFast dense optical flow based on PyrLK sparse matches interpolation.\n* calc_optical_flow_sparse_to_dense_defFast dense optical flow based on PyrLK sparse matches interpolation.\n* create_opt_flow_deep_flowDeepFlow optical flow algorithm implementation.\n* create_opt_flow_dense_rlofAdditional interface to the Dense RLOF algorithm - optflow::calcOpticalFlowDenseRLOF()\n* create_opt_flow_dual_tvl1Creates instance of cv::DenseOpticalFlow\n* create_opt_flow_farnebackAdditional interface to the Farneback’s algorithm - calcOpticalFlowFarneback()\n* create_opt_flow_pca_flowCreates an instance of PCAFlow\n* create_opt_flow_simple_flowAdditional interface to the SimpleFlow algorithm - calcOpticalFlowSF()\n* create_opt_flow_sparse_rlofAdditional interface to the Sparse RLOF algorithm - optflow::calcOpticalFlowSparseRLOF()\n* create_opt_flow_sparse_to_denseAdditional interface to the SparseToDenseFlow algorithm - calcOpticalFlowSparseToDense()\n* read\n* segment_motionSplits a motion history image into a few parts corresponding to separate independent motions (for example, left hand, right hand).\n* update_motion_historyUpdates the motion history image by a moving silhouette.\n* write\n\nType Aliases\n---\n\n* GPCSamplesVector\n\nModule opencv::ovis\n===\n\nOGRE 3D Visualiser\n---\n\novis is a simplified rendering wrapper around ogre3d.\nThe Ogre terminology is used in the API and Ogre Script is assumed to be used for advanced customization.\n\nBesides the API you see here, there are several environment variables that control the behavior of ovis.\nThey are documented in [createWindow].\n\n### Loading geometry\n\nYou can create geometry on the fly or by loading Ogre `.mesh` files.\n\n#### Blender\n\nFor converting/ creating geometry Blender is recommended.\n\n* Blender 2.7x is better tested, but Blender 2.8x should work too\n* install blender2ogre matching your Blender version\n* download the Ogre MSVC SDK which contains `OgreXMLConverter.exe` (in `bin/`) and set the path in the blender2ogre settings\n* get ogre-meshviewer to enable the preview function in blender2ogre as well as for verifying the exported files\n* in case the exported materials are not exactly how you want them, consult the Ogre Manual\n\n#### Assimp\n\nWhen using Ogre 1.12.9 or later, enabling the Assimp plugin allows to load arbitrary geometry.\nSimply pass `bunny.obj` instead of `bunny.mesh` as `meshname` in [WindowScene::createEntity].\n\nYou should still use ogre-meshviewer to verify that the geometry is converted correctly.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* WindowSceneA 3D viewport and the associated scene\n\nEnums\n---\n\n* EntityProperty\n* MaterialProperty\n* SceneSettings\n\nConstants\n---\n\n* ENTITY_AABB_WORLD\n* ENTITY_ANIMBLEND_MODE\n* ENTITY_CAST_SHADOWS\n* ENTITY_MATERIAL\n* ENTITY_SCALE\n* MATERIAL_DIFFUSE\n* MATERIAL_EMISSIVE\n* MATERIAL_LINE_WIDTH\n* MATERIAL_OPACITY\n* MATERIAL_POINT_SIZE\n* MATERIAL_TEXTURE\n* MATERIAL_TEXTURE0\n* MATERIAL_TEXTURE1\n* MATERIAL_TEXTURE2\n* MATERIAL_TEXTURE3\n* SCENE_AAApply anti-aliasing. The first window determines the setting for all windows.\n* SCENE_INTERACTIVEallow the user to control the camera.\n* SCENE_OFFSCREENRender off-screen without a window. Allows separate AA setting. Requires manual update via WindowScene::update\n* SCENE_SEPARATEthe window will use a separate scene. The scene will be shared otherwise.\n* SCENE_SHADOWSEnable real-time shadows in the scene. All entities cast shadows by default. Control via ENTITY_CAST_SHADOWS\n* SCENE_SHOW_CS_CROSSdraw coordinate system crosses for debugging\n\nTraits\n---\n\n* WindowSceneTraitMutable methods for crate::ovis::WindowScene\n* WindowSceneTraitConstConstant methods for crate::ovis::WindowScene\n\nFunctions\n---\n\n* add_resource_locationAdd an additional resource location that is search for meshes, textures and materials\n* create_grid_meshcreates a grid\n* create_grid_mesh_defcreates a grid\n* create_plane_meshcreate a 2D plane, X right, Y down, Z up\n* create_plane_mesh_defcreate a 2D plane, X right, Y down, Z up\n* create_point_cloud_meshcreates a point cloud mesh\n* create_point_cloud_mesh_defcreates a point cloud mesh\n* create_triangle_meshcreates a triangle mesh from vertex-vertex or face-vertex representation\n* create_triangle_mesh_defcreates a triangle mesh from vertex-vertex or face-vertex representation\n* create_windowcreate a new rendering window/ viewport\n* create_window_defcreate a new rendering window/ viewport\n* set_material_propertyset the property of a material to the given value\n* set_material_property_1set the property of a material to the given value\n* set_material_property_2set the shader property of a material to the given value\n* set_material_textureset the texture of a material to the given value\n* update_textureDeprecated**Deprecated**: use setMaterialProperty\n* wait_keyupdate all windows and wait for keyboard event\n* wait_key_defupdate all windows and wait for keyboard event\n\nModule opencv::phase_unwrapping\n===\n\nPhase Unwrapping API\n---\n\nTwo-dimensional phase unwrapping is found in different applications like terrain elevation estimation in synthetic aperture radar (SAR), field mapping in magnetic resonance imaging or as a way of finding corresponding pixels in structured light reconstruction with sinusoidal patterns.\n\nGiven a phase map, wrapped between [-pi; pi], phase unwrapping aims at finding the “true” phase map by adding the right number of 2*pi to each pixel.\n\nThe problem is straightforward for perfect wrapped phase map, but real data are usually not noise-free.\nAmong the different algorithms that were developed, quality-guided phase unwrapping methods are fast and efficient. They follow a path that unwraps high quality pixels first,\navoiding error propagation from the start.\n\nIn this module, a quality-guided phase unwrapping is implemented following the approach described in histogramUnwrapping .\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* HistogramPhaseUnwrappingClass implementing two-dimensional phase unwrapping based on histogramUnwrapping This algorithm belongs to the quality-guided phase unwrapping methods.\nFirst, it computes a reliability map from second differences between a pixel and its eight neighbours.\nReliability values lie between 0 and 16*pi*pi. Then, this reliability map is used to compute the reliabilities of “edges”. An edge is an entity defined by two pixels that are connected horizontally or vertically. Its reliability is found by adding the the reliabilities of the two pixels connected through it. Edges are sorted in a histogram based on their reliability values.\nThis histogram is then used to unwrap pixels, starting from the highest quality pixel.\n* HistogramPhaseUnwrapping_ParamsParameters of phaseUnwrapping constructor.\n* PhaseUnwrappingAbstract base class for phase unwrapping.\n\nTraits\n---\n\n* HistogramPhaseUnwrappingTraitMutable methods for crate::phase_unwrapping::HistogramPhaseUnwrapping\n* HistogramPhaseUnwrappingTraitConstConstant methods for crate::phase_unwrapping::HistogramPhaseUnwrapping\n* PhaseUnwrappingTraitMutable methods for crate::phase_unwrapping::PhaseUnwrapping\n* PhaseUnwrappingTraitConstConstant methods for crate::phase_unwrapping::PhaseUnwrapping\n\nModule opencv::photo\n===\n\nComputational Photography\n---\n\nThis module includes photo processing algorithms\n\nInpainting\n---\n\nDenoising\n---\n\nHDR imaging\n---\n\nThis section describes high dynamic range imaging algorithms namely tonemapping, exposure alignment,\ncamera calibration with multiple exposures and exposure fusion.\n\nContrast Preserving Decolorization\n---\n\nUseful links:\n\nhttp://www.cse.cuhk.edu.hk/leojia/projects/color2gray/index.html\n\nSeamless Cloning\n---\n\nUseful links:\n\nhttps://www.learnopencv.com/seamless-cloning-using-opencv-python-cpp\n\nNon-Photorealistic Rendering\n---\n\nUseful links:\n\nhttp://www.inf.ufrgs.br/~eslgastal/DomainTransform\n\nhttps://www.learnopencv.com/non-photorealistic-rendering-using-opencv-python-c/\n\nC API\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AlignExposuresThe base class for algorithms that align images of the same scene with different exposures\n* AlignMTBThis algorithm converts images to median threshold bitmaps (1 for pixels brighter than median luminance and 0 otherwise) and than aligns the resulting bitmaps using bit operations.\n* CalibrateCRFThe base class for camera response calibration algorithms.\n* CalibrateDebevecInverse camera response function is extracted for each brightness value by minimizing an objective function as linear system. Objective function is constructed using pixel values on the same position in all images, extra term is added to make the result smoother.\n* CalibrateRobertsonInverse camera response function is extracted for each brightness value by minimizing an objective function as linear system. This algorithm uses all image pixels.\n* MergeDebevecThe resulting HDR image is calculated as weighted average of the exposures considering exposure values and camera response.\n* MergeExposuresThe base class algorithms that can merge exposure sequence to a single image.\n* MergeMertensPixels are weighted using contrast, saturation and well-exposedness measures, than images are combined using laplacian pyramids.\n* MergeRobertsonThe resulting HDR image is calculated as weighted average of the exposures considering exposure values and camera response.\n* TonemapBase class for tonemapping algorithms - tools that are used to map HDR image to 8-bit range.\n* TonemapDragoAdaptive logarithmic mapping is a fast global tonemapping algorithm that scales the image in logarithmic domain.\n* TonemapMantiukThis algorithm transforms image to contrast using gradients on all levels of gaussian pyramid,\ntransforms contrast values to HVS response and scales the response. After this the image is reconstructed from new contrast values.\n* TonemapReinhardThis is a global tonemapping operator that models human visual system.\n\nConstants\n---\n\n* INPAINT_NSUse Navier-Stokes based method\n* INPAINT_TELEAUse the algorithm proposed by <NAME>\n* LDR_SIZE\n* MIXED_CLONEThe classic method, color-based selection and alpha masking might be time consuming and often leaves an undesirable halo. Seamless cloning, even averaged with the original image, is not effective. Mixed seamless cloning based on a loose selection proves effective.\n* MONOCHROME_TRANSFERMonochrome transfer allows the user to easily replace certain features of one object by alternative features.\n* NORMAL_CLONEThe power of the method is fully expressed when inserting objects with complex outlines into a new background\n* NORMCONV_FILTERNormalized Convolution Filtering\n* RECURS_FILTERRecursive Filtering\n\nTraits\n---\n\n* AlignExposuresTraitMutable methods for crate::photo::AlignExposures\n* AlignExposuresTraitConstConstant methods for crate::photo::AlignExposures\n* AlignMTBTraitMutable methods for crate::photo::AlignMTB\n* AlignMTBTraitConstConstant methods for crate::photo::AlignMTB\n* CalibrateCRFTraitMutable methods for crate::photo::CalibrateCRF\n* CalibrateCRFTraitConstConstant methods for crate::photo::CalibrateCRF\n* CalibrateDebevecTraitMutable methods for crate::photo::CalibrateDebevec\n* CalibrateDebevecTraitConstConstant methods for crate::photo::CalibrateDebevec\n* CalibrateRobertsonTraitMutable methods for crate::photo::CalibrateRobertson\n* CalibrateRobertsonTraitConstConstant methods for crate::photo::CalibrateRobertson\n* MergeDebevecTraitMutable methods for crate::photo::MergeDebevec\n* MergeDebevecTraitConstConstant methods for crate::photo::MergeDebevec\n* MergeExposuresTraitMutable methods for crate::photo::MergeExposures\n* MergeExposuresTraitConstConstant methods for crate::photo::MergeExposures\n* MergeMertensTraitMutable methods for crate::photo::MergeMertens\n* MergeMertensTraitConstConstant methods for crate::photo::MergeMertens\n* MergeRobertsonTraitMutable methods for crate::photo::MergeRobertson\n* MergeRobertsonTraitConstConstant methods for crate::photo::MergeRobertson\n* TonemapDragoTraitMutable methods for crate::photo::TonemapDrago\n* TonemapDragoTraitConstConstant methods for crate::photo::TonemapDrago\n* TonemapMantiukTraitMutable methods for crate::photo::TonemapMantiuk\n* TonemapMantiukTraitConstConstant methods for crate::photo::TonemapMantiuk\n* TonemapReinhardTraitMutable methods for crate::photo::TonemapReinhard\n* TonemapReinhardTraitConstConstant methods for crate::photo::TonemapReinhard\n* TonemapTraitMutable methods for crate::photo::Tonemap\n* TonemapTraitConstConstant methods for crate::photo::Tonemap\n\nFunctions\n---\n\n* color_changeGiven an original color image, two differently colored versions of this image can be mixed seamlessly.\n* color_change_defGiven an original color image, two differently colored versions of this image can be mixed seamlessly.\n* create_align_mtbCreates AlignMTB object\n* create_align_mtb_defCreates AlignMTB object\n* create_calibrate_debevecCreates CalibrateDebevec object\n* create_calibrate_debevec_defCreates CalibrateDebevec object\n* create_calibrate_robertsonCreates CalibrateRobertson object\n* create_calibrate_robertson_defCreates CalibrateRobertson object\n* create_merge_debevecCreates MergeDebevec object\n* create_merge_mertensCreates MergeMertens object\n* create_merge_mertens_defCreates MergeMertens object\n* create_merge_robertsonCreates MergeRobertson object\n* create_tonemapCreates simple linear mapper with gamma correction\n* create_tonemap_defCreates simple linear mapper with gamma correction\n* create_tonemap_dragoCreates TonemapDrago object\n* create_tonemap_drago_defCreates TonemapDrago object\n* create_tonemap_mantiukCreates TonemapMantiuk object\n* create_tonemap_mantiuk_defCreates TonemapMantiuk object\n* create_tonemap_reinhardCreates TonemapReinhard object\n* create_tonemap_reinhard_defCreates TonemapReinhard object\n* decolorTransforms a color image to a grayscale image. It is a basic tool in digital printing, stylized black-and-white photograph rendering, and in many single channel image processing applications CL12 .\n* denoise_tvl1Primal-dual algorithm is an algorithm for solving special types of variational problems (that is,\nfinding a function to minimize some functional). As the image denoising, in particular, may be seen as the variational problem, primal-dual algorithm then can be used to perform denoising and this is exactly what is implemented.\n* denoise_tvl1_defPrimal-dual algorithm is an algorithm for solving special types of variational problems (that is,\nfinding a function to minimize some functional). As the image denoising, in particular, may be seen as the variational problem, primal-dual algorithm then can be used to perform denoising and this is exactly what is implemented.\n* detail_enhanceThis filter enhances the details of a particular image.\n* detail_enhance_defThis filter enhances the details of a particular image.\n* edge_preserving_filterFiltering is the fundamental operation in image and video processing. Edge-preserving smoothing filters are used in many different applications EM11 .\n* edge_preserving_filter_defFiltering is the fundamental operation in image and video processing. Edge-preserving smoothing filters are used in many different applications EM11 .\n* fast_nl_means_denoisingPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising/ with several computational optimizations. Noise expected to be a gaussian white noise\n* fast_nl_means_denoising_1C++ default parameters\n* fast_nl_means_denoising_1_defNote\n* fast_nl_means_denoising_coloredModification of fastNlMeansDenoising function for colored images\n* fast_nl_means_denoising_colored_1C++ default parameters\n* fast_nl_means_denoising_colored_1_defNote\n* fast_nl_means_denoising_colored_cudaModification of fastNlMeansDenoising function for colored images\n* fast_nl_means_denoising_colored_cuda_defModification of fastNlMeansDenoising function for colored images\n* fast_nl_means_denoising_colored_defModification of fastNlMeansDenoising function for colored images\n* fast_nl_means_denoising_colored_multiModification of fastNlMeansDenoisingMulti function for colored images sequences\n* fast_nl_means_denoising_colored_multi_defModification of fastNlMeansDenoisingMulti function for colored images sequences\n* fast_nl_means_denoising_cudaPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising with several computational optimizations. Noise expected to be a gaussian white noise\n* fast_nl_means_denoising_cuda_defPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising with several computational optimizations. Noise expected to be a gaussian white noise\n* fast_nl_means_denoising_defPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising/ with several computational optimizations. Noise expected to be a gaussian white noise\n* fast_nl_means_denoising_multiModification of fastNlMeansDenoising function for images sequence where consecutive images have been captured in small period of time. For example video. This version of the function is for grayscale images or for manual manipulation with colorspaces. See Buades2005DenoisingIS for more details\n(open access here).\n* fast_nl_means_denoising_multi_defModification of fastNlMeansDenoising function for images sequence where consecutive images have been captured in small period of time. For example video. This version of the function is for grayscale images or for manual manipulation with colorspaces. See Buades2005DenoisingIS for more details\n(open access here).\n* fast_nl_means_denoising_multi_vecModification of fastNlMeansDenoising function for images sequence where consecutive images have been captured in small period of time. For example video. This version of the function is for grayscale images or for manual manipulation with colorspaces. See Buades2005DenoisingIS for more details\n(open access here).\n* fast_nl_means_denoising_multi_vec_defModification of fastNlMeansDenoising function for images sequence where consecutive images have been captured in small period of time. For example video. This version of the function is for grayscale images or for manual manipulation with colorspaces. See Buades2005DenoisingIS for more details\n(open access here).\n* fast_nl_means_denoising_vecPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising/ with several computational optimizations. Noise expected to be a gaussian white noise\n* fast_nl_means_denoising_vec_defPerform image denoising using Non-local Means Denoising algorithm http://www.ipol.im/pub/algo/bcm_non_local_means_denoising/ with several computational optimizations. Noise expected to be a gaussian white noise\n* illumination_changeApplying an appropriate non-linear transformation to the gradient field inside the selection and then integrating back with a Poisson solver, modifies locally the apparent illumination of an image.\n* illumination_change_defApplying an appropriate non-linear transformation to the gradient field inside the selection and then integrating back with a Poisson solver, modifies locally the apparent illumination of an image.\n* inpaintRestores the selected region in an image using the region neighborhood.\n* non_local_meansPerforms pure non local means denoising without any simplification, and thus it is not fast.\n* non_local_means_1C++ default parameters\n* non_local_means_1_defNote\n* non_local_means_defPerforms pure non local means denoising without any simplification, and thus it is not fast.\n* pencil_sketch@example samples/cpp/tutorial_code/photo/non_photorealistic_rendering/npr_demo.cpp An example using non-photorealistic line drawing functions\n* pencil_sketch_def@example samples/cpp/tutorial_code/photo/non_photorealistic_rendering/npr_demo.cpp An example using non-photorealistic line drawing functions\n* seamless_clone@example samples/cpp/tutorial_code/photo/seamless_cloning/cloning_demo.cpp An example using seamlessClone function\n* stylizationStylization aims to produce digital imagery with a wide variety of effects not focused on photorealism. Edge-aware filters are ideal for stylization, as they can abstract regions of low contrast while preserving, or enhancing, high-contrast features.\n* stylization_defStylization aims to produce digital imagery with a wide variety of effects not focused on photorealism. Edge-aware filters are ideal for stylization, as they can abstract regions of low contrast while preserving, or enhancing, high-contrast features.\n* texture_flatteningBy retaining only the gradients at edge locations, before integrating with the Poisson solver, one washes out the texture of the selected region, giving its contents a flat aspect. Here Canny Edge %Detector is used.\n* texture_flattening_defBy retaining only the gradients at edge locations, before integrating with the Poisson solver, one washes out the texture of the selected region, giving its contents a flat aspect. Here Canny Edge %Detector is used.\n\nModule opencv::platform_types\n===\n\nReexported platform types that are used by OpenCV\n\nEnums\n---\n\n* FILE\n\nType Aliases\n---\n\n* clock_t\n* ptrdiff_t\n* size_t\n\nModule opencv::plot\n===\n\nPlot function for Mat data\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* Plot2d\n\nTraits\n---\n\n* Plot2dTraitMutable methods for crate::plot::Plot2d\n* Plot2dTraitConstConstant methods for crate::plot::Plot2d\n\nModule opencv::rapid\n===\n\nsilhouette based 3D object tracking\n---\n\nimplements “RAPID-a video rate object tracker” harris1990rapid with the dynamic control point extraction of drummond2002real\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* Rapid_GOSTrackerimplements “Global optimal searching for textureless 3D object tracking” wang2015global\n* Rapid_OLSTrackerimplements “Optimal local searching for fast and robust textureless 3D object tracking in highly cluttered backgrounds” seo2013optimal\n* Rapid_Rapidwrapper around rapid function for uniform access\n* Rapid_TrackerAbstract base class for stateful silhouette trackers\n\nTraits\n---\n\n* Rapid_GOSTrackerTraitMutable methods for crate::rapid::Rapid_GOSTracker\n* Rapid_GOSTrackerTraitConstConstant methods for crate::rapid::Rapid_GOSTracker\n* Rapid_OLSTrackerTraitMutable methods for crate::rapid::Rapid_OLSTracker\n* Rapid_OLSTrackerTraitConstConstant methods for crate::rapid::Rapid_OLSTracker\n* Rapid_RapidTraitMutable methods for crate::rapid::Rapid_Rapid\n* Rapid_RapidTraitConstConstant methods for crate::rapid::Rapid_Rapid\n* Rapid_TrackerTraitMutable methods for crate::rapid::Rapid_Tracker\n* Rapid_TrackerTraitConstConstant methods for crate::rapid::Rapid_Tracker\n\nFunctions\n---\n\n* convert_correspondenciesCollect corresponding 2d and 3d points based on correspondencies and mask\n* convert_correspondencies_defCollect corresponding 2d and 3d points based on correspondencies and mask\n* draw_correspondenciesDebug draw markers of matched correspondences onto a lineBundle\n* draw_correspondencies_defDebug draw markers of matched correspondences onto a lineBundle\n* draw_search_linesDebug draw search lines onto an image\n* draw_wireframeDraw a wireframe of a triangle mesh\n* draw_wireframe_defDraw a wireframe of a triangle mesh\n* extract_control_pointsExtract control points from the projected silhouette of a mesh\n* extract_line_bundleExtract the line bundle from an image\n* find_correspondenciesFind corresponding image locations by searching for a maximal sobel edge along the search line (a single row in the bundle)\n* find_correspondencies_defFind corresponding image locations by searching for a maximal sobel edge along the search line (a single row in the bundle)\n* rapidHigh level function to execute a single rapid harris1990rapid iteration\n* rapid_defHigh level function to execute a single rapid harris1990rapid iteration\n\nModule opencv::rgbd\n===\n\nRGB-Depth Processing\n---\n\n[kinfu_icp]\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ColoredKinfu_ColoredKinFuKinectFusion implementation\n* ColoredKinfu_Params\n* DepthCleanerObject that can clean a noisy depth image\n* Dynafu_DynaFu\n* FastICPOdometryA faster version of ICPOdometry which is used in KinectFusion implementation Partial list of differences:\n* ICPOdometryOdometry based on the paper “KinectFusion: Real-Time Dense Surface Mapping and Tracking”,\n<NAME>, <NAME>, at al, SIGGRAPH, 2011.\n* Kinfu_Detail_PoseGraph\n* Kinfu_Intr\n* Kinfu_Intr_ProjectorProjects camera space vector onto screen\n* Kinfu_Intr_ReprojectorCamera intrinsics Reprojects screen point to camera space given z coord.\n* Kinfu_KinFuKinectFusion implementation\n* Kinfu_Params\n* Kinfu_Volume\n* Kinfu_VolumeParams\n* LargeKinfuLarge Scale Dense Depth Fusion implementation\n* LineMod_ColorGradient\\brief Modality that computes quantized gradient orientations from a color image.\n* LineMod_DepthNormal\\brief Modality that computes quantized surface normals from a dense depth map.\n* LineMod_Detector\\brief Object detector using the LINE template matching algorithm with any set of modalities.\n* LineMod_Feature\\brief Discriminant feature described by its location and label.\n* LineMod_Match\\brief Represents a successful template match.\n* LineMod_Modality\\brief Interface for modalities that plug into the LINE template matching representation.\n* LineMod_QuantizedPyramid\\brief Represents a modality operating over an image pyramid.\n* LineMod_Template\n* OdometryBase class for computation of odometry.\n* OdometryFrameObject that contains a frame data that is possibly needed for the Odometry.\nIt’s used for the efficiency (to pass precomputed/cached data of the frame that participates in the Odometry processing several times).\n* Params\n* RgbdFrameObject that contains a frame data.\n* RgbdICPOdometryOdometry that merges RgbdOdometry and ICPOdometry by minimize sum of their energy functions.\n* RgbdNormalsObject that can compute the normals in an image.\nIt is an object as it can cache data for speed efficiency The implemented methods are either:\n* RgbdOdometryOdometry based on the paper “Real-Time Visual Odometry from Dense RGB-D Images”,\n<NAME>, <NAME>, <NAME>, ICCV, 2011.\n* RgbdPlaneObject that can compute planes in an image\n\nEnums\n---\n\n* DepthCleaner_DEPTH_CLEANER_METHODNIL method is from\n`Modeling Kinect Sensor Noise for Improved 3d Reconstruction and Tracking`\nby <NAME>, <NAME>, <NAME>\n* Kinfu_VolumeType\n* RgbdNormals_RGBD_NORMALS_METHOD\n* RgbdPlane_RGBD_PLANE_METHOD\n\nConstants\n---\n\n* DepthCleaner_DEPTH_CLEANER_NIL\n* Kinfu_VolumeType_COLOREDTSDF\n* Kinfu_VolumeType_HASHTSDF\n* Kinfu_VolumeType_TSDF\n* OdometryFrame_CACHE_ALL\n* OdometryFrame_CACHE_DST\n* OdometryFrame_CACHE_SRC\n* Odometry_RIGID_BODY_MOTION\n* Odometry_ROTATION\n* Odometry_TRANSLATION\n* RgbdNormals_RGBD_NORMALS_METHOD_FALS\n* RgbdNormals_RGBD_NORMALS_METHOD_LINEMOD\n* RgbdNormals_RGBD_NORMALS_METHOD_SRI\n* RgbdPlane_RGBD_PLANE_METHOD_DEFAULT\n\nTraits\n---\n\n* ColoredKinfu_ColoredKinFuTraitMutable methods for crate::rgbd::ColoredKinfu_ColoredKinFu\n* ColoredKinfu_ColoredKinFuTraitConstConstant methods for crate::rgbd::ColoredKinfu_ColoredKinFu\n* ColoredKinfu_ParamsTraitMutable methods for crate::rgbd::ColoredKinfu_Params\n* ColoredKinfu_ParamsTraitConstConstant methods for crate::rgbd::ColoredKinfu_Params\n* DepthCleanerTraitMutable methods for crate::rgbd::DepthCleaner\n* DepthCleanerTraitConstConstant methods for crate::rgbd::DepthCleaner\n* Dynafu_DynaFuTraitMutable methods for crate::rgbd::Dynafu_DynaFu\n* Dynafu_DynaFuTraitConstConstant methods for crate::rgbd::Dynafu_DynaFu\n* FastICPOdometryTraitMutable methods for crate::rgbd::FastICPOdometry\n* FastICPOdometryTraitConstConstant methods for crate::rgbd::FastICPOdometry\n* ICPOdometryTraitMutable methods for crate::rgbd::ICPOdometry\n* ICPOdometryTraitConstConstant methods for crate::rgbd::ICPOdometry\n* Kinfu_Detail_PoseGraphTraitMutable methods for crate::rgbd::Kinfu_Detail_PoseGraph\n* Kinfu_Detail_PoseGraphTraitConstConstant methods for crate::rgbd::Kinfu_Detail_PoseGraph\n* Kinfu_KinFuTraitMutable methods for crate::rgbd::Kinfu_KinFu\n* Kinfu_KinFuTraitConstConstant methods for crate::rgbd::Kinfu_KinFu\n* Kinfu_ParamsTraitMutable methods for crate::rgbd::Kinfu_Params\n* Kinfu_ParamsTraitConstConstant methods for crate::rgbd::Kinfu_Params\n* Kinfu_VolumeParamsTraitMutable methods for crate::rgbd::Kinfu_VolumeParams\n* Kinfu_VolumeParamsTraitConstConstant methods for crate::rgbd::Kinfu_VolumeParams\n* Kinfu_VolumeTraitMutable methods for crate::rgbd::Kinfu_Volume\n* Kinfu_VolumeTraitConstConstant methods for crate::rgbd::Kinfu_Volume\n* LargeKinfuTraitMutable methods for crate::rgbd::LargeKinfu\n* LargeKinfuTraitConstConstant methods for crate::rgbd::LargeKinfu\n* LineMod_ColorGradientTraitMutable methods for crate::rgbd::LineMod_ColorGradient\n* LineMod_ColorGradientTraitConstConstant methods for crate::rgbd::LineMod_ColorGradient\n* LineMod_DepthNormalTraitMutable methods for crate::rgbd::LineMod_DepthNormal\n* LineMod_DepthNormalTraitConstConstant methods for crate::rgbd::LineMod_DepthNormal\n* LineMod_DetectorTraitMutable methods for crate::rgbd::LineMod_Detector\n* LineMod_DetectorTraitConstConstant methods for crate::rgbd::LineMod_Detector\n* LineMod_MatchTraitMutable methods for crate::rgbd::LineMod_Match\n* LineMod_MatchTraitConstConstant methods for crate::rgbd::LineMod_Match\n* LineMod_ModalityTraitMutable methods for crate::rgbd::LineMod_Modality\n* LineMod_ModalityTraitConstConstant methods for crate::rgbd::LineMod_Modality\n* LineMod_QuantizedPyramidTraitMutable methods for crate::rgbd::LineMod_QuantizedPyramid\n* LineMod_QuantizedPyramidTraitConstConstant methods for crate::rgbd::LineMod_QuantizedPyramid\n* LineMod_TemplateTraitMutable methods for crate::rgbd::LineMod_Template\n* LineMod_TemplateTraitConstConstant methods for crate::rgbd::LineMod_Template\n* OdometryFrameTraitMutable methods for crate::rgbd::OdometryFrame\n* OdometryFrameTraitConstConstant methods for crate::rgbd::OdometryFrame\n* OdometryTraitMutable methods for crate::rgbd::Odometry\n* OdometryTraitConstConstant methods for crate::rgbd::Odometry\n* ParamsTraitMutable methods for crate::rgbd::Params\n* ParamsTraitConstConstant methods for crate::rgbd::Params\n* RgbdFrameTraitMutable methods for crate::rgbd::RgbdFrame\n* RgbdFrameTraitConstConstant methods for crate::rgbd::RgbdFrame\n* RgbdICPOdometryTraitMutable methods for crate::rgbd::RgbdICPOdometry\n* RgbdICPOdometryTraitConstConstant methods for crate::rgbd::RgbdICPOdometry\n* RgbdNormalsTraitMutable methods for crate::rgbd::RgbdNormals\n* RgbdNormalsTraitConstConstant methods for crate::rgbd::RgbdNormals\n* RgbdOdometryTraitMutable methods for crate::rgbd::RgbdOdometry\n* RgbdOdometryTraitConstConstant methods for crate::rgbd::RgbdOdometry\n* RgbdPlaneTraitMutable methods for crate::rgbd::RgbdPlane\n* RgbdPlaneTraitConstConstant methods for crate::rgbd::RgbdPlane\n\nFunctions\n---\n\n* colormap\\brief Debug function to colormap a quantized image for viewing.\n* depth_to3dConverts a depth image to an organized set of 3d points.\nThe coordinate system is x pointing left, y down and z away from the camera\n* depth_to3d_defConverts a depth image to an organized set of 3d points.\nThe coordinate system is x pointing left, y down and z away from the camera\n* depth_to3d_sparseParameters\n* draw_features\\brief Debug function to draw linemod features\n* draw_features_def\\brief Debug function to draw linemod features\n* get_default_line\\brief Factory function for detector using LINE algorithm with color gradients.\n* get_default_linemod\\brief Factory function for detector using LINE-MOD algorithm with color gradients and depth normals.\n* is_valid_depthChecks if the value is a valid depth. For CV_16U or CV_16S, the convention is to be invalid if it is a limit. For a float/double, we just check if it is a NaN\n* is_valid_depth_1\n* is_valid_depth_2\n* is_valid_depth_3\n* is_valid_depth_4\n* is_valid_depth_5\n* make_volume\n* register_depthRegisters depth data to an external camera Registration is performed by creating a depth cloud, transforming the cloud by the rigid body transformation between the cameras, and then projecting the transformed points into the RGB camera.\n* register_depth_defRegisters depth data to an external camera Registration is performed by creating a depth cloud, transforming the cloud by the rigid body transformation between the cameras, and then projecting the transformed points into the RGB camera.\n* rescale_depthIf the input image is of type CV_16UC1 (like the Kinect one), the image is converted to floats, divided by depth_factor to get a depth in meters, and the values 0 are converted to std::numeric_limits::quiet_NaN()\nOtherwise, the image is simply converted to floats\n* rescale_depth_defIf the input image is of type CV_16UC1 (like the Kinect one), the image is converted to floats, divided by depth_factor to get a depth in meters, and the values 0 are converted to std::numeric_limits::quiet_NaN()\nOtherwise, the image is simply converted to floats\n* warp_frameWarp the image: compute 3d points from the depth, transform them using given transformation,\nthen project color point cloud to an image plane.\nThis function can be used to visualize results of the Odometry algorithm.\n* warp_frame_defWarp the image: compute 3d points from the depth, transform them using given transformation,\nthen project color point cloud to an image plane.\nThis function can be used to visualize results of the Odometry algorithm.\n\nType Aliases\n---\n\n* Dynafu_ParamsBackwards compatibility for old versions\n\nModule opencv::saliency\n===\n\nSaliency API\n---\n\nMany computer vision applications may benefit from understanding where humans focus given a scene.\nOther than cognitively understanding the way human perceive images and scenes, finding salient regions and objects in the images helps various tasks such as speeding up object detection, object recognition, object tracking and content-aware image editing.\n\nAbout the saliency, there is a rich literature but the development is very fragmented. The principal purpose of this API is to give a unique interface, a unique framework for use and plug sever saliency algorithms, also with very different nature and methodology, but they share the same purpose, organizing algorithms into three main categories:\n\n**Static Saliency**: algorithms belonging to this category, exploit different image features that allow to detect salient objects in a non dynamic scenarios.\n\n**Motion Saliency**: algorithms belonging to this category, are particularly focused to detect salient objects over time (hence also over frame), then there is a temporal component sealing cosider that allows to detect “moving” objects as salient, meaning therefore also the more general sense of detection the changes in the scene.\n\n**Objectness**: Objectness is usually represented as a value which reflects how likely an image window covers an object of any category. Algorithms belonging to this category, avoid making decisions early on, by proposing a small number of category-independent proposals, that are expected to cover all objects in an image. Being able to perceive objects before identifying them is closely related to bottom up visual attention (saliency).\n\n\n\nTo see how API works, try tracker demo:\nhttps://github.com/fpuja/opencv_contrib/blob/saliencyModuleDevelop/modules/saliency/samples/computeSaliency.cpp\n\nNote: This API has been designed with PlantUML. If you modify this API please change UML.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* MotionSaliency********************************* Motion Saliency Base Class ***********************************\n* MotionSaliencyBinWangApr2014!\n* Objectness********************************* Objectness Base Class ***********************************\n* ObjectnessBINGthe Binarized normed gradients algorithm from BING\n* Saliency********************************* Saliency Base Class ***********************************\n* StaticSaliency********************************* Static Saliency Base Class ***********************************\n* StaticSaliencyFineGrainedthe Fine Grained Saliency approach from FGS\n* StaticSaliencySpectralResidualthe Spectral Residual approach from SR\n\nTraits\n---\n\n* MotionSaliencyBinWangApr2014TraitMutable methods for crate::saliency::MotionSaliencyBinWangApr2014\n* MotionSaliencyBinWangApr2014TraitConstConstant methods for crate::saliency::MotionSaliencyBinWangApr2014\n* MotionSaliencyTraitMutable methods for crate::saliency::MotionSaliency\n* MotionSaliencyTraitConstConstant methods for crate::saliency::MotionSaliency\n* ObjectnessBINGTraitMutable methods for crate::saliency::ObjectnessBING\n* ObjectnessBINGTraitConstConstant methods for crate::saliency::ObjectnessBING\n* ObjectnessTraitMutable methods for crate::saliency::Objectness\n* ObjectnessTraitConstConstant methods for crate::saliency::Objectness\n* SaliencyTraitMutable methods for crate::saliency::Saliency\n* SaliencyTraitConstConstant methods for crate::saliency::Saliency\n* StaticSaliencyFineGrainedTraitMutable methods for crate::saliency::StaticSaliencyFineGrained\n* StaticSaliencyFineGrainedTraitConstConstant methods for crate::saliency::StaticSaliencyFineGrained\n* StaticSaliencySpectralResidualTraitMutable methods for crate::saliency::StaticSaliencySpectralResidual\n* StaticSaliencySpectralResidualTraitConstConstant methods for crate::saliency::StaticSaliencySpectralResidual\n* StaticSaliencyTraitMutable methods for crate::saliency::StaticSaliency\n* StaticSaliencyTraitConstConstant methods for crate::saliency::StaticSaliency\n\nModule opencv::sfm\n===\n\nStructure From Motion\n---\n\nThe opencv_sfm module contains algorithms to perform 3d reconstruction from 2d images.\n\nThe core of the module is based on a light version of Libmv originally developed by <NAME> and <NAME>.\n\n**Whats is libmv?** \n\nlibmv, also known as the Library for Multiview Reconstruction (or LMV),\nis the computer vision backend for Blender’s motion tracking abilities.\nUnlike other vision libraries with general ambitions, libmv is focused on algorithms for match moving, specifically targeting Blender as the primary customer. Dense reconstruction, reconstruction from unorganized photo collections, image recognition, and other tasks are not a focus of libmv.\n\n**Development** \n\nlibmv is officially under the Blender umbrella, and so is developed on developer.blender.org. The source repository can get checked out independently from Blender.\n\nThis module has been originally developed as a project for Google Summer of Code 2012-2015.\n\nNote:\n\n* Notice that it is compiled only when Eigen, GLog and GFlags are correctly installed.\n\nCheck installation instructions in the following tutorial: [tutorial_sfm_installation]\n\nConditioning\n---\n\nFundamental\n---\n\nInput/Output\n---\n\nNumeric\n---\n\nProjection\n---\n\nRobust Estimation\n---\n\nTriangulation\n---\n\nReconstruction\n---\n\nNote:\n- Notice that it is compiled only when Ceres Solver is correctly installed.\n```\n Check installation instructions in the following tutorial: [tutorial_sfm_installation]\n```\nSimple Pipeline\n---\n\nNote:\n- Notice that it is compiled only when Ceres Solver is correctly installed.\n```\n Check installation instructions in the following tutorial: [tutorial_sfm_installation]\n```\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BaseSFMbase class BaseSFM declares a common API that would be used in a typical scene reconstruction scenario\n* SFMLibmvEuclideanReconstructionSFMLibmvEuclideanReconstruction class provides an interface with the Libmv Structure From Motion pipeline.\n* libmv_CameraIntrinsicsOptionsData structure describing the camera model and its parameters.\n* libmv_ReconstructionOptionsData structure describing the reconstruction options.\n\nConstants\n---\n\n* SFM_DISTORTION_MODEL_DIVISION\n* SFM_DISTORTION_MODEL_POLYNOMIAL\n* SFM_IO_BUNDLER\n* SFM_IO_OPENMVG\n* SFM_IO_OPENSFM\n* SFM_IO_THEIASFM\n* SFM_IO_VISUALSFM\n* SFM_REFINE_FOCAL_LENGTH\n* SFM_REFINE_PRINCIPAL_POINT\n* SFM_REFINE_RADIAL_DISTORTION_K1\n* SFM_REFINE_RADIAL_DISTORTION_K2\n\nTraits\n---\n\n* BaseSFMTraitMutable methods for crate::sfm::BaseSFM\n* BaseSFMTraitConstConstant methods for crate::sfm::BaseSFM\n* SFMLibmvEuclideanReconstructionTraitMutable methods for crate::sfm::SFMLibmvEuclideanReconstruction\n* SFMLibmvEuclideanReconstructionTraitConstConstant methods for crate::sfm::SFMLibmvEuclideanReconstruction\n\nFunctions\n---\n\n* apply_transformation_to_pointsApply Transformation to points.\n* compute_orientationComputes Absolute or Exterior Orientation (Pose Estimation) between 2 sets of 3D point.\n* depthReturns the depth of a point transformed by a rigid transform.\n* essential_from_fundamentalGet Essential matrix from Fundamental and Camera matrices.\n* essential_from_rtGet Essential matrix from Motion (R’s and t’s ).\n* euclidean_to_homogeneousConverts points from Euclidean to homogeneous space. E.g., ((x,y)->(x,y,1))\n* fundamental_from_correspondences7_point_robustEstimate robustly the fundamental matrix between two dataset of 2D point (image coords space).\n* fundamental_from_correspondences7_point_robust_defEstimate robustly the fundamental matrix between two dataset of 2D point (image coords space).\n* fundamental_from_correspondences8_point_robustEstimate robustly the fundamental matrix between two dataset of 2D point (image coords space).\n* fundamental_from_correspondences8_point_robust_defEstimate robustly the fundamental matrix between two dataset of 2D point (image coords space).\n* fundamental_from_essentialGet Essential matrix from Fundamental and Camera matrices.\n* fundamental_from_projectionsGet Fundamental matrix from Projection matrices.\n* homogeneous_to_euclideanConverts point coordinates from homogeneous to euclidean pixel coordinates. E.g., ((x,y,z)->(x/z, y/z))\n* import_reconstructionImport a reconstruction file.\n* import_reconstruction_defImport a reconstruction file.\n* isotropic_preconditioner_from_pointsPoint conditioning (isotropic).\n* k_rt_from_projectionGet K, R and t from projection matrix P, decompose using the RQ decomposition.\n* mean_and_variance_along_rowsComputes the mean and variance of a given matrix along its rows.\n* motion_from_essentialGet Motion (R’s and t’s ) from Essential matrix.\n* motion_from_essential_choose_solutionChoose one of the four possible motion solutions from an essential matrix.\n* normalize_fundamentalNormalizes the Fundamental matrix.\n* normalize_isotropic_pointsThis function normalizes points. (isotropic).\n* normalize_pointsThis function normalizes points (non isotropic).\n* normalized_eight_point_solverEstimate the fundamental matrix between two dataset of 2D point (image coords space).\n* preconditioner_from_pointsPoint conditioning (non isotropic).\n* projection_from_k_rtGet projection matrix P from K, R and t.\n* projections_from_fundamentalGet projection matrices from Fundamental matrix\n* reconstructReconstruct 3d points from 2d correspondences while performing autocalibration.\n* reconstruct_1Reconstruct 3d points from 2d correspondences while performing autocalibration.\n* reconstruct_1_defReconstruct 3d points from 2d correspondences while performing autocalibration.\n* reconstruct_2Reconstruct 3d points from 2d images while performing autocalibration.\n* reconstruct_2_defReconstruct 3d points from 2d images while performing autocalibration.\n* reconstruct_3Reconstruct 3d points from 2d images while performing autocalibration.\n* reconstruct_3_defReconstruct 3d points from 2d images while performing autocalibration.\n* reconstruct_defReconstruct 3d points from 2d correspondences while performing autocalibration.\n* relative_camera_motionComputes the relative camera motion between two cameras.\n* skewReturns the 3x3 skew symmetric matrix of a vector.\n* triangulate_pointsReconstructs bunch of points by triangulation.\n\nModule opencv::shape\n===\n\nShape Distance and Matching\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AffineTransformerWrapper class for the OpenCV Affine Transformation algorithm. :\n* ChiHistogramCostExtractorAn Chi based cost extraction. :\n* EMDHistogramCostExtractorAn EMD based cost extraction. :\n* EMDL1HistogramCostExtractorAn EMD-L1 based cost extraction. :\n* HausdorffDistanceExtractor\n\n---\n* HistogramCostExtractorAbstract base class for histogram cost algorithms.\n* NormHistogramCostExtractorA norm based cost extraction. :\n* ShapeContextDistanceExtractor\n\n---\n* ShapeDistanceExtractor@example modules/shape/samples/shape_example.cpp An example using shape distance algorithm\n* ShapeTransformerAbstract base class for shape transformation algorithms.\n* ThinPlateSplineShapeTransformerDefinition of the transformation\n\nTraits\n---\n\n* AffineTransformerTraitMutable methods for crate::shape::AffineTransformer\n* AffineTransformerTraitConstConstant methods for crate::shape::AffineTransformer\n* ChiHistogramCostExtractorTraitMutable methods for crate::shape::ChiHistogramCostExtractor\n* ChiHistogramCostExtractorTraitConstConstant methods for crate::shape::ChiHistogramCostExtractor\n* EMDHistogramCostExtractorTraitMutable methods for crate::shape::EMDHistogramCostExtractor\n* EMDHistogramCostExtractorTraitConstConstant methods for crate::shape::EMDHistogramCostExtractor\n* EMDL1HistogramCostExtractorTraitMutable methods for crate::shape::EMDL1HistogramCostExtractor\n* EMDL1HistogramCostExtractorTraitConstConstant methods for crate::shape::EMDL1HistogramCostExtractor\n* HausdorffDistanceExtractorTraitMutable methods for crate::shape::HausdorffDistanceExtractor\n* HausdorffDistanceExtractorTraitConstConstant methods for crate::shape::HausdorffDistanceExtractor\n* HistogramCostExtractorTraitMutable methods for crate::shape::HistogramCostExtractor\n* HistogramCostExtractorTraitConstConstant methods for crate::shape::HistogramCostExtractor\n* NormHistogramCostExtractorTraitMutable methods for crate::shape::NormHistogramCostExtractor\n* NormHistogramCostExtractorTraitConstConstant methods for crate::shape::NormHistogramCostExtractor\n* ShapeContextDistanceExtractorTraitMutable methods for crate::shape::ShapeContextDistanceExtractor\n* ShapeContextDistanceExtractorTraitConstConstant methods for crate::shape::ShapeContextDistanceExtractor\n* ShapeDistanceExtractorTraitMutable methods for crate::shape::ShapeDistanceExtractor\n* ShapeDistanceExtractorTraitConstConstant methods for crate::shape::ShapeDistanceExtractor\n* ShapeTransformerTraitMutable methods for crate::shape::ShapeTransformer\n* ShapeTransformerTraitConstConstant methods for crate::shape::ShapeTransformer\n* ThinPlateSplineShapeTransformerTraitMutable methods for crate::shape::ThinPlateSplineShapeTransformer\n* ThinPlateSplineShapeTransformerTraitConstConstant methods for crate::shape::ThinPlateSplineShapeTransformer\n\nFunctions\n---\n\n* create_affine_transformerComplete constructor\n* create_chi_histogram_cost_extractorC++ default parameters\n* create_chi_histogram_cost_extractor_defNote\n* create_emd_histogram_cost_extractorC++ default parameters\n* create_emd_histogram_cost_extractor_defNote\n* create_emdl1_histogram_cost_extractorC++ default parameters\n* create_emdl1_histogram_cost_extractor_defNote\n* create_hausdorff_distance_extractorC++ default parameters\n* create_hausdorff_distance_extractor_defNote\n* create_norm_histogram_cost_extractorC++ default parameters\n* create_norm_histogram_cost_extractor_defNote\n* create_shape_context_distance_extractorC++ default parameters\n* create_shape_context_distance_extractor_defNote\n* create_thin_plate_spline_shape_transformerComplete constructor\n* create_thin_plate_spline_shape_transformer_defComplete constructor\n* emdl1Computes the “minimal work” distance between two weighted point configurations base on the papers\n“EMD-L1: An efficient and Robust Algorithm for comparing histogram-based descriptors”, by <NAME> and <NAME>; and “The Earth Mover’s Distance is the Mallows Distance: Some Insights from Statistics”, by <NAME> and <NAME>.\n\nModule opencv::stereo\n===\n\nStereo Correspondance Algorithms\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* MatchQuasiDense\\addtogroup stereo\n* PropagationParameters\n* QuasiDenseStereoClass containing the methods needed for Quasi Dense Stereo computation.\n\nConstants\n---\n\n* CV_CS_CENSUS\n* CV_DENSE_CENSUS\n* CV_MEAN_VARIATION\n* CV_MODIFIED_CENSUS_TRANSFORM\n* CV_MODIFIED_CS_CENSUS\n* CV_QUADRATIC_INTERPOLATION\n* CV_SIMETRICV_INTERPOLATION\n* CV_SPARSE_CENSUS\n* CV_SPECKLE_REMOVAL_ALGORITHM\n* CV_SPECKLE_REMOVAL_AVG_ALGORITHM\n* CV_STAR_KERNEL\n\nTraits\n---\n\n* QuasiDenseStereoTraitMutable methods for crate::stereo::QuasiDenseStereo\n* QuasiDenseStereoTraitConstConstant methods for crate::stereo::QuasiDenseStereo\n\nFunctions\n---\n\n* census_transformTwo variations of census applied on input images Implementation of a census transform which is taking into account just the some pixels from the census kernel thus allowing for larger block sizes\n*\n* census_transform_1single image census transform\n* modified_census_transformSTANDARD_MCT - Modified census which is memorizing for each pixel 2 bits and includes a tolerance to the pixel comparison MCT_MEAN_VARIATION - Implementation of a modified census transform which is also taking into account the variation to the mean of the window not just the center pixel\n*\n* modified_census_transform_1single version of modified census transform descriptor\n* modified_census_transform_1_defsingle version of modified census transform descriptor\n* modified_census_transform_defSTANDARD_MCT - Modified census which is memorizing for each pixel 2 bits and includes a tolerance to the pixel comparison MCT_MEAN_VARIATION - Implementation of a modified census transform which is also taking into account the variation to the mean of the window not just the center pixel\n*\n* star_census_transformin a 9x9 kernel only certain positions are choosen\n* star_census_transform_1single image version of star kernel\n* symetric_census_transformThe classical center symetric census A modified version of cs census which is comparing a pixel with its correspondent after the center\n*\n* symetric_census_transform_1single version of census transform\n\nModule opencv::stitching\n===\n\nImages stitching\n---\n\nThis figure illustrates the stitching module pipeline implemented in the Stitcher class. Using that class it’s possible to configure/remove some steps, i.e. adjust the stitching pipeline according to the particular needs. All building blocks from the pipeline are available in the detail namespace,\none can combine and use them separately.\n\nThe implemented stitching pipeline is very similar to the one proposed in BL07 .\n\n\n\n### Camera models\n\nThere are currently 2 camera models implemented in stitching pipeline.\n\n* *Homography model* expecting perspective transformations between images implemented in [cv::detail::BestOf2NearestMatcher] cv::detail::HomographyBasedEstimator cv::detail::BundleAdjusterReproj cv::detail::BundleAdjusterRay\n* *Affine model* expecting affine transformation with 6 DOF or 4 DOF implemented in\n[cv::detail::AffineBestOf2NearestMatcher] cv::detail::AffineBasedEstimator cv::detail::BundleAdjusterAffine cv::detail::BundleAdjusterAffinePartial cv::AffineWarper\n\nHomography model is useful for creating photo panoramas captured by camera,\nwhile affine-based model can be used to stitch scans and object captured by specialized devices. Use [cv::Stitcher::create] to get preconfigured pipeline for one of those models.\n\nNote:\nCertain detailed settings of [cv::Stitcher] might not make sense. Especially you should not mix classes implementing affine model and classes implementing Homography model, as they work with different transformations.\n\nFeatures Finding and Images Matching\n---\n\nRotation Estimation\n---\n\nAutocalibration\n---\n\nImages Warping\n---\n\nSeam Estimation\n---\n\nExposure Compensation\n---\n\nImage Blenders\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AffineWarperAffine warper factory class.\n* CompressedRectilinearPortraitWarper\n* CompressedRectilinearWarper\n* CylindricalWarperCylindrical warper factory class.\n* CylindricalWarperGpu\n* Detail_AffineBasedEstimatorAffine transformation based estimator.\n* Detail_AffineBestOf2NearestMatcherFeatures matcher similar to cv::detail::BestOf2NearestMatcher which finds two best matches for each feature and leaves the best one only if the ratio between descriptor distances is greater than the threshold match_conf.\n* Detail_AffineWarperAffine warper that uses rotations and translations\n* Detail_BestOf2NearestMatcherFeatures matcher which finds two best matches for each feature and leaves the best one only if the ratio between descriptor distances is greater than the threshold match_conf\n* Detail_BestOf2NearestRangeMatcher\n* Detail_BlenderBase class for all blenders.\n* Detail_BlocksChannelsCompensatorExposure compensator which tries to remove exposure related artifacts by adjusting image block on each channel.\n* Detail_BlocksCompensatorExposure compensator which tries to remove exposure related artifacts by adjusting image blocks.\n* Detail_BlocksGainCompensatorExposure compensator which tries to remove exposure related artifacts by adjusting image block intensities, see UES01 for details.\n* Detail_BundleAdjusterAffineBundle adjuster that expects affine transformation represented in homogeneous coordinates in R for each camera param. Implements camera parameters refinement algorithm which minimizes sum of the reprojection error squares\n* Detail_BundleAdjusterAffinePartialBundle adjuster that expects affine transformation with 4 DOF represented in homogeneous coordinates in R for each camera param. Implements camera parameters refinement algorithm which minimizes sum of the reprojection error squares\n* Detail_BundleAdjusterBaseBase class for all camera parameters refinement methods.\n* Detail_BundleAdjusterRayImplementation of the camera parameters refinement algorithm which minimizes sum of the distances between the rays passing through the camera center and a feature. :\n* Detail_BundleAdjusterReprojImplementation of the camera parameters refinement algorithm which minimizes sum of the reprojection error squares\n* Detail_CameraParamsDescribes camera parameters.\n* Detail_ChannelsCompensatorExposure compensator which tries to remove exposure related artifacts by adjusting image intensities on each channel independently.\n* Detail_CompressedRectilinearPortraitProjector\n* Detail_CompressedRectilinearPortraitWarper\n* Detail_CompressedRectilinearProjector\n* Detail_CompressedRectilinearWarper\n* Detail_CylindricalPortraitProjector\n* Detail_CylindricalPortraitWarper\n* Detail_CylindricalProjector\n* Detail_CylindricalWarperWarper that maps an image onto the x*x + z*z = 1 cylinder.\n* Detail_CylindricalWarperGpu\n* Detail_DisjointSets\n* Detail_DpSeamFinder\n* Detail_EstimatorRotation estimator base class.\n* Detail_ExposureCompensatorBase class for all exposure compensators.\n* Detail_FeatherBlenderSimple blender which mixes images at its borders.\n* Detail_FeaturesMatcherFeature matchers base class.\n* Detail_FisheyeProjector\n* Detail_FisheyeWarper\n* Detail_GainCompensatorExposure compensator which tries to remove exposure related artifacts by adjusting image intensities, see BL07 and WJ10 for details.\n* Detail_Graph\n* Detail_GraphCutSeamFinderMinimum graph cut-based seam estimator. See details in V03 .\n* Detail_GraphCutSeamFinderBaseBase class for all minimum graph-cut-based seam estimators.\n* Detail_GraphCutSeamFinderGpu\n* Detail_GraphEdge\n* Detail_HomographyBasedEstimatorHomography based rotation estimator.\n* Detail_ImageFeaturesStructure containing image keypoints and descriptors.\n* Detail_MatchesInfoStructure containing information about matches between two images.\n* Detail_MercatorProjector\n* Detail_MercatorWarper\n* Detail_MultiBandBlenderBlender which uses multi-band blending algorithm (see BA83).\n* Detail_NoBundleAdjusterStub bundle adjuster that does nothing.\n* Detail_NoExposureCompensatorStub exposure compensator which does nothing.\n* Detail_NoSeamFinderStub seam estimator which does nothing.\n* Detail_PairwiseSeamFinderBase class for all pairwise seam estimators.\n* Detail_PaniniPortraitProjector\n* Detail_PaniniPortraitWarper\n* Detail_PaniniProjector\n* Detail_PaniniWarper\n* Detail_PlanePortraitProjector\n* Detail_PlanePortraitWarper\n* Detail_PlaneProjector\n* Detail_PlaneWarperWarper that maps an image onto the z = 1 plane.\n* Detail_PlaneWarperGpu\n* Detail_ProjectorBaseBase class for warping logic implementation.\n* Detail_RotationWarperRotation-only model image warper interface.\n* Detail_SeamFinderBase class for a seam estimator.\n* Detail_SphericalPortraitProjector\n* Detail_SphericalPortraitWarper\n* Detail_SphericalProjector\n* Detail_SphericalWarperWarper that maps an image onto the unit sphere located at the origin.\n* Detail_SphericalWarperGpu\n* Detail_StereographicProjector\n* Detail_StereographicWarper\n* Detail_TransverseMercatorProjector\n* Detail_TransverseMercatorWarper\n* Detail_VoronoiSeamFinderVoronoi diagram-based seam estimator.\n* FisheyeWarper\n* MercatorWarper\n* PaniniPortraitWarper\n* PaniniWarper\n* PlaneWarperPlane warper factory class.\n* PlaneWarperGpu\n* PyRotationWarper\n* SphericalWarperSpherical warper factory class\n* SphericalWarperGpu\n* StereographicWarper\n* StitcherHigh level image stitcher.\n* TransverseMercatorWarper\n* WarperCreatorImage warper factories base class.\n\nEnums\n---\n\n* Detail_DpSeamFinder_CostFunction\n* Detail_GraphCutSeamFinderBase_CostType\n* Detail_WaveCorrectKind\n* Stitcher_Mode\n* Stitcher_Status\n\nConstants\n---\n\n* Detail_Blender_FEATHER\n* Detail_Blender_MULTI_BAND\n* Detail_Blender_NO\n* Detail_DpSeamFinder_COLOR\n* Detail_DpSeamFinder_COLOR_GRAD\n* Detail_ExposureCompensator_CHANNELS\n* Detail_ExposureCompensator_CHANNELS_BLOCKS\n* Detail_ExposureCompensator_GAIN\n* Detail_ExposureCompensator_GAIN_BLOCKS\n* Detail_ExposureCompensator_NO\n* Detail_GraphCutSeamFinderBase_COST_COLOR\n* Detail_GraphCutSeamFinderBase_COST_COLOR_GRAD\n* Detail_SeamFinder_DP_SEAM\n* Detail_SeamFinder_NO\n* Detail_SeamFinder_VORONOI_SEAM\n* Detail_WAVE_CORRECT_AUTO\n* Detail_WAVE_CORRECT_HORIZ\n* Detail_WAVE_CORRECT_VERT\n* Stitcher_ERR_CAMERA_PARAMS_ADJUST_FAIL\n* Stitcher_ERR_HOMOGRAPHY_EST_FAIL\n* Stitcher_ERR_NEED_MORE_IMGS\n* Stitcher_OK\n* Stitcher_PANORAMAMode for creating photo panoramas. Expects images under perspective transformation and projects resulting pano to sphere.\n* Stitcher_SCANSMode for composing scans. Expects images under affine transformation does not compensate exposure by default.\n\nTraits\n---\n\n* AffineWarperTraitMutable methods for crate::stitching::AffineWarper\n* AffineWarperTraitConstConstant methods for crate::stitching::AffineWarper\n* CompressedRectilinearPortraitWarperTraitMutable methods for crate::stitching::CompressedRectilinearPortraitWarper\n* CompressedRectilinearPortraitWarperTraitConstConstant methods for crate::stitching::CompressedRectilinearPortraitWarper\n* CompressedRectilinearWarperTraitMutable methods for crate::stitching::CompressedRectilinearWarper\n* CompressedRectilinearWarperTraitConstConstant methods for crate::stitching::CompressedRectilinearWarper\n* CylindricalWarperGpuTraitMutable methods for crate::stitching::CylindricalWarperGpu\n* CylindricalWarperGpuTraitConstConstant methods for crate::stitching::CylindricalWarperGpu\n* CylindricalWarperTraitMutable methods for crate::stitching::CylindricalWarper\n* CylindricalWarperTraitConstConstant methods for crate::stitching::CylindricalWarper\n* Detail_AffineBasedEstimatorTraitMutable methods for crate::stitching::Detail_AffineBasedEstimator\n* Detail_AffineBasedEstimatorTraitConstConstant methods for crate::stitching::Detail_AffineBasedEstimator\n* Detail_AffineBestOf2NearestMatcherTraitMutable methods for crate::stitching::Detail_AffineBestOf2NearestMatcher\n* Detail_AffineBestOf2NearestMatcherTraitConstConstant methods for crate::stitching::Detail_AffineBestOf2NearestMatcher\n* Detail_AffineWarperTraitMutable methods for crate::stitching::Detail_AffineWarper\n* Detail_AffineWarperTraitConstConstant methods for crate::stitching::Detail_AffineWarper\n* Detail_BestOf2NearestMatcherTraitMutable methods for crate::stitching::Detail_BestOf2NearestMatcher\n* Detail_BestOf2NearestMatcherTraitConstConstant methods for crate::stitching::Detail_BestOf2NearestMatcher\n* Detail_BestOf2NearestRangeMatcherTraitMutable methods for crate::stitching::Detail_BestOf2NearestRangeMatcher\n* Detail_BestOf2NearestRangeMatcherTraitConstConstant methods for crate::stitching::Detail_BestOf2NearestRangeMatcher\n* Detail_BlenderTraitMutable methods for crate::stitching::Detail_Blender\n* Detail_BlenderTraitConstConstant methods for crate::stitching::Detail_Blender\n* Detail_BlocksChannelsCompensatorTraitMutable methods for crate::stitching::Detail_BlocksChannelsCompensator\n* Detail_BlocksChannelsCompensatorTraitConstConstant methods for crate::stitching::Detail_BlocksChannelsCompensator\n* Detail_BlocksCompensatorTraitMutable methods for crate::stitching::Detail_BlocksCompensator\n* Detail_BlocksCompensatorTraitConstConstant methods for crate::stitching::Detail_BlocksCompensator\n* Detail_BlocksGainCompensatorTraitMutable methods for crate::stitching::Detail_BlocksGainCompensator\n* Detail_BlocksGainCompensatorTraitConstConstant methods for crate::stitching::Detail_BlocksGainCompensator\n* Detail_BundleAdjusterAffinePartialTraitMutable methods for crate::stitching::Detail_BundleAdjusterAffinePartial\n* Detail_BundleAdjusterAffinePartialTraitConstConstant methods for crate::stitching::Detail_BundleAdjusterAffinePartial\n* Detail_BundleAdjusterAffineTraitMutable methods for crate::stitching::Detail_BundleAdjusterAffine\n* Detail_BundleAdjusterAffineTraitConstConstant methods for crate::stitching::Detail_BundleAdjusterAffine\n* Detail_BundleAdjusterBaseTraitMutable methods for crate::stitching::Detail_BundleAdjusterBase\n* Detail_BundleAdjusterBaseTraitConstConstant methods for crate::stitching::Detail_BundleAdjusterBase\n* Detail_BundleAdjusterRayTraitMutable methods for crate::stitching::Detail_BundleAdjusterRay\n* Detail_BundleAdjusterRayTraitConstConstant methods for crate::stitching::Detail_BundleAdjusterRay\n* Detail_BundleAdjusterReprojTraitMutable methods for crate::stitching::Detail_BundleAdjusterReproj\n* Detail_BundleAdjusterReprojTraitConstConstant methods for crate::stitching::Detail_BundleAdjusterReproj\n* Detail_CameraParamsTraitMutable methods for crate::stitching::Detail_CameraParams\n* Detail_CameraParamsTraitConstConstant methods for crate::stitching::Detail_CameraParams\n* Detail_ChannelsCompensatorTraitMutable methods for crate::stitching::Detail_ChannelsCompensator\n* Detail_ChannelsCompensatorTraitConstConstant methods for crate::stitching::Detail_ChannelsCompensator\n* Detail_CompressedRectilinearPortraitProjectorTraitMutable methods for crate::stitching::Detail_CompressedRectilinearPortraitProjector\n* Detail_CompressedRectilinearPortraitProjectorTraitConstConstant methods for crate::stitching::Detail_CompressedRectilinearPortraitProjector\n* Detail_CompressedRectilinearPortraitWarperTraitMutable methods for crate::stitching::Detail_CompressedRectilinearPortraitWarper\n* Detail_CompressedRectilinearPortraitWarperTraitConstConstant methods for crate::stitching::Detail_CompressedRectilinearPortraitWarper\n* Detail_CompressedRectilinearProjectorTraitMutable methods for crate::stitching::Detail_CompressedRectilinearProjector\n* Detail_CompressedRectilinearProjectorTraitConstConstant methods for crate::stitching::Detail_CompressedRectilinearProjector\n* Detail_CompressedRectilinearWarperTraitMutable methods for crate::stitching::Detail_CompressedRectilinearWarper\n* Detail_CompressedRectilinearWarperTraitConstConstant methods for crate::stitching::Detail_CompressedRectilinearWarper\n* Detail_CylindricalPortraitProjectorTraitMutable methods for crate::stitching::Detail_CylindricalPortraitProjector\n* Detail_CylindricalPortraitProjectorTraitConstConstant methods for crate::stitching::Detail_CylindricalPortraitProjector\n* Detail_CylindricalPortraitWarperTraitMutable methods for crate::stitching::Detail_CylindricalPortraitWarper\n* Detail_CylindricalPortraitWarperTraitConstConstant methods for crate::stitching::Detail_CylindricalPortraitWarper\n* Detail_CylindricalProjectorTraitMutable methods for crate::stitching::Detail_CylindricalProjector\n* Detail_CylindricalProjectorTraitConstConstant methods for crate::stitching::Detail_CylindricalProjector\n* Detail_CylindricalWarperGpuTraitMutable methods for crate::stitching::Detail_CylindricalWarperGpu\n* Detail_CylindricalWarperGpuTraitConstConstant methods for crate::stitching::Detail_CylindricalWarperGpu\n* Detail_CylindricalWarperTraitMutable methods for crate::stitching::Detail_CylindricalWarper\n* Detail_CylindricalWarperTraitConstConstant methods for crate::stitching::Detail_CylindricalWarper\n* Detail_DisjointSetsTraitMutable methods for crate::stitching::Detail_DisjointSets\n* Detail_DisjointSetsTraitConstConstant methods for crate::stitching::Detail_DisjointSets\n* Detail_DpSeamFinderTraitMutable methods for crate::stitching::Detail_DpSeamFinder\n* Detail_DpSeamFinderTraitConstConstant methods for crate::stitching::Detail_DpSeamFinder\n* Detail_EstimatorTraitMutable methods for crate::stitching::Detail_Estimator\n* Detail_EstimatorTraitConstConstant methods for crate::stitching::Detail_Estimator\n* Detail_ExposureCompensatorTraitMutable methods for crate::stitching::Detail_ExposureCompensator\n* Detail_ExposureCompensatorTraitConstConstant methods for crate::stitching::Detail_ExposureCompensator\n* Detail_FeatherBlenderTraitMutable methods for crate::stitching::Detail_FeatherBlender\n* Detail_FeatherBlenderTraitConstConstant methods for crate::stitching::Detail_FeatherBlender\n* Detail_FeaturesMatcherTraitMutable methods for crate::stitching::Detail_FeaturesMatcher\n* Detail_FeaturesMatcherTraitConstConstant methods for crate::stitching::Detail_FeaturesMatcher\n* Detail_FisheyeProjectorTraitMutable methods for crate::stitching::Detail_FisheyeProjector\n* Detail_FisheyeProjectorTraitConstConstant methods for crate::stitching::Detail_FisheyeProjector\n* Detail_FisheyeWarperTraitMutable methods for crate::stitching::Detail_FisheyeWarper\n* Detail_FisheyeWarperTraitConstConstant methods for crate::stitching::Detail_FisheyeWarper\n* Detail_GainCompensatorTraitMutable methods for crate::stitching::Detail_GainCompensator\n* Detail_GainCompensatorTraitConstConstant methods for crate::stitching::Detail_GainCompensator\n* Detail_GraphCutSeamFinderBaseTraitMutable methods for crate::stitching::Detail_GraphCutSeamFinderBase\n* Detail_GraphCutSeamFinderBaseTraitConstConstant methods for crate::stitching::Detail_GraphCutSeamFinderBase\n* Detail_GraphCutSeamFinderGpuTraitMutable methods for crate::stitching::Detail_GraphCutSeamFinderGpu\n* Detail_GraphCutSeamFinderGpuTraitConstConstant methods for crate::stitching::Detail_GraphCutSeamFinderGpu\n* Detail_GraphCutSeamFinderTraitMutable methods for crate::stitching::Detail_GraphCutSeamFinder\n* Detail_GraphCutSeamFinderTraitConstConstant methods for crate::stitching::Detail_GraphCutSeamFinder\n* Detail_GraphEdgeTraitMutable methods for crate::stitching::Detail_GraphEdge\n* Detail_GraphEdgeTraitConstConstant methods for crate::stitching::Detail_GraphEdge\n* Detail_GraphTraitMutable methods for crate::stitching::Detail_Graph\n* Detail_GraphTraitConstConstant methods for crate::stitching::Detail_Graph\n* Detail_HomographyBasedEstimatorTraitMutable methods for crate::stitching::Detail_HomographyBasedEstimator\n* Detail_HomographyBasedEstimatorTraitConstConstant methods for crate::stitching::Detail_HomographyBasedEstimator\n* Detail_ImageFeaturesTraitMutable methods for crate::stitching::Detail_ImageFeatures\n* Detail_ImageFeaturesTraitConstConstant methods for crate::stitching::Detail_ImageFeatures\n* Detail_MatchesInfoTraitMutable methods for crate::stitching::Detail_MatchesInfo\n* Detail_MatchesInfoTraitConstConstant methods for crate::stitching::Detail_MatchesInfo\n* Detail_MercatorProjectorTraitMutable methods for crate::stitching::Detail_MercatorProjector\n* Detail_MercatorProjectorTraitConstConstant methods for crate::stitching::Detail_MercatorProjector\n* Detail_MercatorWarperTraitMutable methods for crate::stitching::Detail_MercatorWarper\n* Detail_MercatorWarperTraitConstConstant methods for crate::stitching::Detail_MercatorWarper\n* Detail_MultiBandBlenderTraitMutable methods for crate::stitching::Detail_MultiBandBlender\n* Detail_MultiBandBlenderTraitConstConstant methods for crate::stitching::Detail_MultiBandBlender\n* Detail_NoBundleAdjusterTraitMutable methods for crate::stitching::Detail_NoBundleAdjuster\n* Detail_NoBundleAdjusterTraitConstConstant methods for crate::stitching::Detail_NoBundleAdjuster\n* Detail_NoExposureCompensatorTraitMutable methods for crate::stitching::Detail_NoExposureCompensator\n* Detail_NoExposureCompensatorTraitConstConstant methods for crate::stitching::Detail_NoExposureCompensator\n* Detail_NoSeamFinderTraitMutable methods for crate::stitching::Detail_NoSeamFinder\n* Detail_NoSeamFinderTraitConstConstant methods for crate::stitching::Detail_NoSeamFinder\n* Detail_PairwiseSeamFinderTraitMutable methods for crate::stitching::Detail_PairwiseSeamFinder\n* Detail_PairwiseSeamFinderTraitConstConstant methods for crate::stitching::Detail_PairwiseSeamFinder\n* Detail_PaniniPortraitProjectorTraitMutable methods for crate::stitching::Detail_PaniniPortraitProjector\n* Detail_PaniniPortraitProjectorTraitConstConstant methods for crate::stitching::Detail_PaniniPortraitProjector\n* Detail_PaniniPortraitWarperTraitMutable methods for crate::stitching::Detail_PaniniPortraitWarper\n* Detail_PaniniPortraitWarperTraitConstConstant methods for crate::stitching::Detail_PaniniPortraitWarper\n* Detail_PaniniProjectorTraitMutable methods for crate::stitching::Detail_PaniniProjector\n* Detail_PaniniProjectorTraitConstConstant methods for crate::stitching::Detail_PaniniProjector\n* Detail_PaniniWarperTraitMutable methods for crate::stitching::Detail_PaniniWarper\n* Detail_PaniniWarperTraitConstConstant methods for crate::stitching::Detail_PaniniWarper\n* Detail_PlanePortraitProjectorTraitMutable methods for crate::stitching::Detail_PlanePortraitProjector\n* Detail_PlanePortraitProjectorTraitConstConstant methods for crate::stitching::Detail_PlanePortraitProjector\n* Detail_PlanePortraitWarperTraitMutable methods for crate::stitching::Detail_PlanePortraitWarper\n* Detail_PlanePortraitWarperTraitConstConstant methods for crate::stitching::Detail_PlanePortraitWarper\n* Detail_PlaneProjectorTraitMutable methods for crate::stitching::Detail_PlaneProjector\n* Detail_PlaneProjectorTraitConstConstant methods for crate::stitching::Detail_PlaneProjector\n* Detail_PlaneWarperGpuTraitMutable methods for crate::stitching::Detail_PlaneWarperGpu\n* Detail_PlaneWarperGpuTraitConstConstant methods for crate::stitching::Detail_PlaneWarperGpu\n* Detail_PlaneWarperTraitMutable methods for crate::stitching::Detail_PlaneWarper\n* Detail_PlaneWarperTraitConstConstant methods for crate::stitching::Detail_PlaneWarper\n* Detail_ProjectorBaseTraitMutable methods for crate::stitching::Detail_ProjectorBase\n* Detail_ProjectorBaseTraitConstConstant methods for crate::stitching::Detail_ProjectorBase\n* Detail_RotationWarperTraitMutable methods for crate::stitching::Detail_RotationWarper\n* Detail_RotationWarperTraitConstConstant methods for crate::stitching::Detail_RotationWarper\n* Detail_SeamFinderTraitMutable methods for crate::stitching::Detail_SeamFinder\n* Detail_SeamFinderTraitConstConstant methods for crate::stitching::Detail_SeamFinder\n* Detail_SphericalPortraitProjectorTraitMutable methods for crate::stitching::Detail_SphericalPortraitProjector\n* Detail_SphericalPortraitProjectorTraitConstConstant methods for crate::stitching::Detail_SphericalPortraitProjector\n* Detail_SphericalPortraitWarperTraitMutable methods for crate::stitching::Detail_SphericalPortraitWarper\n* Detail_SphericalPortraitWarperTraitConstConstant methods for crate::stitching::Detail_SphericalPortraitWarper\n* Detail_SphericalProjectorTraitMutable methods for crate::stitching::Detail_SphericalProjector\n* Detail_SphericalProjectorTraitConstConstant methods for crate::stitching::Detail_SphericalProjector\n* Detail_SphericalWarperGpuTraitMutable methods for crate::stitching::Detail_SphericalWarperGpu\n* Detail_SphericalWarperGpuTraitConstConstant methods for crate::stitching::Detail_SphericalWarperGpu\n* Detail_SphericalWarperTraitMutable methods for crate::stitching::Detail_SphericalWarper\n* Detail_SphericalWarperTraitConstConstant methods for crate::stitching::Detail_SphericalWarper\n* Detail_StereographicProjectorTraitMutable methods for crate::stitching::Detail_StereographicProjector\n* Detail_StereographicProjectorTraitConstConstant methods for crate::stitching::Detail_StereographicProjector\n* Detail_StereographicWarperTraitMutable methods for crate::stitching::Detail_StereographicWarper\n* Detail_StereographicWarperTraitConstConstant methods for crate::stitching::Detail_StereographicWarper\n* Detail_TransverseMercatorProjectorTraitMutable methods for crate::stitching::Detail_TransverseMercatorProjector\n* Detail_TransverseMercatorProjectorTraitConstConstant methods for crate::stitching::Detail_TransverseMercatorProjector\n* Detail_TransverseMercatorWarperTraitMutable methods for crate::stitching::Detail_TransverseMercatorWarper\n* Detail_TransverseMercatorWarperTraitConstConstant methods for crate::stitching::Detail_TransverseMercatorWarper\n* Detail_VoronoiSeamFinderTraitMutable methods for crate::stitching::Detail_VoronoiSeamFinder\n* Detail_VoronoiSeamFinderTraitConstConstant methods for crate::stitching::Detail_VoronoiSeamFinder\n* FisheyeWarperTraitMutable methods for crate::stitching::FisheyeWarper\n* FisheyeWarperTraitConstConstant methods for crate::stitching::FisheyeWarper\n* MercatorWarperTraitMutable methods for crate::stitching::MercatorWarper\n* MercatorWarperTraitConstConstant methods for crate::stitching::MercatorWarper\n* PaniniPortraitWarperTraitMutable methods for crate::stitching::PaniniPortraitWarper\n* PaniniPortraitWarperTraitConstConstant methods for crate::stitching::PaniniPortraitWarper\n* PaniniWarperTraitMutable methods for crate::stitching::PaniniWarper\n* PaniniWarperTraitConstConstant methods for crate::stitching::PaniniWarper\n* PlaneWarperGpuTraitMutable methods for crate::stitching::PlaneWarperGpu\n* PlaneWarperGpuTraitConstConstant methods for crate::stitching::PlaneWarperGpu\n* PlaneWarperTraitMutable methods for crate::stitching::PlaneWarper\n* PlaneWarperTraitConstConstant methods for crate::stitching::PlaneWarper\n* PyRotationWarperTraitMutable methods for crate::stitching::PyRotationWarper\n* PyRotationWarperTraitConstConstant methods for crate::stitching::PyRotationWarper\n* SphericalWarperGpuTraitMutable methods for crate::stitching::SphericalWarperGpu\n* SphericalWarperGpuTraitConstConstant methods for crate::stitching::SphericalWarperGpu\n* SphericalWarperTraitMutable methods for crate::stitching::SphericalWarper\n* SphericalWarperTraitConstConstant methods for crate::stitching::SphericalWarper\n* StereographicWarperTraitMutable methods for crate::stitching::StereographicWarper\n* StereographicWarperTraitConstConstant methods for crate::stitching::StereographicWarper\n* StitcherTraitMutable methods for crate::stitching::Stitcher\n* StitcherTraitConstConstant methods for crate::stitching::Stitcher\n* TransverseMercatorWarperTraitMutable methods for crate::stitching::TransverseMercatorWarper\n* TransverseMercatorWarperTraitConstConstant methods for crate::stitching::TransverseMercatorWarper\n* WarperCreatorTraitMutable methods for crate::stitching::WarperCreator\n* WarperCreatorTraitConstConstant methods for crate::stitching::WarperCreator\n\nFunctions\n---\n\n* auto_detect_wave_correct_kindTries to detect the wave correction kind depending on whether a panorama spans horizontally or vertically\n* compute_image_featuresParameters\n* compute_image_features2Parameters\n* compute_image_features2_defParameters\n* compute_image_features_defParameters\n* create_laplace_pyr\n* create_laplace_pyr_gpu\n* create_weight_map\n* find_max_spanning_tree\n* leave_biggest_component\n* matches_graph_as_string///////////////////////////////////////////////////////////////////////////\n* normalize_using_weight_map///////////////////////////////////////////////////////////////////////////\n* overlap_roi///////////////////////////////////////////////////////////////////////////\n* restore_image_from_laplace_pyr\n* restore_image_from_laplace_pyr_gpu\n* result_roi\n* result_roi_1\n* result_roi_intersection\n* result_tl\n* select_random_subset\n* stitching_log_level\n* wave_correctTries to make panorama more horizontal (or vertical).\n\nModule opencv::structured_light\n===\n\nStructured Light API\n---\n\nStructured light is considered one of the most effective techniques to acquire 3D models.\nThis technique is based on projecting a light pattern and capturing the illuminated scene from one or more points of view. Since the pattern is coded, correspondences between image points and points of the projected pattern can be quickly found and 3D information easily retrieved.\n\nOne of the most commonly exploited coding strategies is based on trmatime-multiplexing. In this case, a set of patterns are successively projected onto the measuring surface.\nThe codeword for a given pixel is usually formed by the sequence of illuminance values for that pixel across the projected patterns. Thus, the codification is called temporal because the bits of the codewords are multiplexed in time pattern .\n\nIn this module a time-multiplexing coding strategy based on Gray encoding is implemented following the\n(stereo) approach described in 3DUNDERWORLD algorithm UNDERWORLD .\nFor more details, see [tutorial_structured_light].\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* GrayCodePatternClass implementing the Gray-code pattern, based on UNDERWORLD.\n* GrayCodePattern_ParamsParameters of StructuredLightPattern constructor.\n* SinusoidalPatternClass implementing Fourier transform profilometry (FTP) , phase-shifting profilometry (PSP)\nand Fourier-assisted phase-shifting profilometry (FAPS) based on faps.\n* SinusoidalPattern_ParamsParameters of SinusoidalPattern constructor\n* StructuredLightPatternAbstract base class for generating and decoding structured light patterns.\n\nConstants\n---\n\n* DECODE_3D_UNDERWORLDK<NAME>, <NAME>. “3DUNDERWORLD-SLS: An Open-Source Structured-Light Scanning System for Rapid Geometry Acquisition”, arXiv preprint arXiv:1406.6595 (2014).\n* FAPS\n* FTP\n* PSP\n\nTraits\n---\n\n* GrayCodePatternTraitMutable methods for crate::structured_light::GrayCodePattern\n* GrayCodePatternTraitConstConstant methods for crate::structured_light::GrayCodePattern\n* GrayCodePattern_ParamsTraitMutable methods for crate::structured_light::GrayCodePattern_Params\n* GrayCodePattern_ParamsTraitConstConstant methods for crate::structured_light::GrayCodePattern_Params\n* SinusoidalPatternTraitMutable methods for crate::structured_light::SinusoidalPattern\n* SinusoidalPatternTraitConstConstant methods for crate::structured_light::SinusoidalPattern\n* SinusoidalPattern_ParamsTraitMutable methods for crate::structured_light::SinusoidalPattern_Params\n* SinusoidalPattern_ParamsTraitConstConstant methods for crate::structured_light::SinusoidalPattern_Params\n* StructuredLightPatternTraitMutable methods for crate::structured_light::StructuredLightPattern\n* StructuredLightPatternTraitConstConstant methods for crate::structured_light::StructuredLightPattern\n\nModule opencv::superres\n===\n\nSuper Resolution\n---\n\nThe Super Resolution module contains a set of functions and classes that can be used to solve the problem of resolution enhancement. There are a few methods implemented, most of them are described in the papers Farsiu03 and Mitzel09 .\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* SuperRes_BroxOpticalFlow\n* SuperRes_DenseOpticalFlowExt\n* SuperRes_DualTVL1OpticalFlow\n* SuperRes_FarnebackOpticalFlow\n* SuperRes_FrameSource\n* SuperRes_PyrLKOpticalFlow\n* SuperRes_SuperResolutionBase class for Super Resolution algorithms.\n\nTraits\n---\n\n* SuperRes_BroxOpticalFlowTraitMutable methods for crate::superres::SuperRes_BroxOpticalFlow\n* SuperRes_BroxOpticalFlowTraitConstConstant methods for crate::superres::SuperRes_BroxOpticalFlow\n* SuperRes_DenseOpticalFlowExtTraitMutable methods for crate::superres::SuperRes_DenseOpticalFlowExt\n* SuperRes_DenseOpticalFlowExtTraitConstConstant methods for crate::superres::SuperRes_DenseOpticalFlowExt\n* SuperRes_DualTVL1OpticalFlowTraitMutable methods for crate::superres::SuperRes_DualTVL1OpticalFlow\n* SuperRes_DualTVL1OpticalFlowTraitConstConstant methods for crate::superres::SuperRes_DualTVL1OpticalFlow\n* SuperRes_FarnebackOpticalFlowTraitMutable methods for crate::superres::SuperRes_FarnebackOpticalFlow\n* SuperRes_FarnebackOpticalFlowTraitConstConstant methods for crate::superres::SuperRes_FarnebackOpticalFlow\n* SuperRes_FrameSourceTraitMutable methods for crate::superres::SuperRes_FrameSource\n* SuperRes_FrameSourceTraitConstConstant methods for crate::superres::SuperRes_FrameSource\n* SuperRes_PyrLKOpticalFlowTraitMutable methods for crate::superres::SuperRes_PyrLKOpticalFlow\n* SuperRes_PyrLKOpticalFlowTraitConstConstant methods for crate::superres::SuperRes_PyrLKOpticalFlow\n* SuperRes_SuperResolutionTraitMutable methods for crate::superres::SuperRes_SuperResolution\n* SuperRes_SuperResolutionTraitConstConstant methods for crate::superres::SuperRes_SuperResolution\n\nFunctions\n---\n\n* create_frame_source_cameraC++ default parameters\n* create_frame_source_camera_defNote\n* create_frame_source_empty\n* create_frame_source_video\n* create_frame_source_video_cuda\n* create_opt_flow_brox_cuda\n* create_opt_flow_dual_tvl1\n* create_opt_flow_dual_tvl1_cuda\n* create_opt_flow_farneback\n* create_opt_flow_farneback_cuda\n* create_opt_flow_pyr_lk_cuda\n* create_super_resolution_btvl1Create Bilateral TV-L1 Super Resolution.\n* create_super_resolution_btvl1_cuda\n\nModule opencv::surface_matching\n===\n\nSurface Matching\n---\n\n### Note about the License and Patents\n\nThe following patents have been issued for methods embodied in this software: “Recognition and pose determination of 3D objects in 3D scenes using geometric point pair descriptors and the generalized Hough Transform”, <NAME>, <NAME>, EP Patent 2385483\n(Nov. 21, 2012), assignee: MVTec Software GmbH, 81675 Muenchen\n(Germany); “Recognition and pose determination of 3D objects in 3D scenes”, <NAME>, <NAME>, US Patent 8830229 (Sept.\n9, 2014), assignee: MVTec Software GmbH, 81675 Muenchen (Germany).\nFurther patents are pending. For further details, contact MVTec Software GmbH (<EMAIL>).\n\nNote that restrictions imposed by these patents (and possibly others)\nexist independently of and may be in conflict with the freedoms granted in this license, which refers to copyright of the program, not patents for any methods that it implements. Both copyright and patent law must be obeyed to legally use and redistribute this program and it is not the purpose of this license to induce you to infringe any patents or other property right claims or to contest validity of any such claims. If you redistribute or use the program, then this license merely protects you from committing copyright infringement. It does not protect you from committing patent infringement. So, before you do anything with this program, make sure that you have permission to do so not merely in terms of copyright, but also in terms of patent law.\n\nPlease note that this license is not to be understood as a guarantee either. If you use the program according to this license, but in conflict with patent law, it does not mean that the licensor will refund you for any losses that you incur if you are sued for your patent infringement.\n\n### Introduction to Surface Matching\n\nCameras and similar devices with the capability of sensation of 3D structure are becoming more common. Thus, using depth and intensity information for matching 3D objects (or parts) are of crucial importance for computer vision. Applications range from industrial control to guiding everyday actions for visually impaired people. The task in recognition and pose estimation in range images aims to identify and localize a queried 3D free-form object by matching it to the acquired database.\n\nFrom an industrial perspective, enabling robots to automatically locate and pick up randomly placed and oriented objects from a bin is an important challenge in factory automation, replacing tedious and heavy manual labor. A system should be able to recognize and locate objects with a predefined shape and estimate the position with the precision necessary for a gripping robot to pick it up.\nThis is where vision guided robotics takes the stage. Similar tools are also capable of guiding robots (and even people) through unstructured environments, leading to automated navigation. These properties make 3D matching from point clouds a ubiquitous necessity. Within this context, I will now describe the OpenCV implementation of a 3D object recognition and pose estimation algorithm using 3D features.\n\n### Surface Matching Algorithm Through 3D Features\n\nThe state of the algorithms in order to achieve the task 3D matching is heavily based on drost2010, which is one of the first and main practical methods presented in this area. The approach is composed of extracting 3D feature points randomly from depth images or generic point clouds, indexing them and later in runtime querying them efficiently. Only the 3D structure is considered, and a trivial hash table is used for feature queries.\n\nWhile being fully aware that utilization of the nice CAD model structure in order to achieve a smart point sampling, I will be leaving that aside now in order to respect the generalizability of the methods (Typically for such algorithms training on a CAD model is not needed, and a point cloud would be sufficient). Below is the outline of the entire algorithm:\n\n\n\nAs explained, the algorithm relies on the extraction and indexing of point pair features, which are defined as follows:\n\n\n\nwhere  and  are feature two selected points on the model (or scene),\n is the difference vector,  and  are the normals at  and\n. During the training stage, this vector is quantized, indexed. In the test stage, same features are extracted from the scene and compared to the database. With a few tricks like separation of the rotational components, the pose estimation part can also be made efficient (check the reference for more details). A Hough-like voting and clustering is employed to estimate the object pose. To cluster the poses, the raw pose hypotheses are sorted in decreasing order of the number of votes. From the highest vote, a new cluster is created. If the next pose hypothesis is close to one of the existing clusters, the hypothesis is added to the cluster and the cluster center is updated as the average of the pose hypotheses within the cluster. If the next hypothesis is not close to any of the clusters, it creates a new cluster. The proximity testing is done with fixed thresholds in translation and rotation. Distance computation and averaging for translation are performed in the 3D Euclidean space, while those for rotation are performed using quaternion representation. After clustering, the clusters are sorted in decreasing order of the total number of votes which determines confidence of the estimated poses.\n\nThis pose is further refined using  in order to obtain the final pose.\n\nPPF presented above depends largely on robust computation of angles between 3D vectors. Even though not reported in the paper, the naive way of doing this (\nremains numerically unstable. A better way to do this is then use inverse tangents, like:\n\n\n\n### Rough Computation of Object Pose Given PPF\n\nLet me summarize the following notation:\n\n* :  point of the model ( accordingly)\n* : Normal of the  point of the model ( accordingly)\n* :  point of the scene ( accordingly)\n* : Normal of the  point of the scene ( accordingly)\n* : The transformation required to translate  to the origin and rotate its normal  onto the -axis.\n* : Rotational component of .\n* : Translational component of .\n* :  point of the model transformed by . (\naccordingly).\n* : Axis angle representation of rotation .\n* : The angular component of the axis angle representation\n.\n\nThe transformation in a point pair feature is computed by first finding the transformation\n from the first point, and applying the same transformation to the second one.\nTransforming each point, together with the normal, to the ground plane leaves us with an angle to find out, during a comparison with a new point pair.\n\nWe could now simply start writing\n\n\n\nwhere\n\n\n\nNote that this is nothing but a stacked transformation. The translational component\n reads\n\n\n\nand the rotational being\n\n\n\nin axis angle format. Note that bold refers to the vector form. After this transformation, the feature vectors of the model are registered onto the ground plane X and the angle with respect to\n is called . Similarly, for the scene, it is called .\n\n#### Hough-like Voting Scheme\n\nAs shown in the outline, PPF (point pair features) are extracted from the model, quantized, stored in the hashtable and indexed, during the training stage. During the runtime however, the similar operation is perfomed on the input scene with the exception that this time a similarity lookup over the hashtable is performed, instead of an insertion. This lookup also allows us to compute a transformation to the ground plane for the scene pairs. After this point, computing the rotational component of the pose reduces to computation of the difference . This component carries the cue about the object pose. A Hough-like voting scheme is performed over the local model coordinate vector and . The highest poses achieved for every scene point lets us recover the object pose.\n\n#### Source Code for PPF Matching\n```\n// pc is the loaded point cloud of the model\n// (Nx6) and pcTest is a loaded point cloud of\n// the scene (Mx6)\nppf_match_3d::PPF3DDetector detector(0.03, 0.05);\ndetector.trainModel(pc);\nvector<Pose3DPtr> results;\ndetector.match(pcTest, results, 1.0/10.0, 0.05);\ncout << \"Poses: \" << endl;\n// print the poses for (size_t i=0; i<results.size(); i++)\n{\n Pose3DPtr pose = results[i];\n cout << \"Pose Result \" << i << endl;\n pose->printPose();\n}\n```\n### Pose Registration via ICP\n\nThe matching process terminates with the attainment of the pose. However, due to the multiple matching points, erroneous hypothesis, pose averaging and etc. such pose is very open to noise and many times is far from being perfect. Although the visual results obtained in that stage are pleasing, the quantitative evaluation shows  degrees variation (error), which is an acceptable level of matching. Many times, the requirement might be set well beyond this margin and it is desired to refine the computed pose.\n\nFurthermore, in typical RGBD scenes and point clouds, 3D structure can capture only less than half of the model due to the visibility in the scene. Therefore, a robust pose refinement algorithm,\nwhich can register occluded and partially visible shapes quickly and correctly is not an unrealistic wish.\n\nAt this point, a trivial option would be to use the well known iterative closest point algorithm .\nHowever, utilization of the basic ICP leads to slow convergence, bad registration, outlier sensitivity and failure to register partial shapes. Thus, it is definitely not suited to the problem. For this reason, many variants have been proposed . Different variants contribute to different stages of the pose estimation process.\n\nICP is composed of  stages and the improvements I propose for each stage is summarized below.\n\n#### Sampling\n\nTo improve convergence speed and computation time, it is common to use less points than the model actually has. However, sampling the correct points to register is an issue in itself. The naive way would be to sample uniformly and hope to get a reasonable subset. More smarter ways try to identify the critical points, which are found to highly contribute to the registration process. Gelfand et.\nal. exploit the covariance matrix in order to constrain the eigenspace, so that a set of points which affect both translation and rotation are used. This is a clever way of subsampling, which I will optionally be using in the implementation.\n\n#### Correspondence Search\n\nAs the name implies, this step is actually the assignment of the points in the data and the model in a closest point fashion. Correct assignments will lead to a correct pose, where wrong assignments strongly degrade the result. In general, KD-trees are used in the search of nearest neighbors, to increase the speed. However this is not an optimality guarantee and many times causes wrong points to be matched. Luckily the assignments are corrected over iterations.\n\nTo overcome some of the limitations, Picky ICP pickyicp and BC-ICP (ICP using bi-unique correspondences) are two well-known methods. Picky ICP first finds the correspondences in the old-fashioned way and then among the resulting corresponding pairs, if more than one scene point\n is assigned to the same model point , it selects  that corresponds to the minimum distance. BC-ICP on the other hand, allows multiple correspondences first and then resolves the assignments by establishing bi-unique correspondences. It also defines a novel no-correspondence outlier, which intrinsically eases the process of identifying outliers.\n\nFor reference, both methods are used. Because P-ICP is a bit faster, with not-so-significant performance drawback, it will be the method of choice in refinment of correspondences.\n\n#### Weighting of Pairs\n\nIn my implementation, I currently do not use a weighting scheme. But the common approaches involve\n*normal compatibility* () or assigning lower weights to point pairs with greater distances ().\n\n#### Rejection of Pairs\n\nThe rejections are done using a dynamic thresholding based on a robust estimate of the standard deviation. In other words, in each iteration, I find the MAD estimate of the Std. Dev. I denote this as . I reject the pairs with distances . Here  is the threshold of rejection and by default set to . The weighting is applied prior to Picky refinement, explained in the previous stage.\n\n#### Error Metric\n\nAs described in , a linearization of point to plane as in koklimlow error metric is used. This both speeds up the registration process and improves convergence.\n\n#### Minimization\n\nEven though many non-linear optimizers (such as Levenberg Mardquardt) are proposed, due to the linearization in the previous step, pose estimation reduces to solving a linear system of equations.\nThis is what I do exactly using cv::solve with DECOMP_SVD option.\n\n#### ICP Algorithm\n\nHaving described the steps above, here I summarize the layout of the ICP algorithm.\n\n##### Efficient ICP Through Point Cloud Pyramids\n\nWhile the up-to-now-proposed variants deal well with some outliers and bad initializations, they require significant number of iterations. Yet, multi-resolution scheme can help reducing the number of iterations by allowing the registration to start from a coarse level and propagate to the lower and finer levels. Such approach both improves the performances and enhances the runtime.\n\nThe search is done through multiple levels, in a hierarchical fashion. The registration starts with a very coarse set of samples of the model. Iteratively, the points are densified and sought. After each iteration the previously estimated pose is used as an initial pose and refined with the ICP.\n\n##### Visual Results\n\n###### Results on Synthetic Data\n\nIn all of the results, the pose is initiated by PPF and the rest is left as:\n\n\n#### Source Code for Pose Refinement Using ICP\n```\nICP icp(200, 0.001f, 2.5f, 8);\n// Using the previously declared pc and pcTest\n// This will perform registration for every pose\n// contained in results icp.registerModelToScene(pc, pcTest, results);\n \n// results now contain the refined poses\n```\n### Results\n\nThis section is dedicated to the results of surface matching (point-pair-feature matching and a following ICP refinement):\n\n\n\nMatches of different models for Mian dataset is presented below:\n\n\n\nYou might checkout the video on youTube here.\n\n### A Complete Sample\n\n#### Parameter Tuning\n\nSurface matching module treats its parameters relative to the model diameter (diameter of the axis parallel bounding box), whenever it can. This makes the parameters independent from the model size.\nThis is why, both model and scene cloud were subsampled such that all points have a minimum distance of , where  is the distance along a given dimension. All three dimensions are sampled in similar manner. For example, if\n is set to 0.05 and the diameter of model is 1m (1000mm), the points sampled from the object’s surface will be approximately 50 mm apart. From another point of view, if the sampling RelativeSamplingStep is set to 0.05, at most  model points are generated\n(depending on how the model fills in the volume). Consequently this results in at most 8000x8000 pairs. In practice, because the models are not uniformly distributed over a rectangular prism, much less points are to be expected. Decreasing this value, results in more model points and thus a more accurate representation. However, note that number of point pair features to be computed is now quadratically increased as the complexity is O(N^2). This is especially a concern for 32 bit systems, where large models can easily overshoot the available memory. Typically, values in the range of 0.025 - 0.05 seem adequate for most of the applications, where the default value is 0.03.\n(Note that there is a difference in this paremeter with the one presented in drost2010 . In drost2010 a uniform cuboid is used for quantization and model diameter is used for reference of sampling. In my implementation, the cuboid is a rectangular prism, and each dimension is quantized independently. I do not take reference from the diameter but along the individual dimensions.\n\nIt would very wise to remove the outliers from the model and prepare an ideal model initially. This is because, the outliers directly affect the relative computations and degrade the matching accuracy.\n\nDuring runtime stage, the scene is again sampled by , as described above.\nHowever this time, only a portion of the scene points are used as reference. This portion is controlled by the parameter , where\n. In other words, if the\n, the subsampled scene will once again be uniformly sampled to 1/5 of the number of points. Maximum value of this parameter is 1 and increasing this parameter also increases the stability, but decreases the speed. Again, because of the initial scene-independent relative sampling, fine tuning this parameter is not a big concern. This would only be an issue when the model shape occupies a volume uniformly, or when the model shape is condensed in a tiny place within the quantization volume (e.g. The octree representation would have too much empty cells).\n\n acts as a step of discretization over the hash table. The point pair features are quantized to be mapped to the buckets of the hashtable. This discretization involves a multiplication and a casting to the integer. Adjusting RelativeDistanceStep in theory controls the collision rate. Note that, more collisions on the hashtable results in less accurate estimations.\nReducing this parameter increases the affect of quantization but starts to assign non-similar point pairs to the same bins. Increasing it however, wanes the ability to group the similar pairs.\nGenerally, because during the sampling stage, the training model points are selected uniformly with a distance controlled by RelativeSamplingStep, RelativeDistanceStep is expected to equate to this value. Yet again, values in the range of 0.025-0.05 are sensible. This time however, when the model is dense, it is not advised to decrease this value. For noisy scenes, the value can be increased to improve the robustness of the matching against noisy points.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ICPThis class implements a very efficient and robust variant of the iterative closest point (ICP) algorithm.\nThe task is to register a 3D model (or point cloud) against a set of noisy target data. The variants are put together by myself after certain tests. The task is to be able to match partial, noisy point clouds in cluttered scenes, quickly.\nYou will find that my emphasis is on the performance, while retaining the accuracy.\nThis implementation is based on Tolga Birdal’s MATLAB implementation in here:\nhttp://www.mathworks.com/matlabcentral/fileexchange/47152-icp-registration-using-efficient-variants-and-multi-resolution-scheme The main contributions come from:\n* PPF3DDetectorClass, allowing the load and matching 3D models.\nTypical Use:\n* Pose3DClass, allowing the storage of a pose. The data structure stores both the quaternions and the matrix forms. It supports IO functionality together with various helper methods to work with poses\n* PoseCluster3DWhen multiple poses (see Pose3D) are grouped together (contribute to the same transformation)\npose clusters occur. This class is a general container for such groups of poses. It is possible to store,\nload and perform IO on these poses.\n\nConstants\n---\n\n* ICP_ICP_SAMPLING_TYPE_GELFAND\n* ICP_ICP_SAMPLING_TYPE_UNIFORM\n\nTraits\n---\n\n* ICPTraitMutable methods for crate::surface_matching::ICP\n* ICPTraitConstConstant methods for crate::surface_matching::ICP\n* PPF3DDetectorTraitMutable methods for crate::surface_matching::PPF3DDetector\n* PPF3DDetectorTraitConstConstant methods for crate::surface_matching::PPF3DDetector\n* Pose3DTraitMutable methods for crate::surface_matching::Pose3D\n* Pose3DTraitConstConstant methods for crate::surface_matching::Pose3D\n* PoseCluster3DTraitMutable methods for crate::surface_matching::PoseCluster3D\n* PoseCluster3DTraitConstConstant methods for crate::surface_matching::PoseCluster3D\n\nType Aliases\n---\n\n* Pose3DPtr\n* PoseCluster3DPtr\n* key_type\n\nModule opencv::text\n===\n\nScene Text Detection and Recognition\n---\n\nThe opencv_text module provides different algorithms for text detection and recognition in natural scene images.\n\nScene Text Detection\n---\n\n### Class-specific Extremal Regions for Scene Text Detection\n\nThe scene text detection algorithm described below has been initially proposed by <NAME> &\n<NAME>. The main idea behind Class-specific Extremal Regions is similar to the MSER in that suitable Extremal Regions (ERs) are selected from the whole component tree of the image.\nHowever, this technique differs from MSER in that selection of suitable ERs is done by a sequential classifier trained for character detection, i.e. dropping the stability requirement of MSERs and selecting class-specific (not necessarily stable) regions.\n\nThe component tree of an image is constructed by thresholding by an increasing value step-by-step from 0 to 255 and then linking the obtained connected components from successive levels in a hierarchy by their inclusion relation:\n\n\n\nThe component tree may contain a huge number of regions even for a very simple image as shown in the previous image. This number can easily reach the order of 1 x 10^6 regions for an average 1 Megapixel image. In order to efficiently select suitable regions among all the ERs the algorithm make use of a sequential classifier with two differentiated stages.\n\nIn the first stage incrementally computable descriptors (area, perimeter, bounding box, and Euler’s number) are computed (in O(1)) for each region r and used as features for a classifier which estimates the class-conditional probability p(r|character). Only the ERs which correspond to local maximum of the probability p(r|character) are selected (if their probability is above a global limit p_min and the difference between local maximum and local minimum is greater than a delta_min value).\n\nIn the second stage, the ERs that passed the first stage are classified into character and non-character classes using more informative but also more computationally expensive features. (Hole area ratio, convex hull ratio, and the number of outer boundary inflexion points).\n\nThis ER filtering process is done in different single-channel projections of the input image in order to increase the character localization recall.\n\nAfter the ER filtering is done on each input channel, character candidates must be grouped in high-level text blocks (i.e. words, text lines, paragraphs, …). The opencv_text module implements two different grouping algorithms: the Exhaustive Search algorithm proposed in Neumann12 for grouping horizontally aligned text, and the method proposed by <NAME> and <NAME> in Gomez13 Gomez14 for grouping arbitrary oriented text (see erGrouping).\n\nTo see the text detector at work, have a look at the textdetection demo:\nhttps://github.com/opencv/opencv_contrib/blob/master/modules/text/samples/textdetection.cpp\n\nScene Text Recognition\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BaseOCR\n* ERFilterBase class for 1st and 2nd stages of Neumann and Matas scene text detection algorithm Neumann12. :\n* ERFilter_CallbackCallback with the classifier is made a class.\n* ERStatThe ERStat structure represents a class-specific Extremal Region (ER).\n* OCRBeamSearchDecoderOCRBeamSearchDecoder class provides an interface for OCR using Beam Search algorithm.\n* OCRBeamSearchDecoder_ClassifierCallbackCallback with the character classifier is made a class.\n* OCRHMMDecoderOCRHMMDecoder class provides an interface for OCR using Hidden Markov Models.\n* OCRHMMDecoder_ClassifierCallbackCallback with the character classifier is made a class.\n* OCRHolisticWordRecognizerOCRHolisticWordRecognizer class provides the functionallity of segmented wordspotting.\nGiven a predefined vocabulary , a DictNet is employed to select the most probable word given an input image.\n* OCRTesseractOCRTesseract class provides an interface with the tesseract-ocr API (v3.02.02) in C++.\n* TextDetectorAn abstract class providing interface for text detection algorithms\n* TextDetectorCNNTextDetectorCNN class provides the functionallity of text bounding box detection.\nThis class is representing to find bounding boxes of text words given an input image.\nThis class uses OpenCV dnn module to load pre-trained model described in LiaoSBWL17.\nThe original repository with the modified SSD Caffe version: https://github.com/MhLiao/TextBoxes.\nModel can be downloaded from DropBox.\nModified .prototxt file with the model description can be found in `opencv_contrib/modules/text/samples/textbox.prototxt`.\n\nEnums\n---\n\n* classifier_type\n* decoder_mode\n* erGrouping_Modestext::erGrouping operation modes\n* ocr_engine_modeTesseract.OcrEngineMode Enumeration\n* page_seg_modeTesseract.PageSegMode Enumeration\n\nConstants\n---\n\n* ERFILTER_NM_IHSGrad\n* ERFILTER_NM_RGBLGrad\n* ERGROUPING_ORIENTATION_ANYText grouping method proposed in Gomez13 Gomez14 for grouping arbitrary oriented text. Regions are agglomerated by Single Linkage Clustering in a weighted feature space that combines proximity\n(x,y coordinates) and similarity measures (color, size, gradient magnitude, stroke width, etc.).\nSLC provides a dendrogram where each node represents a text group hypothesis. Then the algorithm finds the branches corresponding to text groups by traversing this dendrogram with a stopping rule that combines the output of a rotation invariant text group classifier and a probabilistic measure for hierarchical clustering validity assessment.\n* ERGROUPING_ORIENTATION_HORIZExhaustive Search algorithm proposed in Neumann11 for grouping horizontally aligned text.\nThe algorithm models a verification function for all the possible ER sequences. The verification fuction for ER pairs consists in a set of threshold-based pairwise rules which compare measurements of two regions (height ratio, centroid angle, and region distance). The verification function for ER triplets creates a word text line estimate using Least Median-Squares fitting for a given triplet and then verifies that the estimate is valid (based on thresholds created during training). Verification functions for sequences larger than 3 are approximated by verifying that the text line parameters of all (sub)sequences of length 3 are consistent.\n* OCR_CNN_CLASSIFIER\n* OCR_DECODER_VITERBI\n* OCR_KNN_CLASSIFIER\n* OCR_LEVEL_TEXTLINE\n* OCR_LEVEL_WORD\n* OEM_CUBE_ONLY\n* OEM_DEFAULT\n* OEM_TESSERACT_CUBE_COMBINED\n* OEM_TESSERACT_ONLY\n* PSM_AUTO\n* PSM_AUTO_ONLY\n* PSM_AUTO_OSD\n* PSM_CIRCLE_WORD\n* PSM_OSD_ONLY\n* PSM_SINGLE_BLOCK\n* PSM_SINGLE_BLOCK_VERT_TEXT\n* PSM_SINGLE_CHAR\n* PSM_SINGLE_COLUMN\n* PSM_SINGLE_LINE\n* PSM_SINGLE_WORD\n\nTraits\n---\n\n* BaseOCRTraitMutable methods for crate::text::BaseOCR\n* BaseOCRTraitConstConstant methods for crate::text::BaseOCR\n* ERFilterTraitMutable methods for crate::text::ERFilter\n* ERFilterTraitConstConstant methods for crate::text::ERFilter\n* ERFilter_CallbackTraitMutable methods for crate::text::ERFilter_Callback\n* ERFilter_CallbackTraitConstConstant methods for crate::text::ERFilter_Callback\n* ERStatTraitMutable methods for crate::text::ERStat\n* ERStatTraitConstConstant methods for crate::text::ERStat\n* OCRBeamSearchDecoderTraitMutable methods for crate::text::OCRBeamSearchDecoder\n* OCRBeamSearchDecoderTraitConstConstant methods for crate::text::OCRBeamSearchDecoder\n* OCRBeamSearchDecoder_ClassifierCallbackTraitMutable methods for crate::text::OCRBeamSearchDecoder_ClassifierCallback\n* OCRBeamSearchDecoder_ClassifierCallbackTraitConstConstant methods for crate::text::OCRBeamSearchDecoder_ClassifierCallback\n* OCRHMMDecoderTraitMutable methods for crate::text::OCRHMMDecoder\n* OCRHMMDecoderTraitConstConstant methods for crate::text::OCRHMMDecoder\n* OCRHMMDecoder_ClassifierCallbackTraitMutable methods for crate::text::OCRHMMDecoder_ClassifierCallback\n* OCRHMMDecoder_ClassifierCallbackTraitConstConstant methods for crate::text::OCRHMMDecoder_ClassifierCallback\n* OCRHolisticWordRecognizerTraitMutable methods for crate::text::OCRHolisticWordRecognizer\n* OCRHolisticWordRecognizerTraitConstConstant methods for crate::text::OCRHolisticWordRecognizer\n* OCRTesseractTraitMutable methods for crate::text::OCRTesseract\n* OCRTesseractTraitConstConstant methods for crate::text::OCRTesseract\n* TextDetectorCNNTraitMutable methods for crate::text::TextDetectorCNN\n* TextDetectorCNNTraitConstConstant methods for crate::text::TextDetectorCNN\n* TextDetectorTraitMutable methods for crate::text::TextDetector\n* TextDetectorTraitConstConstant methods for crate::text::TextDetector\n\nFunctions\n---\n\n* compute_nm_channelsCompute the different channels to be processed independently in the N&M algorithm Neumann12.\n* compute_nm_channels_defCompute the different channels to be processed independently in the N&M algorithm Neumann12.\n* create_er_filter_nm1Create an Extremal Region Filter for the 1st stage classifier of N&M algorithm Neumann12.\n* create_er_filter_nm1_defCreate an Extremal Region Filter for the 1st stage classifier of N&M algorithm Neumann12.\n* create_er_filter_nm1_from_fileReads an Extremal Region Filter for the 1st stage classifier of N&M algorithm from the provided path e.g. /path/to/cpp/trained_classifierNM1.xml\n* create_er_filter_nm1_from_file_defReads an Extremal Region Filter for the 1st stage classifier of N&M algorithm from the provided path e.g. /path/to/cpp/trained_classifierNM1.xml\n* create_er_filter_nm2Create an Extremal Region Filter for the 2nd stage classifier of N&M algorithm Neumann12.\n* create_er_filter_nm2_defCreate an Extremal Region Filter for the 2nd stage classifier of N&M algorithm Neumann12.\n* create_er_filter_nm2_from_fileReads an Extremal Region Filter for the 2nd stage classifier of N&M algorithm from the provided path e.g. /path/to/cpp/trained_classifierNM2.xml\n* create_er_filter_nm2_from_file_defReads an Extremal Region Filter for the 2nd stage classifier of N&M algorithm from the provided path e.g. /path/to/cpp/trained_classifierNM2.xml\n* create_ocrhmm_transitions_tableUtility function to create a tailored language model transitions table from a given list of words (lexicon).\n* create_ocrhmm_transitions_table_1\n* detect_regions\n* detect_regions_from_fileExtracts text regions from image.\n* detect_regions_from_file_defExtracts text regions from image.\n* detect_text_swtApplies the Stroke Width Transform operator followed by filtering of connected components of similar Stroke Widths to return letter candidates. It also chain them by proximity and size, saving the result in chainBBs.\n* detect_text_swt_defApplies the Stroke Width Transform operator followed by filtering of connected components of similar Stroke Widths to return letter candidates. It also chain them by proximity and size, saving the result in chainBBs.\n* er_groupingFind groups of Extremal Regions that are organized as text blocks.\n* er_grouping_1C++ default parameters\n* er_grouping_1_defNote\n* er_grouping_defFind groups of Extremal Regions that are organized as text blocks.\n* load_classifier_nm1Allow to implicitly load the default classifier when creating an ERFilter object.\n* load_classifier_nm2Allow to implicitly load the default classifier when creating an ERFilter object.\n* load_ocr_beam_search_classifier_cnnAllow to implicitly load the default character classifier when creating an OCRBeamSearchDecoder object.\n* load_ocrhmm_classifierAllow to implicitly load the default character classifier when creating an OCRHMMDecoder object.\n* load_ocrhmm_classifier_cnnDeprecatedAllow to implicitly load the default character classifier when creating an OCRHMMDecoder object.\n* load_ocrhmm_classifier_nmDeprecatedAllow to implicitly load the default character classifier when creating an OCRHMMDecoder object.\n* mse_rs_to_er_statsConverts MSER contours (vector<Point>) to ERStat regions.\n\nModule opencv::tracking\n===\n\nTracking API\n---\n\nTracking API implementation details\n---\n\nLegacy Tracking API\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* TrackerCSRTthe CSRT tracker\n* TrackerCSRT_Params\n* TrackerKCFthe KCF (Kernelized Correlation Filter) tracker\n* TrackerKCF_Params\n\nEnums\n---\n\n* TrackerKCF_MODE\\brief Feature type to be used in the tracking grayscale, colornames, compressed color-names The modes available now:\n\nConstants\n---\n\n* TrackerKCF_CN\n* TrackerKCF_CUSTOM\n* TrackerKCF_GRAY\n\nTraits\n---\n\n* TrackerCSRTTraitMutable methods for crate::tracking::TrackerCSRT\n* TrackerCSRTTraitConstConstant methods for crate::tracking::TrackerCSRT\n* TrackerCSRT_ParamsTraitMutable methods for crate::tracking::TrackerCSRT_Params\n* TrackerCSRT_ParamsTraitConstConstant methods for crate::tracking::TrackerCSRT_Params\n* TrackerKCFTraitMutable methods for crate::tracking::TrackerKCF\n* TrackerKCFTraitConstConstant methods for crate::tracking::TrackerKCF\n\nType Aliases\n---\n\n* TrackerKCF_FeatureExtractorCallbackFN\n\nModule opencv::video\n===\n\nVideo Analysis\n---\n\nMotion Analysis\n---\n\nObject Tracking\n---\n\nC API\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* BackgroundSubtractorBase class for background/foreground segmentation. :\n* BackgroundSubtractorKNNK-nearest neighbours - based Background/Foreground Segmentation Algorithm.\n* BackgroundSubtractorMOG2Gaussian Mixture-based Background/Foreground Segmentation Algorithm.\n* DISOpticalFlowDIS optical flow algorithm.\n* DenseOpticalFlowBase class for dense optical flow algorithms\n* FarnebackOpticalFlowClass computing a dense optical flow using the Gunnar Farneback’s algorithm.\n* KalmanFilterKalman filter class.\n* SparseOpticalFlowBase interface for sparse optical flow algorithms.\n* SparsePyrLKOpticalFlowClass used for calculating a sparse optical flow.\n* TrackerBase abstract class for the long-term tracker\n* TrackerDaSiamRPN\n* TrackerDaSiamRPN_Params\n* TrackerGOTURNthe GOTURN (Generic Object Tracking Using Regression Networks) tracker\n* TrackerGOTURN_Params\n* TrackerMILThe MIL algorithm trains a classifier in an online manner to separate the object from the background.\n* TrackerMIL_Params\n* TrackerNanothe Nano tracker is a super lightweight dnn-based general object tracking.\n* TrackerNano_Params\n* VariationalRefinementVariational optical flow refinement\n\nConstants\n---\n\n* DISOpticalFlow_PRESET_FAST\n* DISOpticalFlow_PRESET_MEDIUM\n* DISOpticalFlow_PRESET_ULTRAFAST\n* MOTION_AFFINE\n* MOTION_EUCLIDEAN\n* MOTION_HOMOGRAPHY\n* MOTION_TRANSLATION\n* OPTFLOW_FARNEBACK_GAUSSIAN\n* OPTFLOW_LK_GET_MIN_EIGENVALS\n* OPTFLOW_USE_INITIAL_FLOW\n\nTraits\n---\n\n* BackgroundSubtractorKNNTraitMutable methods for crate::video::BackgroundSubtractorKNN\n* BackgroundSubtractorKNNTraitConstConstant methods for crate::video::BackgroundSubtractorKNN\n* BackgroundSubtractorMOG2TraitMutable methods for crate::video::BackgroundSubtractorMOG2\n* BackgroundSubtractorMOG2TraitConstConstant methods for crate::video::BackgroundSubtractorMOG2\n* BackgroundSubtractorTraitMutable methods for crate::video::BackgroundSubtractor\n* BackgroundSubtractorTraitConstConstant methods for crate::video::BackgroundSubtractor\n* DISOpticalFlowTraitMutable methods for crate::video::DISOpticalFlow\n* DISOpticalFlowTraitConstConstant methods for crate::video::DISOpticalFlow\n* DenseOpticalFlowTraitMutable methods for crate::video::DenseOpticalFlow\n* DenseOpticalFlowTraitConstConstant methods for crate::video::DenseOpticalFlow\n* FarnebackOpticalFlowTraitMutable methods for crate::video::FarnebackOpticalFlow\n* FarnebackOpticalFlowTraitConstConstant methods for crate::video::FarnebackOpticalFlow\n* KalmanFilterTraitMutable methods for crate::video::KalmanFilter\n* KalmanFilterTraitConstConstant methods for crate::video::KalmanFilter\n* SparseOpticalFlowTraitMutable methods for crate::video::SparseOpticalFlow\n* SparseOpticalFlowTraitConstConstant methods for crate::video::SparseOpticalFlow\n* SparsePyrLKOpticalFlowTraitMutable methods for crate::video::SparsePyrLKOpticalFlow\n* SparsePyrLKOpticalFlowTraitConstConstant methods for crate::video::SparsePyrLKOpticalFlow\n* TrackerDaSiamRPNTraitMutable methods for crate::video::TrackerDaSiamRPN\n* TrackerDaSiamRPNTraitConstConstant methods for crate::video::TrackerDaSiamRPN\n* TrackerDaSiamRPN_ParamsTraitMutable methods for crate::video::TrackerDaSiamRPN_Params\n* TrackerDaSiamRPN_ParamsTraitConstConstant methods for crate::video::TrackerDaSiamRPN_Params\n* TrackerGOTURNTraitMutable methods for crate::video::TrackerGOTURN\n* TrackerGOTURNTraitConstConstant methods for crate::video::TrackerGOTURN\n* TrackerGOTURN_ParamsTraitMutable methods for crate::video::TrackerGOTURN_Params\n* TrackerGOTURN_ParamsTraitConstConstant methods for crate::video::TrackerGOTURN_Params\n* TrackerMILTraitMutable methods for crate::video::TrackerMIL\n* TrackerMILTraitConstConstant methods for crate::video::TrackerMIL\n* TrackerNanoTraitMutable methods for crate::video::TrackerNano\n* TrackerNanoTraitConstConstant methods for crate::video::TrackerNano\n* TrackerNano_ParamsTraitMutable methods for crate::video::TrackerNano_Params\n* TrackerNano_ParamsTraitConstConstant methods for crate::video::TrackerNano_Params\n* TrackerTraitMutable methods for crate::video::Tracker\n* TrackerTraitConstConstant methods for crate::video::Tracker\n* VariationalRefinementTraitMutable methods for crate::video::VariationalRefinement\n* VariationalRefinementTraitConstConstant methods for crate::video::VariationalRefinement\n\nFunctions\n---\n\n* build_optical_flow_pyramidConstructs the image pyramid which can be passed to calcOpticalFlowPyrLK.\n* build_optical_flow_pyramid_defConstructs the image pyramid which can be passed to calcOpticalFlowPyrLK.\n* calc_optical_flow_farnebackComputes a dense optical flow using the Gunnar Farneback’s algorithm.\n* calc_optical_flow_pyr_lkCalculates an optical flow for a sparse feature set using the iterative Lucas-Kanade method with pyramids.\n* calc_optical_flow_pyr_lk_defCalculates an optical flow for a sparse feature set using the iterative Lucas-Kanade method with pyramids.\n* cam_shiftFinds an object center, size, and orientation.\n* compute_eccComputes the Enhanced Correlation Coefficient value between two images EP08 .\n* compute_ecc_defComputes the Enhanced Correlation Coefficient value between two images EP08 .\n* create_background_subtractor_knnCreates KNN Background Subtractor\n* create_background_subtractor_knn_defCreates KNN Background Subtractor\n* create_background_subtractor_mog2Creates MOG2 Background Subtractor\n* create_background_subtractor_mog2_defCreates MOG2 Background Subtractor\n* estimate_rigid_transformDeprecatedComputes an optimal affine transformation between two 2D point sets.\n* find_transform_eccFinds the geometric transform (warp) between two images in terms of the ECC criterion EP08 .\n* find_transform_ecc_1Finds the geometric transform (warp) between two images in terms of the ECC criterion EP08 .\n* find_transform_ecc_1_def@overload\n* mean_shiftFinds an object on a back projection image.\n* read_optical_flowRead a .flo file\n* write_optical_flowWrite a .flo to disk\n\nModule opencv::videoio\n===\n\nVideo I/O\n---\n\nRead and write video or images sequence with OpenCV\n\n#### See also:\n\n* [videoio_overview]\n* Tutorials: [tutorial_table_of_content_app]Flags for video I/O\n---\n\nAdditional flags for video I/O API backends\n---\n\nHardware-accelerated video decoding and encoding\n---\n\nC API for video I/O\n---\n\niOS glue for video I/O\n---\n\nWinRT glue for video I/O\n---\n\nQuery I/O API backends registry\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* VideoCaptureClass for video capturing from video files, image sequences or cameras.\n* VideoWriterVideo writer class.\n\nEnums\n---\n\n* VideoAccelerationTypeVideo Acceleration type\n* VideoCaptureAPIscv::VideoCapture API backends identifier.\n* VideoCaptureOBSensorDataTypeOBSENSOR (for Orbbec 3D-Sensor device/module )\n* VideoCaptureOBSensorGeneratorsOBSENSOR stream generator\n* VideoCaptureOBSensorPropertiesOBSENSOR properties\n* VideoCapturePropertiescv::VideoCapture generic properties identifier.\n* VideoWriterPropertiescv::VideoWriter generic properties identifier.\n\nConstants\n---\n\n* CAP_ANDROIDAndroid - not used\n* CAP_ANYAuto detect == 0\n* CAP_ARAVISAravis SDK\n* CAP_AVFOUNDATIONAVFoundation framework for iOS (OS X Lion will have the same API)\n* CAP_CMU1394Same value as CAP_FIREWIRE\n* CAP_DC1394Same value as CAP_FIREWIRE\n* CAP_DSHOWDirectShow (via videoInput)\n* CAP_FFMPEGOpen and record video file or stream using the FFMPEG library\n* CAP_FIREWARESame value as CAP_FIREWIRE\n* CAP_FIREWIREIEEE 1394 drivers\n* CAP_GIGANETIXSmartek Giganetix GigEVisionSDK\n* CAP_GPHOTO2gPhoto2 connection\n* CAP_GSTREAMERGStreamer\n* CAP_IEEE1394Same value as CAP_FIREWIRE\n* CAP_IMAGESOpenCV Image Sequence (e.g. img_%02d.jpg)\n* CAP_INTELPERCRealSense (former Intel Perceptual Computing SDK)\n* CAP_INTELPERC_DEPTH_GENERATOR\n* CAP_INTELPERC_DEPTH_MAPEach pixel is a 16-bit integer. The value indicates the distance from an object to the camera’s XY plane or the Cartesian depth.\n* CAP_INTELPERC_GENERATORS_MASK\n* CAP_INTELPERC_IMAGE\n* CAP_INTELPERC_IMAGE_GENERATOR\n* CAP_INTELPERC_IR_GENERATOR\n* CAP_INTELPERC_IR_MAPEach pixel is a 16-bit integer. The value indicates the intensity of the reflected laser beam.\n* CAP_INTELPERC_UVDEPTH_MAPEach pixel contains two 32-bit floating point values in the range of 0-1, representing the mapping of depth coordinates to the color coordinates.\n* CAP_INTEL_MFXIntel MediaSDK\n* CAP_MSMFMicrosoft Media Foundation (via videoInput). See platform specific notes above.\n* CAP_OBSENSORFor Orbbec 3D-Sensor device/module (Astra+, Femto)\n* CAP_OBSENSOR_BGR_IMAGEData given from BGR stream generator\n* CAP_OBSENSOR_DEPTH_GENERATOR\n* CAP_OBSENSOR_DEPTH_MAPDepth values in mm (CV_16UC1)\n* CAP_OBSENSOR_GENERATORS_MASK\n* CAP_OBSENSOR_IMAGE_GENERATOR\n* CAP_OBSENSOR_IR_GENERATOR\n* CAP_OBSENSOR_IR_IMAGEData given from IR stream generator(CV_16UC1)\n* CAP_OPENCV_MJPEGBuilt-in OpenCV MotionJPEG codec\n* CAP_OPENNIOpenNI (for Kinect)\n* CAP_OPENNI2OpenNI2 (for Kinect)\n* CAP_OPENNI2_ASTRAOpenNI2 (for Orbbec Astra)\n* CAP_OPENNI2_ASUSOpenNI2 (for Asus Xtion and Occipital Structure sensors)\n* CAP_OPENNI_ASUSOpenNI (for Asus Xtion)\n* CAP_OPENNI_BGR_IMAGEData given from RGB image generator\n* CAP_OPENNI_DEPTH_GENERATOR\n* CAP_OPENNI_DEPTH_GENERATOR_BASELINE\n* CAP_OPENNI_DEPTH_GENERATOR_FOCAL_LENGTH\n* CAP_OPENNI_DEPTH_GENERATOR_PRESENT\n* CAP_OPENNI_DEPTH_GENERATOR_REGISTRATION\n* CAP_OPENNI_DEPTH_GENERATOR_REGISTRATION_ON\n* CAP_OPENNI_DEPTH_MAPDepth values in mm (CV_16UC1)\n* CAP_OPENNI_DISPARITY_MAPDisparity in pixels (CV_8UC1)\n* CAP_OPENNI_DISPARITY_MAP_32FDisparity in pixels (CV_32FC1)\n* CAP_OPENNI_GENERATORS_MASK\n* CAP_OPENNI_GRAY_IMAGEData given from RGB image generator\n* CAP_OPENNI_IMAGE_GENERATOR\n* CAP_OPENNI_IMAGE_GENERATOR_OUTPUT_MODE\n* CAP_OPENNI_IMAGE_GENERATOR_PRESENT\n* CAP_OPENNI_IR_GENERATOR\n* CAP_OPENNI_IR_GENERATOR_PRESENT\n* CAP_OPENNI_IR_IMAGEData given from IR image generator\n* CAP_OPENNI_POINT_CLOUD_MAPXYZ in meters (CV_32FC3)\n* CAP_OPENNI_QVGA_30HZ\n* CAP_OPENNI_QVGA_60HZ\n* CAP_OPENNI_SXGA_15HZ\n* CAP_OPENNI_SXGA_30HZ\n* CAP_OPENNI_VALID_DEPTH_MASKCV_8UC1\n* CAP_OPENNI_VGA_30HZ\n* CAP_PROP_APERTUREAperture. Can be readonly, depends on camera program.\n* CAP_PROP_ARAVIS_AUTOTRIGGERAutomatically trigger frame capture if camera is configured with software trigger\n* CAP_PROP_AUDIO_BASE_INDEX(read-only) Index of the first audio channel for .retrieve() calls. That audio channel number continues enumeration after video channels.\n* CAP_PROP_AUDIO_DATA_DEPTH(open, read) Alternative definition to bits-per-sample, but with clear handling of 32F / 32S\n* CAP_PROP_AUDIO_POS(read-only) Audio position is measured in samples. Accurate audio sample timestamp of previous grabbed fragment. See CAP_PROP_AUDIO_SAMPLES_PER_SECOND and CAP_PROP_AUDIO_SHIFT_NSEC.\n* CAP_PROP_AUDIO_SAMPLES_PER_SECOND(open, read) determined from file/codec input. If not specified, then selected audio sample rate is 44100\n* CAP_PROP_AUDIO_SHIFT_NSEC(read only) Contains the time difference between the start of the audio stream and the video stream in nanoseconds. Positive value means that audio is started after the first video frame. Negative value means that audio is started before the first video frame.\n* CAP_PROP_AUDIO_STREAM(**open-only**) Specify stream in multi-language media files, -1 - disable audio processing or microphone. Default value is -1.\n* CAP_PROP_AUDIO_SYNCHRONIZE(open, read) Enables audio synchronization.\n* CAP_PROP_AUDIO_TOTAL_CHANNELS(read-only) Number of audio channels in the selected audio stream (mono, stereo, etc)\n* CAP_PROP_AUDIO_TOTAL_STREAMS(read-only) Number of audio streams.\n* CAP_PROP_AUTOFOCUS\n* CAP_PROP_AUTO_EXPOSUREDC1394: exposure control done by camera, user can adjust reference level using this feature.\n* CAP_PROP_AUTO_WBenable/ disable auto white-balance\n* CAP_PROP_BACKENDCurrent backend (enum VideoCaptureAPIs). Read-only property\n* CAP_PROP_BACKLIGHT\n* CAP_PROP_BITRATE(read-only) Video bitrate in kbits/s\n* CAP_PROP_BRIGHTNESSBrightness of the image (only for those cameras that support).\n* CAP_PROP_BUFFERSIZE\n* CAP_PROP_CHANNELVideo input or Channel Number (only for those cameras that support)\n* CAP_PROP_CODEC_EXTRADATA_INDEXPositive index indicates that returning extra data is supported by the video back end. This can be retrieved as cap.retrieve(data, ). E.g. When reading from a h264 encoded RTSP stream, the FFmpeg backend could return the SPS and/or PPS if available (if sent in reply to a DESCRIBE request), from calls to cap.retrieve(data, ).\n* CAP_PROP_CODEC_PIXEL_FORMAT(read-only) codec’s pixel format. 4-character code - see VideoWriter::fourcc . Subset of AV_PIX_FMT_* or -1 if unknown\n* CAP_PROP_CONTRASTContrast of the image (only for cameras).\n* CAP_PROP_CONVERT_RGBBoolean flags indicating whether images should be converted to RGB. \n\n*GStreamer note*: The flag is ignored in case if custom pipeline is used. It’s user responsibility to interpret pipeline output.\n* CAP_PROP_DC1394_MAX\n* CAP_PROP_DC1394_MODE_AUTO\n* CAP_PROP_DC1394_MODE_MANUALset automatically when a value of the feature is set by the user.\n* CAP_PROP_DC1394_MODE_ONE_PUSH_AUTO\n* CAP_PROP_DC1394_OFFturn the feature off (not controlled manually nor automatically).\n* CAP_PROP_EXPOSUREExposure (only for those cameras that support).\n* CAP_PROP_EXPOSUREPROGRAMCamera exposure program.\n* CAP_PROP_FOCUS\n* CAP_PROP_FORMATFormat of the %Mat objects (see Mat::type()) returned by VideoCapture::retrieve().\nSet value -1 to fetch undecoded RAW video streams (as Mat 8UC1).\n* CAP_PROP_FOURCC4-character code of codec. see VideoWriter::fourcc .\n* CAP_PROP_FPSFrame rate.\n* CAP_PROP_FRAME_COUNTNumber of frames in the video file.\n* CAP_PROP_FRAME_HEIGHTHeight of the frames in the video stream.\n* CAP_PROP_FRAME_TYPE(read-only) FFmpeg back-end only - Frame type ascii code (73 = ‘I’, 80 = ‘P’, 66 = ‘B’ or 63 = ‘?’ if unknown) of the most recently read frame.\n* CAP_PROP_FRAME_WIDTHWidth of the frames in the video stream.\n* CAP_PROP_GAINGain of the image (only for those cameras that support).\n* CAP_PROP_GAMMA\n* CAP_PROP_GIGA_FRAME_HEIGH_MAX\n* CAP_PROP_GIGA_FRAME_OFFSET_X\n* CAP_PROP_GIGA_FRAME_OFFSET_Y\n* CAP_PROP_GIGA_FRAME_SENS_HEIGH\n* CAP_PROP_GIGA_FRAME_SENS_WIDTH\n* CAP_PROP_GIGA_FRAME_WIDTH_MAX\n* CAP_PROP_GPHOTO2_COLLECT_MSGSCollect messages with details.\n* CAP_PROP_GPHOTO2_FLUSH_MSGSReadonly, returns (const char *).\n* CAP_PROP_GPHOTO2_PREVIEWCapture only preview from liveview mode.\n* CAP_PROP_GPHOTO2_RELOAD_CONFIGTrigger, only by set. Reload camera settings.\n* CAP_PROP_GPHOTO2_RELOAD_ON_CHANGEReload all settings on set.\n* CAP_PROP_GPHOTO2_WIDGET_ENUMERATEReadonly, returns (const char *).\n* CAP_PROP_GSTREAMER_QUEUE_LENGTHDefault is 1\n* CAP_PROP_GUID\n* CAP_PROP_HUEHue of the image (only for cameras).\n* CAP_PROP_HW_ACCELERATION(**open-only**) Hardware acceleration type (see #VideoAccelerationType). Setting supported only via `params` parameter in cv::VideoCapture constructor / .open() method. Default value is backend-specific.\n* CAP_PROP_HW_ACCELERATION_USE_OPENCL(**open-only**) If non-zero, create new OpenCL context and bind it to current thread. The OpenCL context created with Video Acceleration context attached it (if not attached yet) for optimized GPU data copy between HW accelerated decoder and cv::UMat.\n* CAP_PROP_HW_DEVICE(**open-only**) Hardware device index (select GPU if multiple available). Device enumeration is acceleration type specific.\n* CAP_PROP_IMAGES_BASE\n* CAP_PROP_IMAGES_LAST\n* CAP_PROP_INTELPERC_DEPTH_CONFIDENCE_THRESHOLD\n* CAP_PROP_INTELPERC_DEPTH_FOCAL_LENGTH_HORZ\n* CAP_PROP_INTELPERC_DEPTH_FOCAL_LENGTH_VERT\n* CAP_PROP_INTELPERC_DEPTH_LOW_CONFIDENCE_VALUE\n* CAP_PROP_INTELPERC_DEPTH_SATURATION_VALUE\n* CAP_PROP_INTELPERC_PROFILE_COUNT\n* CAP_PROP_INTELPERC_PROFILE_IDX\n* CAP_PROP_IOS_DEVICE_EXPOSURE\n* CAP_PROP_IOS_DEVICE_FLASH\n* CAP_PROP_IOS_DEVICE_FOCUS\n* CAP_PROP_IOS_DEVICE_TORCH\n* CAP_PROP_IOS_DEVICE_WHITEBALANCE\n* CAP_PROP_IRIS\n* CAP_PROP_ISO_SPEED\n* CAP_PROP_LRF_HAS_KEY_FRAMEFFmpeg back-end only - Indicates whether the Last Raw Frame (LRF), output from VideoCapture::read() when VideoCapture is initialized with VideoCapture::open(CAP_FFMPEG, {CAP_PROP_FORMAT, -1}) or VideoCapture::set(CAP_PROP_FORMAT,-1) is called before the first call to VideoCapture::read(), contains encoded data for a key frame.\n* CAP_PROP_MODEBackend-specific value indicating the current capture mode.\n* CAP_PROP_MONOCHROME\n* CAP_PROP_N_THREADS(**open-only**) Set the maximum number of threads to use. Use 0 to use as many threads as CPU cores (applicable for FFmpeg back-end only).\n* CAP_PROP_OBSENSOR_INTRINSIC_CX\n* CAP_PROP_OBSENSOR_INTRINSIC_CY\n* CAP_PROP_OBSENSOR_INTRINSIC_FX\n* CAP_PROP_OBSENSOR_INTRINSIC_FY\n* CAP_PROP_OPENNI2_MIRROR\n* CAP_PROP_OPENNI2_SYNC\n* CAP_PROP_OPENNI_APPROX_FRAME_SYNC\n* CAP_PROP_OPENNI_BASELINEIn mm\n* CAP_PROP_OPENNI_CIRCLE_BUFFER\n* CAP_PROP_OPENNI_FOCAL_LENGTHIn pixels\n* CAP_PROP_OPENNI_FRAME_MAX_DEPTHIn mm\n* CAP_PROP_OPENNI_GENERATOR_PRESENT\n* CAP_PROP_OPENNI_MAX_BUFFER_SIZE\n* CAP_PROP_OPENNI_MAX_TIME_DURATION\n* CAP_PROP_OPENNI_OUTPUT_MODE\n* CAP_PROP_OPENNI_REGISTRATIONFlag that synchronizes the remapping depth map to image map by changing depth generator’s view point (if the flag is “on”) or sets this view point to its normal one (if the flag is “off”).\n* CAP_PROP_OPENNI_REGISTRATION_ON\n* CAP_PROP_OPEN_TIMEOUT_MSEC(**open-only**) timeout in milliseconds for opening a video capture (applicable for FFmpeg and GStreamer back-ends only)\n* CAP_PROP_ORIENTATION_AUTOif true - rotates output frames of CvCapture considering video file’s metadata (applicable for FFmpeg and AVFoundation back-ends only) (https://github.com/opencv/opencv/issues/15499)\n* CAP_PROP_ORIENTATION_META(read-only) Frame rotation defined by stream meta (applicable for FFmpeg and AVFoundation back-ends only)\n* CAP_PROP_PAN\n* CAP_PROP_POS_AVI_RATIORelative position of the video file: 0=start of the film, 1=end of the film.\n* CAP_PROP_POS_FRAMES0-based index of the frame to be decoded/captured next.\n* CAP_PROP_POS_MSECCurrent position of the video file in milliseconds.\n* CAP_PROP_PVAPI_BINNINGXHorizontal binning factor.\n* CAP_PROP_PVAPI_BINNINGYVertical binning factor.\n* CAP_PROP_PVAPI_DECIMATIONHORIZONTALHorizontal sub-sampling of the image.\n* CAP_PROP_PVAPI_DECIMATIONVERTICALVertical sub-sampling of the image.\n* CAP_PROP_PVAPI_FRAMESTARTTRIGGERMODEFrameStartTriggerMode: Determines how a frame is initiated.\n* CAP_PROP_PVAPI_MULTICASTIPIP for enable multicast master mode. 0 for disable multicast.\n* CAP_PROP_PVAPI_PIXELFORMATPixel format.\n* CAP_PROP_READ_TIMEOUT_MSEC(**open-only**) timeout in milliseconds for reading from a video capture (applicable for FFmpeg and GStreamer back-ends only)\n* CAP_PROP_RECTIFICATIONRectification flag for stereo cameras (note: only supported by DC1394 v 2.x backend currently).\n* CAP_PROP_ROLL\n* CAP_PROP_SAR_DENSample aspect ratio: num/den (den)\n* CAP_PROP_SAR_NUMSample aspect ratio: num/den (num)\n* CAP_PROP_SATURATIONSaturation of the image (only for cameras).\n* CAP_PROP_SETTINGSPop up video/camera filter dialog (note: only supported by DSHOW backend currently. The property value is ignored)\n* CAP_PROP_SHARPNESS\n* CAP_PROP_SPEEDExposure speed. Can be readonly, depends on camera program.\n* CAP_PROP_STREAM_OPEN_TIME_USEC\n* CAP_PROP_TEMPERATURE\n* CAP_PROP_TILT\n* CAP_PROP_TRIGGER\n* CAP_PROP_TRIGGER_DELAY\n* CAP_PROP_VIDEO_STREAM(**open-only**) Specify video stream, 0-based index. Use -1 to disable video stream from file or IP cameras. Default value is 0.\n* CAP_PROP_VIDEO_TOTAL_CHANNELS(read-only) Number of video channels\n* CAP_PROP_VIEWFINDEREnter liveview mode.\n* CAP_PROP_WB_TEMPERATUREwhite-balance color temperature\n* CAP_PROP_WHITE_BALANCE_BLUE_UCurrently unsupported.\n* CAP_PROP_WHITE_BALANCE_RED_V\n* CAP_PROP_XI_ACQ_BUFFER_SIZEAcquisition buffer size in buffer_size_unit. Default bytes.\n* CAP_PROP_XI_ACQ_BUFFER_SIZE_UNITAcquisition buffer size unit in bytes. Default 1. E.g. Value 1024 means that buffer_size is in KiBytes.\n* CAP_PROP_XI_ACQ_FRAME_BURST_COUNTSets number of frames acquired by burst. This burst is used only if trigger is set to FrameBurstStart.\n* CAP_PROP_XI_ACQ_TIMING_MODEType of sensor frames timing.\n* CAP_PROP_XI_ACQ_TRANSPORT_BUFFER_COMMITNumber of buffers to commit to low level.\n* CAP_PROP_XI_ACQ_TRANSPORT_BUFFER_SIZEAcquisition transport buffer size in bytes.\n* CAP_PROP_XI_AEAGAutomatic exposure/gain.\n* CAP_PROP_XI_AEAG_LEVELAverage intensity of output signal AEAG should achieve(in %).\n* CAP_PROP_XI_AEAG_ROI_HEIGHTAutomatic exposure/gain ROI Height.\n* CAP_PROP_XI_AEAG_ROI_OFFSET_XAutomatic exposure/gain ROI offset X.\n* CAP_PROP_XI_AEAG_ROI_OFFSET_YAutomatic exposure/gain ROI offset Y.\n* CAP_PROP_XI_AEAG_ROI_WIDTHAutomatic exposure/gain ROI Width.\n* CAP_PROP_XI_AE_MAX_LIMITMaximum limit of exposure in AEAG procedure.\n* CAP_PROP_XI_AG_MAX_LIMITMaximum limit of gain in AEAG procedure.\n* CAP_PROP_XI_APPLY_CMSEnable applying of CMS profiles to xiGetImage (see XI_PRM_INPUT_CMS_PROFILE, XI_PRM_OUTPUT_CMS_PROFILE).\n* CAP_PROP_XI_AUTO_BANDWIDTH_CALCULATIONAutomatic bandwidth calculation.\n* CAP_PROP_XI_AUTO_WBAutomatic white balance.\n* CAP_PROP_XI_AVAILABLE_BANDWIDTHCalculate and returns available interface bandwidth(int Megabits).\n* CAP_PROP_XI_BINNING_HORIZONTALHorizontal Binning - number of horizontal photo-sensitive cells to combine together.\n* CAP_PROP_XI_BINNING_PATTERNBinning pattern type.\n* CAP_PROP_XI_BINNING_SELECTORBinning engine selector.\n* CAP_PROP_XI_BINNING_VERTICALVertical Binning - number of vertical photo-sensitive cells to combine together.\n* CAP_PROP_XI_BPCCorrection of bad pixels.\n* CAP_PROP_XI_BUFFERS_QUEUE_SIZEQueue of field/frame buffers.\n* CAP_PROP_XI_BUFFER_POLICYData move policy.\n* CAP_PROP_XI_CC_MATRIX_00Color Correction Matrix element [0][0].\n* CAP_PROP_XI_CC_MATRIX_01Color Correction Matrix element [0][1].\n* CAP_PROP_XI_CC_MATRIX_02Color Correction Matrix element [0][2].\n* CAP_PROP_XI_CC_MATRIX_03Color Correction Matrix element [0][3].\n* CAP_PROP_XI_CC_MATRIX_10Color Correction Matrix element [1][0].\n* CAP_PROP_XI_CC_MATRIX_11Color Correction Matrix element [1][1].\n* CAP_PROP_XI_CC_MATRIX_12Color Correction Matrix element [1][2].\n* CAP_PROP_XI_CC_MATRIX_13Color Correction Matrix element [1][3].\n* CAP_PROP_XI_CC_MATRIX_20Color Correction Matrix element [2][0].\n* CAP_PROP_XI_CC_MATRIX_21Color Correction Matrix element [2][1].\n* CAP_PROP_XI_CC_MATRIX_22Color Correction Matrix element [2][2].\n* CAP_PROP_XI_CC_MATRIX_23Color Correction Matrix element [2][3].\n* CAP_PROP_XI_CC_MATRIX_30Color Correction Matrix element [3][0].\n* CAP_PROP_XI_CC_MATRIX_31Color Correction Matrix element [3][1].\n* CAP_PROP_XI_CC_MATRIX_32Color Correction Matrix element [3][2].\n* CAP_PROP_XI_CC_MATRIX_33Color Correction Matrix element [3][3].\n* CAP_PROP_XI_CHIP_TEMPCamera sensor temperature.\n* CAP_PROP_XI_CMSMode of color management system.\n* CAP_PROP_XI_COLOR_FILTER_ARRAYReturns color filter array type of RAW data.\n* CAP_PROP_XI_COLUMN_FPN_CORRECTIONCorrection of column FPN.\n* CAP_PROP_XI_COOLINGStart camera cooling.\n* CAP_PROP_XI_COUNTER_SELECTORSelect counter.\n* CAP_PROP_XI_COUNTER_VALUECounter status.\n* CAP_PROP_XI_DATA_FORMATOutput data format.\n* CAP_PROP_XI_DEBOUNCE_ENEnable/Disable debounce to selected GPI.\n* CAP_PROP_XI_DEBOUNCE_POLDebounce polarity (pol = 1 t0 - falling edge, t1 - rising edge).\n* CAP_PROP_XI_DEBOUNCE_T0Debounce time (x * 10us).\n* CAP_PROP_XI_DEBOUNCE_T1Debounce time (x * 10us).\n* CAP_PROP_XI_DEBUG_LEVELSet debug level.\n* CAP_PROP_XI_DECIMATION_HORIZONTALHorizontal Decimation - horizontal sub-sampling of the image - reduces the horizontal resolution of the image by the specified vertical decimation factor.\n* CAP_PROP_XI_DECIMATION_PATTERNDecimation pattern type.\n* CAP_PROP_XI_DECIMATION_SELECTORDecimation engine selector.\n* CAP_PROP_XI_DECIMATION_VERTICALVertical Decimation - vertical sub-sampling of the image - reduces the vertical resolution of the image by the specified vertical decimation factor.\n* CAP_PROP_XI_DEFAULT_CC_MATRIXSet default Color Correction Matrix.\n* CAP_PROP_XI_DEVICE_MODEL_IDReturns device model id.\n* CAP_PROP_XI_DEVICE_RESETResets the camera to default state.\n* CAP_PROP_XI_DEVICE_SNReturns device serial number.\n* CAP_PROP_XI_DOWNSAMPLINGChange image resolution by binning or skipping.\n* CAP_PROP_XI_DOWNSAMPLING_TYPEChange image downsampling type.\n* CAP_PROP_XI_EXPOSUREExposure time in microseconds.\n* CAP_PROP_XI_EXPOSURE_BURST_COUNTSets the number of times of exposure in one frame.\n* CAP_PROP_XI_EXP_PRIORITYExposure priority (0.5 - exposure 50%, gain 50%).\n* CAP_PROP_XI_FFS_ACCESS_KEYSetting of key enables file operations on some cameras.\n* CAP_PROP_XI_FFS_FILE_IDFile number.\n* CAP_PROP_XI_FFS_FILE_SIZESize of file.\n* CAP_PROP_XI_FRAMERATEDefine framerate in Hz.\n* CAP_PROP_XI_FREE_FFS_SIZESize of free camera FFS.\n* CAP_PROP_XI_GAINGain in dB.\n* CAP_PROP_XI_GAIN_SELECTORGain selector for parameter Gain allows to select different type of gains.\n* CAP_PROP_XI_GAMMACChromaticity gamma.\n* CAP_PROP_XI_GAMMAYLuminosity gamma.\n* CAP_PROP_XI_GPI_LEVELGet general purpose level.\n* CAP_PROP_XI_GPI_MODESet general purpose input mode.\n* CAP_PROP_XI_GPI_SELECTORSelects general purpose input.\n* CAP_PROP_XI_GPO_MODESet general purpose output mode.\n* CAP_PROP_XI_GPO_SELECTORSelects general purpose output.\n* CAP_PROP_XI_HDREnable High Dynamic Range feature.\n* CAP_PROP_XI_HDR_KNEEPOINT_COUNTThe number of kneepoints in the PWLR.\n* CAP_PROP_XI_HDR_T1Position of first kneepoint(in % of XI_PRM_EXPOSURE).\n* CAP_PROP_XI_HDR_T2Position of second kneepoint (in % of XI_PRM_EXPOSURE).\n* CAP_PROP_XI_HEIGHTHeight of the Image provided by the device (in pixels).\n* CAP_PROP_XI_HOUS_BACK_SIDE_TEMPCamera housing back side temperature.\n* CAP_PROP_XI_HOUS_TEMPCamera housing temperature.\n* CAP_PROP_XI_HW_REVISIONReturns hardware revision number.\n* CAP_PROP_XI_IMAGE_BLACK_LEVELLast image black level counts. Can be used for Offline processing to recall it.\n* CAP_PROP_XI_IMAGE_DATA_BIT_DEPTHbitdepth of data returned by function xiGetImage.\n* CAP_PROP_XI_IMAGE_DATA_FORMATOutput data format.\n* CAP_PROP_XI_IMAGE_DATA_FORMAT_RGB32_ALPHAThe alpha channel of RGB32 output image format.\n* CAP_PROP_XI_IMAGE_IS_COLORReturns 1 for color cameras.\n* CAP_PROP_XI_IMAGE_PAYLOAD_SIZEBuffer size in bytes sufficient for output image returned by xiGetImage.\n* CAP_PROP_XI_IS_COOLEDReturns 1 for cameras that support cooling.\n* CAP_PROP_XI_IS_DEVICE_EXISTReturns 1 if camera connected and works properly.\n* CAP_PROP_XI_KNEEPOINT1Value of first kneepoint (% of sensor saturation).\n* CAP_PROP_XI_KNEEPOINT2Value of second kneepoint (% of sensor saturation).\n* CAP_PROP_XI_LED_MODEDefine camera signalling LED functionality.\n* CAP_PROP_XI_LED_SELECTORSelects camera signalling LED.\n* CAP_PROP_XI_LENS_APERTURE_VALUECurrent lens aperture value in stops. Examples: 2.8, 4, 5.6, 8, 11.\n* CAP_PROP_XI_LENS_FEATUREAllows access to lens feature value currently selected by XI_PRM_LENS_FEATURE_SELECTOR.\n* CAP_PROP_XI_LENS_FEATURE_SELECTORSelects the current feature which is accessible by XI_PRM_LENS_FEATURE.\n* CAP_PROP_XI_LENS_FOCAL_LENGTHLens focal distance in mm.\n* CAP_PROP_XI_LENS_FOCUS_DISTANCELens focus distance in cm.\n* CAP_PROP_XI_LENS_FOCUS_MOVEMoves lens focus motor by steps set in XI_PRM_LENS_FOCUS_MOVEMENT_VALUE.\n* CAP_PROP_XI_LENS_FOCUS_MOVEMENT_VALUELens current focus movement value to be used by XI_PRM_LENS_FOCUS_MOVE in motor steps.\n* CAP_PROP_XI_LENS_MODEStatus of lens control interface. This shall be set to XI_ON before any Lens operations.\n* CAP_PROP_XI_LIMIT_BANDWIDTHSet/get bandwidth(datarate)(in Megabits).\n* CAP_PROP_XI_LUT_ENActivates LUT.\n* CAP_PROP_XI_LUT_INDEXControl the index (offset) of the coefficient to access in the LUT.\n* CAP_PROP_XI_LUT_VALUEValue at entry LUTIndex of the LUT.\n* CAP_PROP_XI_MANUAL_WBCalculates White Balance(must be called during acquisition).\n* CAP_PROP_XI_OFFSET_XHorizontal offset from the origin to the area of interest (in pixels).\n* CAP_PROP_XI_OFFSET_YVertical offset from the origin to the area of interest (in pixels).\n* CAP_PROP_XI_OUTPUT_DATA_BIT_DEPTHDevice output data bit depth.\n* CAP_PROP_XI_OUTPUT_DATA_PACKINGDevice output data packing (or grouping) enabled. Packing could be enabled if output_data_bit_depth > 8 and packing capability is available.\n* CAP_PROP_XI_OUTPUT_DATA_PACKING_TYPEData packing type. Some cameras supports only specific packing type.\n* CAP_PROP_XI_RECENT_FRAMEGetImage returns most recent frame.\n* CAP_PROP_XI_REGION_MODEActivates/deactivates Region selected by Region Selector.\n* CAP_PROP_XI_REGION_SELECTORSelects Region in Multiple ROI which parameters are set by width, height, … ,region mode.\n* CAP_PROP_XI_ROW_FPN_CORRECTIONCorrection of row FPN.\n* CAP_PROP_XI_SENSOR_BOARD_TEMPCamera sensor board temperature.\n* CAP_PROP_XI_SENSOR_CLOCK_FREQ_HZSensor clock frequency in Hz.\n* CAP_PROP_XI_SENSOR_CLOCK_FREQ_INDEXSensor clock frequency index. Sensor with selected frequencies have possibility to set the frequency only by this index.\n* CAP_PROP_XI_SENSOR_DATA_BIT_DEPTHSensor output data bit depth.\n* CAP_PROP_XI_SENSOR_FEATURE_SELECTORSelects the current feature which is accessible by XI_PRM_SENSOR_FEATURE_VALUE.\n* CAP_PROP_XI_SENSOR_FEATURE_VALUEAllows access to sensor feature value currently selected by XI_PRM_SENSOR_FEATURE_SELECTOR.\n* CAP_PROP_XI_SENSOR_MODECurrent sensor mode. Allows to select sensor mode by one integer. Setting of this parameter affects: image dimensions and downsampling.\n* CAP_PROP_XI_SENSOR_OUTPUT_CHANNEL_COUNTNumber of output channels from sensor used for data transfer.\n* CAP_PROP_XI_SENSOR_TAPSNumber of taps.\n* CAP_PROP_XI_SHARPNESSSharpness Strength.\n* CAP_PROP_XI_SHUTTER_TYPEChange sensor shutter type(CMOS sensor).\n* CAP_PROP_XI_TARGET_TEMPSet sensor target temperature for cooling.\n* CAP_PROP_XI_TEST_PATTERNSelects which test pattern type is generated by the selected generator.\n* CAP_PROP_XI_TEST_PATTERN_GENERATOR_SELECTORSelects which test pattern generator is controlled by the TestPattern feature.\n* CAP_PROP_XI_TIMEOUTImage capture timeout in milliseconds.\n* CAP_PROP_XI_TRANSPORT_PIXEL_FORMATCurrent format of pixels on transport layer.\n* CAP_PROP_XI_TRG_DELAYSpecifies the delay in microseconds (us) to apply after the trigger reception before activating it.\n* CAP_PROP_XI_TRG_SELECTORSelects the type of trigger.\n* CAP_PROP_XI_TRG_SOFTWAREGenerates an internal trigger. PRM_TRG_SOURCE must be set to TRG_SOFTWARE.\n* CAP_PROP_XI_TRG_SOURCEDefines source of trigger.\n* CAP_PROP_XI_TS_RST_MODEDefines how time stamp reset engine will be armed.\n* CAP_PROP_XI_TS_RST_SOURCEDefines which source will be used for timestamp reset. Writing this parameter will trigger settings of engine (arming).\n* CAP_PROP_XI_USED_FFS_SIZESize of used camera FFS.\n* CAP_PROP_XI_WB_KBWhite balance blue coefficient.\n* CAP_PROP_XI_WB_KGWhite balance green coefficient.\n* CAP_PROP_XI_WB_KRWhite balance red coefficient.\n* CAP_PROP_XI_WIDTHWidth of the Image provided by the device (in pixels).\n* CAP_PROP_ZOOM\n* CAP_PVAPIPvAPI, Prosilica GigE SDK\n* CAP_PVAPI_DECIMATION_2OUTOF42 out of 4 decimation\n* CAP_PVAPI_DECIMATION_2OUTOF82 out of 8 decimation\n* CAP_PVAPI_DECIMATION_2OUTOF162 out of 16 decimation\n* CAP_PVAPI_DECIMATION_OFFOff\n* CAP_PVAPI_FSTRIGMODE_FIXEDRATEFixedRate\n* CAP_PVAPI_FSTRIGMODE_FREERUNFreerun\n* CAP_PVAPI_FSTRIGMODE_SOFTWARESoftware\n* CAP_PVAPI_FSTRIGMODE_SYNCIN1SyncIn1\n* CAP_PVAPI_FSTRIGMODE_SYNCIN2SyncIn2\n* CAP_PVAPI_PIXELFORMAT_BAYER8Bayer8\n* CAP_PVAPI_PIXELFORMAT_BAYER16Bayer16\n* CAP_PVAPI_PIXELFORMAT_BGR24Bgr24\n* CAP_PVAPI_PIXELFORMAT_BGRA32Bgra32\n* CAP_PVAPI_PIXELFORMAT_MONO8Mono8\n* CAP_PVAPI_PIXELFORMAT_MONO16Mono16\n* CAP_PVAPI_PIXELFORMAT_RGB24Rgb24\n* CAP_PVAPI_PIXELFORMAT_RGBA32Rgba32\n* CAP_QTQuickTime (obsolete, removed)\n* CAP_REALSENSESynonym for CAP_INTELPERC\n* CAP_UEYEuEye Camera API\n* CAP_UNICAPUnicap drivers (obsolete, removed)\n* CAP_V4LV4L/V4L2 capturing support\n* CAP_V4L2Same as CAP_V4L\n* CAP_VFWVideo For Windows (obsolete, removed)\n* CAP_WINRTMicrosoft Windows Runtime using Media Foundation\n* CAP_XIAPIXIMEA Camera API\n* CAP_XINEXINE engine (Linux)\n* CV__CAP_PROP_LATEST\n* CV__VIDEOWRITER_PROP_LATEST\n* VIDEOWRITER_PROP_DEPTHDefaults to CV_8U.\n* VIDEOWRITER_PROP_FRAMEBYTES(Read-only): Size of just encoded video frame. Note that the encoding order may be different from representation order.\n* VIDEOWRITER_PROP_HW_ACCELERATION(**open-only**) Hardware acceleration type (see #VideoAccelerationType). Setting supported only via `params` parameter in VideoWriter constructor / .open() method. Default value is backend-specific.\n* VIDEOWRITER_PROP_HW_ACCELERATION_USE_OPENCL(**open-only**) If non-zero, create new OpenCL context and bind it to current thread. The OpenCL context created with Video Acceleration context attached it (if not attached yet) for optimized GPU data copy between cv::UMat and HW accelerated encoder.\n* VIDEOWRITER_PROP_HW_DEVICE(**open-only**) Hardware device index (select GPU if multiple available). Device enumeration is acceleration type specific.\n* VIDEOWRITER_PROP_IS_COLORIf it is not zero, the encoder will expect and encode color frames, otherwise it will work with grayscale frames.\n* VIDEOWRITER_PROP_NSTRIPESNumber of stripes for parallel encoding. -1 for auto detection.\n* VIDEOWRITER_PROP_QUALITYCurrent quality (0..100%) of the encoded videostream. Can be adjusted dynamically in some codecs.\n* VIDEO_ACCELERATION_ANYPrefer to use H/W acceleration. If no one supported, then fallback to software processing.\n* VIDEO_ACCELERATION_D3D11DirectX 11\n* VIDEO_ACCELERATION_MFXlibmfx (Intel MediaSDK/oneVPL)\n* VIDEO_ACCELERATION_NONEDo not require any specific H/W acceleration, prefer software processing.\nReading of this value means that special H/W accelerated handling is not added or not detected by OpenCV.\n* VIDEO_ACCELERATION_VAAPIVAAPI\n\nTraits\n---\n\n* VideoCaptureTraitMutable methods for crate::videoio::VideoCapture\n* VideoCaptureTraitConstConstant methods for crate::videoio::VideoCapture\n* VideoWriterTraitMutable methods for crate::videoio::VideoWriter\n* VideoWriterTraitConstConstant methods for crate::videoio::VideoWriter\n\nFunctions\n---\n\n* get_backend_nameReturns backend API name or “UnknownVideoAPI(xxx)”\n* get_backendsReturns list of all available backends\n* get_camera_backend_plugin_versionReturns description and ABI/API version of videoio plugin’s camera interface\n* get_camera_backendsReturns list of available backends which works via `cv::VideoCapture(int index)`\n* get_stream_backend_plugin_versionReturns description and ABI/API version of videoio plugin’s stream capture interface\n* get_stream_backendsReturns list of available backends which works via `cv::VideoCapture(filename)`\n* get_writer_backend_plugin_versionReturns description and ABI/API version of videoio plugin’s writer interface\n* get_writer_backendsReturns list of available backends which works via `cv::VideoWriter()`\n* has_backendReturns true if backend is available\n* is_backend_built_inReturns true if backend is built in (false if backend is used as plugin)\n\nModule opencv::videostab\n===\n\nVideo Stabilization\n---\n\nThe video stabilization module contains a set of functions and classes that can be used to solve the problem of video stabilization. There are a few methods implemented, most of them are described in the papers OF06 and G11 . However, there are some extensions and deviations from the original paper methods.\n\n#### References\n\n1. “Full-Frame Video Stabilization with Motion Inpainting”\n<NAME>, <NAME>, <NAME>, <NAME>, Senior Member, and Heung-<NAME> 2. “Auto-Directed Video Stabilization with Robust L1 Optimal Camera Paths”\n<NAME>, <NAME>, <NAME>\n# Global Motion Estimation\n\nThe video stabilization module contains a set of functions and classes for global motion estimation between point clouds or between images. In the last case features are extracted and matched internally. For the sake of convenience the motion estimation functions are wrapped into classes.\nBoth the functions and the classes are available.\n\nThe Fast Marching Method Telea04 is used in of the video stabilization routines to do motion and color inpainting. The method is implemented is a flexible way and it’s made public for other users.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* ColorAverageInpainter\n* ColorInpainter\n* ConsistentMosaicInpainter\n* DeblurerBase\n* DensePyrLkOptFlowEstimatorGpu\n* FastMarchingMethodDescribes the Fast Marching Method implementation.\n* FromFileMotionReader\n* GaussianMotionFilter\n* IDenseOptFlowEstimator\n* IFrameSource\n* ILog\n* IMotionStabilizer\n* IOutlierRejector\n* ISparseOptFlowEstimator\n* ImageMotionEstimatorBaseBase class for global 2D motion estimation methods which take frames as input.\n* InpainterBase\n* InpaintingPipeline\n* KeypointBasedMotionEstimatorDescribes a global 2D motion estimation method which uses keypoints detection and optical flow for matching.\n* KeypointBasedMotionEstimatorGpu\n* LogToStdout\n* LpMotionStabilizer\n* MaskFrameSource\n* MoreAccurateMotionWobbleSuppressor\n* MoreAccurateMotionWobbleSuppressorBase\n* MoreAccurateMotionWobbleSuppressorGpu\n* MotionEstimatorBaseBase class for all global motion estimation methods.\n* MotionEstimatorL1Describes a global 2D motion estimation method which minimizes L1 error.\n* MotionEstimatorRansacL2Describes a robust RANSAC-based global 2D motion estimation method which minimizes L2 error.\n* MotionFilterBase\n* MotionInpainter\n* MotionStabilizationPipeline\n* NullDeblurer\n* NullFrameSource\n* NullInpainter\n* NullLog\n* NullOutlierRejector\n* NullWobbleSuppressor\n* OnePassStabilizer\n* PyrLkOptFlowEstimatorBase\n* RansacParamsDescribes RANSAC method parameters.\n* SparsePyrLkOptFlowEstimator\n* SparsePyrLkOptFlowEstimatorGpu\n* StabilizerBase\n* ToFileMotionWriter\n* TranslationBasedLocalOutlierRejector\n* TwoPassStabilizer\n* VideoFileSource\n* WeightingDeblurer\n* WobbleSuppressorBase\n\nEnums\n---\n\n* MotionModelDescribes motion model between two point clouds.\n\nConstants\n---\n\n* MM_AFFINE\n* MM_HOMOGRAPHY\n* MM_RIGID\n* MM_ROTATION\n* MM_SIMILARITY\n* MM_TRANSLATION\n* MM_TRANSLATION_AND_SCALE\n* MM_UNKNOWN\n\nTraits\n---\n\n* ColorAverageInpainterTraitMutable methods for crate::videostab::ColorAverageInpainter\n* ColorAverageInpainterTraitConstConstant methods for crate::videostab::ColorAverageInpainter\n* ColorInpainterTraitMutable methods for crate::videostab::ColorInpainter\n* ColorInpainterTraitConstConstant methods for crate::videostab::ColorInpainter\n* ConsistentMosaicInpainterTraitMutable methods for crate::videostab::ConsistentMosaicInpainter\n* ConsistentMosaicInpainterTraitConstConstant methods for crate::videostab::ConsistentMosaicInpainter\n* DeblurerBaseTraitMutable methods for crate::videostab::DeblurerBase\n* DeblurerBaseTraitConstConstant methods for crate::videostab::DeblurerBase\n* DensePyrLkOptFlowEstimatorGpuTraitMutable methods for crate::videostab::DensePyrLkOptFlowEstimatorGpu\n* DensePyrLkOptFlowEstimatorGpuTraitConstConstant methods for crate::videostab::DensePyrLkOptFlowEstimatorGpu\n* FastMarchingMethodTraitMutable methods for crate::videostab::FastMarchingMethod\n* FastMarchingMethodTraitConstConstant methods for crate::videostab::FastMarchingMethod\n* FromFileMotionReaderTraitMutable methods for crate::videostab::FromFileMotionReader\n* FromFileMotionReaderTraitConstConstant methods for crate::videostab::FromFileMotionReader\n* GaussianMotionFilterTraitMutable methods for crate::videostab::GaussianMotionFilter\n* GaussianMotionFilterTraitConstConstant methods for crate::videostab::GaussianMotionFilter\n* IDenseOptFlowEstimatorTraitMutable methods for crate::videostab::IDenseOptFlowEstimator\n* IDenseOptFlowEstimatorTraitConstConstant methods for crate::videostab::IDenseOptFlowEstimator\n* IFrameSourceTraitMutable methods for crate::videostab::IFrameSource\n* IFrameSourceTraitConstConstant methods for crate::videostab::IFrameSource\n* ILogTraitMutable methods for crate::videostab::ILog\n* ILogTraitConstConstant methods for crate::videostab::ILog\n* IMotionStabilizerTraitMutable methods for crate::videostab::IMotionStabilizer\n* IMotionStabilizerTraitConstConstant methods for crate::videostab::IMotionStabilizer\n* IOutlierRejectorTraitMutable methods for crate::videostab::IOutlierRejector\n* IOutlierRejectorTraitConstConstant methods for crate::videostab::IOutlierRejector\n* ISparseOptFlowEstimatorTraitMutable methods for crate::videostab::ISparseOptFlowEstimator\n* ISparseOptFlowEstimatorTraitConstConstant methods for crate::videostab::ISparseOptFlowEstimator\n* ImageMotionEstimatorBaseTraitMutable methods for crate::videostab::ImageMotionEstimatorBase\n* ImageMotionEstimatorBaseTraitConstConstant methods for crate::videostab::ImageMotionEstimatorBase\n* InpainterBaseTraitMutable methods for crate::videostab::InpainterBase\n* InpainterBaseTraitConstConstant methods for crate::videostab::InpainterBase\n* InpaintingPipelineTraitMutable methods for crate::videostab::InpaintingPipeline\n* InpaintingPipelineTraitConstConstant methods for crate::videostab::InpaintingPipeline\n* KeypointBasedMotionEstimatorGpuTraitMutable methods for crate::videostab::KeypointBasedMotionEstimatorGpu\n* KeypointBasedMotionEstimatorGpuTraitConstConstant methods for crate::videostab::KeypointBasedMotionEstimatorGpu\n* KeypointBasedMotionEstimatorTraitMutable methods for crate::videostab::KeypointBasedMotionEstimator\n* KeypointBasedMotionEstimatorTraitConstConstant methods for crate::videostab::KeypointBasedMotionEstimator\n* LogToStdoutTraitMutable methods for crate::videostab::LogToStdout\n* LogToStdoutTraitConstConstant methods for crate::videostab::LogToStdout\n* LpMotionStabilizerTraitMutable methods for crate::videostab::LpMotionStabilizer\n* LpMotionStabilizerTraitConstConstant methods for crate::videostab::LpMotionStabilizer\n* MaskFrameSourceTraitMutable methods for crate::videostab::MaskFrameSource\n* MaskFrameSourceTraitConstConstant methods for crate::videostab::MaskFrameSource\n* MoreAccurateMotionWobbleSuppressorBaseTraitMutable methods for crate::videostab::MoreAccurateMotionWobbleSuppressorBase\n* MoreAccurateMotionWobbleSuppressorBaseTraitConstConstant methods for crate::videostab::MoreAccurateMotionWobbleSuppressorBase\n* MoreAccurateMotionWobbleSuppressorGpuTraitMutable methods for crate::videostab::MoreAccurateMotionWobbleSuppressorGpu\n* MoreAccurateMotionWobbleSuppressorGpuTraitConstConstant methods for crate::videostab::MoreAccurateMotionWobbleSuppressorGpu\n* MoreAccurateMotionWobbleSuppressorTraitMutable methods for crate::videostab::MoreAccurateMotionWobbleSuppressor\n* MoreAccurateMotionWobbleSuppressorTraitConstConstant methods for crate::videostab::MoreAccurateMotionWobbleSuppressor\n* MotionEstimatorBaseTraitMutable methods for crate::videostab::MotionEstimatorBase\n* MotionEstimatorBaseTraitConstConstant methods for crate::videostab::MotionEstimatorBase\n* MotionEstimatorL1TraitMutable methods for crate::videostab::MotionEstimatorL1\n* MotionEstimatorL1TraitConstConstant methods for crate::videostab::MotionEstimatorL1\n* MotionEstimatorRansacL2TraitMutable methods for crate::videostab::MotionEstimatorRansacL2\n* MotionEstimatorRansacL2TraitConstConstant methods for crate::videostab::MotionEstimatorRansacL2\n* MotionFilterBaseTraitMutable methods for crate::videostab::MotionFilterBase\n* MotionFilterBaseTraitConstConstant methods for crate::videostab::MotionFilterBase\n* MotionInpainterTraitMutable methods for crate::videostab::MotionInpainter\n* MotionInpainterTraitConstConstant methods for crate::videostab::MotionInpainter\n* MotionStabilizationPipelineTraitMutable methods for crate::videostab::MotionStabilizationPipeline\n* MotionStabilizationPipelineTraitConstConstant methods for crate::videostab::MotionStabilizationPipeline\n* NullDeblurerTraitMutable methods for crate::videostab::NullDeblurer\n* NullDeblurerTraitConstConstant methods for crate::videostab::NullDeblurer\n* NullFrameSourceTraitMutable methods for crate::videostab::NullFrameSource\n* NullFrameSourceTraitConstConstant methods for crate::videostab::NullFrameSource\n* NullInpainterTraitMutable methods for crate::videostab::NullInpainter\n* NullInpainterTraitConstConstant methods for crate::videostab::NullInpainter\n* NullLogTraitMutable methods for crate::videostab::NullLog\n* NullLogTraitConstConstant methods for crate::videostab::NullLog\n* NullOutlierRejectorTraitMutable methods for crate::videostab::NullOutlierRejector\n* NullOutlierRejectorTraitConstConstant methods for crate::videostab::NullOutlierRejector\n* NullWobbleSuppressorTraitMutable methods for crate::videostab::NullWobbleSuppressor\n* NullWobbleSuppressorTraitConstConstant methods for crate::videostab::NullWobbleSuppressor\n* OnePassStabilizerTraitMutable methods for crate::videostab::OnePassStabilizer\n* OnePassStabilizerTraitConstConstant methods for crate::videostab::OnePassStabilizer\n* PyrLkOptFlowEstimatorBaseTraitMutable methods for crate::videostab::PyrLkOptFlowEstimatorBase\n* PyrLkOptFlowEstimatorBaseTraitConstConstant methods for crate::videostab::PyrLkOptFlowEstimatorBase\n* RansacParamsTraitMutable methods for crate::videostab::RansacParams\n* RansacParamsTraitConstConstant methods for crate::videostab::RansacParams\n* SparsePyrLkOptFlowEstimatorGpuTraitMutable methods for crate::videostab::SparsePyrLkOptFlowEstimatorGpu\n* SparsePyrLkOptFlowEstimatorGpuTraitConstConstant methods for crate::videostab::SparsePyrLkOptFlowEstimatorGpu\n* SparsePyrLkOptFlowEstimatorTraitMutable methods for crate::videostab::SparsePyrLkOptFlowEstimator\n* SparsePyrLkOptFlowEstimatorTraitConstConstant methods for crate::videostab::SparsePyrLkOptFlowEstimator\n* StabilizerBaseTraitMutable methods for crate::videostab::StabilizerBase\n* StabilizerBaseTraitConstConstant methods for crate::videostab::StabilizerBase\n* ToFileMotionWriterTraitMutable methods for crate::videostab::ToFileMotionWriter\n* ToFileMotionWriterTraitConstConstant methods for crate::videostab::ToFileMotionWriter\n* TranslationBasedLocalOutlierRejectorTraitMutable methods for crate::videostab::TranslationBasedLocalOutlierRejector\n* TranslationBasedLocalOutlierRejectorTraitConstConstant methods for crate::videostab::TranslationBasedLocalOutlierRejector\n* TwoPassStabilizerTraitMutable methods for crate::videostab::TwoPassStabilizer\n* TwoPassStabilizerTraitConstConstant methods for crate::videostab::TwoPassStabilizer\n* VideoFileSourceTraitMutable methods for crate::videostab::VideoFileSource\n* VideoFileSourceTraitConstConstant methods for crate::videostab::VideoFileSource\n* WeightingDeblurerTraitMutable methods for crate::videostab::WeightingDeblurer\n* WeightingDeblurerTraitConstConstant methods for crate::videostab::WeightingDeblurer\n* WobbleSuppressorBaseTraitMutable methods for crate::videostab::WobbleSuppressorBase\n* WobbleSuppressorBaseTraitConstConstant methods for crate::videostab::WobbleSuppressorBase\n\nFunctions\n---\n\n* calc_blurriness\n* calc_flow_mask\n* complete_frame_according_to_flow\n* ensure_inclusion_constraint\n* estimate_global_motion_least_squaresEstimates best global motion between two 2D point clouds in the least-squares sense.\n* estimate_global_motion_least_squares_defEstimates best global motion between two 2D point clouds in the least-squares sense.\n* estimate_global_motion_ransacEstimates best global motion between two 2D point clouds robustly (using RANSAC method).\n* estimate_global_motion_ransac_defEstimates best global motion between two 2D point clouds robustly (using RANSAC method).\n* estimate_optimal_trim_ratio\n* get_motionComputes motion between two frames assuming that all the intermediate motions are known.\n\nModule opencv::viz\n===\n\n3D Visualizer\n---\n\nThis section describes 3D visualization window as well as classes and methods that are used to interact with it.\n\n3D visualization window (see Viz3d) is used to display widgets (see Widget), and it provides several methods to interact with scene and widgets.\n\nWidget\n---\n\nIn this section, the widget framework is explained. Widgets represent 2D or 3D objects, varying from simple ones such as lines to complex ones such as point clouds and meshes.\n\nWidgets are **implicitly shared**. Therefore, one can add a widget to the scene, and modify the widget without re-adding the widget.\n```\n// Create a cloud widget viz::WCloud cw(cloud, viz::Color::red());\n// Display it in a window myWindow.showWidget(\"CloudWidget1\", cw);\n// Modify it, and it will be modified in the window.\ncw.setColor(viz::Color::yellow());\n```\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* CameraThis class wraps intrinsic parameters of a camera.\n* ColorThis class represents color in BGR order.\n* KeyboardEventThis class represents a keyboard event.\n* MeshThis class wraps mesh attributes, and it can load a mesh from a ply file. :\n* MouseEventThis class represents a mouse event.\n* Viz3dThe Viz3d class represents a 3D visualizer window. This class is implicitly shared.\n* WArrowThis 3D Widget defines an arrow.\n* WCameraPositionThis 3D Widget represents camera position in a scene by its axes or viewing frustum. :\n* WCircleThis 3D Widget defines a circle.\n* WCloudThis 3D Widget defines a point cloud. :\n* WCloudCollectionThis 3D Widget defines a collection of clouds. :\n* WCloudNormalsThis 3D Widget represents normals of a point cloud. :\n* WConeThis 3D Widget defines a cone. :\n* WCoordinateSystemThis 3D Widget represents a coordinate system. :\n* WCubeThis 3D Widget defines a cube.\n* WCylinderThis 3D Widget defines a cylinder. :\n* WGridThis 3D Widget defines a grid. :\n* WImage3DThis 3D Widget represents an image in 3D space. :\n* WImageOverlayThis 2D Widget represents an image overlay. :\n* WLineThis 3D Widget defines a finite line.\n* WMeshConstructs a WMesh.\n* WPaintedCloud\n* WPlaneThis 3D Widget defines a finite plane.\n* WPolyLineThis 3D Widget defines a poly line. :\n* WSphereThis 3D Widget defines a sphere. :\n* WTextThis 2D Widget represents text overlay.\n* WText3DThis 3D Widget represents 3D text. The text always faces the camera.\n* WTrajectoryThis 3D Widget represents a trajectory. :\n* WTrajectoryFrustumsThis 3D Widget represents a trajectory. :\n* WTrajectorySpheresThis 3D Widget represents a trajectory using spheres and lines\n* WWidgetMergerThis class allows to merge several widgets to single one.\n* WidgetBase class of all widgets. Widget is implicitly shared.\n* Widget2DBase class of all 2D widgets.\n* Widget3DBase class of all 3D widgets.\n\nEnums\n---\n\n* KeyboardEvent_Action\n* MouseEvent_MouseButton\n* MouseEvent_Type\n* RenderingProperties//////////////////////////////////////////////////////////////////////////\nWidget rendering properties\n* RepresentationValues\n* ShadingValues\n\nConstants\n---\n\n* AMBIENT\n* FONT_SIZE\n* IMMEDIATE_RENDERING\n* KeyboardEvent_ALT\n* KeyboardEvent_CTRL\n* KeyboardEvent_KEY_DOWN\n* KeyboardEvent_KEY_UP\n* KeyboardEvent_NONE\n* KeyboardEvent_SHIFT\n* LIGHTING\n* LINE_WIDTH\n* Mesh_LOAD_AUTO\n* Mesh_LOAD_OBJ\n* Mesh_LOAD_PLY\n* MouseEvent_LeftButton\n* MouseEvent_MiddleButton\n* MouseEvent_MouseButtonPress\n* MouseEvent_MouseButtonRelease\n* MouseEvent_MouseDblClick\n* MouseEvent_MouseMove\n* MouseEvent_MouseScrollDown\n* MouseEvent_MouseScrollUp\n* MouseEvent_NoButton\n* MouseEvent_RightButton\n* MouseEvent_VScroll\n* OPACITY\n* POINT_SIZE\n* REPRESENTATION\n* REPRESENTATION_POINTS\n* REPRESENTATION_SURFACE\n* REPRESENTATION_WIREFRAME\n* SHADING\n* SHADING_FLAT\n* SHADING_GOURAUD\n* SHADING_PHONG\n* WTrajectory_BOTH\n* WTrajectory_FRAMES\n* WTrajectory_PATH\n\nTraits\n---\n\n* CameraTraitMutable methods for crate::viz::Camera\n* CameraTraitConstConstant methods for crate::viz::Camera\n* ColorTraitMutable methods for crate::viz::Color\n* ColorTraitConstConstant methods for crate::viz::Color\n* KeyboardEventTraitMutable methods for crate::viz::KeyboardEvent\n* KeyboardEventTraitConstConstant methods for crate::viz::KeyboardEvent\n* MeshTraitMutable methods for crate::viz::Mesh\n* MeshTraitConstConstant methods for crate::viz::Mesh\n* MouseEventTraitMutable methods for crate::viz::MouseEvent\n* MouseEventTraitConstConstant methods for crate::viz::MouseEvent\n* Viz3dTraitMutable methods for crate::viz::Viz3d\n* Viz3dTraitConstConstant methods for crate::viz::Viz3d\n* WArrowTraitMutable methods for crate::viz::WArrow\n* WArrowTraitConstConstant methods for crate::viz::WArrow\n* WCameraPositionTraitMutable methods for crate::viz::WCameraPosition\n* WCameraPositionTraitConstConstant methods for crate::viz::WCameraPosition\n* WCircleTraitMutable methods for crate::viz::WCircle\n* WCircleTraitConstConstant methods for crate::viz::WCircle\n* WCloudCollectionTraitMutable methods for crate::viz::WCloudCollection\n* WCloudCollectionTraitConstConstant methods for crate::viz::WCloudCollection\n* WCloudNormalsTraitMutable methods for crate::viz::WCloudNormals\n* WCloudNormalsTraitConstConstant methods for crate::viz::WCloudNormals\n* WCloudTraitMutable methods for crate::viz::WCloud\n* WCloudTraitConstConstant methods for crate::viz::WCloud\n* WConeTraitMutable methods for crate::viz::WCone\n* WConeTraitConstConstant methods for crate::viz::WCone\n* WCoordinateSystemTraitMutable methods for crate::viz::WCoordinateSystem\n* WCoordinateSystemTraitConstConstant methods for crate::viz::WCoordinateSystem\n* WCubeTraitMutable methods for crate::viz::WCube\n* WCubeTraitConstConstant methods for crate::viz::WCube\n* WCylinderTraitMutable methods for crate::viz::WCylinder\n* WCylinderTraitConstConstant methods for crate::viz::WCylinder\n* WGridTraitMutable methods for crate::viz::WGrid\n* WGridTraitConstConstant methods for crate::viz::WGrid\n* WImage3DTraitMutable methods for crate::viz::WImage3D\n* WImage3DTraitConstConstant methods for crate::viz::WImage3D\n* WImageOverlayTraitMutable methods for crate::viz::WImageOverlay\n* WImageOverlayTraitConstConstant methods for crate::viz::WImageOverlay\n* WLineTraitMutable methods for crate::viz::WLine\n* WLineTraitConstConstant methods for crate::viz::WLine\n* WMeshTraitMutable methods for crate::viz::WMesh\n* WMeshTraitConstConstant methods for crate::viz::WMesh\n* WPaintedCloudTraitMutable methods for crate::viz::WPaintedCloud\n* WPaintedCloudTraitConstConstant methods for crate::viz::WPaintedCloud\n* WPlaneTraitMutable methods for crate::viz::WPlane\n* WPlaneTraitConstConstant methods for crate::viz::WPlane\n* WPolyLineTraitMutable methods for crate::viz::WPolyLine\n* WPolyLineTraitConstConstant methods for crate::viz::WPolyLine\n* WSphereTraitMutable methods for crate::viz::WSphere\n* WSphereTraitConstConstant methods for crate::viz::WSphere\n* WText3DTraitMutable methods for crate::viz::WText3D\n* WText3DTraitConstConstant methods for crate::viz::WText3D\n* WTextTraitMutable methods for crate::viz::WText\n* WTextTraitConstConstant methods for crate::viz::WText\n* WTrajectoryFrustumsTraitMutable methods for crate::viz::WTrajectoryFrustums\n* WTrajectoryFrustumsTraitConstConstant methods for crate::viz::WTrajectoryFrustums\n* WTrajectorySpheresTraitMutable methods for crate::viz::WTrajectorySpheres\n* WTrajectorySpheresTraitConstConstant methods for crate::viz::WTrajectorySpheres\n* WTrajectoryTraitMutable methods for crate::viz::WTrajectory\n* WTrajectoryTraitConstConstant methods for crate::viz::WTrajectory\n* WWidgetMergerTraitMutable methods for crate::viz::WWidgetMerger\n* WWidgetMergerTraitConstConstant methods for crate::viz::WWidgetMerger\n* Widget2DTraitMutable methods for crate::viz::Widget2D\n* Widget2DTraitConstConstant methods for crate::viz::Widget2D\n* Widget3DTraitMutable methods for crate::viz::Widget3D\n* Widget3DTraitConstConstant methods for crate::viz::Widget3D\n* WidgetTraitMutable methods for crate::viz::Widget\n* WidgetTraitConstConstant methods for crate::viz::Widget\n\nFunctions\n---\n\n* compute_normals////////////////////////////////////////////////////////////////////////////////////////////\nComputing normals for mesh\n* get_window_by_nameRetrieves a window by its name.\n* imshowDisplays image in specified window\n* imshow_defDisplays image in specified window\n* make_camera_poseConstructs camera pose from position, focal_point and up_vector (see gluLookAt() for more information).\n* make_transform_to_globalTakes coordinate frame data and builds transform to global coordinate frame.\n* make_transform_to_global_defTakes coordinate frame data and builds transform to global coordinate frame.\n* read_cloudParameters\n* read_cloud_defParameters\n* read_mesh////////////////////////////////////////////////////////////////////////////////////////////\nReads mesh. Only ply format is supported now and no texture load support\n* read_poseParameters\n* read_pose_defParameters\n* read_trajectorytakes vector<Affine3> with T = float/double and loads poses from sequence of files\n* read_trajectory_deftakes vector<Affine3> with T = float/double and loads poses from sequence of files\n* unregister_all_windowsUnregisters all Viz windows from internal database. After it ‘getWindowByName()’ will create new windows instead of getting existing from the database.\n* write_cloudParameters\n* write_cloud_defParameters\n* write_poseParameters\n* write_pose_defParameters\n* write_trajectorytakes vector<Affine3> with T = float/double and writes to a sequence of files with given filename format\n* write_trajectory_deftakes vector<Affine3> with T = float/double and writes to a sequence of files with given filename format\n\nType Aliases\n---\n\n* Viz3d_Color\n* Viz3d_KeyboardCallback\n* Viz3d_MouseCallback\n\nModule opencv::wechat_qrcode\n===\n\nWeChat QR code detector for detecting and parsing QR code.\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* WeChatQRCodeWeChat QRCode includes two CNN-based models:A object detection model and a super resolution model.Object detection model is applied to detect QRCode with the bounding box.super resolution model is applied to zoom in QRCode when it is small.\n\nTraits\n---\n\n* WeChatQRCodeTraitMutable methods for crate::wechat_qrcode::WeChatQRCode\n* WeChatQRCodeTraitConstConstant methods for crate::wechat_qrcode::WeChatQRCode\n\nModule opencv::xfeatures2d\n===\n\nExtra 2D Features Framework\n---\n\nExperimental 2D Features Algorithms\n---\n\nThis section describes experimental algorithms for 2d feature detection.\n\nNon-free 2D Features Algorithms\n---\n\nThis section describes two popular algorithms for 2d feature detection, SIFT and SURF, that are known to be patented. You need to set the OPENCV_ENABLE_NONFREE option in cmake to use those. Use them at your own risk.\n\nExperimental 2D Features Matching Algorithm\n---\n\nThis section describes the following matching strategies:\n\n* GMS: Grid-based Motion Statistics, Bian2017gms\n* LOGOS: Local geometric support for high-outlier spatial verification, Lowry2018LOGOSLG\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AffineFeature2DClass implementing affine adaptation for key points.\n* BEBLIDClass implementing BEBLID (Boosted Efficient Binary Local Image Descriptor),\ndescribed in Suarez2020BEBLID .\n* BoostDescClass implementing BoostDesc (Learning Image Descriptors with Boosting), described in Trzcinski13a and Trzcinski13b.\n* BriefDescriptorExtractorClass for computing BRIEF descriptors described in calon2010 .\n* DAISYClass implementing DAISY descriptor, described in Tola10\n* Elliptic_KeyPointElliptic region around an interest point.\n* FREAKClass implementing the FREAK (*Fast Retina Keypoint*) keypoint descriptor, described in AOV12 .\n* HarrisLaplaceFeatureDetectorClass implementing the Harris-Laplace feature detector as described in Mikolajczyk2004.\n* LATCHlatch Class for computing the LATCH descriptor.\nIf you find this code useful, please add a reference to the following paper in your work:\n<NAME> and <NAME>, “LATCH: Learned Arrangements of Three Patch Codes”, arXiv preprint arXiv:1501.03719, 15 Jan. 2015\n* LUCIDClass implementing the locally uniform comparison image descriptor, described in LUCID\n* MSDDetectorClass implementing the MSD (*Maximal Self-Dissimilarity*) keypoint detector, described in Tombari14.\n* PCTSignaturesClass implementing PCT (position-color-texture) signature extraction as described in KrulisLS16.\nThe algorithm is divided to a feature sampler and a clusterizer.\nFeature sampler produces samples at given set of coordinates.\nClusterizer then produces clusters of these samples using k-means algorithm.\nResulting set of clusters is the signature of the input image.\n* PCTSignaturesSQFDClass implementing Signature Quadratic Form Distance (SQFD).\n* SURFClass for extracting Speeded Up Robust Features from an image Bay06 .\n* SURF_CUDAClass used for extracting Speeded Up Robust Features (SURF) from an image. :\n* StarDetectorThe class implements the keypoint detector introduced by Agrawal08, synonym of StarDetector. :\n* TBMRClass implementing the Tree Based Morse Regions (TBMR) as described in Najman2014 extended with scaled extraction ability.\n* TEBLIDClass implementing TEBLID (Triplet-based Efficient Binary Local Image Descriptor),\ndescribed in Suarez2021TEBLID.\n* VGGClass implementing VGG (Oxford Visual Geometry Group) descriptor trained end to end using “Descriptor Learning Using Convex Optimisation” (DLCO) aparatus described in Simonyan14.\n\nEnums\n---\n\n* BEBLID_BeblidSizeDescriptor number of bits, each bit is a boosting weak-learner.\nThe user can choose between 512 or 256 bits.\n* DAISY_NormalizationType\n* PCTSignatures_DistanceFunctionLp distance function selector.\n* PCTSignatures_PointDistributionPoint distributions supported by random point generator.\n* PCTSignatures_SimilarityFunctionSimilarity function selector.\n* SURF_CUDA_KeypointLayout\n* TEBLID_TeblidSizeDescriptor number of bits, each bit is a box average difference.\nThe user can choose between 256 or 512 bits.\n\nConstants\n---\n\n* BEBLID_SIZE_256_BITS\n* BEBLID_SIZE_512_BITS\n* BoostDesc_BGM\n* BoostDesc_BGM_BILINEAR\n* BoostDesc_BGM_HARD\n* BoostDesc_BINBOOST_64\n* BoostDesc_BINBOOST_128\n* BoostDesc_BINBOOST_256\n* BoostDesc_LBGM\n* DAISY_NRM_FULL\n* DAISY_NRM_NONE\n* DAISY_NRM_PARTIAL\n* DAISY_NRM_SIFT\n* PCTSignatures_GAUSSIANblock formula\n* PCTSignatures_HEURISTICblock formula\n* PCTSignatures_L0_5\n* PCTSignatures_L0_25\n* PCTSignatures_L1\n* PCTSignatures_L2\n* PCTSignatures_L2SQUARED\n* PCTSignatures_L5\n* PCTSignatures_L_INFINITY\n* PCTSignatures_MINUSblock formula\n* PCTSignatures_NORMALGenerate points with normal (gaussian) distribution.\n* PCTSignatures_REGULARGenerate points in a regular grid.\n* PCTSignatures_UNIFORMGenerate numbers uniformly.\n* SURF_CUDA_ANGLE_ROW\n* SURF_CUDA_HESSIAN_ROW\n* SURF_CUDA_LAPLACIAN_ROW\n* SURF_CUDA_OCTAVE_ROW\n* SURF_CUDA_ROWS_COUNT\n* SURF_CUDA_SIZE_ROW\n* SURF_CUDA_X_ROW\n* SURF_CUDA_Y_ROW\n* TEBLID_SIZE_256_BITS\n* TEBLID_SIZE_512_BITS\n* VGG_VGG_48\n* VGG_VGG_64\n* VGG_VGG_80\n* VGG_VGG_120\n\nTraits\n---\n\n* AffineFeature2DTraitMutable methods for crate::xfeatures2d::AffineFeature2D\n* AffineFeature2DTraitConstConstant methods for crate::xfeatures2d::AffineFeature2D\n* BEBLIDTraitMutable methods for crate::xfeatures2d::BEBLID\n* BEBLIDTraitConstConstant methods for crate::xfeatures2d::BEBLID\n* BoostDescTraitMutable methods for crate::xfeatures2d::BoostDesc\n* BoostDescTraitConstConstant methods for crate::xfeatures2d::BoostDesc\n* BriefDescriptorExtractorTraitMutable methods for crate::xfeatures2d::BriefDescriptorExtractor\n* BriefDescriptorExtractorTraitConstConstant methods for crate::xfeatures2d::BriefDescriptorExtractor\n* DAISYTraitMutable methods for crate::xfeatures2d::DAISY\n* DAISYTraitConstConstant methods for crate::xfeatures2d::DAISY\n* Elliptic_KeyPointTraitMutable methods for crate::xfeatures2d::Elliptic_KeyPoint\n* Elliptic_KeyPointTraitConstConstant methods for crate::xfeatures2d::Elliptic_KeyPoint\n* FREAKTraitMutable methods for crate::xfeatures2d::FREAK\n* FREAKTraitConstConstant methods for crate::xfeatures2d::FREAK\n* HarrisLaplaceFeatureDetectorTraitMutable methods for crate::xfeatures2d::HarrisLaplaceFeatureDetector\n* HarrisLaplaceFeatureDetectorTraitConstConstant methods for crate::xfeatures2d::HarrisLaplaceFeatureDetector\n* LATCHTraitMutable methods for crate::xfeatures2d::LATCH\n* LATCHTraitConstConstant methods for crate::xfeatures2d::LATCH\n* LUCIDTraitMutable methods for crate::xfeatures2d::LUCID\n* LUCIDTraitConstConstant methods for crate::xfeatures2d::LUCID\n* MSDDetectorTraitMutable methods for crate::xfeatures2d::MSDDetector\n* MSDDetectorTraitConstConstant methods for crate::xfeatures2d::MSDDetector\n* PCTSignaturesSQFDTraitMutable methods for crate::xfeatures2d::PCTSignaturesSQFD\n* PCTSignaturesSQFDTraitConstConstant methods for crate::xfeatures2d::PCTSignaturesSQFD\n* PCTSignaturesTraitMutable methods for crate::xfeatures2d::PCTSignatures\n* PCTSignaturesTraitConstConstant methods for crate::xfeatures2d::PCTSignatures\n* SURFTraitMutable methods for crate::xfeatures2d::SURF\n* SURFTraitConstConstant methods for crate::xfeatures2d::SURF\n* SURF_CUDATraitMutable methods for crate::xfeatures2d::SURF_CUDA\n* SURF_CUDATraitConstConstant methods for crate::xfeatures2d::SURF_CUDA\n* StarDetectorTraitMutable methods for crate::xfeatures2d::StarDetector\n* StarDetectorTraitConstConstant methods for crate::xfeatures2d::StarDetector\n* TBMRTraitMutable methods for crate::xfeatures2d::TBMR\n* TBMRTraitConstConstant methods for crate::xfeatures2d::TBMR\n* TEBLIDTraitMutable methods for crate::xfeatures2d::TEBLID\n* TEBLIDTraitConstConstant methods for crate::xfeatures2d::TEBLID\n* VGGTraitMutable methods for crate::xfeatures2d::VGG\n* VGGTraitConstConstant methods for crate::xfeatures2d::VGG\n\nFunctions\n---\n\n* fast_for_point_setEstimates cornerness for prespecified KeyPoints using the FAST algorithm\n* fast_for_point_set_defEstimates cornerness for prespecified KeyPoints using the FAST algorithm\n* match_gmsGMS (Grid-based Motion Statistics) feature matching strategy described in Bian2017gms .\n* match_gms_defGMS (Grid-based Motion Statistics) feature matching strategy described in Bian2017gms .\n* match_logosLOGOS (Local geometric support for high-outlier spatial verification) feature matching strategy described in Lowry2018LOGOSLG .\n\nType Aliases\n---\n\n* SurfDescriptorExtractor\n* SurfFeatureDetector\n\nModule opencv::ximgproc\n===\n\nExtended Image Processing\n---\n\nStructured forests for fast edge detection\n---\n\nThis module contains implementations of modern structured edge detection algorithms,\ni.e. algorithms which somehow takes into account pixel affinities in natural images.\n\nEdgeBoxes\n---\n\nFilters\n---\n\nSuperpixels\n---\n\nImage segmentation\n---\n\nFast line detector\n---\n\nEdgeDrawing\n---\n\nEDGE DRAWING LIBRARY FOR GEOMETRIC FEATURE EXTRACTION AND VALIDATION\n\nEdge Drawing (ED) algorithm is an proactive approach on edge detection problem. In contrast to many other existing edge detection algorithms which follow a subtractive approach (i.e. after applying gradient filters onto an image eliminating pixels w.r.t. several rules, e.g. non-maximal suppression and hysteresis in Canny), ED algorithm works via an additive strategy, i.e. it picks edge pixels one by one, hence the name Edge Drawing. Then we process those random shaped edge segments to extract higher level edge features, i.e. lines, circles, ellipses, etc. The popular method of extraction edge pixels from the thresholded gradient magnitudes is non-maximal supression that tests every pixel whether it has the maximum gradient response along its gradient direction and eliminates if it does not. However, this method does not check status of the neighboring pixels, and therefore might result low quality (in terms of edge continuity, smoothness, thinness, localization) edge segments. Instead of non-maximal supression,\nED points a set of edge pixels and join them by maximizing the total gradient response of edge segments. Therefore it can extract high quality edge segments without need for an additional hysteresis step.\n\nFourier descriptors\n---\n\nBinary morphology on run-length encoded image\n---\n\nThese functions support morphological operations on binary images. In order to be fast and space efficient binary images are encoded with a run-length representation.\nThis representation groups continuous horizontal sequences of “on” pixels together in a “run”. A run is charactarized by the column position of the first pixel in the run, the column position of the last pixel in the run and the row position. This representation is very compact for binary images which contain large continuous areas of “on” and “off” pixels. A checkerboard pattern would be a good example. The representation is not so suitable for binary images created from random noise images or other images where little correlation between neighboring pixels exists.\n\nThe morphological operations supported here are very similar to the operations supported in the imgproc module. In general they are fast. However on several occasions they are slower than the functions from imgproc. The structuring elements of cv::MORPH_RECT and cv::MORPH_CROSS have very good support from the imgproc module. Also small structuring elements are very fast in imgproc (presumably due to opencl support). Therefore the functions from this module are recommended for larger structuring elements (cv::MORPH_ELLIPSE or self defined structuring elements). A sample application\n(run_length_morphology_demo) is supplied which allows to compare the speed of some morphological operations for the functions using run-length encoding and the imgproc functions for a given image.\n\nRun length encoded images are stored in standard opencv images. Images have a single column of cv::Point3i elements. The number of rows is the number of run + 1. The first row contains the size of the original (not encoded) image. For the runs the following mapping is used (x: column begin, y: column end (last column), z: row).\n\nThe size of the original image is required for compatibility with the imgproc functions when the boundary handling requires that pixel outside the image boundary are\n“on”.\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* AdaptiveManifoldFilterInterface for Adaptive Manifold Filter realizations.\n* Box\n* ContourFittingClass for ContourFitting algorithms.\nContourFitting match two contours inline formula and inline formula minimizing distance block formula where inline formula and inline formula are Fourier descriptors of inline formula and inline formula and s is a scaling factor and inline formula is angle rotation and inline formula is starting point factor adjustement\n* DTFilterInterface for realizations of Domain Transform filter.\n* DisparityFilterMain interface for all disparity map filters.\n* DisparityWLSFilterDisparity map filter based on Weighted Least Squares filter (in form of Fast Global Smoother that is a lot faster than traditional Weighted Least Squares filter implementations) and optional use of left-right-consistency-based confidence to refine the results in half-occlusions and uniform areas.\n* EdgeAwareInterpolatorSparse match interpolation algorithm based on modified locally-weighted affine estimator from Revaud2015 and Fast Global Smoother as post-processing filter.\n* EdgeBoxesClass implementing EdgeBoxes algorithm from ZitnickECCV14edgeBoxes :\n* EdgeDrawingClass implementing the ED (EdgeDrawing) topal2012edge, EDLines akinlar2011edlines, EDPF akinlar2012edpf and EDCircles akinlar2013edcircles algorithms\n* EdgeDrawing_Params\n* FastBilateralSolverFilterInterface for implementations of Fast Bilateral Solver.\n* FastGlobalSmootherFilterInterface for implementations of Fast Global Smoother filter.\n* FastLineDetector@include samples/fld_lines.cpp\n* GraphSegmentationGraph Based Segmentation Algorithm.\nThe class implements the algorithm described in PFF2004 .\n* GuidedFilterInterface for realizations of Guided Filter.\n* RFFeatureGetter!\nHelper class for training part of [<NAME> and <NAME>. Structured Forests for Fast Edge Detection, 2013].\n* RICInterpolatorSparse match interpolation algorithm based on modified piecewise locally-weighted affine estimator called Robust Interpolation method of Correspondences or RIC from Hu2017 and Variational and Fast Global Smoother as post-processing filter. The RICInterpolator is a extension of the EdgeAwareInterpolator.\nMain concept of this extension is an piece-wise affine model based on over-segmentation via SLIC superpixel estimation.\nThe method contains an efficient propagation mechanism to estimate among the pieces-wise models.\n* RidgeDetectionFilterApplies Ridge Detection Filter to an input image.\nImplements Ridge detection similar to the one in Mathematica using the eigen values from the Hessian Matrix of the input image using Sobel Derivatives.\nAdditional refinement can be done using Skeletonization and Binarization. Adapted from segleafvein and M_RF\n* ScanSegmentClass implementing the F-DBSCAN (Accelerated superpixel image segmentation with a parallelized DBSCAN algorithm) superpixels algorithm by Loke SC, et al. loke2021accelerated for original paper.\n* SelectiveSearchSegmentationSelective search segmentation algorithm The class implements the algorithm described in uijlings2013selective.\n* SelectiveSearchSegmentationStrategyStrategie for the selective search segmentation algorithm The class implements a generic stragery for the algorithm described in uijlings2013selective.\n* SelectiveSearchSegmentationStrategyColorColor-based strategy for the selective search segmentation algorithm The class is implemented from the algorithm described in uijlings2013selective.\n* SelectiveSearchSegmentationStrategyFillFill-based strategy for the selective search segmentation algorithm The class is implemented from the algorithm described in uijlings2013selective.\n* SelectiveSearchSegmentationStrategyMultipleRegroup multiple strategies for the selective search segmentation algorithm\n* SelectiveSearchSegmentationStrategySizeSize-based strategy for the selective search segmentation algorithm The class is implemented from the algorithm described in uijlings2013selective.\n* SelectiveSearchSegmentationStrategyTextureTexture-based strategy for the selective search segmentation algorithm The class is implemented from the algorithm described in uijlings2013selective.\n* SparseMatchInterpolatorMain interface for all filters, that take sparse matches as an input and produce a dense per-pixel matching (optical flow) as an output.\n* StructuredEdgeDetectionClass implementing edge detection algorithm from Dollar2013 :\n* SuperpixelLSCClass implementing the LSC (Linear Spectral Clustering) superpixels algorithm described in LiCVPR2015LSC.\n* SuperpixelSEEDSClass implementing the SEEDS (Superpixels Extracted via Energy-Driven Sampling) superpixels algorithm described in VBRV14 .\n* SuperpixelSLICClass implementing the SLIC (Simple Linear Iterative Clustering) superpixels algorithm described in Achanta2012.\n\nEnums\n---\n\n* AngleRangeOptionSpecifies the part of Hough space to calculate\n@details The enum specifies the part of Hough space to calculate. Each member specifies primarily direction of lines (horizontal or vertical)\nand the direction of angle changes.\nDirection of angle changes is from multiples of 90 to odd multiples of 45.\nThe image considered to be written top-down and left-to-right.\nAngles are started from vertical line and go clockwise.\nSeparate quarters and halves are written in orientation they should be in full Hough space.\n* EdgeAwareFiltersList\n* EdgeDrawing_GradientOperator\n* HoughDeskewOptionSpecifies to do or not to do skewing of Hough transform image\n@details The enum specifies to do or not to do skewing of Hough transform image so it would be no cycling in Hough transform image through borders of image.\n* HoughOpSpecifies binary operations.\n@details The enum specifies binary operations, that is such ones which involve two operands. Formally, a binary operation @f$ f @f$ on a set @f$ S @f$\nis a binary relation that maps elements of the Cartesian product\n@f$ S \\times S @f$ to @f$ S @f$:\n@f[ f: S \\times S \\to S @f]\n@ingroup MinUtils_MathOper\n* LocalBinarizationMethodsSpecifies the binarization method to use in cv::ximgproc::niBlackThreshold\n* RulesOptionSpecifies the degree of rules validation.\n@details The enum specifies the degree of rules validation. This can be used,\nfor example, to choose a proper way of input arguments validation.\n* SLICType\n* ThinningTypes\n* WMFWeightTypeSpecifies weight types of weighted median filter.\n\nConstants\n---\n\n* AM_FILTER\n* ARO_0_45\n* ARO_45_90\n* ARO_45_135\n* ARO_90_135\n* ARO_315_0\n* ARO_315_45\n* ARO_315_135\n* ARO_CTR_HOR\n* ARO_CTR_VER\n* BINARIZATION_NIBLACKClassic Niblack binarization. See Niblack1985 .\n* BINARIZATION_NICKNICK technique. See Khurshid2009 .\n* BINARIZATION_SAUVOLASauvola’s technique. See Sauvola1997 .\n* BINARIZATION_WOLFWolf’s technique. See Wolf2004 .\n* DTF_IC\n* DTF_NC\n* DTF_RF\n* EdgeDrawing_LSD\n* EdgeDrawing_PREWITT\n* EdgeDrawing_SCHARR\n* EdgeDrawing_SOBEL\n* FHT_ADD\n* FHT_AVE\n* FHT_MAX\n* FHT_MIN\n* GUIDED_FILTER\n* HDO_DESKEW\n* HDO_RAW\n* MSLIC\n* RO_IGNORE_BORDERSSkip validations of image borders.\n* RO_STRICTValidate each rule in a proper way.\n* SLIC\n* SLICO\n* THINNING_GUOHALL\n* THINNING_ZHANGSUEN\n* WMF_COSinline formula\n* WMF_EXPinline formula\n* WMF_IV1inline formula\n* WMF_IV2inline formula\n* WMF_JACinline formula\n* WMF_OFFunweighted\n\nTraits\n---\n\n* AdaptiveManifoldFilterTraitMutable methods for crate::ximgproc::AdaptiveManifoldFilter\n* AdaptiveManifoldFilterTraitConstConstant methods for crate::ximgproc::AdaptiveManifoldFilter\n* ContourFittingTraitMutable methods for crate::ximgproc::ContourFitting\n* ContourFittingTraitConstConstant methods for crate::ximgproc::ContourFitting\n* DTFilterTraitMutable methods for crate::ximgproc::DTFilter\n* DTFilterTraitConstConstant methods for crate::ximgproc::DTFilter\n* DisparityFilterTraitMutable methods for crate::ximgproc::DisparityFilter\n* DisparityFilterTraitConstConstant methods for crate::ximgproc::DisparityFilter\n* DisparityWLSFilterTraitMutable methods for crate::ximgproc::DisparityWLSFilter\n* DisparityWLSFilterTraitConstConstant methods for crate::ximgproc::DisparityWLSFilter\n* EdgeAwareInterpolatorTraitMutable methods for crate::ximgproc::EdgeAwareInterpolator\n* EdgeAwareInterpolatorTraitConstConstant methods for crate::ximgproc::EdgeAwareInterpolator\n* EdgeBoxesTraitMutable methods for crate::ximgproc::EdgeBoxes\n* EdgeBoxesTraitConstConstant methods for crate::ximgproc::EdgeBoxes\n* EdgeDrawingTraitMutable methods for crate::ximgproc::EdgeDrawing\n* EdgeDrawingTraitConstConstant methods for crate::ximgproc::EdgeDrawing\n* FastBilateralSolverFilterTraitMutable methods for crate::ximgproc::FastBilateralSolverFilter\n* FastBilateralSolverFilterTraitConstConstant methods for crate::ximgproc::FastBilateralSolverFilter\n* FastGlobalSmootherFilterTraitMutable methods for crate::ximgproc::FastGlobalSmootherFilter\n* FastGlobalSmootherFilterTraitConstConstant methods for crate::ximgproc::FastGlobalSmootherFilter\n* FastLineDetectorTraitMutable methods for crate::ximgproc::FastLineDetector\n* FastLineDetectorTraitConstConstant methods for crate::ximgproc::FastLineDetector\n* GraphSegmentationTraitMutable methods for crate::ximgproc::GraphSegmentation\n* GraphSegmentationTraitConstConstant methods for crate::ximgproc::GraphSegmentation\n* GuidedFilterTraitMutable methods for crate::ximgproc::GuidedFilter\n* GuidedFilterTraitConstConstant methods for crate::ximgproc::GuidedFilter\n* RFFeatureGetterTraitMutable methods for crate::ximgproc::RFFeatureGetter\n* RFFeatureGetterTraitConstConstant methods for crate::ximgproc::RFFeatureGetter\n* RICInterpolatorTraitMutable methods for crate::ximgproc::RICInterpolator\n* RICInterpolatorTraitConstConstant methods for crate::ximgproc::RICInterpolator\n* RidgeDetectionFilterTraitMutable methods for crate::ximgproc::RidgeDetectionFilter\n* RidgeDetectionFilterTraitConstConstant methods for crate::ximgproc::RidgeDetectionFilter\n* ScanSegmentTraitMutable methods for crate::ximgproc::ScanSegment\n* ScanSegmentTraitConstConstant methods for crate::ximgproc::ScanSegment\n* SelectiveSearchSegmentationStrategyColorTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategyColor\n* SelectiveSearchSegmentationStrategyColorTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategyColor\n* SelectiveSearchSegmentationStrategyFillTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategyFill\n* SelectiveSearchSegmentationStrategyFillTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategyFill\n* SelectiveSearchSegmentationStrategyMultipleTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategyMultiple\n* SelectiveSearchSegmentationStrategyMultipleTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategyMultiple\n* SelectiveSearchSegmentationStrategySizeTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategySize\n* SelectiveSearchSegmentationStrategySizeTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategySize\n* SelectiveSearchSegmentationStrategyTextureTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategyTexture\n* SelectiveSearchSegmentationStrategyTextureTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategyTexture\n* SelectiveSearchSegmentationStrategyTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentationStrategy\n* SelectiveSearchSegmentationStrategyTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentationStrategy\n* SelectiveSearchSegmentationTraitMutable methods for crate::ximgproc::SelectiveSearchSegmentation\n* SelectiveSearchSegmentationTraitConstConstant methods for crate::ximgproc::SelectiveSearchSegmentation\n* SparseMatchInterpolatorTraitMutable methods for crate::ximgproc::SparseMatchInterpolator\n* SparseMatchInterpolatorTraitConstConstant methods for crate::ximgproc::SparseMatchInterpolator\n* StructuredEdgeDetectionTraitMutable methods for crate::ximgproc::StructuredEdgeDetection\n* StructuredEdgeDetectionTraitConstConstant methods for crate::ximgproc::StructuredEdgeDetection\n* SuperpixelLSCTraitMutable methods for crate::ximgproc::SuperpixelLSC\n* SuperpixelLSCTraitConstConstant methods for crate::ximgproc::SuperpixelLSC\n* SuperpixelSEEDSTraitMutable methods for crate::ximgproc::SuperpixelSEEDS\n* SuperpixelSEEDSTraitConstConstant methods for crate::ximgproc::SuperpixelSEEDS\n* SuperpixelSLICTraitMutable methods for crate::ximgproc::SuperpixelSLIC\n* SuperpixelSLICTraitConstConstant methods for crate::ximgproc::SuperpixelSLIC\n\nFunctions\n---\n\n* am_filterSimple one-line Adaptive Manifold Filter call.\n* am_filter_defSimple one-line Adaptive Manifold Filter call.\n* anisotropic_diffusionPerforms anisotropic diffusion on an image.\n* bilateral_texture_filterApplies the bilateral texture filter to an image. It performs structure-preserving texture filter.\nFor more details about this filter see Cho2014.\n* bilateral_texture_filter_defApplies the bilateral texture filter to an image. It performs structure-preserving texture filter.\nFor more details about this filter see Cho2014.\n* bright_edgesC++ default parameters\n* bright_edges_defNote\n* color_match_templateCompares a color template against overlapped color image regions.\n* compute_bad_pixel_percentFunction for computing the percent of “bad” pixels in the disparity map\n(pixels where error is higher than a specified threshold)\n* compute_bad_pixel_percent_defFunction for computing the percent of “bad” pixels in the disparity map\n(pixels where error is higher than a specified threshold)\n* compute_mseFunction for computing mean square error for disparity maps\n* contour_samplingContour sampling .\n* covariance_estimationComputes the estimated covariance matrix of an image using the sliding window forumlation.\n* create_am_filterFactory method, create instance of AdaptiveManifoldFilter and produce some initialization routines.\n* create_am_filter_defFactory method, create instance of AdaptiveManifoldFilter and produce some initialization routines.\n* create_contour_fittingcreate ContourFitting algorithm object\n* create_contour_fitting_defcreate ContourFitting algorithm object\n* create_disparity_wls_filterConvenience factory method that creates an instance of DisparityWLSFilter and sets up all the relevant filter parameters automatically based on the matcher instance. Currently supports only StereoBM and StereoSGBM.\n* create_disparity_wls_filter_genericMore generic factory method, create instance of DisparityWLSFilter and execute basic initialization routines. When using this method you will need to set-up the ROI, matchers and other parameters by yourself.\n* create_dt_filterFactory method, create instance of DTFilter and produce initialization routines.\n* create_dt_filter_defFactory method, create instance of DTFilter and produce initialization routines.\n* create_edge_aware_interpolatorFactory method that creates an instance of the EdgeAwareInterpolator.\n* create_edge_boxesCreates a Edgeboxes\n* create_edge_boxes_defCreates a Edgeboxes\n* create_edge_drawingCreates a smart pointer to a EdgeDrawing object and initializes it\n* create_fast_bilateral_solver_filterFactory method, create instance of FastBilateralSolverFilter and execute the initialization routines.\n* create_fast_bilateral_solver_filter_defFactory method, create instance of FastBilateralSolverFilter and execute the initialization routines.\n* create_fast_global_smoother_filterFactory method, create instance of FastGlobalSmootherFilter and execute the initialization routines.\n* create_fast_global_smoother_filter_defFactory method, create instance of FastGlobalSmootherFilter and execute the initialization routines.\n* create_fast_line_detectorCreates a smart pointer to a FastLineDetector object and initializes it\n* create_fast_line_detector_defCreates a smart pointer to a FastLineDetector object and initializes it\n* create_graph_segmentationCreates a graph based segmentor\n* create_graph_segmentation_defCreates a graph based segmentor\n* create_guided_filterFactory method, create instance of GuidedFilter and produce initialization routines.\n* create_quaternion_imagecreates a quaternion image.\n* create_rf_feature_getter\n* create_ric_interpolatorFactory method that creates an instance of the RICInterpolator.\n* create_right_matcherConvenience method to set up the matcher for computing the right-view disparity map that is required in case of filtering with confidence.\n* create_rle_imageCreates a run-length encoded image from a vector of runs (column begin, column end, row)\n* create_rle_image_defCreates a run-length encoded image from a vector of runs (column begin, column end, row)\n* create_scan_segmentInitializes a ScanSegment object.\n* create_scan_segment_defInitializes a ScanSegment object.\n* create_selective_search_segmentationCreate a new SelectiveSearchSegmentation class.\n* create_selective_search_segmentation_strategy_colorCreate a new color-based strategy\n* create_selective_search_segmentation_strategy_fillCreate a new fill-based strategy\n* create_selective_search_segmentation_strategy_multipleCreate a new multiple strategy\n* create_selective_search_segmentation_strategy_multiple_1Create a new multiple strategy and set one subtrategy\n* create_selective_search_segmentation_strategy_multiple_2Create a new multiple strategy and set two subtrategies, with equal weights\n* create_selective_search_segmentation_strategy_multiple_3Create a new multiple strategy and set three subtrategies, with equal weights\n* create_selective_search_segmentation_strategy_multiple_4Create a new multiple strategy and set four subtrategies, with equal weights\n* create_selective_search_segmentation_strategy_sizeCreate a new size-based strategy\n* create_selective_search_segmentation_strategy_textureCreate a new size-based strategy\n* create_structured_edge_detection!\n* create_structured_edge_detection_def!\n* create_superpixel_lscClass implementing the LSC (Linear Spectral Clustering) superpixels\n* create_superpixel_lsc_defClass implementing the LSC (Linear Spectral Clustering) superpixels\n* create_superpixel_seedsInitializes a SuperpixelSEEDS object.\n* create_superpixel_seeds_defInitializes a SuperpixelSEEDS object.\n* create_superpixel_slicInitialize a SuperpixelSLIC object\n* create_superpixel_slic_defInitialize a SuperpixelSLIC object\n* dilateDilates an run-length encoded binary image by using a specific structuring element.\n* dilate_defDilates an run-length encoded binary image by using a specific structuring element.\n* dt_filterSimple one-line Domain Transform filter call. If you have multiple images to filter with the same guided image then use DTFilter interface to avoid extra computations on initialization stage.\n* dt_filter_defSimple one-line Domain Transform filter call. If you have multiple images to filter with the same guided image then use DTFilter interface to avoid extra computations on initialization stage.\n* edge_preserving_filterSmoothes an image using the Edge-Preserving filter.\n* erodeErodes an run-length encoded binary image by using a specific structuring element.\n* erode_defErodes an run-length encoded binary image by using a specific structuring element.\n* fast_bilateral_solver_filterSimple one-line Fast Bilateral Solver filter call. If you have multiple images to filter with the same guide then use FastBilateralSolverFilter interface to avoid extra computations.\n* fast_bilateral_solver_filter_defSimple one-line Fast Bilateral Solver filter call. If you have multiple images to filter with the same guide then use FastBilateralSolverFilter interface to avoid extra computations.\n* fast_global_smoother_filterSimple one-line Fast Global Smoother filter call. If you have multiple images to filter with the same guide then use FastGlobalSmootherFilter interface to avoid extra computations.\n* fast_global_smoother_filter_defSimple one-line Fast Global Smoother filter call. If you have multiple images to filter with the same guide then use FastGlobalSmootherFilter interface to avoid extra computations.\n* fast_hough_transformCalculates 2D Fast Hough transform of an image.\n* fast_hough_transform_defCalculates 2D Fast Hough transform of an image.\n* find_ellipsesFinds ellipses fastly in an image using projective invariant pruning.\n* find_ellipses_defFinds ellipses fastly in an image using projective invariant pruning.\n* fourier_descriptorFourier descriptors for planed closed curves\n* fourier_descriptor_defFourier descriptors for planed closed curves\n* get_disparity_visFunction for creating a disparity map visualization (clamped CV_8U image)\n* get_disparity_vis_defFunction for creating a disparity map visualization (clamped CV_8U image)\n* get_structuring_elementReturns a run length encoded structuring element of the specified size and shape.\n* gradient_deriche_xApplies X Deriche filter to an image.\n* gradient_deriche_yApplies Y Deriche filter to an image.\n* gradient_paillou_x\n* gradient_paillou_yApplies Paillou filter to an image.\n* guided_filterSimple one-line Guided Filter call.\n* guided_filter_defSimple one-line Guided Filter call.\n* hough_point2_lineCalculates coordinates of line segment corresponded by point in Hough space.\n* hough_point2_line_defCalculates coordinates of line segment corresponded by point in Hough space.\n* is_rl_morphology_possibleCheck whether a custom made structuring element can be used with run length morphological operations.\n(It must consist of a continuous array of single runs per row)\n* joint_bilateral_filterApplies the joint bilateral filter to an image.\n* joint_bilateral_filter_defApplies the joint bilateral filter to an image.\n* l0_smoothGlobal image smoothing via L0 gradient minimization.\n* l0_smooth_defGlobal image smoothing via L0 gradient minimization.\n* morphology_exApplies a morphological operation to a run-length encoded binary image.\n* morphology_ex_defApplies a morphological operation to a run-length encoded binary image.\n* ni_black_thresholdPerforms thresholding on input images using Niblack’s technique or some of the popular variations it inspired.\n* ni_black_threshold_defPerforms thresholding on input images using Niblack’s technique or some of the popular variations it inspired.\n* paintPaint run length encoded binary image into an image.\n* pei_lin_normalizationCalculates an affine transformation that normalize given image using Pei&Lin Normalization.\n* pei_lin_normalization_1Calculates an affine transformation that normalize given image using Pei&Lin Normalization.\n* qconjcalculates conjugate of a quaternion image.\n* qdftPerforms a forward or inverse Discrete quaternion Fourier transform of a 2D quaternion array.\n* qmultiplyCalculates the per-element quaternion product of two arrays\n* qunitarydivides each element by its modulus.\n* radon_transformCalculate Radon Transform of an image.\n* radon_transform_defCalculate Radon Transform of an image.\n* read_gtFunction for reading ground truth disparity maps. Supports basic Middlebury and MPI-Sintel formats. Note that the resulting disparity map is scaled by 16.\n* rolling_guidance_filterApplies the rolling guidance filter to an image.\n* rolling_guidance_filter_defApplies the rolling guidance filter to an image.\n* thinningApplies a binary blob thinning operation, to achieve a skeletization of the input image.\n* thinning_defApplies a binary blob thinning operation, to achieve a skeletization of the input image.\n* thresholdApplies a fixed-level threshold to each array element.\n* transform_fdtransform a contour\n* transform_fd_deftransform a contour\n* weighted_median_filterApplies weighted median filter to an image.\n* weighted_median_filter_defApplies weighted median filter to an image.\n\nType Aliases\n---\n\n* Boxes\n\nModule opencv::xobjdetect\n===\n\nExtended object detection\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* WBDetectorWaldBoost detector\n\nTraits\n---\n\n* WBDetectorTraitMutable methods for crate::xobjdetect::WBDetector\n* WBDetectorTraitConstConstant methods for crate::xobjdetect::WBDetector\n\nModule opencv::xphoto\n===\n\nAdditional photo processing algorithms\n---\n\nModules\n---\n\n* prelude\n\nStructs\n---\n\n* GrayworldWBGray-world white balance algorithm\n* LearningBasedWBMore sophisticated learning-based automatic white balance algorithm.\n* SimpleWBA simple white balance algorithm that works by independently stretching each of the input image channels to the specified range. For increased robustness it ignores the top and bottom inline formula of pixel values.\n* TonemapDurandThis algorithm decomposes image into two layers: base layer and detail layer using bilateral filter and compresses contrast of the base layer thus preserving all the details.\n* WhiteBalancerThe base class for auto white balance algorithms.\n\nEnums\n---\n\n* Bm3dStepsBM3D algorithm steps\n* InpaintTypesVarious inpainting algorithms\n* TransformTypesBM3D transform types\n\nConstants\n---\n\n* BM3D_STEP1Execute only first step of the algorithm\n* BM3D_STEP2Execute only second step of the algorithm\n* BM3D_STEPALLExecute all steps of the algorithm\n* HAARUn-normalized Haar transform\n* INPAINT_FSR_BESTPerforms Frequency Selective Reconstruction (FSR).\nOne of the two quality profiles BEST and FAST can be chosen, depending on the time available for reconstruction.\nSee GenserPCS2018 and SeilerTIP2015 for details.\n* INPAINT_FSR_FASTSee #INPAINT_FSR_BEST\n* INPAINT_SHIFTMAPThis algorithm searches for dominant correspondences (transformations) of image patches and tries to seamlessly fill-in the area to be inpainted using this transformations\n\nTraits\n---\n\n* GrayworldWBTraitMutable methods for crate::xphoto::GrayworldWB\n* GrayworldWBTraitConstConstant methods for crate::xphoto::GrayworldWB\n* LearningBasedWBTraitMutable methods for crate::xphoto::LearningBasedWB\n* LearningBasedWBTraitConstConstant methods for crate::xphoto::LearningBasedWB\n* SimpleWBTraitMutable methods for crate::xphoto::SimpleWB\n* SimpleWBTraitConstConstant methods for crate::xphoto::SimpleWB\n* TonemapDurandTraitMutable methods for crate::xphoto::TonemapDurand\n* TonemapDurandTraitConstConstant methods for crate::xphoto::TonemapDurand\n* WhiteBalancerTraitMutable methods for crate::xphoto::WhiteBalancer\n* WhiteBalancerTraitConstConstant methods for crate::xphoto::WhiteBalancer\n\nFunctions\n---\n\n* apply_channel_gainsImplements an efficient fixed-point approximation for applying channel gains, which is the last step of multiple white balance algorithms.\n* bm3d_denoisingPerforms image denoising using the Block-Matching and 3D-filtering algorithm http://www.cs.tut.fi/~foi/GCF-BM3D/BM3D_TIP_2007.pdf with several computational optimizations. Noise expected to be a gaussian white noise.\n* bm3d_denoising_1Performs image denoising using the Block-Matching and 3D-filtering algorithm http://www.cs.tut.fi/~foi/GCF-BM3D/BM3D_TIP_2007.pdf with several computational optimizations. Noise expected to be a gaussian white noise.\n* bm3d_denoising_1_defPerforms image denoising using the Block-Matching and 3D-filtering algorithm http://www.cs.tut.fi/~foi/GCF-BM3D/BM3D_TIP_2007.pdf with several computational optimizations. Noise expected to be a gaussian white noise.\n* bm3d_denoising_defPerforms image denoising using the Block-Matching and 3D-filtering algorithm http://www.cs.tut.fi/~foi/GCF-BM3D/BM3D_TIP_2007.pdf with several computational optimizations. Noise expected to be a gaussian white noise.\n* create_grayworld_wbCreates an instance of GrayworldWB\n* create_learning_based_wbCreates an instance of LearningBasedWB\n* create_learning_based_wb_defCreates an instance of LearningBasedWB\n* create_simple_wbCreates an instance of SimpleWB\n* create_tonemap_durandCreates TonemapDurand object\n* create_tonemap_durand_defCreates TonemapDurand object\n* dct_denoisingThe function implements simple dct-based denoising\n* dct_denoising_defThe function implements simple dct-based denoising\n* inpaintThe function implements different single-image inpainting algorithms.\n* oil_paintingoilPainting See the book Holzmann1988 for details.\n* oil_painting_1oilPainting See the book Holzmann1988 for details.\n\nMacro opencv::not_opencv_branch_4\n===\n\n\n```\nmacro_rules! not_opencv_branch_4 {\n ($($tt:tt)*) => { ... };\n}\n```\nConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nMacro opencv::not_opencv_branch_32\n===\n\n\n```\nmacro_rules! not_opencv_branch_32 {\n ($($tt:tt)*) => { ... };\n}\n```\n👎Deprecated: OpenCV 3.2 is no longer supportedConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nMacro opencv::not_opencv_branch_34\n===\n\n\n```\nmacro_rules! not_opencv_branch_34 {\n ($($tt:tt)*) => { ... };\n}\n```\nConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nMacro opencv::opencv_branch_4\n===\n\n\n```\nmacro_rules! opencv_branch_4 {\n ($($tt:tt)*) => { ... };\n}\n```\nConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nMacro opencv::opencv_branch_32\n===\n\n\n```\nmacro_rules! opencv_branch_32 {\n ($($tt:tt)*) => { ... };\n}\n```\n👎Deprecated: OpenCV 3.2 is no longer supportedConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nMacro opencv::opencv_branch_34\n===\n\n\n```\nmacro_rules! opencv_branch_34 {\n ($($tt:tt)*) => { ... };\n}\n```\nConditional compilation macro based on OpenCV branch version for usage in external crates.\n\nExamples\n---\n\nAlternative import:\n```\nopencv::opencv_branch_4! {\n use opencv::imgproc::LINE_8;\n}\nopencv::not_opencv_branch_4! {\n use opencv::core::LINE_8;\n}\n```\nAlternative function call:\n```\nopencv::opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new_default(0)?;\n}\nopencv::not_opencv_branch_32! {\n let mut cam = opencv::videoio::VideoCapture::new(0, videoio::CAP_ANY)?;\n}\n```\n\nStruct opencv::Error\n===\n\n\n```\npub struct Error {\n pub code: i32,\n pub message: String,\n}\n```\nFields\n---\n\n`code: i32``message: String`Implementations\n---\n\n### impl Error\n\n#### pub fn new(code: i32, message: impl Into<String>) -> Self\n\nTrait Implementations\n---\n\n### impl Debug for Error\n\n#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. \n\n#### fn fmt(&self, f: &mut Formatter<'_>) -> Result\n\nFormats the value using the given formatter. \n\n1.30.0 · source#### fn source(&self) -> Option<&(dyn Error + 'static)The lower-level source of this error, if any. Read more1.0.0 · source#### fn description(&self) -> &str\n\n👎Deprecated since 1.42.0: use the Display impl or to_string() Read more1.0.0 · source#### fn cause(&self) -> Option<&dyn Error👎Deprecated since 1.33.0: replaced by Error::source, which can support downcasting#### fn provide<'a>(&'a self, request: &mut Request<'a>)\n\n🔬This is a nightly-only experimental API. (`error_generic_member_access`)Provides type based access to context intended for error reports. \n\n#### fn from(_: NulError) -> Self\n\nConverts to this type from the input type.### impl From<TryFromCharError> for Error\n\n#### fn from(_: TryFromCharError) -> Self\n\nConverts to this type from the input type.Auto Trait Implementations\n---\n\n### impl RefUnwindSafe for Error\n\n### impl Send for Error\n\n### impl Sync for Error\n\n### impl Unpin for Error\n\n### impl UnwindSafe for Error\n\nBlanket Implementations\n---\n\n### impl<T> Any for Twhere\n T: 'static + ?Sized,\n\n#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. \n T: ?Sized,\n\n#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. \n T: ?Sized,\n\n#### fn borrow_mut(&mut self) -> &mut T\n\nMutably borrows from an owned value. \n\n#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\n### impl<T, U> Into<U> for Twhere\n U: From<T>,\n\n#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\n### impl<T> ToString for Twhere\n T: Display + ?Sized,\n\n#### default fn to_string(&self) -> String\n\nConverts the given value to a `String`. \n U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.### impl<T, U> TryInto<U> for Twhere\n U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion.\n\nType Alias opencv::Result\n===\n\n\n```\npub type Result<T, E = Error> = Result<T, E>;\n```\nAliased Type\n---\n```\nenum Result<T, E = Error> {\n Ok(T),\n Err(E),\n}\n```\nVariants\n---\n\n1.0.0### Ok(T)\n\nContains the success value\n\n1.0.0### Err(E)\n\nContains the error value"}}},{"rowIdx":59479,"cells":{"project":{"kind":"string","value":"@ckeditor/ckeditor5-build-multi-root"},"source":{"kind":"string","value":"npm"},"language":{"kind":"string","value":"JavaScript"},"content":{"kind":"string","value":"[CKEditor 5 multi-root editor build](#ckeditor5-multi-root-editor-build)\n===\n\nThe multi-root editor build for CKEditor 5. Read more about the [multi-root editor build](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/predefined-builds.html#multi-root-editor) and see the [demo](https://ckeditor.com/docs/ckeditor5/latest/examples/builds/multi-root-editor.html).\n\n[Documentation](#documentation)\n---\n\nSee:\n\n* [Installation](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/quick-start.html) for how to install this package and what it contains.\n* [Editor lifecycle](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/editor-lifecycle.html) for how to create an editor and interact with it.\n* [Configuration](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/configuration.html) for how to configure the editor.\n* [Creating custom builds](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/quick-start.html#building-the-editor-from-source) for how to customize the build (configure and rebuild the editor bundle).\n\n[Quick start](#quick-start)\n---\n\nFirst, install the build from npm:\n```\nnpm install --save @ckeditor/ckeditor5-build-multi-root\n```\nAnd use it in your website:\n```\n<div id=\"toolbar\"></div>\n<div id=\"header\">\n\t<p>Content for header.</p>\n</div>\n<div id=\"content\">\n\t<p>Main editor content.</p>\n</div>\n<div class=\"boxes\">\n\t<div class=\"box box-left editor\">\n\t\t<div id=\"left-side\">\n\t\t\t<p>Content for left-side box.</p>\n\t\t</div>\n\t</div>\n\t<div class=\"box box-right editor\">\n\t\t<div id=\"right-side\">\n\t\t\t<p>Content for right-side box.</p>\n\t\t</div>\n\t</div>\n</div>\n<script src=\"./node_modules/@ckeditor/ckeditor5-build-multi-root/build/ckeditor.js\"></script>\n<script>\n\tMultiRootEditor\n\t\t\t.create( {\n\t\t\t\theader: document.getElementById( 'header' ),\n\t\t\t\tcontent: document.getElementById( 'content' ),\n\t\t\t\tleftSide: document.getElementById( 'left-side' ),\n\t\t\t\trightSide: document.getElementById( 'right-side' )\n\t\t\t} )\n\t\t\t.then( editor => {\n\t\t\t\twindow.editor = editor;\n\n\t\t\t\t// Append toolbar to a proper container.\n\t\t\t\tconst toolbarContainer = document.getElementById( 'toolbar' );\n\t\t\t\ttoolbarContainer.appendChild( editor.ui.view.toolbar.element );\n\t\t\t} )\n\t\t\t.catch( error => {\n\t\t\t\tconsole.error( 'There was a problem initializing the editor.', error );\n\t\t\t} );\n</script>\n```\nOr in your JavaScript application:\n```\nimport MultiRootEditor from '@ckeditor/ckeditor5-build-multi-root';\n\n// Or using the CommonJS version:\n// const MultiRootEditor = require( '@ckeditor/ckeditor5-build-multi-root' );\n\nMultiRootEditor\n\t.create( {\n\t\theader: document.getElementById( 'header' ),\n\t\tcontent: document.getElementById( 'content' ),\n\t\tleftSide: document.getElementById( 'left-side' ),\n\t\trightSide: document.getElementById( 'right-side' )\n\t} )\n\t.then( editor => {\n\t\twindow.editor = editor;\n\n\t\t// Append toolbar to a proper container.\n\t\tconst toolbarContainer = document.getElementById( 'toolbar' );\n\t\ttoolbarContainer.appendChild( editor.ui.view.toolbar.element );\n\t} )\n\t.catch( error => {\n\t\tconsole.error( 'There was a problem initializing the editor.', error );\n\t} );\n```\n**Note:** If you are planning to integrate CKEditor 5 deep into your application, it is actually more convenient and recommended to install and import the source modules directly (like it happens in `ckeditor.js`). Read more in the [Advanced setup guide](https://ckeditor.com/docs/ckeditor5/latest/installation/advanced/advanced-setup.html).\n\n[License](#license)\n---\n\nLicensed under the terms of [GNU General Public License Version 2 or later](http://www.gnu.org/licenses/gpl.html). For full details about the license, please check the `LICENSE.md` file or <https://ckeditor.com/legal/ckeditor-oss-license>.\nReadme\n---\n\n### Keywords\n\n* ckeditor5-build\n* ckeditor\n* ckeditor5\n* ckeditor 5\n* wysiwyg\n* rich text\n* editor\n* html\n* contentEditable\n* editing\n* operational transformation\n* ot\n* collaboration\n* collaborative\n* real-time\n* framework"}}},{"rowIdx":59480,"cells":{"project":{"kind":"string","value":"@thi.ng/rdom-canvas"},"source":{"kind":"string","value":"npm"},"language":{"kind":"string","value":"JavaScript"},"content":{"kind":"string","value":"This project is part of the\n[@thi.ng/umbrella](https://github.com/thi-ng/umbrella/) monorepo and anti-framework.\n\n* [About](#about)\n\t+ [General usage](#general-usage)\n\t+ [Control attributes](#control-attributes)\n* [Status](#status)\n* [Related packages](#related-packages)\n* [Installation](#installation)\n* [Dependencies](#dependencies)\n* [Usage examples](#usage-examples)\n* [API](#api)\n* [Authors](#authors)\n* [License](#license)\n\n[About](#about)\n---\n\n[@thi.ng/rdom](https://github.com/thi-ng/umbrella/tree/develop/packages/rdom) component wrapper for [@thi.ng/hiccup-canvas](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-canvas) and declarative canvas drawing. Please consult these packages' READMEs for further background information...\n\n### [General usage](#general-usage)\n\nAs with most thi.ng/rdom components, the state (aka geometry/scenegraph) for the canvas component is being sourced from a\n[thi.ng/rstream](https://github.com/thi-ng/umbrella/tree/develop/packages/rstream)\nsubscription. The canvas redraws every time that subscription delivers a new value. The size of the canvas can be given as a subscription too and if so will also automatically trigger resizing of the canvas.\n\nThe geometry to rendered to the canvas is expressed as\n[thi.ng/hiccup](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup),\nspecifically the flavor used by\n[thi.ng/hiccup-canvas](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-canvas),\nwhich (not just coincidentally) is the same as also used by\n[thi.ng/geom](https://github.com/thi-ng/umbrella/tree/develop/packages/geom)\nshapes.\n```\nimport { circle, group } from \"@thi.ng/geom\";\nimport { $canvas } from \"@thi.ng/rdom-canvas\";\nimport { fromRAF } from \"@thi.ng/rstream\";\nimport { repeatedly } from \"@thi.ng/transducers\";\n\n// create geometry stream/subscription const geo = fromRAF().map((t) =>\n // shape group w/ attribs (also see section in readme)\n group({ __background: \"#0ff\" }, [\n // create 10 circles\n ...repeatedly(\n (i) =>\n circle(\n [\n Math.sin(t * 0.01 + i * 0.5) * 150 + 300,\n Math.sin(t * 0.03 + i * 0.5) * 150 + 300\n ],\n 50,\n // colors can be given as RGBA vectors or CSS\n { fill: [i * 0.1, 0, i * 0.05] }\n ),\n 10\n )\n ])\n);\n\n// create & mount canvas component (w/ fixed size)\n$canvas(geo, [600, 600]).mount(document.body);\n```\n### [Control attributes](#control-attributes)\n\nThe root shape/group support the following special attributes:\n\n* `__background`: background color. If given, fills the canvas will given color before drawing\n* `__clear`: clear background flag. If true clears the canvas before drawing\n\nAlso see relevant section in the [thi.ng/hiccup-canvas README](https://github.com/thi-ng/umbrella/blob/develop/packages/hiccup-canvas/README.md#special-attributes)...\n\n[Status](#status)\n---\n\n**ALPHA** - bleeding edge / work-in-progress\n\n[Search or submit any issues for this package](https://github.com/thi-ng/umbrella/issues?q=%5Brdom-canvas%5D+in%3Atitle)\n\n[Related packages](#related-packages)\n---\n\n* [@thi.ng/hiccup-canvas](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-canvas) - Hiccup shape tree renderer for vanilla Canvas 2D contexts\n* [@thi.ng/hiccup-svg](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-svg) - SVG element functions for [@thi.ng/hiccup](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup) & related tooling\n* [@thi.ng/geom](https://github.com/thi-ng/umbrella/tree/develop/packages/geom) - Functional, polymorphic API for 2D geometry types & SVG generation\n* [@thi.ng/scenegraph](https://github.com/thi-ng/umbrella/tree/develop/packages/scenegraph) - Extensible 2D/3D scene graph with [@thi.ng/hiccup-canvas](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-canvas) support\n\n[Installation](#installation)\n---\n```\nyarn add @thi.ng/rdom-canvas\n```\nES module import:\n```\n<script type=\"module\" src=\"https://cdn.skypack.dev/@thi.ng/rdom-canvas\"></script>\n```\n[Skypack documentation](https://docs.skypack.dev/)\n\nFor Node.js REPL:\n```\nconst rdomCanvas = await import(\"@thi.ng/rdom-canvas\");\n```\nPackage sizes (brotli'd, pre-treeshake): ESM: 596 bytes\n\n[Dependencies](#dependencies)\n---\n\n* [@thi.ng/adapt-dpi](https://github.com/thi-ng/umbrella/tree/develop/packages/adapt-dpi)\n* [@thi.ng/api](https://github.com/thi-ng/umbrella/tree/develop/packages/api)\n* [@thi.ng/associative](https://github.com/thi-ng/umbrella/tree/develop/packages/associative)\n* [@thi.ng/checks](https://github.com/thi-ng/umbrella/tree/develop/packages/checks)\n* [@thi.ng/hiccup-canvas](https://github.com/thi-ng/umbrella/tree/develop/packages/hiccup-canvas)\n* [@thi.ng/rdom](https://github.com/thi-ng/umbrella/tree/develop/packages/rdom)\n* [@thi.ng/rstream](https://github.com/thi-ng/umbrella/tree/develop/packages/rstream)\n\n[Usage examples](#usage-examples)\n---\n\nSeveral demos in this repo's\n[/examples](https://github.com/thi-ng/umbrella/tree/develop/examples)\ndirectory are using this package.\n\nA selection:\n\n| Screenshot | Description | Live demo | Source |\n| --- | --- | --- | --- |\n| | Interactive visualization of closest points on ellipses | [Demo](https://demo.thi.ng/umbrella/ellipse-proximity/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/ellipse-proximity) |\n| | 2.5D hidden line visualization of digital elevation files (DEM) | [Demo](https://demo.thi.ng/umbrella/geom-terrain-viz/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/geom-terrain-viz) |\n| | Quasi-random lattice generator | [Demo](https://demo.thi.ng/umbrella/quasi-lattice/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/quasi-lattice) |\n| | Minimal rdom-canvas animation | [Demo](https://demo.thi.ng/umbrella/rdom-canvas-basics/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/rdom-canvas-basics) |\n| | rdom & hiccup-canvas interop test | [Demo](https://demo.thi.ng/umbrella/rdom-lissajous/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/rdom-lissajous) |\n| | Fitting, transforming & plotting 10k data points per frame using SIMD | [Demo](https://demo.thi.ng/umbrella/simd-plot/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/simd-plot) |\n| | Multi-layer vectorization & dithering of bitmap images | [Demo](https://demo.thi.ng/umbrella/trace-bitmap/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/trace-bitmap) |\n\n[API](#api)\n---\n\n[Generated API docs](https://docs.thi.ng/umbrella/rdom-canvas/)\n\nTODO\n\n[Authors](#authors)\n---\n\n* [<NAME>](https://thi.ng)\n\nIf this project contributes to an academic publication, please cite it as:\n```\n@misc{thing-rdom-canvas,\n title = \"@thi.ng/rdom-canvas\",\n author = \"<NAME>\",\n note = \"https://thi.ng/rdom-canvas\",\n year = 2020\n}\n```\n[License](#license)\n---\n\n© 2020 - 2023 <NAME> // Apache License 2.0\nReadme\n---\n\n### Keywords\n\n* animation\n* browser\n* canvas\n* component\n* declarative\n* graphics\n* hiccup\n* scenegraph\n* typescript\n* ui\n* wrapper"}}},{"rowIdx":59481,"cells":{"project":{"kind":"string","value":"GRMustache"},"source":{"kind":"string","value":"cocoapods"},"language":{"kind":"string","value":"Objective-C"},"content":{"kind":"string","value":"grmustache.swift\n===\n\nWelcome to the documentation for the grmustache.swift framework! In this guide, we will explore the features, usage, and advantages of using grmustache.swift in your Swift projects.\n\nWhat is grmustache.swift?\n---\n\ngrmustache.swift is a powerful and lightweight implementation of the Mustache templating language for Swift. Mustache is a logic-less template system that allows you to define templates with placeholders that are then replaced with actual values at runtime.\n\nThis framework provides an intuitive way to render Mustache templates, making it easy to generate dynamic content such as HTML, emails, source code, configuration files, and more.\n\nInstallation\n---\n\nTo install grmustache.swift, follow these steps:\n\n* Open your Xcode project\n* Go to File > Swift Packages > Add Package Dependency\n* Enter the repository URL: `https://github.com/your-repo/grmustache.swift`\n* Choose the latest version of grmustache.swift\n* Click Next and follow the prompts to complete the installation\n\nUsage\n---\n\ngrmustache.swift offers a simple and elegant API for rendering Mustache templates. Here’s an example of how to use it:\n```\nimport GRMustache\n\n// Create a Mustache template let template = try Template(string: \"Hello, {{name}}!\")\n\n// Define a context let context = [\"name\": \"<NAME>\"]\n\n// Render the template with the context let rendered = try template.render(with: Box(context))\n\nprint(rendered)\n// Output: Hello, <NAME>!\n```\nAdvantages\n---\n\ngrmustache.swift offers several advantages over other templating solutions:\n\n* Lightweight and efficient\n* Excellent performance\n* Supports advanced Mustache features like lambdas, filters, and partials\n* Extensive documentation and active community support\n* Compatible with macOS, iOS, tvOS, and watchOS\n\nAdditional Resources\n---\n\n* [grmustache.swift GitHub Repository](https://github.com/your-repo/grmustache.swift)\n* [Mustache Documentation](https://mustache.github.io/mustache.5.html)\n* [Swift Programming Language](https://www.swift.org)\n\nThat’s all you need to know to get started with grmustache.swift. Happy templating!"}}},{"rowIdx":59482,"cells":{"project":{"kind":"string","value":"atsame54_xpro"},"source":{"kind":"string","value":"rust"},"language":{"kind":"string","value":"Rust"},"content":{"kind":"string","value":"Module atsame54_xpro::pins\n===\n\nSAM E54 XPlained Pro Pin Definitions\n\nStructs\n---\n\n* PinsBSP replacement for the HAL\n`Pins` type\n\nConstants\n---\n\n* ADC0_ANALOG0_IDDynPinId \nfor the `Adc0Analog0` alias.\n* ADC0_ANALOG0_MODEDynPinMode \nfor the `Adc0Analog0` alias.\n* ADC0_ANALOG1_IDDynPinId \nfor the `Adc0Analog1` alias.\n* ADC0_ANALOG1_MODEDynPinMode \nfor the `Adc0Analog1` alias.\n* ADC0_ANALOG2_IDDynPinId \nfor the `Adc0Analog2` alias.\n* ADC0_ANALOG2_MODEDynPinMode \nfor the `Adc0Analog2` alias.\n* ADC0_ANALOG3_IDDynPinId \nfor the `Adc0Analog3` alias.\n* ADC0_ANALOG3_MODEDynPinMode \nfor the `Adc0Analog3` alias.\n* ADC0_ANALOG4_IDDynPinId \nfor the `Adc0Analog4` alias.\n* ADC0_ANALOG4_MODEDynPinMode \nfor the `Adc0Analog4` alias.\n* ADC0_ANALOG5_IDDynPinId \nfor the `Adc0Analog5` alias.\n* ADC0_ANALOG5_MODEDynPinMode \nfor the `Adc0Analog5` alias.\n* ADC0_ANALOG6_IDDynPinId \nfor the `Adc0Analog6` alias.\n* ADC0_ANALOG6_MODEDynPinMode \nfor the `Adc0Analog6` alias.\n* ADC0_ANALOG7_IDDynPinId \nfor the `Adc0Analog7` alias.\n* ADC0_ANALOG7_MODEDynPinMode \nfor the `Adc0Analog7` alias.\n* ADC1_ANALOG0_IDDynPinId \nfor the `Adc1Analog0` alias.\n* ADC1_ANALOG0_MODEDynPinMode \nfor the `Adc1Analog0` alias.\n* ADC1_ANALOG1_IDDynPinId \nfor the `Adc1Analog1` alias.\n* ADC1_ANALOG1_MODEDynPinMode \nfor the `Adc1Analog1` alias.\n* ADC1_ANALOG4_IDDynPinId \nfor the `Adc1Analog4` alias.\n* ADC1_ANALOG4_MODEDynPinMode \nfor the `Adc1Analog4` alias.\n* ADC1_ANALOG5_IDDynPinId \nfor the `Adc1Analog5` alias.\n* ADC1_ANALOG5_MODEDynPinMode \nfor the `Adc1Analog5` alias.\n* ADC1_ANALOG6_IDDynPinId \nfor the `Adc1Analog6` alias.\n* ADC1_ANALOG6_MODEDynPinMode \nfor the `Adc1Analog6` alias.\n* ADC1_ANALOG7_IDDynPinId \nfor the `Adc1Analog7` alias.\n* ADC1_ANALOG7_MODEDynPinMode \nfor the `Adc1Analog7` alias.\n* ADC1_ANALOG8_IDDynPinId \nfor the `Adc1Analog8` alias.\n* ADC1_ANALOG8_MODEDynPinMode \nfor the `Adc1Analog8` alias.\n* ADC1_ANALOG9_IDDynPinId \nfor the `Adc1Analog9` alias.\n* ADC1_ANALOG9_MODEDynPinMode \nfor the `Adc1Analog9` alias.\n* ADC1_ANALOG14_IDDynPinId \nfor the `Adc1Analog14` alias.\n* ADC1_ANALOG14_MODEDynPinMode \nfor the `Adc1Analog14` alias.\n* ADC1_ANALOG15_IDDynPinId \nfor the `Adc1Analog15` alias.\n* ADC1_ANALOG15_MODEDynPinMode \nfor the `Adc1Analog15` alias.\n* ADC_DAC_HEADER_IDDynPinId \nfor the `AdcDacHeader` alias.\n* ADC_DAC_HEADER_MODEDynPinMode \nfor the `AdcDacHeader` alias.\n* ATA6561_RX_IDDynPinId \nfor the `Ata6561Rx` alias.\n* ATA6561_RX_MODEDynPinMode \nfor the `Ata6561Rx` alias.\n* ATA6561_STANDBY_IDDynPinId \nfor the `Ata6561Standby` alias.\n* ATA6561_STANDBY_MODEDynPinMode \nfor the `Ata6561Standby` alias.\n* ATA6561_TX_IDDynPinId \nfor the `Ata6561Tx` alias.\n* ATA6561_TX_MODEDynPinMode \nfor the `Ata6561Tx` alias.\n* BUTTON_IDDynPinId \nfor the `Button` alias.\n* BUTTON_MODEDynPinMode \nfor the `Button` alias.\n* DGI_I2C_SCL_IDDynPinId \nfor the `DgiI2cScl` alias.\n* DGI_I2C_SCL_MODEDynPinMode \nfor the `DgiI2cScl` alias.\n* DGI_I2C_SDA_IDDynPinId \nfor the `DgiI2cSda` alias.\n* DGI_I2C_SDA_MODEDynPinMode \nfor the `DgiI2cSda` alias.\n* DGI_SPI_CS_IDDynPinId \nfor the `DgiSpiCs` alias.\n* DGI_SPI_CS_MODEDynPinMode \nfor the `DgiSpiCs` alias.\n* DGI_SPI_MISO_IDDynPinId \nfor the `DgiSpiMiso` alias.\n* DGI_SPI_MISO_MODEDynPinMode \nfor the `DgiSpiMiso` alias.\n* DGI_SPI_MOSI_IDDynPinId \nfor the `DgiSpiMosi` alias.\n* DGI_SPI_MOSI_MODEDynPinMode \nfor the `DgiSpiMosi` alias.\n* DGI_SPI_SCK_IDDynPinId \nfor the `DgiSpiSck` alias.\n* DGI_SPI_SCK_MODEDynPinMode \nfor the `DgiSpiSck` alias.\n* EDBG_GPIO0_IN_IDDynPinId \nfor the `EdbgGpio0In` alias.\n* EDBG_GPIO0_IN_MODEDynPinMode \nfor the `EdbgGpio0In` alias.\n* EDBG_GPIO0_OUT_IDDynPinId \nfor the `EdbgGpio0Out` alias.\n* EDBG_GPIO0_OUT_MODEDynPinMode \nfor the `EdbgGpio0Out` alias.\n* EDBG_GPIO1_IN_IDDynPinId \nfor the `EdbgGpio1In` alias.\n* EDBG_GPIO1_IN_MODEDynPinMode \nfor the `EdbgGpio1In` alias.\n* EDBG_GPIO1_OUT_IDDynPinId \nfor the `EdbgGpio1Out` alias.\n* EDBG_GPIO1_OUT_MODEDynPinMode \nfor the `EdbgGpio1Out` alias.\n* EDBG_GPIO2_IN_IDDynPinId \nfor the `EdbgGpio2In` alias.\n* EDBG_GPIO2_IN_MODEDynPinMode \nfor the `EdbgGpio2In` alias.\n* EDBG_GPIO2_OUT_IDDynPinId \nfor the `EdbgGpio2Out` alias.\n* EDBG_GPIO2_OUT_MODEDynPinMode \nfor the `EdbgGpio2Out` alias.\n* EDBG_UART_RX_IDDynPinId \nfor the `EdbgUartRx` alias.\n* EDBG_UART_RX_MODEDynPinMode \nfor the `EdbgUartRx` alias.\n* EDBG_UART_TX_IDDynPinId \nfor the `EdbgUartTx` alias.\n* EDBG_UART_TX_MODEDynPinMode \nfor the `EdbgUartTx` alias.\n* ETH_CRS_DV_IDDynPinId \nfor the `EthCrsDv` alias.\n* ETH_CRS_DV_MODEDynPinMode \nfor the `EthCrsDv` alias.\n* ETH_GMDIO_IDDynPinId \nfor the `EthGmdio` alias.\n* ETH_GMDIO_MODEDynPinMode \nfor the `EthGmdio` alias.\n* ETH_INTERRUPT_IDDynPinId \nfor the `EthInterrupt` alias.\n* ETH_INTERRUPT_MODEDynPinMode \nfor the `EthInterrupt` alias.\n* ETH_MDC_IDDynPinId \nfor the `EthMdc` alias.\n* ETH_MDC_MODEDynPinMode \nfor the `EthMdc` alias.\n* ETH_REF_CLK_IDDynPinId \nfor the `EthRefClk` alias.\n* ETH_REF_CLK_MODEDynPinMode \nfor the `EthRefClk` alias.\n* ETH_RESET_IDDynPinId \nfor the `EthReset` alias.\n* ETH_RESET_MODEDynPinMode \nfor the `EthReset` alias.\n* ETH_RXD0_IDDynPinId \nfor the `EthRxd0` alias.\n* ETH_RXD0_MODEDynPinMode \nfor the `EthRxd0` alias.\n* ETH_RXD1_IDDynPinId \nfor the `EthRxd1` alias.\n* ETH_RXD1_MODEDynPinMode \nfor the `EthRxd1` alias.\n* ETH_RXER_IDDynPinId \nfor the `EthRxer` alias.\n* ETH_RXER_MODEDynPinMode \nfor the `EthRxer` alias.\n* ETH_TXD0_IDDynPinId \nfor the `EthTxd0` alias.\n* ETH_TXD0_MODEDynPinMode \nfor the `EthTxd0` alias.\n* ETH_TXD1_IDDynPinId \nfor the `EthTxd1` alias.\n* ETH_TXD1_MODEDynPinMode \nfor the `EthTxd1` alias.\n* ETH_TXEN_IDDynPinId \nfor the `EthTxen` alias.\n* ETH_TXEN_MODEDynPinMode \nfor the `EthTxen` alias.\n* EXT1_ADC_MINUS_IDDynPinId \nfor the `Ext1AdcMinus` alias.\n* EXT1_ADC_MINUS_MODEDynPinMode \nfor the `Ext1AdcMinus` alias.\n* EXT1_ADC_PLUS_IDDynPinId \nfor the `Ext1AdcPlus` alias.\n* EXT1_ADC_PLUS_MODEDynPinMode \nfor the `Ext1AdcPlus` alias.\n* EXT1_GPIO1_IN_IDDynPinId \nfor the `Ext1Gpio1In` alias.\n* EXT1_GPIO1_IN_MODEDynPinMode \nfor the `Ext1Gpio1In` alias.\n* EXT1_GPIO1_OUT_IDDynPinId \nfor the `Ext1Gpio1Out` alias.\n* EXT1_GPIO1_OUT_MODEDynPinMode \nfor the `Ext1Gpio1Out` alias.\n* EXT1_GPIO2_IN_IDDynPinId \nfor the `Ext1Gpio2In` alias.\n* EXT1_GPIO2_IN_MODEDynPinMode \nfor the `Ext1Gpio2In` alias.\n* EXT1_GPIO2_OUT_IDDynPinId \nfor the `Ext1Gpio2Out` alias.\n* EXT1_GPIO2_OUT_MODEDynPinMode \nfor the `Ext1Gpio2Out` alias.\n* EXT1_I2C_SCL_IDDynPinId \nfor the `Ext1I2cScl` alias.\n* EXT1_I2C_SCL_MODEDynPinMode \nfor the `Ext1I2cScl` alias.\n* EXT1_I2C_SDA_IDDynPinId \nfor the `Ext1I2cSda` alias.\n* EXT1_I2C_SDA_MODEDynPinMode \nfor the `Ext1I2cSda` alias.\n* EXT1_IRQ_GPIO_IN_IDDynPinId \nfor the `Ext1IrqGpioIn` alias.\n* EXT1_IRQ_GPIO_IN_MODEDynPinMode \nfor the `Ext1IrqGpioIn` alias.\n* EXT1_IRQ_GPIO_OUT_IDDynPinId \nfor the `Ext1IrqGpioOut` alias.\n* EXT1_IRQ_GPIO_OUT_MODEDynPinMode \nfor the `Ext1IrqGpioOut` alias.\n* EXT1_PWM_MINUS_IDDynPinId \nfor the `Ext1PwmMinus` alias.\n* EXT1_PWM_MINUS_MODEDynPinMode \nfor the `Ext1PwmMinus` alias.\n* EXT1_PWM_PLUS_IDDynPinId \nfor the `Ext1PwmPlus` alias.\n* EXT1_PWM_PLUS_MODEDynPinMode \nfor the `Ext1PwmPlus` alias.\n* EXT1_SPI_CS_A_IDDynPinId \nfor the `Ext1SpiCsA` alias.\n* EXT1_SPI_CS_A_MODEDynPinMode \nfor the `Ext1SpiCsA` alias.\n* EXT1_SPI_CS_B_IDDynPinId \nfor the `Ext1SpiCsB` alias.\n* EXT1_SPI_CS_B_MODEDynPinMode \nfor the `Ext1SpiCsB` alias.\n* EXT1_SPI_MISO_IDDynPinId \nfor the `Ext1SpiMiso` alias.\n* EXT1_SPI_MISO_MODEDynPinMode \nfor the `Ext1SpiMiso` alias.\n* EXT1_SPI_MOSI_IDDynPinId \nfor the `Ext1SpiMosi` alias.\n* EXT1_SPI_MOSI_MODEDynPinMode \nfor the `Ext1SpiMosi` alias.\n* EXT1_SPI_SCK_IDDynPinId \nfor the `Ext1SpiSck` alias.\n* EXT1_SPI_SCK_MODEDynPinMode \nfor the `Ext1SpiSck` alias.\n* EXT1_UART_CTS_IDDynPinId \nfor the `Ext1UartCts` alias.\n* EXT1_UART_CTS_MODEDynPinMode \nfor the `Ext1UartCts` alias.\n* EXT1_UART_RTS_IDDynPinId \nfor the `Ext1UartRts` alias.\n* EXT1_UART_RTS_MODEDynPinMode \nfor the `Ext1UartRts` alias.\n* EXT1_UART_RX_IDDynPinId \nfor the `Ext1UartRx` alias.\n* EXT1_UART_RX_MODEDynPinMode \nfor the `Ext1UartRx` alias.\n* EXT1_UART_TX_IDDynPinId \nfor the `Ext1UartTx` alias.\n* EXT1_UART_TX_MODEDynPinMode \nfor the `Ext1UartTx` alias.\n* EXT2_ADC_MINUS_IDDynPinId \nfor the `Ext2AdcMinus` alias.\n* EXT2_ADC_MINUS_MODEDynPinMode \nfor the `Ext2AdcMinus` alias.\n* EXT2_ADC_PLUS_IDDynPinId \nfor the `Ext2AdcPlus` alias.\n* EXT2_ADC_PLUS_MODEDynPinMode \nfor the `Ext2AdcPlus` alias.\n* EXT2_GPIO1_IN_IDDynPinId \nfor the `Ext2Gpio1In` alias.\n* EXT2_GPIO1_IN_MODEDynPinMode \nfor the `Ext2Gpio1In` alias.\n* EXT2_GPIO1_OUT_IDDynPinId \nfor the `Ext2Gpio1Out` alias.\n* EXT2_GPIO1_OUT_MODEDynPinMode \nfor the `Ext2Gpio1Out` alias.\n* EXT2_GPIO2_IN_IDDynPinId \nfor the `Ext2Gpio2In` alias.\n* EXT2_GPIO2_IN_MODEDynPinMode \nfor the `Ext2Gpio2In` alias.\n* EXT2_GPIO2_OUT_IDDynPinId \nfor the `Ext2Gpio2Out` alias.\n* EXT2_GPIO2_OUT_MODEDynPinMode \nfor the `Ext2Gpio2Out` alias.\n* EXT2_I2C_SCL_IDDynPinId \nfor the `Ext2I2cScl` alias.\n* EXT2_I2C_SCL_MODEDynPinMode \nfor the `Ext2I2cScl` alias.\n* EXT2_I2C_SDA_IDDynPinId \nfor the `Ext2I2cSda` alias.\n* EXT2_I2C_SDA_MODEDynPinMode \nfor the `Ext2I2cSda` alias.\n* EXT2_IRQ_GPIO_IN_IDDynPinId \nfor the `Ext2IrqGpioIn` alias.\n* EXT2_IRQ_GPIO_IN_MODEDynPinMode \nfor the `Ext2IrqGpioIn` alias.\n* EXT2_IRQ_GPIO_OUT_IDDynPinId \nfor the `Ext2IrqGpioOut` alias.\n* EXT2_IRQ_GPIO_OUT_MODEDynPinMode \nfor the `Ext2IrqGpioOut` alias.\n* EXT2_PWM_MINUS_IDDynPinId \nfor the `Ext2PwmMinus` alias.\n* EXT2_PWM_MINUS_MODEDynPinMode \nfor the `Ext2PwmMinus` alias.\n* EXT2_PWM_PLUS_IDDynPinId \nfor the `Ext2PwmPlus` alias.\n* EXT2_PWM_PLUS_MODEDynPinMode \nfor the `Ext2PwmPlus` alias.\n* EXT2_SPI_CS_A_IDDynPinId \nfor the `Ext2SpiCsA` alias.\n* EXT2_SPI_CS_A_MODEDynPinMode \nfor the `Ext2SpiCsA` alias.\n* EXT2_SPI_CS_B_IDDynPinId \nfor the `Ext2SpiCsB` alias.\n* EXT2_SPI_CS_B_MODEDynPinMode \nfor the `Ext2SpiCsB` alias.\n* EXT2_SPI_MISO_IDDynPinId \nfor the `Ext2SpiMiso` alias.\n* EXT2_SPI_MISO_MODEDynPinMode \nfor the `Ext2SpiMiso` alias.\n* EXT2_SPI_MOSI_IDDynPinId \nfor the `Ext2SpiMosi` alias.\n* EXT2_SPI_MOSI_MODEDynPinMode \nfor the `Ext2SpiMosi` alias.\n* EXT2_SPI_SCK_IDDynPinId \nfor the `Ext2SpiSck` alias.\n* EXT2_SPI_SCK_MODEDynPinMode \nfor the `Ext2SpiSck` alias.\n* EXT2_UART_RX_IDDynPinId \nfor the `Ext2UartRx` alias.\n* EXT2_UART_RX_MODEDynPinMode \nfor the `Ext2UartRx` alias.\n* EXT2_UART_TX_IDDynPinId \nfor the `Ext2UartTx` alias.\n* EXT2_UART_TX_MODEDynPinMode \nfor the `Ext2UartTx` alias.\n* EXT3_ADC_MINUS_IDDynPinId \nfor the `Ext3AdcMinus` alias.\n* EXT3_ADC_MINUS_MODEDynPinMode \nfor the `Ext3AdcMinus` alias.\n* EXT3_ADC_PLUS_IDDynPinId \nfor the `Ext3AdcPlus` alias.\n* EXT3_ADC_PLUS_MODEDynPinMode \nfor the `Ext3AdcPlus` alias.\n* EXT3_GPIO1_IN_IDDynPinId \nfor the `Ext3Gpio1In` alias.\n* EXT3_GPIO1_IN_MODEDynPinMode \nfor the `Ext3Gpio1In` alias.\n* EXT3_GPIO1_OUT_IDDynPinId \nfor the `Ext3Gpio1Out` alias.\n* EXT3_GPIO1_OUT_MODEDynPinMode \nfor the `Ext3Gpio1Out` alias.\n* EXT3_GPIO2_IN_IDDynPinId \nfor the `Ext3Gpio2In` alias.\n* EXT3_GPIO2_IN_MODEDynPinMode \nfor the `Ext3Gpio2In` alias.\n* EXT3_GPIO2_OUT_IDDynPinId \nfor the `Ext3Gpio2Out` alias.\n* EXT3_GPIO2_OUT_MODEDynPinMode \nfor the `Ext3Gpio2Out` alias.\n* EXT3_I2C_SCL_IDDynPinId \nfor the `Ext3I2cScl` alias.\n* EXT3_I2C_SCL_MODEDynPinMode \nfor the `Ext3I2cScl` alias.\n* EXT3_I2C_SDA_IDDynPinId \nfor the `Ext3I2cSda` alias.\n* EXT3_I2C_SDA_MODEDynPinMode \nfor the `Ext3I2cSda` alias.\n* EXT3_IRQ_GPIO_IN_IDDynPinId \nfor the `Ext3IrqGpioIn` alias.\n* EXT3_IRQ_GPIO_IN_MODEDynPinMode \nfor the `Ext3IrqGpioIn` alias.\n* EXT3_IRQ_GPIO_OUT_IDDynPinId \nfor the `Ext3IrqGpioOut` alias.\n* EXT3_IRQ_GPIO_OUT_MODEDynPinMode \nfor the `Ext3IrqGpioOut` alias.\n* EXT3_PWM_MINUS_IDDynPinId \nfor the `Ext3PwmMinus` alias.\n* EXT3_PWM_MINUS_MODEDynPinMode \nfor the `Ext3PwmMinus` alias.\n* EXT3_PWM_PLUS_IDDynPinId \nfor the `Ext3PwmPlus` alias.\n* EXT3_PWM_PLUS_MODEDynPinMode \nfor the `Ext3PwmPlus` alias.\n* EXT3_SPI_CS_A_IDDynPinId \nfor the `Ext3SpiCsA` alias.\n* EXT3_SPI_CS_A_MODEDynPinMode \nfor the `Ext3SpiCsA` alias.\n* EXT3_SPI_CS_B_IDDynPinId \nfor the `Ext3SpiCsB` alias.\n* EXT3_SPI_CS_B_MODEDynPinMode \nfor the `Ext3SpiCsB` alias.\n* EXT3_SPI_MISO_IDDynPinId \nfor the `Ext3SpiMiso` alias.\n* EXT3_SPI_MISO_MODEDynPinMode \nfor the `Ext3SpiMiso` alias.\n* EXT3_SPI_MOSI_IDDynPinId \nfor the `Ext3SpiMosi` alias.\n* EXT3_SPI_MOSI_MODEDynPinMode \nfor the `Ext3SpiMosi` alias.\n* EXT3_SPI_SCK_IDDynPinId \nfor the `Ext3SpiSck` alias.\n* EXT3_SPI_SCK_MODEDynPinMode \nfor the `Ext3SpiSck` alias.\n* EXT3_UART_RX_IDDynPinId \nfor the `Ext3UartRx` alias.\n* EXT3_UART_RX_MODEDynPinMode \nfor the `Ext3UartRx` alias.\n* EXT3_UART_TX_IDDynPinId \nfor the `Ext3UartTx` alias.\n* EXT3_UART_TX_MODEDynPinMode \nfor the `Ext3UartTx` alias.\n* I2S_FS0_IDDynPinId \nfor the `I2sFs0` alias.\n* I2S_FS0_MODEDynPinMode \nfor the `I2sFs0` alias.\n* I2S_FS1_IDDynPinId \nfor the `I2sFs1` alias.\n* I2S_FS1_MODEDynPinMode \nfor the `I2sFs1` alias.\n* I2S_SDI_IDDynPinId \nfor the `I2sSdi` alias.\n* I2S_SDI_MODEDynPinMode \nfor the `I2sSdi` alias.\n* I2S_SDO_IDDynPinId \nfor the `I2sSdo` alias.\n* I2S_SDO_MODEDynPinMode \nfor the `I2sSdo` alias.\n* LED_IDDynPinId \nfor the `Led` alias.\n* LED_MODEDynPinMode \nfor the `Led` alias.\n* PCC_DOUT00_IDDynPinId \nfor the `PccDout00` alias.\n* PCC_DOUT00_MODEDynPinMode \nfor the `PccDout00` alias.\n* PCC_DOUT01_IDDynPinId \nfor the `PccDout01` alias.\n* PCC_DOUT01_MODEDynPinMode \nfor the `PccDout01` alias.\n* PCC_DOUT02_IDDynPinId \nfor the `PccDout02` alias.\n* PCC_DOUT02_MODEDynPinMode \nfor the `PccDout02` alias.\n* PCC_DOUT03_IDDynPinId \nfor the `PccDout03` alias.\n* PCC_DOUT03_MODEDynPinMode \nfor the `PccDout03` alias.\n* PCC_DOUT04_IDDynPinId \nfor the `PccDout04` alias.\n* PCC_DOUT04_MODEDynPinMode \nfor the `PccDout04` alias.\n* PCC_DOUT05_IDDynPinId \nfor the `PccDout05` alias.\n* PCC_DOUT05_MODEDynPinMode \nfor the `PccDout05` alias.\n* PCC_DOUT06_IDDynPinId \nfor the `PccDout06` alias.\n* PCC_DOUT06_MODEDynPinMode \nfor the `PccDout06` alias.\n* PCC_DOUT07_IDDynPinId \nfor the `PccDout07` alias.\n* PCC_DOUT07_MODEDynPinMode \nfor the `PccDout07` alias.\n* PCC_DOUT08_IDDynPinId \nfor the `PccDout08` alias.\n* PCC_DOUT08_MODEDynPinMode \nfor the `PccDout08` alias.\n* PCC_DOUT09_IDDynPinId \nfor the `PccDout09` alias.\n* PCC_DOUT09_MODEDynPinMode \nfor the `PccDout09` alias.\n* PCC_HSYNC_IDDynPinId \nfor the `PccHsync` alias.\n* PCC_HSYNC_MODEDynPinMode \nfor the `PccHsync` alias.\n* PCC_PCLK_IDDynPinId \nfor the `PccPclk` alias.\n* PCC_PCLK_MODEDynPinMode \nfor the `PccPclk` alias.\n* PCC_PWDN_IDDynPinId \nfor the `PccPwdn` alias.\n* PCC_PWDN_MODEDynPinMode \nfor the `PccPwdn` alias.\n* PCC_RESET_IDDynPinId \nfor the `PccReset` alias.\n* PCC_RESET_MODEDynPinMode \nfor the `PccReset` alias.\n* PCC_VSYNC_IDDynPinId \nfor the `PccVsync` alias.\n* PCC_VSYNC_MODEDynPinMode \nfor the `PccVsync` alias.\n* PCC_XCLK_IDDynPinId \nfor the `PccXclk` alias.\n* PCC_XCLK_MODEDynPinMode \nfor the `PccXclk` alias.\n* PDEC_INDEX_IDDynPinId \nfor the `PdecIndex` alias.\n* PDEC_INDEX_MODEDynPinMode \nfor the `PdecIndex` alias.\n* PDEC_PHASE_A_IDDynPinId \nfor the `PdecPhaseA` alias.\n* PDEC_PHASE_A_MODEDynPinMode \nfor the `PdecPhaseA` alias.\n* PDEC_PHASE_B_IDDynPinId \nfor the `PdecPhaseB` alias.\n* PDEC_PHASE_B_MODEDynPinMode \nfor the `PdecPhaseB` alias.\n* QSPI_DATA0_IDDynPinId \nfor the `QspiData0` alias.\n* QSPI_DATA0_MODEDynPinMode \nfor the `QspiData0` alias.\n* QSPI_DATA1_IDDynPinId \nfor the `QspiData1` alias.\n* QSPI_DATA1_MODEDynPinMode \nfor the `QspiData1` alias.\n* QSPI_DATA2_IDDynPinId \nfor the `QspiData2` alias.\n* QSPI_DATA2_MODEDynPinMode \nfor the `QspiData2` alias.\n* QSPI_DATA3_IDDynPinId \nfor the `QspiData3` alias.\n* QSPI_DATA3_MODEDynPinMode \nfor the `QspiData3` alias.\n* QSPI_SCK_IDDynPinId \nfor the `QspiSck` alias.\n* QSPI_SCK_MODEDynPinMode \nfor the `QspiSck` alias.\n* QSPI_SCS_IDDynPinId \nfor the `QspiScs` alias.\n* QSPI_SCS_MODEDynPinMode \nfor the `QspiScs` alias.\n* QT_BUTTON_IDDynPinId \nfor the `QtButton` alias.\n* QT_BUTTON_MODEDynPinMode \nfor the `QtButton` alias.\n* SD_CD_IDDynPinId \nfor the `SdCd` alias.\n* SD_CD_MODEDynPinMode \nfor the `SdCd` alias.\n* SD_CLK_IDDynPinId \nfor the `SdClk` alias.\n* SD_CLK_MODEDynPinMode \nfor the `SdClk` alias.\n* SD_CMD_IDDynPinId \nfor the `SdCmd` alias.\n* SD_CMD_MODEDynPinMode \nfor the `SdCmd` alias.\n* SD_DATA0_IDDynPinId \nfor the `SdData0` alias.\n* SD_DATA0_MODEDynPinMode \nfor the `SdData0` alias.\n* SD_DATA1_IDDynPinId \nfor the `SdData1` alias.\n* SD_DATA1_MODEDynPinMode \nfor the `SdData1` alias.\n* SD_DATA2_IDDynPinId \nfor the `SdData2` alias.\n* SD_DATA2_MODEDynPinMode \nfor the `SdData2` alias.\n* SD_DATA3_IDDynPinId \nfor the `SdData3` alias.\n* SD_DATA3_MODEDynPinMode \nfor the `SdData3` alias.\n* SD_WP_IDDynPinId \nfor the `SdWp` alias.\n* SD_WP_MODEDynPinMode \nfor the `SdWp` alias.\n* SWCLK_IDDynPinId \nfor the `Swclk` alias.\n* SWCLK_MODEDynPinMode \nfor the `Swclk` alias.\n* SWDIO_IDDynPinId \nfor the `Swdio` alias.\n* SWDIO_MODEDynPinMode \nfor the `Swdio` alias.\n* SWO_IDDynPinId \nfor the `Swo` alias.\n* SWO_MODEDynPinMode \nfor the `Swo` alias.\n* USB_DM_IDDynPinId \nfor the `UsbDm` alias.\n* USB_DM_MODEDynPinMode \nfor the `UsbDm` alias.\n* USB_DP_IDDynPinId \nfor the `UsbDp` alias.\n* USB_DP_MODEDynPinMode \nfor the `UsbDp` alias.\n* XOSC1_CLOCK_IDDynPinId \nfor the `Xosc1Clock` alias.\n* XOSC1_CLOCK_MODEDynPinMode \nfor the `Xosc1Clock` alias.\n* XOSC1_X_IN_IDDynPinId \nfor the `Xosc1XIn` alias.\n* XOSC1_X_IN_MODEDynPinMode \nfor the `Xosc1XIn` alias.\n* XOSC1_X_OUT_IDDynPinId \nfor the `Xosc1XOut` alias.\n* XOSC1_X_OUT_MODEDynPinMode \nfor the `Xosc1XOut` alias.\n\nType Definitions\n---\n\n* Adc0Analog0Alias for a configured `Pin`\n* Adc0Analog0Id`PinId` for the `Adc0Analog0` alias\n* Adc0Analog0Mode`PinMode` for the `Adc0Analog0` alias\n* Adc0Analog1Alias for a configured `Pin`\n* Adc0Analog1Id`PinId` for the `Adc0Analog1` alias\n* Adc0Analog1Mode`PinMode` for the `Adc0Analog1` alias\n* Adc0Analog2Alias for a configured `Pin`\n* Adc0Analog2Id`PinId` for the `Adc0Analog2` alias\n* Adc0Analog2Mode`PinMode` for the `Adc0Analog2` alias\n* Adc0Analog3Alias for a configured `Pin`\n* Adc0Analog3Id`PinId` for the `Adc0Analog3` alias\n* Adc0Analog3Mode`PinMode` for the `Adc0Analog3` alias\n* Adc0Analog4Alias for a configured `Pin`\n* Adc0Analog4Id`PinId` for the `Adc0Analog4` alias\n* Adc0Analog4Mode`PinMode` for the `Adc0Analog4` alias\n* Adc0Analog5Alias for a configured `Pin`\n* Adc0Analog5Id`PinId` for the `Adc0Analog5` alias\n* Adc0Analog5Mode`PinMode` for the `Adc0Analog5` alias\n* Adc0Analog6Alias for a configured `Pin`\n* Adc0Analog6Id`PinId` for the `Adc0Analog6` alias\n* Adc0Analog6Mode`PinMode` for the `Adc0Analog6` alias\n* Adc0Analog7Alias for a configured `Pin`\n* Adc0Analog7Id`PinId` for the `Adc0Analog7` alias\n* Adc0Analog7Mode`PinMode` for the `Adc0Analog7` alias\n* Adc1Analog0Alias for a configured `Pin`\n* Adc1Analog0Id`PinId` for the `Adc1Analog0` alias\n* Adc1Analog0Mode`PinMode` for the `Adc1Analog0` alias\n* Adc1Analog1Alias for a configured `Pin`\n* Adc1Analog1Id`PinId` for the `Adc1Analog1` alias\n* Adc1Analog1Mode`PinMode` for the `Adc1Analog1` alias\n* Adc1Analog4Alias for a configured `Pin`\n* Adc1Analog4Id`PinId` for the `Adc1Analog4` alias\n* Adc1Analog4Mode`PinMode` for the `Adc1Analog4` alias\n* Adc1Analog5Alias for a configured `Pin`\n* Adc1Analog5Id`PinId` for the `Adc1Analog5` alias\n* Adc1Analog5Mode`PinMode` for the `Adc1Analog5` alias\n* Adc1Analog6Alias for a configured `Pin`\n* Adc1Analog6Id`PinId` for the `Adc1Analog6` alias\n* Adc1Analog6Mode`PinMode` for the `Adc1Analog6` alias\n* Adc1Analog7Alias for a configured `Pin`\n* Adc1Analog7Id`PinId` for the `Adc1Analog7` alias\n* Adc1Analog7Mode`PinMode` for the `Adc1Analog7` alias\n* Adc1Analog8Alias for a configured `Pin`\n* Adc1Analog8Id`PinId` for the `Adc1Analog8` alias\n* Adc1Analog8Mode`PinMode` for the `Adc1Analog8` alias\n* Adc1Analog9Alias for a configured `Pin`\n* Adc1Analog9Id`PinId` for the `Adc1Analog9` alias\n* Adc1Analog9Mode`PinMode` for the `Adc1Analog9` alias\n* Adc1Analog14Alias for a configured `Pin`\n* Adc1Analog14Id`PinId` for the `Adc1Analog14` alias\n* Adc1Analog14Mode`PinMode` for the `Adc1Analog14` alias\n* Adc1Analog15Alias for a configured `Pin`\n* Adc1Analog15Id`PinId` for the `Adc1Analog15` alias\n* Adc1Analog15Mode`PinMode` for the `Adc1Analog15` alias\n* AdcDacHeaderAlias for a configured `Pin`\n* AdcDacHeaderId`PinId` for the `AdcDacHeader` alias\n* AdcDacHeaderMode`PinMode` for the `AdcDacHeader` alias\n* Ata6561RxAlias for a configured `Pin`\n* Ata6561RxId`PinId` for the `Ata6561Rx` alias\n* Ata6561RxMode`PinMode` for the `Ata6561Rx` alias\n* Ata6561StandbyAlias for a configured `Pin`\n* Ata6561StandbyId`PinId` for the `Ata6561Standby` alias\n* Ata6561StandbyMode`PinMode` for the `Ata6561Standby` alias\n* Ata6561TxAlias for a configured `Pin`\n* Ata6561TxId`PinId` for the `Ata6561Tx` alias\n* Ata6561TxMode`PinMode` for the `Ata6561Tx` alias\n* ButtonAlias for a configured `Pin`\n* ButtonId`PinId` for the `Button` alias\n* ButtonMode`PinMode` for the `Button` alias\n* DgiI2cSclAlias for a configured `Pin`\n* DgiI2cSclId`PinId` for the `DgiI2cScl` alias\n* DgiI2cSclMode`PinMode` for the `DgiI2cScl` alias\n* DgiI2cSdaAlias for a configured `Pin`\n* DgiI2cSdaId`PinId` for the `DgiI2cSda` alias\n* DgiI2cSdaMode`PinMode` for the `DgiI2cSda` alias\n* DgiSpiCsAlias for a configured `Pin`\n* DgiSpiCsId`PinId` for the `DgiSpiCs` alias\n* DgiSpiCsMode`PinMode` for the `DgiSpiCs` alias\n* DgiSpiMisoAlias for a configured `Pin`\n* DgiSpiMisoId`PinId` for the `DgiSpiMiso` alias\n* DgiSpiMisoMode`PinMode` for the `DgiSpiMiso` alias\n* DgiSpiMosiAlias for a configured `Pin`\n* DgiSpiMosiId`PinId` for the `DgiSpiMosi` alias\n* DgiSpiMosiMode`PinMode` for the `DgiSpiMosi` alias\n* DgiSpiSckAlias for a configured `Pin`\n* DgiSpiSckId`PinId` for the `DgiSpiSck` alias\n* DgiSpiSckMode`PinMode` for the `DgiSpiSck` alias\n* EdbgGpio0InAlias for a configured `Pin`\n* EdbgGpio0InId`PinId` for the `EdbgGpio0In` alias\n* EdbgGpio0InMode`PinMode` for the `EdbgGpio0In` alias\n* EdbgGpio0OutAlias for a configured `Pin`\n* EdbgGpio0OutId`PinId` for the `EdbgGpio0Out` alias\n* EdbgGpio0OutMode`PinMode` for the `EdbgGpio0Out` alias\n* EdbgGpio1InAlias for a configured `Pin`\n* EdbgGpio1InId`PinId` for the `EdbgGpio1In` alias\n* EdbgGpio1InMode`PinMode` for the `EdbgGpio1In` alias\n* EdbgGpio1OutAlias for a configured `Pin`\n* EdbgGpio1OutId`PinId` for the `EdbgGpio1Out` alias\n* EdbgGpio1OutMode`PinMode` for the `EdbgGpio1Out` alias\n* EdbgGpio2InAlias for a configured `Pin`\n* EdbgGpio2InId`PinId` for the `EdbgGpio2In` alias\n* EdbgGpio2InMode`PinMode` for the `EdbgGpio2In` alias\n* EdbgGpio2OutAlias for a configured `Pin`\n* EdbgGpio2OutId`PinId` for the `EdbgGpio2Out` alias\n* EdbgGpio2OutMode`PinMode` for the `EdbgGpio2Out` alias\n* EdbgUartRxAlias for a configured `Pin`\n* EdbgUartRxId`PinId` for the `EdbgUartRx` alias\n* EdbgUartRxMode`PinMode` for the `EdbgUartRx` alias\n* EdbgUartTxAlias for a configured `Pin`\n* EdbgUartTxId`PinId` for the `EdbgUartTx` alias\n* EdbgUartTxMode`PinMode` for the `EdbgUartTx` alias\n* EthCrsDvAlias for a configured `Pin`\n* EthCrsDvId`PinId` for the `EthCrsDv` alias\n* EthCrsDvMode`PinMode` for the `EthCrsDv` alias\n* EthGmdioAlias for a configured `Pin`\n* EthGmdioId`PinId` for the `EthGmdio` alias\n* EthGmdioMode`PinMode` for the `EthGmdio` alias\n* EthInterruptAlias for a configured `Pin`\n* EthInterruptId`PinId` for the `EthInterrupt` alias\n* EthInterruptMode`PinMode` for the `EthInterrupt` alias\n* EthMdcAlias for a configured `Pin`\n* EthMdcId`PinId` for the `EthMdc` alias\n* EthMdcMode`PinMode` for the `EthMdc` alias\n* EthRefClkAlias for a configured `Pin`\n* EthRefClkId`PinId` for the `EthRefClk` alias\n* EthRefClkMode`PinMode` for the `EthRefClk` alias\n* EthResetAlias for a configured `Pin`\n* EthResetId`PinId` for the `EthReset` alias\n* EthResetMode`PinMode` for the `EthReset` alias\n* EthRxd0Alias for a configured `Pin`\n* EthRxd0Id`PinId` for the `EthRxd0` alias\n* EthRxd0Mode`PinMode` for the `EthRxd0` alias\n* EthRxd1Alias for a configured `Pin`\n* EthRxd1Id`PinId` for the `EthRxd1` alias\n* EthRxd1Mode`PinMode` for the `EthRxd1` alias\n* EthRxerAlias for a configured `Pin`\n* EthRxerId`PinId` for the `EthRxer` alias\n* EthRxerMode`PinMode` for the `EthRxer` alias\n* EthTxd0Alias for a configured `Pin`\n* EthTxd0Id`PinId` for the `EthTxd0` alias\n* EthTxd0Mode`PinMode` for the `EthTxd0` alias\n* EthTxd1Alias for a configured `Pin`\n* EthTxd1Id`PinId` for the `EthTxd1` alias\n* EthTxd1Mode`PinMode` for the `EthTxd1` alias\n* EthTxenAlias for a configured `Pin`\n* EthTxenId`PinId` for the `EthTxen` alias\n* EthTxenMode`PinMode` for the `EthTxen` alias\n* Ext1AdcMinusAlias for a configured `Pin`\n* Ext1AdcMinusId`PinId` for the `Ext1AdcMinus` alias\n* Ext1AdcMinusMode`PinMode` for the `Ext1AdcMinus` alias\n* Ext1AdcPlusAlias for a configured `Pin`\n* Ext1AdcPlusId`PinId` for the `Ext1AdcPlus` alias\n* Ext1AdcPlusMode`PinMode` for the `Ext1AdcPlus` alias\n* Ext1Gpio1InAlias for a configured `Pin`\n* Ext1Gpio1InId`PinId` for the `Ext1Gpio1In` alias\n* Ext1Gpio1InMode`PinMode` for the `Ext1Gpio1In` alias\n* Ext1Gpio1OutAlias for a configured `Pin`\n* Ext1Gpio1OutId`PinId` for the `Ext1Gpio1Out` alias\n* Ext1Gpio1OutMode`PinMode` for the `Ext1Gpio1Out` alias\n* Ext1Gpio2InAlias for a configured `Pin`\n* Ext1Gpio2InId`PinId` for the `Ext1Gpio2In` alias\n* Ext1Gpio2InMode`PinMode` for the `Ext1Gpio2In` alias\n* Ext1Gpio2OutAlias for a configured `Pin`\n* Ext1Gpio2OutId`PinId` for the `Ext1Gpio2Out` alias\n* Ext1Gpio2OutMode`PinMode` for the `Ext1Gpio2Out` alias\n* Ext1I2cSclAlias for a configured `Pin`\n* Ext1I2cSclId`PinId` for the `Ext1I2cScl` alias\n* Ext1I2cSclMode`PinMode` for the `Ext1I2cScl` alias\n* Ext1I2cSdaAlias for a configured `Pin`\n* Ext1I2cSdaId`PinId` for the `Ext1I2cSda` alias\n* Ext1I2cSdaMode`PinMode` for the `Ext1I2cSda` alias\n* Ext1IrqGpioInAlias for a configured `Pin`\n* Ext1IrqGpioInId`PinId` for the `Ext1IrqGpioIn` alias\n* Ext1IrqGpioInMode`PinMode` for the `Ext1IrqGpioIn` alias\n* Ext1IrqGpioOutAlias for a configured `Pin`\n* Ext1IrqGpioOutId`PinId` for the `Ext1IrqGpioOut` alias\n* Ext1IrqGpioOutMode`PinMode` for the `Ext1IrqGpioOut` alias\n* Ext1PwmMinusAlias for a configured `Pin`\n* Ext1PwmMinusId`PinId` for the `Ext1PwmMinus` alias\n* Ext1PwmMinusMode`PinMode` for the `Ext1PwmMinus` alias\n* Ext1PwmPlusAlias for a configured `Pin`\n* Ext1PwmPlusId`PinId` for the `Ext1PwmPlus` alias\n* Ext1PwmPlusMode`PinMode` for the `Ext1PwmPlus` alias\n* Ext1SpiCsAAlias for a configured `Pin`\n* Ext1SpiCsAId`PinId` for the `Ext1SpiCsA` alias\n* Ext1SpiCsAMode`PinMode` for the `Ext1SpiCsA` alias\n* Ext1SpiCsBAlias for a configured `Pin`\n* Ext1SpiCsBId`PinId` for the `Ext1SpiCsB` alias\n* Ext1SpiCsBMode`PinMode` for the `Ext1SpiCsB` alias\n* Ext1SpiMisoAlias for a configured `Pin`\n* Ext1SpiMisoId`PinId` for the `Ext1SpiMiso` alias\n* Ext1SpiMisoMode`PinMode` for the `Ext1SpiMiso` alias\n* Ext1SpiMosiAlias for a configured `Pin`\n* Ext1SpiMosiId`PinId` for the `Ext1SpiMosi` alias\n* Ext1SpiMosiMode`PinMode` for the `Ext1SpiMosi` alias\n* Ext1SpiSckAlias for a configured `Pin`\n* Ext1SpiSckId`PinId` for the `Ext1SpiSck` alias\n* Ext1SpiSckMode`PinMode` for the `Ext1SpiSck` alias\n* Ext1UartCtsAlias for a configured `Pin`\n* Ext1UartCtsId`PinId` for the `Ext1UartCts` alias\n* Ext1UartCtsMode`PinMode` for the `Ext1UartCts` alias\n* Ext1UartRtsAlias for a configured `Pin`\n* Ext1UartRtsId`PinId` for the `Ext1UartRts` alias\n* Ext1UartRtsMode`PinMode` for the `Ext1UartRts` alias\n* Ext1UartRxAlias for a configured `Pin`\n* Ext1UartRxId`PinId` for the `Ext1UartRx` alias\n* Ext1UartRxMode`PinMode` for the `Ext1UartRx` alias\n* Ext1UartTxAlias for a configured `Pin`\n* Ext1UartTxId`PinId` for the `Ext1UartTx` alias\n* Ext1UartTxMode`PinMode` for the `Ext1UartTx` alias\n* Ext2AdcMinusAlias for a configured `Pin`\n* Ext2AdcMinusId`PinId` for the `Ext2AdcMinus` alias\n* Ext2AdcMinusMode`PinMode` for the `Ext2AdcMinus` alias\n* Ext2AdcPlusAlias for a configured `Pin`\n* Ext2AdcPlusId`PinId` for the `Ext2AdcPlus` alias\n* Ext2AdcPlusMode`PinMode` for the `Ext2AdcPlus` alias\n* Ext2Gpio1InAlias for a configured `Pin`\n* Ext2Gpio1InId`PinId` for the `Ext2Gpio1In` alias\n* Ext2Gpio1InMode`PinMode` for the `Ext2Gpio1In` alias\n* Ext2Gpio1OutAlias for a configured `Pin`\n* Ext2Gpio1OutId`PinId` for the `Ext2Gpio1Out` alias\n* Ext2Gpio1OutMode`PinMode` for the `Ext2Gpio1Out` alias\n* Ext2Gpio2InAlias for a configured `Pin`\n* Ext2Gpio2InId`PinId` for the `Ext2Gpio2In` alias\n* Ext2Gpio2InMode`PinMode` for the `Ext2Gpio2In` alias\n* Ext2Gpio2OutAlias for a configured `Pin`\n* Ext2Gpio2OutId`PinId` for the `Ext2Gpio2Out` alias\n* Ext2Gpio2OutMode`PinMode` for the `Ext2Gpio2Out` alias\n* Ext2I2cSclAlias for a configured `Pin`\n* Ext2I2cSclId`PinId` for the `Ext2I2cScl` alias\n* Ext2I2cSclMode`PinMode` for the `Ext2I2cScl` alias\n* Ext2I2cSdaAlias for a configured `Pin`\n* Ext2I2cSdaId`PinId` for the `Ext2I2cSda` alias\n* Ext2I2cSdaMode`PinMode` for the `Ext2I2cSda` alias\n* Ext2IrqGpioInAlias for a configured `Pin`\n* Ext2IrqGpioInId`PinId` for the `Ext2IrqGpioIn` alias\n* Ext2IrqGpioInMode`PinMode` for the `Ext2IrqGpioIn` alias\n* Ext2IrqGpioOutAlias for a configured `Pin`\n* Ext2IrqGpioOutId`PinId` for the `Ext2IrqGpioOut` alias\n* Ext2IrqGpioOutMode`PinMode` for the `Ext2IrqGpioOut` alias\n* Ext2PwmMinusAlias for a configured `Pin`\n* Ext2PwmMinusId`PinId` for the `Ext2PwmMinus` alias\n* Ext2PwmMinusMode`PinMode` for the `Ext2PwmMinus` alias\n* Ext2PwmPlusAlias for a configured `Pin`\n* Ext2PwmPlusId`PinId` for the `Ext2PwmPlus` alias\n* Ext2PwmPlusMode`PinMode` for the `Ext2PwmPlus` alias\n* Ext2SpiCsAAlias for a configured `Pin`\n* Ext2SpiCsAId`PinId` for the `Ext2SpiCsA` alias\n* Ext2SpiCsAMode`PinMode` for the `Ext2SpiCsA` alias\n* Ext2SpiCsBAlias for a configured `Pin`\n* Ext2SpiCsBId`PinId` for the `Ext2SpiCsB` alias\n* Ext2SpiCsBMode`PinMode` for the `Ext2SpiCsB` alias\n* Ext2SpiMisoAlias for a configured `Pin`\n* Ext2SpiMisoId`PinId` for the `Ext2SpiMiso` alias\n* Ext2SpiMisoMode`PinMode` for the `Ext2SpiMiso` alias\n* Ext2SpiMosiAlias for a configured `Pin`\n* Ext2SpiMosiId`PinId` for the `Ext2SpiMosi` alias\n* Ext2SpiMosiMode`PinMode` for the `Ext2SpiMosi` alias\n* Ext2SpiSckAlias for a configured `Pin`\n* Ext2SpiSckId`PinId` for the `Ext2SpiSck` alias\n* Ext2SpiSckMode`PinMode` for the `Ext2SpiSck` alias\n* Ext2UartRxAlias for a configured `Pin`\n* Ext2UartRxId`PinId` for the `Ext2UartRx` alias\n* Ext2UartRxMode`PinMode` for the `Ext2UartRx` alias\n* Ext2UartTxAlias for a configured `Pin`\n* Ext2UartTxId`PinId` for the `Ext2UartTx` alias\n* Ext2UartTxMode`PinMode` for the `Ext2UartTx` alias\n* Ext3AdcMinusAlias for a configured `Pin`\n* Ext3AdcMinusId`PinId` for the `Ext3AdcMinus` alias\n* Ext3AdcMinusMode`PinMode` for the `Ext3AdcMinus` alias\n* Ext3AdcPlusAlias for a configured `Pin`\n* Ext3AdcPlusId`PinId` for the `Ext3AdcPlus` alias\n* Ext3AdcPlusMode`PinMode` for the `Ext3AdcPlus` alias\n* Ext3Gpio1InAlias for a configured `Pin`\n* Ext3Gpio1InId`PinId` for the `Ext3Gpio1In` alias\n* Ext3Gpio1InMode`PinMode` for the `Ext3Gpio1In` alias\n* Ext3Gpio1OutAlias for a configured `Pin`\n* Ext3Gpio1OutId`PinId` for the `Ext3Gpio1Out` alias\n* Ext3Gpio1OutMode`PinMode` for the `Ext3Gpio1Out` alias\n* Ext3Gpio2InAlias for a configured `Pin`\n* Ext3Gpio2InId`PinId` for the `Ext3Gpio2In` alias\n* Ext3Gpio2InMode`PinMode` for the `Ext3Gpio2In` alias\n* Ext3Gpio2OutAlias for a configured `Pin`\n* Ext3Gpio2OutId`PinId` for the `Ext3Gpio2Out` alias\n* Ext3Gpio2OutMode`PinMode` for the `Ext3Gpio2Out` alias\n* Ext3I2cSclAlias for a configured `Pin`\n* Ext3I2cSclId`PinId` for the `Ext3I2cScl` alias\n* Ext3I2cSclMode`PinMode` for the `Ext3I2cScl` alias\n* Ext3I2cSdaAlias for a configured `Pin`\n* Ext3I2cSdaId`PinId` for the `Ext3I2cSda` alias\n* Ext3I2cSdaMode`PinMode` for the `Ext3I2cSda` alias\n* Ext3IrqGpioInAlias for a configured `Pin`\n* Ext3IrqGpioInId`PinId` for the `Ext3IrqGpioIn` alias\n* Ext3IrqGpioInMode`PinMode` for the `Ext3IrqGpioIn` alias\n* Ext3IrqGpioOutAlias for a configured `Pin`\n* Ext3IrqGpioOutId`PinId` for the `Ext3IrqGpioOut` alias\n* Ext3IrqGpioOutMode`PinMode` for the `Ext3IrqGpioOut` alias\n* Ext3PwmMinusAlias for a configured `Pin`\n* Ext3PwmMinusId`PinId` for the `Ext3PwmMinus` alias\n* Ext3PwmMinusMode`PinMode` for the `Ext3PwmMinus` alias\n* Ext3PwmPlusAlias for a configured `Pin`\n* Ext3PwmPlusId`PinId` for the `Ext3PwmPlus` alias\n* Ext3PwmPlusMode`PinMode` for the `Ext3PwmPlus` alias\n* Ext3SpiCsAAlias for a configured `Pin`\n* Ext3SpiCsAId`PinId` for the `Ext3SpiCsA` alias\n* Ext3SpiCsAMode`PinMode` for the `Ext3SpiCsA` alias\n* Ext3SpiCsBAlias for a configured `Pin`\n* Ext3SpiCsBId`PinId` for the `Ext3SpiCsB` alias\n* Ext3SpiCsBMode`PinMode` for the `Ext3SpiCsB` alias\n* Ext3SpiMisoAlias for a configured `Pin`\n* Ext3SpiMisoId`PinId` for the `Ext3SpiMiso` alias\n* Ext3SpiMisoMode`PinMode` for the `Ext3SpiMiso` alias\n* Ext3SpiMosiAlias for a configured `Pin`\n* Ext3SpiMosiId`PinId` for the `Ext3SpiMosi` alias\n* Ext3SpiMosiMode`PinMode` for the `Ext3SpiMosi` alias\n* Ext3SpiSckAlias for a configured `Pin`\n* Ext3SpiSckId`PinId` for the `Ext3SpiSck` alias\n* Ext3SpiSckMode`PinMode` for the `Ext3SpiSck` alias\n* Ext3UartRxAlias for a configured `Pin`\n* Ext3UartRxId`PinId` for the `Ext3UartRx` alias\n* Ext3UartRxMode`PinMode` for the `Ext3UartRx` alias\n* Ext3UartTxAlias for a configured `Pin`\n* Ext3UartTxId`PinId` for the `Ext3UartTx` alias\n* Ext3UartTxMode`PinMode` for the `Ext3UartTx` alias\n* I2sFs0Alias for a configured `Pin`\n* I2sFs0Id`PinId` for the `I2sFs0` alias\n* I2sFs0Mode`PinMode` for the `I2sFs0` alias\n* I2sFs1Alias for a configured `Pin`\n* I2sFs1Id`PinId` for the `I2sFs1` alias\n* I2sFs1Mode`PinMode` for the `I2sFs1` alias\n* I2sSdiAlias for a configured `Pin`\n* I2sSdiId`PinId` for the `I2sSdi` alias\n* I2sSdiMode`PinMode` for the `I2sSdi` alias\n* I2sSdoAlias for a configured `Pin`\n* I2sSdoId`PinId` for the `I2sSdo` alias\n* I2sSdoMode`PinMode` for the `I2sSdo` alias\n* LedAlias for a configured `Pin`\n* LedId`PinId` for the `Led` alias\n* LedMode`PinMode` for the `Led` alias\n* PccDout00Alias for a configured `Pin`\n* PccDout00Id`PinId` for the `PccDout00` alias\n* PccDout00Mode`PinMode` for the `PccDout00` alias\n* PccDout01Alias for a configured `Pin`\n* PccDout01Id`PinId` for the `PccDout01` alias\n* PccDout01Mode`PinMode` for the `PccDout01` alias\n* PccDout02Alias for a configured `Pin`\n* PccDout02Id`PinId` for the `PccDout02` alias\n* PccDout02Mode`PinMode` for the `PccDout02` alias\n* PccDout03Alias for a configured `Pin`\n* PccDout03Id`PinId` for the `PccDout03` alias\n* PccDout03Mode`PinMode` for the `PccDout03` alias\n* PccDout04Alias for a configured `Pin`\n* PccDout04Id`PinId` for the `PccDout04` alias\n* PccDout04Mode`PinMode` for the `PccDout04` alias\n* PccDout05Alias for a configured `Pin`\n* PccDout05Id`PinId` for the `PccDout05` alias\n* PccDout05Mode`PinMode` for the `PccDout05` alias\n* PccDout06Alias for a configured `Pin`\n* PccDout06Id`PinId` for the `PccDout06` alias\n* PccDout06Mode`PinMode` for the `PccDout06` alias\n* PccDout07Alias for a configured `Pin`\n* PccDout07Id`PinId` for the `PccDout07` alias\n* PccDout07Mode`PinMode` for the `PccDout07` alias\n* PccDout08Alias for a configured `Pin`\n* PccDout08Id`PinId` for the `PccDout08` alias\n* PccDout08Mode`PinMode` for the `PccDout08` alias\n* PccDout09Alias for a configured `Pin`\n* PccDout09Id`PinId` for the `PccDout09` alias\n* PccDout09Mode`PinMode` for the `PccDout09` alias\n* PccHsyncAlias for a configured `Pin`\n* PccHsyncId`PinId` for the `PccHsync` alias\n* PccHsyncMode`PinMode` for the `PccHsync` alias\n* PccPclkAlias for a configured `Pin`\n* PccPclkId`PinId` for the `PccPclk` alias\n* PccPclkMode`PinMode` for the `PccPclk` alias\n* PccPwdnAlias for a configured `Pin`\n* PccPwdnId`PinId` for the `PccPwdn` alias\n* PccPwdnMode`PinMode` for the `PccPwdn` alias\n* PccResetAlias for a configured `Pin`\n* PccResetId`PinId` for the `PccReset` alias\n* PccResetMode`PinMode` for the `PccReset` alias\n* PccVsyncAlias for a configured `Pin`\n* PccVsyncId`PinId` for the `PccVsync` alias\n* PccVsyncMode`PinMode` for the `PccVsync` alias\n* PccXclkAlias for a configured `Pin`\n* PccXclkId`PinId` for the `PccXclk` alias\n* PccXclkMode`PinMode` for the `PccXclk` alias\n* PdecIndexAlias for a configured `Pin`\n* PdecIndexId`PinId` for the `PdecIndex` alias\n* PdecIndexMode`PinMode` for the `PdecIndex` alias\n* PdecPhaseAAlias for a configured `Pin`\n* PdecPhaseAId`PinId` for the `PdecPhaseA` alias\n* PdecPhaseAMode`PinMode` for the `PdecPhaseA` alias\n* PdecPhaseBAlias for a configured `Pin`\n* PdecPhaseBId`PinId` for the `PdecPhaseB` alias\n* PdecPhaseBMode`PinMode` for the `PdecPhaseB` alias\n* QspiData0Alias for a configured `Pin`\n* QspiData0Id`PinId` for the `QspiData0` alias\n* QspiData0Mode`PinMode` for the `QspiData0` alias\n* QspiData1Alias for a configured `Pin`\n* QspiData1Id`PinId` for the `QspiData1` alias\n* QspiData1Mode`PinMode` for the `QspiData1` alias\n* QspiData2Alias for a configured `Pin`\n* QspiData2Id`PinId` for the `QspiData2` alias\n* QspiData2Mode`PinMode` for the `QspiData2` alias\n* QspiData3Alias for a configured `Pin`\n* QspiData3Id`PinId` for the `QspiData3` alias\n* QspiData3Mode`PinMode` for the `QspiData3` alias\n* QspiSckAlias for a configured `Pin`\n* QspiSckId`PinId` for the `QspiSck` alias\n* QspiSckMode`PinMode` for the `QspiSck` alias\n* QspiScsAlias for a configured `Pin`\n* QspiScsId`PinId` for the `QspiScs` alias\n* QspiScsMode`PinMode` for the `QspiScs` alias\n* QtButtonAlias for a configured `Pin`\n* QtButtonId`PinId` for the `QtButton` alias\n* QtButtonMode`PinMode` for the `QtButton` alias\n* SdCdAlias for a configured `Pin`\n* SdCdId`PinId` for the `SdCd` alias\n* SdCdMode`PinMode` for the `SdCd` alias\n* SdClkAlias for a configured `Pin`\n* SdClkId`PinId` for the `SdClk` alias\n* SdClkMode`PinMode` for the `SdClk` alias\n* SdCmdAlias for a configured `Pin`\n* SdCmdId`PinId` for the `SdCmd` alias\n* SdCmdMode`PinMode` for the `SdCmd` alias\n* SdData0Alias for a configured `Pin`\n* SdData0Id`PinId` for the `SdData0` alias\n* SdData0Mode`PinMode` for the `SdData0` alias\n* SdData1Alias for a configured `Pin`\n* SdData1Id`PinId` for the `SdData1` alias\n* SdData1Mode`PinMode` for the `SdData1` alias\n* SdData2Alias for a configured `Pin`\n* SdData2Id`PinId` for the `SdData2` alias\n* SdData2Mode`PinMode` for the `SdData2` alias\n* SdData3Alias for a configured `Pin`\n* SdData3Id`PinId` for the `SdData3` alias\n* SdData3Mode`PinMode` for the `SdData3` alias\n* SdWpAlias for a configured `Pin`\n* SdWpId`PinId` for the `SdWp` alias\n* SdWpMode`PinMode` for the `SdWp` alias\n* SwclkAlias for a configured `Pin`\n* SwclkId`PinId` for the `Swclk` alias\n* SwclkMode`PinMode` for the `Swclk` alias\n* SwdioAlias for a configured `Pin`\n* SwdioId`PinId` for the `Swdio` alias\n* SwdioMode`PinMode` for the `Swdio` alias\n* SwoAlias for a configured `Pin`\n* SwoId`PinId` for the `Swo` alias\n* SwoMode`PinMode` for the `Swo` alias\n* UsbDmAlias for a configured `Pin`\n* UsbDmId`PinId` for the `UsbDm` alias\n* UsbDmMode`PinMode` for the `UsbDm` alias\n* UsbDpAlias for a configured `Pin`\n* UsbDpId`PinId` for the `UsbDp` alias\n* UsbDpMode`PinMode` for the `UsbDp` alias\n* Xosc1ClockAlias for a configured `Pin`\n* Xosc1ClockId`PinId` for the `Xosc1Clock` alias\n* Xosc1ClockMode`PinMode` for the `Xosc1Clock` alias\n* Xosc1XInAlias for a configured `Pin`\n* Xosc1XInId`PinId` for the `Xosc1XIn` alias\n* Xosc1XInMode`PinMode` for the `Xosc1XIn` alias\n* Xosc1XOutAlias for a configured `Pin`\n* Xosc1XOutId`PinId` for the `Xosc1XOut` alias\n* Xosc1XOutMode`PinMode` for the `Xosc1XOut` alias\n\nModule atsame54_xpro::devices\n===\n\nSAM E54 XPlained Pro sercom device definitions\n\nThese type definitions are used by the Sam E54 Xplained Pro for its various Sercom functions in extensions 1, 2, and 3,\nas well as the DGI and EDBG ports and USB connections.\n\nFunctions\n---\n\n* dgi_i2cSet up the DGI I2C device\n* dgi_spiSet up the DGI SPI device\n* edbg_uartSet up the EDBG UART device\n* ext1_flow_control_uartSet up the extension 1 UART device with flow control\n* ext1_i2cSet up the extension 1 I2C device\n* ext1_spiSet up the extension 1 SPI device\n* ext1_uartSet up the extension 1 UART device\n* ext2_i2cSet up the extension 1 I2C device\n* ext2_spiSet up the extension 2 SPI device\n* ext2_uartSet up the extension 2 UART device\n* ext3_i2cSet up the extension 1 I2C device\n* ext3_spiSet up the extension 3 SPI device\n* ext3_uartSet up the extension 3 UART device\n\nType Definitions\n---\n\n* DgiI2cDGI I2C device\n* DgiI2cPadsI2C pads for the DGI connection\n* DgiI2cSercomAlias for the `SERCOM7` peripheral\n* DgiSpiDGI SPI device\n* DgiSpiPadsSPI pads for the DGI connection\n* DgiSpiSercomAlias for the `SERCOM6` peripheral\n* EdbgUartEDBG connection UART device\n* EdbgUartPadsUART pads for the EDBG connection\n* EdbgUartSercomAlias for the `SERCOM2` peripheral\n* Ext1FlowControlUartExtension 1 UART device with flow control\n* Ext1FlowControlUartPadsUART pads for the extension 1 connection with flow control\n* Ext1I2cExtension 1 I2C device\n* Ext1I2cPadsI2C pads for the extension 1 connection\n* Ext1I2cSercomAlias for the `SERCOM3` peripheral\n* Ext1SpiExtension 1 SPI device\n* Ext1SpiPadsSPI pads for the extension 1 connection\n* Ext1SpiSercomAlias for the `SERCOM4` peripheral\n* Ext1UartExtension 1 UART device\n* Ext1UartPadsUART pads for the extension 1 connection\n* Ext1UartSercomAlias for the `SERCOM0` peripheral\n* Ext2I2cExtension 2 I2C device\n* Ext2I2cPadsI2C pads for the extension 2 connection\n* Ext2I2cSercomAlias for the `SERCOM7` peripheral\n* Ext2SpiExtension 1 SPI device\n* Ext2SpiPadsSPI pads for the extension 2 connection\n* Ext2SpiSercomAlias for the `SERCOM6` peripheral\n* Ext2UartExtension 2 UART device\n* Ext2UartPadsUART pads for the extension 2 connection\n* Ext2UartSercomAlias for the `SERCOM5` peripheral\n* Ext3I2cExtension 3 I2C device\n* Ext3I2cPadsI2C pads for the extension 3 connection\n* Ext3I2cSercomAlias for the `SERCOM7` peripheral\n* Ext3SpiExtension 3 SPI device\n* Ext3SpiPadsSPI pads for the extension 3 connection\n* Ext3SpiSercomAlias for the `SERCOM6` peripheral\n* Ext3UartExtension 3 UART device\n* Ext3UartPadsUART pads for the extension 3 connection\n* Ext3UartSercomAlias for the `SERCOM1` peripheral\n\nMacro atsame54_xpro::periph_alias\n===\n\n\n```\nmacro_rules! periph_alias {\n ($peripherals:ident . ext1_uart_sercom) => { ... };\n ($peripherals:ident . ext3_uart_sercom) => { ... };\n ($peripherals:ident . edbg_uart_sercom) => { ... };\n ($peripherals:ident . ext1_i2c_sercom) => { ... };\n ($peripherals:ident . ext1_spi_sercom) => { ... };\n ($peripherals:ident . ext2_uart_sercom) => { ... };\n ($peripherals:ident . ext2_spi_sercom) => { ... };\n ($peripherals:ident . ext3_spi_sercom) => { ... };\n ($peripherals:ident . dgi_spi_sercom) => { ... };\n ($peripherals:ident . ext2_i2c_sercom) => { ... };\n ($peripherals:ident . ext3_i2c_sercom) => { ... };\n ($peripherals:ident . dgi_i2c_sercom) => { ... };\n}\n```\nRefer to fields of the `Peripherals`\nstruct by alternate names\n\nThis macro can be used to access fields of the `Peripherals`\nstruct by alternate names. The available aliases are:\n\n* `SERCOM0` can be refered to with the type alias `Ext1UartSercom` and accessed as the field name `ext1_uart_sercom`\n* `SERCOM1` can be refered to with the type alias `Ext3UartSercom` and accessed as the field name `ext3_uart_sercom`\n* `SERCOM2` can be refered to with the type alias `EdbgUartSercom` and accessed as the field name `edbg_uart_sercom`\n* `SERCOM3` can be refered to with the type alias `Ext1I2cSercom` and accessed as the field name `ext1_i2c_sercom`\n* `SERCOM4` can be refered to with the type alias `Ext1SpiSercom` and accessed as the field name `ext1_spi_sercom`\n* `SERCOM5` can be refered to with the type alias `Ext2UartSercom` and accessed as the field name `ext2_uart_sercom`\n* `SERCOM6` can be refered to with the type alias `Ext2SpiSercom` and accessed as the field name `ext2_spi_sercom`\n* `SERCOM6` can be refered to with the type alias `Ext3SpiSercom` and accessed as the field name `ext3_spi_sercom`\n* `SERCOM6` can be refered to with the type alias `DgiSpiSercom` and accessed as the field name `dgi_spi_sercom`\n* `SERCOM7` can be refered to with the type alias `Ext2I2cSercom` and accessed as the field name `ext2_i2c_sercom`\n* `SERCOM7` can be refered to with the type alias `Ext3I2cSercom` and accessed as the field name `ext3_i2c_sercom`\n* `SERCOM7` can be refered to with the type alias `DgiI2cSercom` and accessed as the field name `dgi_i2c_sercom`\n\nFor example. suppose `display_spi` were an alternate name for the `SERCOM4` peripheral. You could use the `periph_alias!`\nmacro to access it like this:\n```\nlet mut peripherals = pac::Peripherals::take().unwrap();\n// Replace this let display_spi = peripherals.SERCOM4;\n// With this let display_spi = periph_alias!(peripherals.display_spi);\n```\n\nMacro atsame54_xpro::pin_alias\n===\n\n\n```\nmacro_rules! pin_alias {\n ($pins:ident . pa02) => { ... };\n ($pins:ident . pa03) => { ... };\n ($pins:ident . pa04) => { ... };\n ($pins:ident . pa05) => { ... };\n ($pins:ident . pa06) => { ... };\n ($pins:ident . pa07) => { ... };\n ($pins:ident . pa08) => { ... };\n ($pins:ident . pa09) => { ... };\n ($pins:ident . pa10) => { ... };\n ($pins:ident . pa11) => { ... };\n ($pins:ident . pa12) => { ... };\n ($pins:ident . pa13) => { ... };\n ($pins:ident . pa14) => { ... };\n ($pins:ident . pa15) => { ... };\n ($pins:ident . pa16) => { ... };\n ($pins:ident . pa17) => { ... };\n ($pins:ident . pa18) => { ... };\n ($pins:ident . pa19) => { ... };\n ($pins:ident . pa20) => { ... };\n ($pins:ident . pa21) => { ... };\n ($pins:ident . pa22) => { ... };\n ($pins:ident . pa23) => { ... };\n ($pins:ident . pa24) => { ... };\n ($pins:ident . pa25) => { ... };\n ($pins:ident . pa27) => { ... };\n ($pins:ident . pa30) => { ... };\n ($pins:ident . pa31) => { ... };\n ($pins:ident . pb00) => { ... };\n ($pins:ident . pb01) => { ... };\n ($pins:ident . pb02) => { ... };\n ($pins:ident . pb04) => { ... };\n ($pins:ident . pb05) => { ... };\n ($pins:ident . pb06) => { ... };\n ($pins:ident . pb07) => { ... };\n ($pins:ident . pb08) => { ... };\n ($pins:ident . pb09) => { ... };\n ($pins:ident . pb10) => { ... };\n ($pins:ident . pb11) => { ... };\n ($pins:ident . pb12) => { ... };\n ($pins:ident . pb13) => { ... };\n ($pins:ident . pb14) => { ... };\n ($pins:ident . pb15) => { ... };\n ($pins:ident . pb16) => { ... };\n ($pins:ident . pb17) => { ... };\n ($pins:ident . pb18) => { ... };\n ($pins:ident . pb19) => { ... };\n ($pins:ident . pb20) => { ... };\n ($pins:ident . pb21) => { ... };\n ($pins:ident . pb22) => { ... };\n ($pins:ident . pb23) => { ... };\n ($pins:ident . pb24) => { ... };\n ($pins:ident . pb25) => { ... };\n ($pins:ident . pb26) => { ... };\n ($pins:ident . pb27) => { ... };\n ($pins:ident . pb28) => { ... };\n ($pins:ident . pb29) => { ... };\n ($pins:ident . pb30) => { ... };\n ($pins:ident . pb31) => { ... };\n ($pins:ident . pc01) => { ... };\n ($pins:ident . pc02) => { ... };\n ($pins:ident . pc03) => { ... };\n ($pins:ident . pc04) => { ... };\n ($pins:ident . pc05) => { ... };\n ($pins:ident . pc06) => { ... };\n ($pins:ident . pc07) => { ... };\n ($pins:ident . pc10) => { ... };\n ($pins:ident . pc11) => { ... };\n ($pins:ident . pc12) => { ... };\n ($pins:ident . pc13) => { ... };\n ($pins:ident . pc14) => { ... };\n ($pins:ident . pc16) => { ... };\n ($pins:ident . pc17) => { ... };\n ($pins:ident . pc18) => { ... };\n ($pins:ident . pc20) => { ... };\n ($pins:ident . pc21) => { ... };\n ($pins:ident . pc22) => { ... };\n ($pins:ident . pc23) => { ... };\n ($pins:ident . pc30) => { ... };\n ($pins:ident . pc31) => { ... };\n ($pins:ident . pd00) => { ... };\n ($pins:ident . pd01) => { ... };\n ($pins:ident . pd08) => { ... };\n ($pins:ident . pd09) => { ... };\n ($pins:ident . pd10) => { ... };\n ($pins:ident . pd11) => { ... };\n ($pins:ident . pd12) => { ... };\n ($pins:ident . pd20) => { ... };\n ($pins:ident . pd21) => { ... };\n ($pins:ident . adc_dac_header) => { ... };\n ($pins:ident . adc0_analog0) => { ... };\n ($pins:ident . ext2_adc_minus) => { ... };\n ($pins:ident . adc0_analog1) => { ... };\n ($pins:ident . adc0_analog4) => { ... };\n ($pins:ident . ext1_uart_tx) => { ... };\n ($pins:ident . adc0_analog5) => { ... };\n ($pins:ident . ext1_uart_rx) => { ... };\n ($pins:ident . adc0_analog6) => { ... };\n ($pins:ident . ext1_gpio1_in) => { ... };\n ($pins:ident . ext1_gpio1_out) => { ... };\n ($pins:ident . ext1_uart_rts) => { ... };\n ($pins:ident . ext1_gpio2_in) => { ... };\n ($pins:ident . ext1_gpio2_out) => { ... };\n ($pins:ident . adc0_analog7) => { ... };\n ($pins:ident . ext1_uart_cts) => { ... };\n ($pins:ident . qspi_data0) => { ... };\n ($pins:ident . qspi_data1) => { ... };\n ($pins:ident . qspi_data2) => { ... };\n ($pins:ident . qspi_data3) => { ... };\n ($pins:ident . pcc_vsync) => { ... };\n ($pins:ident . eth_rxd1) => { ... };\n ($pins:ident . pcc_hsync) => { ... };\n ($pins:ident . eth_rxd0) => { ... };\n ($pins:ident . pcc_pclk) => { ... };\n ($pins:ident . eth_ref_clk) => { ... };\n ($pins:ident . pcc_xclk) => { ... };\n ($pins:ident . eth_rxer) => { ... };\n ($pins:ident . qt_button) => { ... };\n ($pins:ident . pcc_dout00) => { ... };\n ($pins:ident . pcc_dout01) => { ... };\n ($pins:ident . eth_txen) => { ... };\n ($pins:ident . pcc_dout02) => { ... };\n ($pins:ident . eth_txd0) => { ... };\n ($pins:ident . pcc_dout03) => { ... };\n ($pins:ident . eth_txd1) => { ... };\n ($pins:ident . sd_cmd) => { ... };\n ($pins:ident . i2s_fs0) => { ... };\n ($pins:ident . pcc_dout04) => { ... };\n ($pins:ident . sd_clk) => { ... };\n ($pins:ident . i2s_sdo) => { ... };\n ($pins:ident . pcc_dout05) => { ... };\n ($pins:ident . ext1_i2c_sda) => { ... };\n ($pins:ident . i2s_sdi) => { ... };\n ($pins:ident . pcc_dout06) => { ... };\n ($pins:ident . ext1_i2c_scl) => { ... };\n ($pins:ident . i2s_fs1) => { ... };\n ($pins:ident . pcc_dout07) => { ... };\n ($pins:ident . usb_dm) => { ... };\n ($pins:ident . usb_dp) => { ... };\n ($pins:ident . ext1_spi_cs_b) => { ... };\n ($pins:ident . swclk) => { ... };\n ($pins:ident . swdio) => { ... };\n ($pins:ident . ext2_adc_plus) => { ... };\n ($pins:ident . ext2_gpio1_in) => { ... };\n ($pins:ident . ext2_gpio1_out) => { ... };\n ($pins:ident . ext2_spi_cs_b) => { ... };\n ($pins:ident . ext1_adc_plus) => { ... };\n ($pins:ident . adc1_analog6) => { ... };\n ($pins:ident . ext1_adc_minus) => { ... };\n ($pins:ident . adc1_analog7) => { ... };\n ($pins:ident . ext2_gpio2_in) => { ... };\n ($pins:ident . ext2_gpio2_out) => { ... };\n ($pins:ident . adc1_analog8) => { ... };\n ($pins:ident . ext1_irq_gpio_in) => { ... };\n ($pins:ident . ext1_irq_gpio_out) => { ... };\n ($pins:ident . adc1_analog9) => { ... };\n ($pins:ident . adc0_analog2) => { ... };\n ($pins:ident . adc1_analog0) => { ... };\n ($pins:ident . ext1_pwm_plus) => { ... };\n ($pins:ident . adc0_analog3) => { ... };\n ($pins:ident . adc1_analog1) => { ... };\n ($pins:ident . ext1_pwm_minus) => { ... };\n ($pins:ident . qspi_sck) => { ... };\n ($pins:ident . qspi_scs) => { ... };\n ($pins:ident . ata6561_tx) => { ... };\n ($pins:ident . ata6561_rx) => { ... };\n ($pins:ident . ext2_pwm_plus) => { ... };\n ($pins:ident . pcc_dout08) => { ... };\n ($pins:ident . ext2_pwm_minus) => { ... };\n ($pins:ident . pcc_dout09) => { ... };\n ($pins:ident . ext2_uart_tx) => { ... };\n ($pins:ident . ext2_uart_rx) => { ... };\n ($pins:ident . sd_data0) => { ... };\n ($pins:ident . sd_data1) => { ... };\n ($pins:ident . sd_data2) => { ... };\n ($pins:ident . sd_data3) => { ... };\n ($pins:ident . xosc1_x_in) => { ... };\n ($pins:ident . xosc1_clock) => { ... };\n ($pins:ident . xosc1_x_out) => { ... };\n ($pins:ident . edbg_uart_rx) => { ... };\n ($pins:ident . edbg_uart_tx) => { ... };\n ($pins:ident . ext1_spi_sck) => { ... };\n ($pins:ident . ext1_spi_mosi) => { ... };\n ($pins:ident . ext1_spi_cs_a) => { ... };\n ($pins:ident . ext1_spi_miso) => { ... };\n ($pins:ident . swo) => { ... };\n ($pins:ident . button) => { ... };\n ($pins:ident . ext3_gpio1_in) => { ... };\n ($pins:ident . ext3_gpio1_out) => { ... };\n ($pins:ident . ext3_adc_plus) => { ... };\n ($pins:ident . adc1_analog4) => { ... };\n ($pins:ident . ext3_adc_minus) => { ... };\n ($pins:ident . adc1_analog5) => { ... };\n ($pins:ident . ext2_spi_mosi) => { ... };\n ($pins:ident . ext3_spi_mosi) => { ... };\n ($pins:ident . dgi_spi_mosi) => { ... };\n ($pins:ident . ext2_spi_sck) => { ... };\n ($pins:ident . ext3_spi_sck) => { ... };\n ($pins:ident . dgi_spi_sck) => { ... };\n ($pins:ident . ext2_spi_cs_a) => { ... };\n ($pins:ident . ext2_spi_miso) => { ... };\n ($pins:ident . ext3_spi_miso) => { ... };\n ($pins:ident . dgi_spi_miso) => { ... };\n ($pins:ident . ext3_gpio2_in) => { ... };\n ($pins:ident . ext3_gpio2_out) => { ... };\n ($pins:ident . pcc_pwdn) => { ... };\n ($pins:ident . eth_mdc) => { ... };\n ($pins:ident . pcc_reset) => { ... };\n ($pins:ident . eth_gmdio) => { ... };\n ($pins:ident . ata6561_standby) => { ... };\n ($pins:ident . ext3_spi_cs_a) => { ... };\n ($pins:ident . pdec_phase_a) => { ... };\n ($pins:ident . edbg_gpio0_in) => { ... };\n ($pins:ident . edbg_gpio0_out) => { ... };\n ($pins:ident . pdec_phase_b) => { ... };\n ($pins:ident . edbg_gpio1_in) => { ... };\n ($pins:ident . edbg_gpio1_out) => { ... };\n ($pins:ident . led) => { ... };\n ($pins:ident . pdec_index) => { ... };\n ($pins:ident . edbg_gpio2_in) => { ... };\n ($pins:ident . edbg_gpio2_out) => { ... };\n ($pins:ident . eth_crs_dv) => { ... };\n ($pins:ident . eth_reset) => { ... };\n ($pins:ident . ext3_uart_tx) => { ... };\n ($pins:ident . ext3_uart_rx) => { ... };\n ($pins:ident . ext3_irq_gpio_in) => { ... };\n ($pins:ident . ext3_irq_gpio_out) => { ... };\n ($pins:ident . ext3_spi_cs_b) => { ... };\n ($pins:ident . ext2_irq_gpio_in) => { ... };\n ($pins:ident . ext2_irq_gpio_out) => { ... };\n ($pins:ident . adc1_analog14) => { ... };\n ($pins:ident . dgi_spi_cs) => { ... };\n ($pins:ident . adc1_analog15) => { ... };\n ($pins:ident . ext2_i2c_sda) => { ... };\n ($pins:ident . ext3_i2c_sda) => { ... };\n ($pins:ident . dgi_i2c_sda) => { ... };\n ($pins:ident . ext2_i2c_scl) => { ... };\n ($pins:ident . ext3_i2c_scl) => { ... };\n ($pins:ident . dgi_i2c_scl) => { ... };\n ($pins:ident . ext3_pwm_plus) => { ... };\n ($pins:ident . ext3_pwm_minus) => { ... };\n ($pins:ident . eth_interrupt) => { ... };\n ($pins:ident . sd_cd) => { ... };\n ($pins:ident . sd_wp) => { ... };\n}\n```\nRefer to fields of the `Pins` struct by alternate names\n\nThis macro can be used to access fields of the `Pins` struct by alternate names. See the `Pins` documentation for a list of the availabe pin aliases.\n\nFor example. suppose `spi_mosi` were an alternate name for the\n`serial_out` pin of the `Pins` struct. You could use the\n`pin_alias!` macro to access it like this:\n```\nlet mut peripherals = pac::Peripherals::take().unwrap();\nlet pins = bsp::Pins::new(peripherals.PORT);\n// Replace this let mosi = pins.serial_out;\n// With this let mosi = pin_alias!(pins.spi_mosi);\n```\n\nStruct atsame54_xpro::pins::Pins\n===\n\n\n```\npub struct Pins {\n pub pa02: Pin<PA02, Reset>,\n pub pa03: Pin<PA03, Reset>,\n pub pa04: Pin<PA04, Reset>,\n pub pa05: Pin<PA05, Reset>,\n pub pa06: Pin<PA06, Reset>,\n pub pa07: Pin<PA07, Reset>,\n pub pa08: Pin<PA08, Reset>,\n pub pa09: Pin<PA09, Reset>,\n pub pa10: Pin<PA10, Reset>,\n pub pa11: Pin<PA11, Reset>,\n pub pa12: Pin<PA12, Reset>,\n pub pa13: Pin<PA13, Reset>,\n pub pa14: Pin<PA14, Reset>,\n pub pa15: Pin<PA15, Reset>,\n pub pa16: Pin<PA16, Reset>,\n pub pa17: Pin<PA17, Reset>,\n pub pa18: Pin<PA18, Reset>,\n pub pa19: Pin<PA19, Reset>,\n pub pa20: Pin<PA20, Reset>,\n pub pa21: Pin<PA21, Reset>,\n pub pa22: Pin<PA22, Reset>,\n pub pa23: Pin<PA23, Reset>,\n pub pa24: Pin<PA24, Reset>,\n pub pa25: Pin<PA25, Reset>,\n pub pa27: Pin<PA27, Reset>,\n pub pa30: Pin<PA30, Reset>,\n pub pa31: Pin<PA31, Reset>,\n pub pb00: Pin<PB00, Reset>,\n pub pb01: Pin<PB01, Reset>,\n pub pb02: Pin<PB02, Reset>,\n pub pb04: Pin<PB04, Reset>,\n pub pb05: Pin<PB05, Reset>,\n pub pb06: Pin<PB06, Reset>,\n pub pb07: Pin<PB07, Reset>,\n pub pb08: Pin<PB08, Reset>,\n pub pb09: Pin<PB09, Reset>,\n pub pb10: Pin<PB10, Reset>,\n pub pb11: Pin<PB11, Reset>,\n pub pb12: Pin<PB12, Reset>,\n pub pb13: Pin<PB13, Reset>,\n pub pb14: Pin<PB14, Reset>,\n pub pb15: Pin<PB15, Reset>,\n pub pb16: Pin<PB16, Reset>,\n pub pb17: Pin<PB17, Reset>,\n pub pb18: Pin<PB18, Reset>,\n pub pb19: Pin<PB19, Reset>,\n pub pb20: Pin<PB20, Reset>,\n pub pb21: Pin<PB21, Reset>,\n pub pb22: Pin<PB22, Reset>,\n pub pb23: Pin<PB23, Reset>,\n pub pb24: Pin<PB24, Reset>,\n pub pb25: Pin<PB25, Reset>,\n pub pb26: Pin<PB26, Reset>,\n pub pb27: Pin<PB27, Reset>,\n pub pb28: Pin<PB28, Reset>,\n pub pb29: Pin<PB29, Reset>,\n pub pb30: Pin<PB30, Reset>,\n pub pb31: Pin<PB31, Reset>,\n pub pc01: Pin<PC01, Reset>,\n pub pc02: Pin<PC02, Reset>,\n pub pc03: Pin<PC03, Reset>,\n pub pc04: Pin<PC04, Reset>,\n pub pc05: Pin<PC05, Reset>,\n pub pc06: Pin<PC06, Reset>,\n pub pc07: Pin<PC07, Reset>,\n pub pc10: Pin<PC10, Reset>,\n pub pc11: Pin<PC11, Reset>,\n pub pc12: Pin<PC12, Reset>,\n pub pc13: Pin<PC13, Reset>,\n pub pc14: Pin<PC14, Reset>,\n pub pc16: Pin<PC16, Reset>,\n pub pc17: Pin<PC17, Reset>,\n pub pc18: Pin<PC18, Reset>,\n pub pc20: Pin<PC20, Reset>,\n pub pc21: Pin<PC21, Reset>,\n pub pc22: Pin<PC22, Reset>,\n pub pc23: Pin<PC23, Reset>,\n pub pc30: Pin<PC30, Reset>,\n pub pc31: Pin<PC31, Reset>,\n pub pd00: Pin<PD00, Reset>,\n pub pd01: Pin<PD01, Reset>,\n pub pd08: Pin<PD08, Reset>,\n pub pd09: Pin<PD09, Reset>,\n pub pd10: Pin<PD10, Reset>,\n pub pd11: Pin<PD11, Reset>,\n pub pd12: Pin<PD12, Reset>,\n pub pd20: Pin<PD20, Reset>,\n pub pd21: Pin<PD21, Reset>,\n /* private fields */\n}\n```\nBSP replacement for the HAL\n`Pins` type\n\nThis type is intended to provide more meaningful names for the given pins.\n\nFields\n---\n\n`pa02: Pin<PA02, Reset>`PA02: ADC/DAC header pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc_dac_header, \nadc0_analog0, \n\n`pa03: Pin<PA03, Reset>`PA03: Extension 2 ADC pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_adc_minus, \nadc0_analog1, \n\n`pa04: Pin<PA04, Reset>`PA04: Extension 1 UART transmit pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc0_analog4, \next1_uart_tx, \n\n`pa05: Pin<PA05, Reset>`PA05: Extension 1 UART receive pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc0_analog5, \next1_uart_rx, \n\n`pa06: Pin<PA06, Reset>`PA06: ADC 0 analog pin 6, Extension 1 GPIO pin 1,\nor Extension 1 UART request to send (RTS) pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc0_analog6, \next1_gpio1_in, \next1_gpio1_out, \next1_uart_rts, \n\n`pa07: Pin<PA07, Reset>`PA07: ADC 0 analog pin 6, Extension 1 GPIO pin 2,\nor Extension 1 UART clear to send (CTS) pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_gpio2_in, \next1_gpio2_out, \nadc0_analog7, \next1_uart_cts, \n\n`pa08: Pin<PA08, Reset>`PA08: QSPI data pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_data0, \n\n`pa09: Pin<PA09, Reset>`PA09: QSPI data pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_data1, \n\n`pa10: Pin<PA10, Reset>`PA10: QSPI data pin 2 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_data2, \n\n`pa11: Pin<PA11, Reset>`PA11: QSPI data pin 3 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_data3, \n\n`pa12: Pin<PA12, Reset>`PA12: PCC VSync pin or Ethernet receive data pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_vsync, \neth_rxd1, \n\n`pa13: Pin<PA13, Reset>`PA13: PCC HSync pin or Ethernet receive data pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_hsync, \neth_rxd0, \n\n`pa14: Pin<PA14, Reset>`PA14: PCC PCLK pin or Ethernet ref clock pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_pclk, \neth_ref_clk, \n\n`pa15: Pin<PA15, Reset>`PA15: PCC XCLK pin or Ethernet receive error pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_xclk, \neth_rxer, \n\n`pa16: Pin<PA16, Reset>`PA16: Capacitive touch button or PCC Data out pin 00 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqt_button, \npcc_dout00, \n\n`pa17: Pin<PA17, Reset>`PA17: PCC data out pin 01 or Ethernet transmit enable pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_dout01, \neth_txen, \n\n`pa18: Pin<PA18, Reset>`PA18: PCC data out pin 02 or Ethernet transmit data pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_dout02, \neth_txd0, \n\n`pa19: Pin<PA19, Reset>`PA19: PCC data out pin 03 or Ethernet transmit data pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_dout03, \neth_txd1, \n\n`pa20: Pin<PA20, Reset>`PA20: SD card command pin, I2S frame sync 0 pin, or PCC data out pin 04 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_cmd, \ni2s_fs0, \npcc_dout04, \n\n`pa21: Pin<PA21, Reset>`PA21: SD card clock pin, I2S serial data out pin, or PCC data out pin 05 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_clk, \ni2s_sdo, \npcc_dout05, \n\n`pa22: Pin<PA22, Reset>`PA22: Extension 1 I2c data pin, I2S serial data pin, or PCC data out pin 06 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_i2c_sda, \ni2s_sdi, \npcc_dout06, \n\n`pa23: Pin<PA23, Reset>`PA23: Extension 1 I2c clock pin, I2S frame sync 1 pin, or PCC data out pin 07 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_i2c_scl, \ni2s_fs1, \npcc_dout07, \n\n`pa24: Pin<PA24, Reset>`PA24: USB Data- pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nusb_dm, \n\n`pa25: Pin<PA25, Reset>`PA25: USB Data+ pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nusb_dp, \n\n`pa27: Pin<PA27, Reset>`PA27: Extension 1 SPI chip select pin B This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_spi_cs_b, \n\n`pa30: Pin<PA30, Reset>`PA30: Serial wire clock pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nswclk, \n\n`pa31: Pin<PA31, Reset>`PA31: Serial wire data in/out This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nswdio, \n\n`pb00: Pin<PB00, Reset>`PB00: Extension 2 ADC pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_adc_plus, \n\n`pb01: Pin<PB01, Reset>`PB01: Extension 2 GPIO pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_gpio1_in, \next2_gpio1_out, \n\n`pb02: Pin<PB02, Reset>`PB02: Extension 2 SPI chip select pin B This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_spi_cs_b, \n\n`pb04: Pin<PB04, Reset>`PB04: Extension 1 ADC plus pin, or ADC 1 analog pin 6 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_adc_plus, \nadc1_analog6, \n\n`pb05: Pin<PB05, Reset>`PB05: Extension 1 ADC minus pin, or ADC 1 analog pin 7 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_adc_minus, \nadc1_analog7, \n\n`pb06: Pin<PB06, Reset>`PB06: Extension 2 GPIO pin 2, or ADC 1 analog pin 8 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_gpio2_in, \next2_gpio2_out, \nadc1_analog8, \n\n`pb07: Pin<PB07, Reset>`PB07: Extension 2 interrupt request/GPIO pin, or ADC 1 analog pin 9 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_irq_gpio_in, \next1_irq_gpio_out, \nadc1_analog9, \n\n`pb08: Pin<PB08, Reset>`PB08: Extension 1 PWM+ pin, ADC 0 analog pin 2, or ADC 1 analog pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc0_analog2, \nadc1_analog0, \next1_pwm_plus, \n\n`pb09: Pin<PB09, Reset>`PB09: Extension 1 PWM- pin, ADC 0 analog pin 3, or ADC 1 analog pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nadc0_analog3, \nadc1_analog1, \next1_pwm_minus, \n\n`pb10: Pin<PB10, Reset>`PB10: QSPI serial clock This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_sck, \n\n`pb11: Pin<PB11, Reset>`PB11: QSPI chip select pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nqspi_scs, \n\n`pb12: Pin<PB12, Reset>`PB12: ATA6561 on-board CAN device transmit pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nata6561_tx, \n\n`pb13: Pin<PB13, Reset>`PB13: ATA6561 on-board CAN device receive pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nata6561_rx, \n\n`pb14: Pin<PB14, Reset>`PB14: Extension 2 PWM+ pin or PCC data out pin 08 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_pwm_plus, \npcc_dout08, \n\n`pb15: Pin<PB15, Reset>`PB15: Extension 2 PWM- pin or PCC data out pin 09 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_pwm_minus, \npcc_dout09, \n\n`pb16: Pin<PB16, Reset>`PB16: Extension 2 UART transmit pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_uart_tx, \n\n`pb17: Pin<PB17, Reset>`PB17: Extension 2 UART receive pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_uart_rx, \n\n`pb18: Pin<PB18, Reset>`PB18: SD card data pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_data0, \n\n`pb19: Pin<PB19, Reset>`PB19: SD card data pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_data1, \n\n`pb20: Pin<PB20, Reset>`PB20: SD card data pin 2 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_data2, \n\n`pb21: Pin<PB21, Reset>`PB21: SD card data pin 3 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_data3, \n\n`pb22: Pin<PB22, Reset>`PB22: Xosc1 XIn/clock pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nxosc1_x_in, \nxosc1_clock, \n\n`pb23: Pin<PB23, Reset>`PB23: Xosc1 XOut pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nxosc1_x_out, \n\n`pb24: Pin<PB24, Reset>`PB24: EDBG connection UART receive pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nedbg_uart_rx, \n\n`pb25: Pin<PB25, Reset>`PB25: EDBG connection UART transmit pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nedbg_uart_tx, \n\n`pb26: Pin<PB26, Reset>`PB26: Extension 1 SPI serial clock pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_spi_sck, \n\n`pb27: Pin<PB27, Reset>`PB27: Extension 1 SPI MOSI pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_spi_mosi, \n\n`pb28: Pin<PB28, Reset>`PB28: Extension 1 SPI chip select pin A This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_spi_cs_a, \n\n`pb29: Pin<PB29, Reset>`PB29: Extension 1 SPI MISO pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next1_spi_miso, \n\n`pb30: Pin<PB30, Reset>`PB30: Serial wire out pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nswo, \n\n`pb31: Pin<PB31, Reset>`PB31: Switch 0, user-controlled button This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nbutton, \n\n`pc01: Pin<PC01, Reset>`PC01: Extension 3 GPIO pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_gpio1_in, \next3_gpio1_out, \n\n`pc02: Pin<PC02, Reset>`PC02: Extension 3 ADC+ pin, or ADC 1 analog pin 4 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_adc_plus, \nadc1_analog4, \n\n`pc03: Pin<PC03, Reset>`PC03: Extension 3 ADC- pin, or ADC 1 analog pin 5 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_adc_minus, \nadc1_analog5, \n\n`pc04: Pin<PC04, Reset>`PC04: SPI MOSI pin for extension 2, 3, or data gateway interface This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_spi_mosi, \next3_spi_mosi, \ndgi_spi_mosi, \n\n`pc05: Pin<PC05, Reset>`PC05: SPI serial clock pin for extension 2, 3, or data gateway interface This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_spi_sck, \next3_spi_sck, \ndgi_spi_sck, \n\n`pc06: Pin<PC06, Reset>`PC06: Extension 2 SPI chip select pin A This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_spi_cs_a, \n\n`pc07: Pin<PC07, Reset>`PC07: SPI MISO pin for extension 2, 3, or data gateway interface This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_spi_miso, \next3_spi_miso, \ndgi_spi_miso, \n\n`pc10: Pin<PC10, Reset>`PC10: Extension 3 GPIO pin 2 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_gpio2_in, \next3_gpio2_out, \n\n`pc11: Pin<PC11, Reset>`PC11: PCC PWDN pin, or Ethernet MDC pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_pwdn, \neth_mdc, \n\n`pc12: Pin<PC12, Reset>`PC12: PCC reset pin, or ethernet GMDIO pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npcc_reset, \neth_gmdio, \n\n`pc13: Pin<PC13, Reset>`PC13: ATA6561 on-board CAN device standby pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nata6561_standby, \n\n`pc14: Pin<PC14, Reset>`PC14: Extension 3 SPI chip select pin A This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_spi_cs_a, \n\n`pc16: Pin<PC16, Reset>`PC16: Position decoder phase A pin, or embedded debugger GPIO pin 0 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npdec_phase_a, \nedbg_gpio0_in, \nedbg_gpio0_out, \n\n`pc17: Pin<PC17, Reset>`PC17: Position decoder phase B pin, or embedded debugger GPIO pin 1 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\npdec_phase_b, \nedbg_gpio1_in, \nedbg_gpio1_out, \n\n`pc18: Pin<PC18, Reset>`PC18: LED output, position decoder index pin, or embedded debugger GPIO pin 2 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nled, \npdec_index, \nedbg_gpio2_in, \nedbg_gpio2_out, \n\n`pc20: Pin<PC20, Reset>`PC20: Ethernet carrier sense / data valid pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\neth_crs_dv, \n\n`pc21: Pin<PC21, Reset>`PC21: Ethernet reset pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\neth_reset, \n\n`pc22: Pin<PC22, Reset>`PC22: Extension 3 UART transmit pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_uart_tx, \n\n`pc23: Pin<PC23, Reset>`PC23: Extension 3 UART receive pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_uart_rx, \n\n`pc30: Pin<PC30, Reset>`PC30: Extension 3 interrupt request/GPIO pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_irq_gpio_in, \next3_irq_gpio_out, \n\n`pc31: Pin<PC31, Reset>`PC31: Extension 3 SPI chip select pin B This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_spi_cs_b, \n\n`pd00: Pin<PD00, Reset>`PD00: Extension 2 interrupt request/GPIO pin, or ADC 1 analog pin 14 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_irq_gpio_in, \next2_irq_gpio_out, \nadc1_analog14, \n\n`pd01: Pin<PD01, Reset>`PD01: Data gateway interface chip select pin, or ADC 1 analog pin 15 This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\ndgi_spi_cs, \nadc1_analog15, \n\n`pd08: Pin<PD08, Reset>`PD08: Extension 2, 3, and data gateway interface I2C serial data pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_i2c_sda, \next3_i2c_sda, \ndgi_i2c_sda, \n\n`pd09: Pin<PD09, Reset>`PD09: Extension 2, 3, and data gateway interface I2C serial clock pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next2_i2c_scl, \next3_i2c_scl, \ndgi_i2c_scl, \n\n`pd10: Pin<PD10, Reset>`PD10: Extension 3 PWM+ pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_pwm_plus, \n\n`pd11: Pin<PD11, Reset>`PD11: Extension 3 PWM- pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\next3_pwm_minus, \n\n`pd12: Pin<PD12, Reset>`PD12: Ethernet interrupt pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\neth_interrupt, \n\n`pd20: Pin<PD20, Reset>`PD20: SD card card detect pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_cd, \n\n`pd21: Pin<PD21, Reset>`PD21: SD card write protect pin This field can also be accessed using the [`pin_alias!`] macro with the following alternate names:\n\nsd_wp, \n\nImplementations\n---\n\n### impl Pins\n\n#### pub fn new(port: PORT) -> Self\n\nTake ownership of the PAC [`PORT`] and split it into discrete [`Pin`]s.\n\nThis struct serves as a replacement for the HAL `Pins`\nstruct. It is intended to provide more meaningful names for each [`Pin`] in a BSP. Any [`Pin`] not defined by the BSP is dropped.\n\n`PORT`\n`Pin`\n`Pins`\n\n#### pub unsafe fn port(&mut self) -> PORT\n\nTake the PAC [`PORT`]\n\nThe [`PORT`] can only be taken once. Subsequent calls to this function will panic.\n\n##### Safety\n\nDirect access to the [`PORT`] could allow you to invalidate the compiler’s type-level tracking, so it is unsafe.\n\n`PORT`\n\nAuto Trait Implementations\n---\n\n### impl RefUnwindSafe for Pins\n\n### impl Send for Pins\n\n### impl !Sync for Pins\n\n### impl Unpin for Pins\n\n### impl UnwindSafe for Pins\n\nBlanket Implementations\n---\n\n### impl<T> Any for Twhere\n T: 'static + ?Sized,\n\n#### fn type_id(&self) -> TypeId\n\nGets the `TypeId` of `self`. \n T: ?Sized,\n\n#### fn borrow(&self) -> &T\n\nImmutably borrows from an owned value. \n T: ?Sized,\n\n#### fn borrow_mut(&mut self) -> &mut T\n\nMutably borrows from an owned value. \n\n#### fn from(t: T) -> T\n\nReturns the argument unchanged.\n\n### impl<T, U> Into<U> for Twhere\n U: From<T>,\n\n#### fn into(self) -> U\n\nCalls `U::from(self)`.\n\nThat is, this conversion is whatever the implementation of\n`From<T> for U` chooses to do.\n\n### impl<T> Same<T> for T\n\n#### type Output = T\n\nShould always be `Self`### impl<T, U> TryFrom<U> for Twhere\n U: Into<T>,\n\n#### type Error = Infallible\n\nThe type returned in the event of a conversion error.#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::ErrorPerforms the conversion.### impl<T, U> TryInto<U> for Twhere\n U: TryFrom<T>,\n\n#### type Error = <U as TryFrom<T>>::Error\n\nThe type returned in the event of a conversion error.#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::ErrorPerforms the conversion."}}},{"rowIdx":59483,"cells":{"project":{"kind":"string","value":"novapo-medusa-payment-manual"},"source":{"kind":"string","value":"npm"},"language":{"kind":"string","value":"JavaScript"},"content":{"kind":"string","value":"Manual Payment\n===\n\nA minimal payment provider that allows merchants to handle payments manually.\n\n[Medusa Website](https://medusajs.com/) | [Medusa Repository](https://github.com/medusajs/medusa)\n\nFeatures\n---\n\n* Provides a restriction-free payment provider that can be used during checkout and while processing orders.\n\n---\n\nPrerequisites\n---\n\n* [Medusa backend](https://docs.medusajs.com/development/backend/install)\n\n---\n\nHow to Install\n---\n\n1. Run the following command in the directory of the Medusa backend:\n```\nnpm install medusa-payment-manual\n```\n2. In `medusa-config.js` add the following at the end of the `plugins` array:\n```\nconst plugins = [\n // ...\n `medusa-payment-manual`\n]\n```\n---\n\nTest the Plugin\n---\n\n1. Run the following command in the directory of the Medusa backend to run the backend:\n```\nnpm run start\n```\n2. Enable the payment provider in a region in the admin. You can refer to [this User Guide](https://docs.medusajs.com/user-guide/regions/providers) to learn how to do that. Alternatively, you can use the [Admin APIs](https://docs.medusajs.com/api/admin#tag/Region/operation/PostRegionsRegion).\n\n3. Place an order using a storefront or the [Store APIs](https://docs.medusajs.com/api/store). You should be able to use Stripe as a payment method.\nReadme\n---\n\n### Keywords\n\n* medusa-plugin\n* medusa-plugin-payment"}}},{"rowIdx":59484,"cells":{"project":{"kind":"string","value":"FME"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘FME’\n July 5, 2023\nVersion 1.3.6.3\nTitle A Flexible Modelling Environment for Inverse Modelling,\n Sensitivity, Identifiability and Monte Carlo Analysis\nAuthor <NAME> [aut, cre] (<https://orcid.org/0000-0003-4603-7100>),\n <NAME> [aut] (<https://orcid.org/0000-0002-4951-6468>)\nMaintainer <NAME> <<EMAIL>>\nDepends R (>= 2.6), deSolve, rootSolve, coda\nImports minpack.lm, MASS, graphics, grDevices, stats, utils, minqa\nSuggests diagram\nDescription Provides functions to help in fitting models to data, to\n perform Monte Carlo, sensitivity and identifiability analysis. It is\n intended to work with models be written as a set of differential\n equations that are solved either by an integration routine from\n package 'deSolve', or a steady-state solver from package\n 'rootSolve'. However, the methods can also be used with other types of\n functions.\nLicense GPL (>= 2)\nURL http://fme.r-forge.r-project.org/\nNeedsCompilation yes\nRepository CRAN\nDate/Publication 2023-07-05 15:03:04 UTC\nR topics documented:\nFME-packag... 2\ncolli... 4\ncross2lon... 7\ngaussianWeight... 10\nGri... 12\nLatinhype... 13\nmodCos... 14\nmodCR... 20\nmodFi... 23\nmodMCM... 30\nNor... 38\nobsplo... 40\npseudoOpti... 42\nsensFu... 44\nsensRang... 48\nUni... 53\n FME-package A Flexible Modelling Environment for Inverse Modelling, Sensitivity,\n Identifiability, Monte Carlo Analysis.\nDescription\n R-package FME contains functions to run complex applications of models that produce output as a\n function of input parameters.\n Although it was created to be used with models consisting of ordinary differential equations (ODE),\n partial differential equations (PDE) or differential algebraic equations (DAE), it can work with other\n models.\n It contains:\n • Functions to allow fitting of the model to data.\n Function modCost estimates the (weighted) residuals between model output and data, variable\n and model costs.\n Function modFit uses the output of modCost to find the best-fit parameters. It provides a\n wrapper around R’s built-in minimisation routines (optim, nlm, nlminb) and nls.lm from\n package minpack.lm.\n Package FME also includes an implementation of the pseudo-random search algorithm (func-\n tion pseudoOptim).\n • Function sensFun estimates the sensitivity functions of selected output variables as a function\n of model parameters. This is the basis of uni-variate, bi-variate and multi-variate sensitivity\n analysis.\n • Function collin uses as input the sensitivity functions and estimates the \"collinearity\" index\n for all possible parameter sets. This multivariate sensitivity estimate measures approximate\n linear dependence and is useful to derive which parameter sets are identifiable given the data\n set.\n • Function sensRange produces ’envelopes’ around the sensitivity variables, consisting of a\n time series or a 1-dimensional set, as a function of the sensitivity parameters. It produces\n \"envelopes\" around the variables.\n • Function modCRL calculates the values of single variables as a function of the sensitivity pa-\n rameters. This function can be used to run simple \"what-if\" scenarios\n • Function modMCMC runs a Markov chain Monte Carlo (Bayesian analysis). It implements the\n delayed rejection - adaptive Metropolis (DRAM) algorithm.\n • FME also contains functions to generate multiple parameter values arranged according to a\n grid (Grid) multinormal (Norm) or uniform (Unif) design, and a latin hypercube sampling\n (Latinhyper) function\nDetails\n bug corrections:\n • version 1.3.6, sensFun: corrected calculation of L2 norm (now consistent with help page),\n • version 1.3, modCost: minlogp was not correctly estimated if more than one observed variable\n (used the wrong sd).\nAuthor(s)\n <NAME>\n <NAME>\nReferences\n Soetaert, K. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## Not run:\n ## show examples (see respective help pages for details)\n example(modCost)\n example(sensFun)\n example(modMCMC)\n example(modCRL)\n ## open the directory with documents\n browseURL(paste(system.file(package = \"FME\"), \"/doc\", sep = \"\"))\n ## open the directory with examples\n browseURL(paste(system.file(package = \"FME\"), \"/doc/examples\", sep = \"\"))\n ## the vignettes\n vignette(\"FME\")\n vignette(\"FMEdyna\")\n vignette(\"FMEsteady\")\n vignette(\"FMEother\")\n vignette(\"FMEmcmc\")\n edit(vignette(\"FME\"))\n edit(vignette(\"FMEdyna\"))\n edit(vignette(\"FMEsteady\"))\n edit(vignette(\"FMEother\"))\n edit(vignette(\"FMEmcmc\"))\n ## End(Not run)\n collin Estimates the Collinearity of Parameter Sets\nDescription\n Based on the sensitivity functions of model variables to a selection of parameters, calculates the\n \"identifiability\" of sets of parameter.\n The sensitivity functions are a matrix whose (i,j)-th element contains\n ∂yi ∆Θj\n ·\n ∂Θj ∆yi\n and where yi is an output variable, at a certain (time) instance, i, ∆yi is the scaling of variable yi ,\n ∆Θj is the scaling of parameter Θj .\n Function collin estimates the collinearity, or identifiability of all parameter sets or of one param-\n eter set.\n As a rule of thumb, a collinearity value less than about 20 is \"identifiable\".\nUsage\n collin(sensfun, parset = NULL, N = NULL, which = NULL, maxcomb = 5000)\n ## S3 method for class 'collin'\n print(x, ...)\n ## S3 method for class 'collin'\n plot(x, ...)\nArguments\n sensfun model sensitivity functions as estimated by SensFun.\n parset one selected parameter combination, a vector with their names or with the in-\n dices to the parameters.\n N the number of parameters in the set; if NULL then all combinations will be tried.\n Ignored if parset is not NULL.\n which the name or the index to the observed variables that should be used. Default =\n all observed variables.\n maxcomb the maximal number of combinations that can be tested. If too large, this may\n produce a huge output. The number of combinations of n parameters out of a\n total of p parameters is choose(p, n).\n x an object of class collin.\n ... additional arguments passed to the methods.\nDetails\n The collinearity is a measure of approximate linear dependence between sets of parameters. The\n higher its value, the more the parameters are related. With \"related\" is meant that several paraemter\n combinations may produce similar values of the output variables.\nValue\n a data.frame of class collin with one row for each parameter combination (parameters as in\n sensfun).\n Each row contains:\n ... for each parameter whether it is present (1) or absent (0) in the set,\n N the number of parameters in the set,\n collinearity the collinearity value.\n The data.frame returned by collin has methods for the generic functions print and plot.\nNote\n It is possible to use collin for selecting parameter sets that can be fine-tuned based on a data set.\n Thus it is a powerful technique to make model calibration routines more robust, because calibration\n routines often fail when parameters are strongly related.\n In general, when the collinearity index exceeds 20, the linear dependence is assumed to be critical\n (i.e. it will not be possible or easy to estimate all the parameters in the combination together).\n The procedure is explained in Omlin et al. (2001).\n 1. First the function collin is used to test how far a dataset can be used for estimating certain\n (combinations of) parameters. After selection of an ’identifiable parameter set’ (which has a low\n \"collinearity\") they are fine-tuned by calibration.\n 2. As the sensitivity analysis is a local analysis (i.e. its outcome depends on the current values of the\n model parameters) and the fitting routine is used to estimate the best values of the parameters, this\n is an iterative procedure. This means that identifiable parameters are determined, fitted to the data,\n then a newly identifiable parameter set is determined, fitted, etcetera until convergenc is reached.\n See the paper by Omlin et al. (2001) for more information.\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n <NAME>., <NAME>. and <NAME>., 2001. Practical Identifiability Analysis of Large Environ-\n mental Simulation Models. Water Resour. Res. 37(4): 1015–1030.\n <NAME>., <NAME>. and <NAME>., 2001. Biogeochemical Model of Lake Zurich: Sensitivity,\n Identifiability and Uncertainty Analysis. Ecol. Modell. 141: 105–123.\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Test collinearity values\n ## =======================================================================\n ## linearly related set... => Infinity\n collin(cbind(1:5, 2*(1:5)))\n ## unrelated set => 1\n MM <- matrix(nr = 4, nc = 2, byrow = TRUE,\n data = c(-0.400, -0.374, 0.255, 0.797, 0.690, -0.472, -0.546, 0.049))\n collin(MM)\n ## =======================================================================\n ## Bacterial model as in Soetaert and Herman, 2009\n ## =======================================================================\n pars <- list(gmax = 0.5,eff = 0.5,\n ks = 0.5, rB = 0.01, dB = 0.01)\n solveBact <- function(pars) {\n derivs <- function(t, state, pars) { # returns rate of change\n with (as.list(c(state, pars)), {\n dBact <- gmax*eff*Sub/(Sub + ks)*Bact - dB*Bact - rB*Bact\n dSub <- -gmax *Sub/(Sub + ks)*Bact + dB*Bact\n return(list(c(dBact, dSub)))\n })\n }\n state <- c(Bact = 0.1, Sub = 100)\n tout <- seq(0, 50, by = 0.5)\n ## ode solves the model by integration...\n return(as.data.frame(ode(y = state, times = tout, func = derivs,\n parms = pars)))\n }\n out <- solveBact(pars)\n ## We wish to estimate parameters gmax and eff by fitting the model to\n ## these data:\n Data <- matrix(nc = 2, byrow = TRUE, data =\n c( 2, 0.14, 4, 0.2, 6, 0.38, 8, 0.42,\n 10, 0.6, 12, 0.107, 14, 1.3, 16, 2.0,\n 18, 3.0, 20, 4.5, 22, 6.15, 24, 11,\n 26, 13.8, 28, 20.0, 30, 31 , 35, 65, 40, 61)\n )\n colnames(Data) <- c(\"time\",\"Bact\")\n head(Data)\n Data2 <- matrix(c(2, 100, 20, 93, 30, 55, 50, 0), ncol = 2, byrow = TRUE)\n colnames(Data2) <- c(\"time\", \"Sub\")\n ## Objective function to minimise\n Objective <- function (x) { # Model cost\n pars[] <- x\n out <- solveBact(x)\n Cost <- modCost(obs = Data2, model = out) # observed data in 2 data.frames\n return(modCost(obs = Data, model = out, cost = Cost))\n }\n ## 1. Estimate sensitivity functions - all parameters\n sF <- sensFun(func = Objective, parms = pars, varscale = 1)\n ## 2. Estimate the collinearity\n Coll <- collin(sF)\n ## The larger the collinearity, the less identifiable the data set\n Coll\n plot(Coll, log = \"y\")\n ## 20 = magical number above which there are identifiability problems\n abline(h = 20, col = \"red\")\n ## select \"identifiable\" sets with 4 parameters\n Coll [Coll[,\"collinearity\"] < 20 & Coll[,\"N\"]==4,]\n ## collinearity of one selected parameter set\n collin(sF, c(1, 3, 5))\n collin(sF, 1:5)\n collin(sF, c(\"gmax\", \"eff\"))\n ## collinearity of all combinations of 3 parameters\n collin(sF, N = 3)\n ## The collinearity depends on the value of the parameters:\n P <- pars\n P[1:2] <- 1 # was: 0.5\n collin(sensFun(Objective, P, varscale = 1))\n cross2long Convert a dataset in wide (crosstab) format to long (database) format\nDescription\n Rearranges a data frame in cross tab format by putting all relevant columns below each other,\n replicating the independent variable and, if necessary, other specified columns. Optionally, an err\n column is added.\nUsage\n cross2long( data, x, select = NULL, replicate = NULL,\n error = FALSE, na.rm = FALSE)\nArguments\n data a data frame (or matrix) with crosstab layout\n x name of the independent variable to be replicated\n select a vector of column names to be included (see details). All columns are included\n if not specified.\n replicate a vector of names of variables (apart from the independent variable that have to\n be replicated for every included column (e.g. experimental treatment specifica-\n tion).\n error boolean indicating whether the final dataset in long format should contain an\n extra column for error values (cf. modCost); here filled with 1’s.\n na.rm whether or not to remove the NAs.\nDetails\n The original data frame is converted from a wide (crosstab) layout (one variable per column) to a\n long (database) layout (all variable value in one column).\n As an example of both formats consider the data, called Dat consisting of two observed variables,\n called \"Obs1\" and \"Obs2\", both containing two observations, at time 1 and 2:\n name time val err\n Obs1 1 50 5\n Obs1 2 150 15\n Obs2 1 1 0.1\n Obs2 2 2 0.2\n for the long format and\n time Obs1 Obs2\n 1 50 1\n 2 150 2\n for the crosstab format.\n The parameters x, select, and replicate should be disjoint. Although the independent variable\n always has to be replicated it should not be given by the replicate parameter.\nValue\n A data frame with the following columns:\n name Column containing the column names of the original crosstab data frame, data\n x A replication of the independent variable\n y The actual data stacked upon each other in one column\n err Optional column, filled with NA values (necessary for some other functions)\n ... all other columns from the original dataset that had to be replicated (indicated\n by the parameter replicate)\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Suppose we have measured sediment oxygen concentration profiles\n ## =======================================================================\n depth <- 0:7\n O2mud <- c( 6, 1, 0.5, 0.1, 0.05,0, 0, 0)\n O2silt <- c( 6, 5, 3, 2, 1.5, 1, 0.5, 0)\n O2sand <- c( 6, 6, 5, 4, 3, 2, 1, 0)\n zones <- c(\"a\", \"b\", \"b\", \"c\", \"c\", \"d\", \"d\", \"e\")\n oxygen <- data.frame(depth = depth,\n zone = zones,\n mud = O2mud,\n silt = O2silt,\n sand = O2sand\n )\n cross2long(data = oxygen, x = depth,\n select = c(silt, mud), replicate = zone)\n cross2long(data = oxygen, x = depth,\n select = c(mud, -silt), replicate = zone)\n # twice the same column name: replicates\n colnames(oxygen)[4] <- \"mud\"\n cross2long(data=oxygen, x = depth, select = mud)\n gaussianWeights A kernel average smoother function to weigh residuals according to\n a Gaussian density function This function is still experimental... use\n with care\nDescription\n A calibration dataset in database format (cf. modCost for the database format) is extended in order\n to fit model output using a weighted least squares approach. To this end, the observations are\n replicated for a certain number of times, and weights are assigned to the replicates according to a\n Gaussian density function. This density has the relevant observation as mean value. The standard\n deviation, provided as a parameter, determines the number of inserted replicate observations (see\n Detail).\n This weighted regression approach may be interesting when discontinuities exist in the observa-\n tional data. Under these circumstances small changes in the timing (or more general the position\n along the axis of the independent variable) of the model output may have a disproportional impact\n on the overall goodness-of-fit (e.g. timing of nutrient depletion). Additionally, this approach may\n be used to model uncertainty in the independent variable (e.g. slices of sediment profiles, or the\n timing of a sampling).\nUsage\n gaussianWeights (obs, x = x, y = y, xmodel, spread, weight = \"none\",\n aggregation = x ,ordering)\nArguments\n obs dataset in long (database) format as is typically used by modCost\n x name of the independent variable (typically x, cf. modCost) in obs. Defaults to\n x (not given as character string; cf. subset)\n y name of the dependent variable in obs. Defaults to y.\n xmodel an ordered vector of unique times at which model output is produced. If not\n given, the independent variable of the observational dataset is used.\n spread standard deviation used to calculate the weights from a normal density function.\n This value also determines the number of points from the model output that are\n compared to a specific observa- tion in obs (2 * 3 * spread + 1; containing 99.7%\n of the Gaussian distribution, centered around the observation of interest).\n weight scaling factor of the modCost function (\"sd\", \"mean\", or \"none\"). The Gaussian\n weights are multiplied by this factor to account for differences in units.\n aggregation vector of column names from the dataset that are used to aggregate observations\n while calculating the scaling factor. Defaults to the variable name, \"name\".\n ordering Optional extra grouping and ordering of observations. Given as a vector of\n variable names. If none given, ordering will be done by variable name and inde-\n pendent variable. If both aggregation and ordering variables are given, ordering\n will be done as follows: x within ordering (in reverse order) within aggregation\n (in reverse order). Aggregation and ordering should be disjoint sets of variable\n names.\nDetails\n Suppose: spread = 1/24 (days; = 1 hour) x = time in days, 1 per hour\n Then: obs_i is replicated 7 times (spread = observational periodicity = 1 hour):\n => obs_i-3 = ... = obs_i-1 = obs_i = obs_i+1 = ... = obs_i+3\n The weights (W_i+j, for j = -3 ...3) are calculated as follows: W’_i+j = 1/(spread * sqrt(2pi)) *\n exp(-1/2 * ((obs_i+j - obs_i)/spread)^2\n W_i+j = W’_i+j/sum(W_i-3,...,W_i+3) (such that their sum equals 1)\nValue\n A modified version of obs is returned with the following extensions:\n 1. Each observation obs[i] is replicated n times were n represents the number of modelx values\n within the interval [obs_i - (3 * spread), obs_i + 3 * spread)].\n 2. These replicate observations get the same x values as their modeled counterparts (xmodel).\n 3. Weights are given in column, called \"err\"\n The returned data frame has the following columns:\n • \"name\" or another name specified by the first element of aggregation. Usually this column\n contains the names of the observed variables.\n • \"x\" or another name specified by x\n • \"y\" or another name specified by y\n • \"err\" containing the calculated weights\n • The rest of the columns of the data frame given by obs in that order.\nAuthor(s)\n <NAME> <<EMAIL>>\nExamples\n ## =======================================================================\n ## A Sediment example\n ## =======================================================================\n ## Sediment oxygen concentration is measured every\n ## centimeter in 3 sediment types\n depth <- 0:7\n observations <- data.frame(\n profile = rep(c(\"mud\",\"silt\",\"sand\"), each=8),\n depth = depth,\n O2 = c(c(6,1,0.5,0.1,0.05,0,0,0),\n c(6,5,3,2,1.5,1,0.5,0),\n c(6,6,5,4,3,2,1,0)\n )\n )\n ## A model generates profiles with a depth resolution of 1 millimeter\n modeldepths <- seq(0, 9, by = 0.05)\n ## All these model outputs are compared with weighed observations.\n gaussianWeights(obs = observations, x = depth, y = O2,\n xmodel = modeldepths,\n spread = 0.1, weight = \"none\",\n aggregation = profile)\n # Weights of one observation in silt at depth 2:\n Sub <- subset(observations, subset = (profile == \"silt\" & depth == 2))\n plot(Sub[,-1])\n SubWW <- gaussianWeights(obs = Sub, x = depth, y = O2,\n xmodel = modeldepths, spread = 0.5,\n weight=\"none\", aggregation = profile)\n SubWW[,-1]\n Grid Grid Distribution\nDescription\n Generates parameter sets arranged on a regular grid.\nUsage\n Grid(parRange, num)\nArguments\n parRange the range (min, max) of the parameters, a matrix or a data.frame with one row\n for each parameter, and two columns with the minimum (1st) and maximum\n (2nd) column.\n num the number of random parameter sets to generate.\nDetails\n The grid design produces the most regular parameter distribution; there is no randomness involved.\n The number of parameter sets generated with Grid will be <= num.\nValue\n a matrix with one row for each generated parameter set, and one column per parameter.\nAuthor(s)\n <NAME> <<EMAIL>>\nSee Also\n Norm for (multi)normally distributed random parameter sets.\n Latinhyper to generates parameter sets using latin hypercube sampling.\n Unif for uniformly distributed random parameter sets.\n seq the R-default for generating regular sequences of numbers.\nExamples\n ## 4 parameters\n parRange <- data.frame(min = c(0, 1, 2, 3), max = c(10, 9, 8, 7))\n rownames(parRange) <- c(\"par1\", \"par2\", \"par3\", \"par4\")\n ## grid\n pairs(Grid(parRange, 500), main = \"Grid\")\n Latinhyper Latin Hypercube Sampling\nDescription\n Generates random parameter sets using a latin hypercube sampling algorithm.\nUsage\n Latinhyper(parRange, num)\nArguments\n parRange the range (min, max) of the parameters, a matrix or a data.frame with one row\n for each parameter, and two columns with the minimum (1st) and maximum\n (2nd) column.\n num the number of random parameter sets to generate.\nDetails\n In the latin hypercube sampling, the space for each parameter is subdivided into num equally-sized\n segments and one parameter value in each of the segments drawn randomly.\nValue\n a matrix with one row for each generated parameter set, and one column per parameter.\nNote\n The latin hypercube distributed parameter sets give better coverage in parameter space than the\n uniform random design (Unif). It is a reasonable choice in case the number of parameter sets is\n limited.\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n Press, <NAME>., <NAME>., <NAME>. and <NAME>. (2007) Numerical Recipes in\n C. Cambridge University Press.\nSee Also\n Norm for (multi)normally distributed random parameter sets.\n Unif for uniformly distributed random parameter sets.\n Grid to generate random parameter sets arranged on a regular grid.\nExamples\n ## 4 parameters\n parRange <- data.frame(min = c(0, 1, 2, 3), max = c(10, 9, 8, 7))\n rownames(parRange) <- c(\"par1\", \"par2\", \"par3\", \"par4\")\n ## Latin hypercube\n pairs(Latinhyper(parRange, 100), main = \"Latin hypercube\")\n modCost Calculates the Discrepancy of a Model Solution with Observations\nDescription\n Given a solution of a model and observed data, estimates the residuals, and the variable and model\n costs (sum of squared residuals).\nUsage\n modCost(model, obs, x = \"time\", y = NULL, err = NULL,\n weight = \"none\", scaleVar = FALSE, cost = NULL, ...)\nArguments\n model model output, as generated by the integration routine or the steady-state solver,\n a matrix or a data.frame, with one column per dependent and independent vari-\n able.\n obs the observed data, either in long (database) format (name, x, y), a data.frame, or\n in wide (crosstable, or matrix) format - see details.\n x the name of the independent variable; it should be a name occurring both in the\n obs and model data structures.\n y either NULL, the name of the column with the dependent variable values,or an in-\n dex to the dependent variable values; if NULL then the observations are assumed\n to be in crosstable (matrix) format, and the names of the independent variables\n are given by the column names of this matrix.\n err either NULL, or the name of the column with the error estimates, used to weigh\n the residuals (see details); if NULL, then the residuals are not weighed.\n cost if not NULL, the output of a previous call to modCost; in this case, the new output\n will combine both.\n weight only if err=NULL: how to weigh the residuals, one of \"none\", \"std\", \"mean\", see\n details.\n scaleVar if TRUE, then the residuals of one observed variable are scaled respectively to the\n number of observations (see details).\n ... additional arguments passed to R-function approx.\nDetails\n This function compares model output with observed data.\n It computes\n 1. the weighted residuals, one for each data point.\n 2. the variable costs, i.e. the sum of squared weight residuals per variable.\n 3. the model cost, the scaled sum of variable costs .\n There are three steps:\n 1. For any observed data point, i, the weighted residuals are estimated as:\n M odi − Obsi\n resi =\n errori\n with weighti = 1/erri and where M odi and Obsi are the modeled, respectively observed value of\n data point i.\n The weights are equal to 1/error, where the latter can be inputted, one for each data point by speci-\n fying err as an extra column in the observed data.\n This can only be done when the data input is in long (database) format.\n When err is not inputted, then the weights are specified via argument weight which is either:\n • \"none\", which sets the weight equal to 1 (the default)\n • \"std\", which sets the weights equal to the reciprocal of the standard deviation of the observed\n data (can only be used if there is more than 1 data point)\n • \"mean\", which uses 1/mean of the absolute value of the observed data (can only be used if not\n 0).\n 2. Then for each observed variable, j, a variable cost is estimated as the sum of squared weighted\n residuals for this variable:\n nj\n X\n Costvarj = resi 2\n where nj is the number of observations for observed variable j.\n 3. Finally, the model Cost is estimated as the scaled sum of variable costs:\n nv\n X Costvarj\n M odCost =\n scalevarj\n and where scalevarj allows to scale the variable costs relative to the number of observations. This\n is set by specifying argument scaleVar. If TRUE, then the variable costs are rescaled. The default\n is NOT to rescale (i.e. scalevarj =1).\n The models typically consist of (a system of) differential equations, which are either solved by:\n • integration routines, e.g. the routines from package deSolve,\n • steady-state estimators, as from package rootSolve.\n The data can be presented in two formats:\n • data table (long) format; this is a two to four column data.frame that contains the name of\n the observed variable (always the FIRST column), the (optional) value of the independent\n variable (default column name = \"time\"), the value of the observation and the (optional)\n value of the error. For data presented in this format, the names of the column(s) with the\n independent variable (x) and the name of the column that has the value of the dependent\n variable y must be passed to function modCost.\n • crosstable (wide) format; this is a matrix, where each column denotes one dependent (or\n independent) variable; the column name is the name of the observed variable. When using this\n format, only the name of the column that contains the dependent variable must be specified\n (x).\n As an example of both formats consider the data, called Dat consisting of two observed variables,\n called \"Obs1\" and \"Obs2\", both containing two observations, at time 1 and 2:\n name time val err\n Obs1 1 50 5\n Obs1 2 150 15\n Obs2 1 1 0.1\n Obs2 2 2 0.2\n for the long format and\n time Obs1 Obs2\n 1 50 1\n 2 150 2\n for the crosstab format. Note, that in the latter case it is not possible to provide separate errors per\n data point.\n By calling modCost several consecutive times (using the cost argument), it is possible to combine\n both types of data files.\nValue\n a list of type modCost containing:\n model one value, the model cost, which equals the sum of scaled variable costs (see\n details).\n minlogp one value, -log(model probablity), where it is assumed that the data are normally\n distributed, with standard deviation = error.\n var the variable costs, a data.frame with, for each observed variable the following\n (see details):\n • name, the name of the observed variable.\n • scale, the scale-factor used to weigh the variable cost, either 1 or 1/(number\n observations), defaults to 1.\n • N, the number of data points per observed variable.\n • SSR.unweighted, the sum of squared residuals per observed variable, un-\n weighted.\n • SSR, the sum of weighted squared residuals per observed variable(see de-\n tails).\n residuals the data residual, a data.frame with several columns:\n • name, the name of the observed variable.\n • x, the value of the independent variable (if present).\n • obs, the observed variable value.\n • mod, the corresponding modeled value.\n • weight, the factor used to weigh the residuals, 1/error, defaults to 1.\n • res, the weighted residuals between model and observations (mod-obs)*weight.\n • res.unweighted, the residuals between model and observations (mod-obs).\nNote\n In the future, it should be possible to have more than one independent variable present. This is not\n yet implemented, but it should allow e.g. to fit time series of spatially dependent variables.\nAuthor(s)\n Karline Soetaert <<EMAIL>>\nReferences\n Soetaert, K. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Type 1 input: name, time, value\n ## =======================================================================\n ## Create new data: two observed variables, \"a\", \"b\"\n Data <- data.frame(name = c(rep(\"a\", 4), rep(\"b\", 4)),\n time = c(1:4, 2:5), val = c(runif(4), 1:4))\n ## \"a nonsense model\"\n Mod <- function (t, y, par) {\n da <- 0\n db <- 1\n return(list(c(da, db)))\n }\n out <- ode(y = c(a = 0.5, b = 0.5), times = 0:6, func = Mod, parms = NULL)\n Data # Show\n out\n ## The cost function\n modCost(model = out, obs = Data, y = \"val\")\n ## The cost function with a data error added\n Dat2 <- cbind(Data, Err = Data$val*0.1) # error = 10% of value\n modCost(model = out, obs = Dat2, y = \"val\", err = \"Err\")\n ## =======================================================================\n ## Type 2 input: Matrix format; column names = variable names\n ## =======================================================================\n ## logistic growth model\n TT <- seq(1, 100, 2.5)\n N0 <- 0.1\n r <- 0.5\n K <- 100\n ## analytical solution\n Ana <- cbind(time = TT, N = K/(1 + (K/N0 - 1) * exp(-r*TT)))\n ## numeric solution\n logist <- function(t, x, parms) {\n with(as.list(parms), {\n dx <- r * x[1] * (1 - x[1]/K)\n list(dx)\n })\n }\n time <- 0:100\n parms <- c(r = r, K = K)\n x <- c(N = N0)\n ## Compare several numerical solutions\n Euler <- ode(x, time, logist, parms, hini = 2, method = \"euler\")\n Rk4 <- ode(x, time, logist, parms, hini = 2, method = \"rk4\")\n Lsoda <- ode(x, time, logist, parms) # lsoda is default method\n Ana2 <- cbind(time = time, N = K/(1 + (K/N0 - 1) * exp(-r * time)))\n ## the SSR and residuals with respect to the \"data\"\n cEuler <- modCost(Euler, Ana)$model\n cRk4 <- modCost(Rk4 , Ana)$model\n cLsoda <- modCost(Lsoda, Ana)$model\n cAna <- modCost(Ana2 , Ana)$model\n compare <- data.frame(method = c(\"euler\", \"rk4\", \"lsoda\", \"Ana\"),\n cost = c(cEuler, cRk4, cLsoda, cAna))\n ## Plot Euler, RK and analytic solution\n plot(Euler, Rk4, col = c(\"red\", \"blue\"), obs = Ana,\n main = \"logistic growth\", xlab = \"time\", ylab = \"N\")\n legend(\"bottomright\", c(\"exact\", \"euler\", \"rk4\"), pch = c(1, NA, NA),\n col = c(\"black\", \"red\", \"blue\"), lty = c(NA, 1, 2))\n legend(\"right\", ncol = 2, title = \"SSR\",\n legend = c(as.character(compare[,1]),\n format(compare[,2], digits = 2)))\n compare\n ## =======================================================================\n ## Now suppose we do not know K and r and they are to be fitted...\n ## The \"observations\" are the analytical solution\n ## =======================================================================\n ## Run the model with initial guess: K = 10, r = 2\n parms[\"K\"] <- 10\n parms[\"r\"] <- 2\n init <- ode(x, time, logist, parms)\n ## FITTING algorithm uses modFit\n ## First define the objective function (model cost) to be minimised\n ## more general: using modFit\n Cost <- function(P) {\n parms[\"K\"] <- P[1]\n parms[\"r\"] <- P[2]\n out <- ode(x, time, logist, parms)\n return(modCost(out, Ana))\n }\n (Fit<-modFit(p = c(K = 10, r = 2), f = Cost))\n summary(Fit)\n ## run model with the optimized value:\n parms[c(\"K\", \"r\")] <- Fit$par\n fitted <- ode(x, time, logist, parms)\n ## show results, compared with \"observations\"\n plot(init, fitted, col = c(\"green\", \"blue\"), lwd = 2, lty = 1,\n obs = Ana, obspar = list(col = \"red\", pch = 16, cex = 2),\n main = \"logistic growth\", xlab = \"time\", ylab = \"N\")\n legend(\"right\", c(\"initial\", \"fitted\"), col = c(\"green\", \"blue\"), lwd = 2)\n Cost(Fit$par)\n modCRL Monte Carlo Analysis\nDescription\n Given a model consisting of differential equations, estimates the global effect of certain (sensitivity)\n parameters on selected sensitivity variables.\n This is done by drawing parameter values according to some predefined distribution, running the\n model with each of these parameter combinations, and calculating the values of the selected output\n variables at each output interval.\n This function is useful for “what-if” scenarios.\n If the output variables consist of a time-series or spatially dependent, use sensRange instead.\nUsage\n modCRL(func, parms = NULL, sensvar = NULL, dist = \"unif\",\n parInput = NULL, parRange = NULL, parMean = NULL, parCovar = NULL,\n num = 100, ...)\n ## S3 method for class 'modCRL'\n summary(object, ...)\n ## S3 method for class 'modCRL'\n plot(x, which = NULL, trace = FALSE, ask = NULL, ...)\n ## S3 method for class 'modCRL'\n pairs(x, which = 1:ncol(x), nsample = NULL, ...)\n ## S3 method for class 'modCRL'\n hist(x, which = 1:ncol(x), ask = NULL, ...)\nArguments\n func an R-function that has as first argument parms and that returns a vector with\n variables whose sensitivity should be estimated.\n parms parameters passed to func; should be either a vector, or a list with named ele-\n ments. If NULL, then the first element of parInput is taken.\n sensvar the output variables for which the sensitivity needs to be estimated. Either NULL,\n the default=all output variables, or a vector with output variable names (which\n should be present in the vector returned by func), or a vector with indices to\n output variables as present in the output vector returned by func.\n dist the distribution according to which the parameters should be generated, one\n of \"unif\" (uniformly random samples), \"norm\", (normally distributed random\n samples), \"latin\" (latin hypercube distribution), \"grid\" (parameters arranged\n on a grid).\n The input parameters for the distribution are specified by parRange (min,max),\n except for the normally distributed parameters, in which case the distribution is\n specified by the parameter means parMean and the variance-covariance matrix,\n parCovar. Note that, if the distribution is \"norm\" and parRange is given, then\n a truncated distribution will be generated. (This is useful to prevent for instance\n that certain parameters become negative). Ignored if parInput is specified.\n parRange the range (min, max) of the sensitivity parameters, a matrix or (preferred) a\n data.frame with one row for each parameter, and two columns with the mini-\n mum (1st) and maximum (2nd) value. The rownames of parRange should be\n parameter names that are known in argument parms. Ignored if parInput is\n specified.\n parInput a matrix with dimension (*, npar) with the values of the sensitivity parameters.\n parMean only when dist is \"norm\": the mean value of each parameter. Ignored if\n parInput is specified.\n parCovar only when dist is \"norm\": the parameter’s variance-covariance matrix.\n num the number of times the model has to be run. Set large enough. If parInput is\n specified, then num parameters are selected randomly (from the rows of parInput.\n object an object of class modCRL.\n x an object of class modCRL.\n which the name or the index to the variables and parameters that should be plotted.\n Default = all variables and parameters.\n nsample the number of xy pairs to be plotted on the upper panel in the pairs plot. When\n NULL all xy pairs plotted. Set to a lower number in case the graph becomes too\n dense (and the exported picture too large). This does not affect the histograms\n on the diagonal plot (which are estimated using all values).\n trace if TRUE, adds smoothed line to the plot.\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask=.) and dev.interactive.\n ... additional arguments passed to function func or to the methods.\nValue\n a data.frame of type modCRL containing the parameter(s) and the corresponding values of the sensi-\n tivity output variables.\n The list returned by modCRL has a method for the generic functions summary and plot – see note.\nNote\n The following methods are included:\n • summary, estimates summary statistics for the sensitivity variables, a table with as many rows\n as there are variables (or elements in the vector returned by func) and the following columns:\n x, the mapping value, Mean, the mean, sd, the standard deviation, Min, the minimal value, Max,\n the maximal value, q25, q50, q75, the 25th, 50 and 75% quantile.\n • plot, produces a plot of the modCRL output, either one plot for each sensitivity variable and\n with the parameter value on the x-axis. This only works when there is only one parameter!\n OR\n one plot for each parameter value on the x-axis. This only works when there is only one\n variable!\n • hist, produces a histogram of the modCRL output parameters and variables.\n • pairs, produces a pairs plot of the modCRL output.\n The data.frame of type modCRL has several attributes, which remain hidden, and which are generally\n not of practical use (they are needed for the S3 methods). There is one exception - see notes in help\n of sensRange.\nAuthor(s)\n <NAME> <<EMAIL>>.\nReferences\n Soetaert, K. and Petzoldt, T. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Bacterial growth model as in Soetaert and Herman, 2009\n ## =======================================================================\n pars <- list(gmax = 0.5,eff = 0.5,\n ks = 0.5, rB = 0.01, dB = 0.01)\n solveBact <- function(pars) {\n derivs <- function(t,state,pars) { # returns rate of change\n with (as.list(c(state,pars)), {\n dBact <- gmax*eff * Sub/(Sub + ks)*Bact - dB*Bact - rB*Bact\n dSub <- -gmax * Sub/(Sub + ks)*Bact + dB*Bact\n return(list(c(dBact, dSub)))\n })\n }\n state <- c(Bact = 0.1, Sub = 100)\n tout <- seq(0, 50, by = 0.5)\n ## ode solves the model by integration...\n return(as.data.frame(ode(y = state, times = tout, func = derivs,\n parms = pars)))\n }\n out <- solveBact(pars)\n plot(out$time, out$Bact, main = \"Bacteria\",\n xlab = \"time, hour\", ylab = \"molC/m3\", type = \"l\", lwd = 2)\n ## Function that returns the last value of the simulation\n SF <- function (p) {\n pars[\"eff\"] <- p\n out <- solveBact(pars)\n return(out[nrow(out), 2:3])\n }\n parRange <- matrix(nr = 1, nc = 2, c(0.2, 0.8),\n dimnames = list(\"eff\", c(\"min\", \"max\")))\n parRange\n CRL <- modCRL(func = SF, parRange = parRange)\n plot(CRL) # plots both variables\n plot(CRL, which = c(\"eff\", \"Bact\"), trace = FALSE) #selects one\n modFit Constrained Fitting of a Model to Data\nDescription\n Fitting a model to data, with lower and/or upper bounds\nUsage\n modFit(f, p, ..., lower = -Inf, upper = Inf,\n method = c(\"Marq\", \"Port\", \"Newton\",\n \"Nelder-Mead\", \"BFGS\", \"CG\", \"L-BFGS-B\", \"SANN\",\n \"Pseudo\", \"bobyqa\"), jac = NULL,\n control = list(), hessian = TRUE)\n ## S3 method for class 'modFit'\n summary(object, cov=TRUE,...)\n ## S3 method for class 'modFit'\n deviance(object, ...)\n ## S3 method for class 'modFit'\n coef(object, ...)\n ## S3 method for class 'modFit'\n residuals(object, ...)\n ## S3 method for class 'modFit'\n df.residual(object, ...)\n ## S3 method for class 'modFit'\n plot(x, ask = NULL, ...)\n ## S3 method for class 'summary.modFit'\n print(x, digits = max(3, getOption(\"digits\") - 3),\n ...)\nArguments\n f a function to be minimized, with first argument the vector of parameters over\n which minimization is to take place. It should return either a vector of residuals\n (of model versus data) or an element of class modCost (as returned by a call to\n modCost.\n p initial values for the parameters to be optimized over.\n ... additional arguments passed to function f (modFit) or passed to the methods.\n lower lower bounds on the parameters; if unbounded set equal to -Inf.\n upper upper bounds on the parameters; if unbounded set equal to Inf.\n method The method to be used, one of \"Marq\", \"Port\", \"Newton\", \"Nelder-Mead\", \"BFGS\",\n \"CG\", \"L-BFGS-B\", \"SANN\", \"Pseudo\", \"bobyqa\" - see details.\n jac A function that calculates the Jacobian; it should be called as jac(x, ...) and\n return the matrix with derivatives of the model residuals as a function of the\n parameters. Supplying the Jacobian can substantially improve performance; see\n last example.\n hessian TRUE if Hessian is to be estimated. Note that, if set to FALSE, then a summary\n cannot be estimated.\n control additional control arguments passed to the optimisation routine - see details of\n nls.lm (\"Marq\"), nlminb (\"Port\"), optim (\"Nelder-Mead\", \"BFGS\", \"CG\", \"L-\n BFGS-B\", \"SANN\"), nlm (\"Newton\") or pseudoOptim(\"Pseudo\").\n object an object of class modFit.\n x an object of class modFit.\n digits number of significant digits in printout.\n cov when TRUE also calculates the parameter covariances.\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask=.) and dev.interactive.\nDetails\n Note that arguments after ... must be matched exactly.\n The method to be used is specified by argument method which can be one of the methods from\n function optim:\n • \"Nelder-Mead\", the default from optim,\n • \"BFGS\", a quasi-Newton method,\n • \"CG\", a conjugate-gradient method,\n • \"L-BFGS-B\", constrained quasi-Newton method,\n • \"SANN\", method of simulated annealing.\n Or one of the following:\n • \"Marq\", the Levenberg-Marquardt algorithm (nls.lm from package minpack) - the default.\n Note that this method is the only least squares method.\n • \"Newton\", a Newton-type algorithm (see nlm),\n • \"Port\", the Port algorithm (see nlminb),\n • \"Pseudo\", a pseudorandom-search algorithm (see pseudoOptim),\n • \"bobyqa\", derivative-free optimization by quadratic approximation from package minqa.\n For difficult problems it may be efficient to perform some iterations with Pseudo, which will bring\n the algorithm near the vicinity of a (the) minimum, after which the default algorithm (Marq) is used\n to locate the minimum more precisely.\n The implementation for the routines from optim differs from constrOptim which implements an\n adaptive barrier algorithm and which allows a more flexible implementation of linear constraints.\n For all methods except L-BFGS-B, Port, Pseudo, and bobyqa that handle box constraints internally,\n bounds on parameters are imposed by a transformation of the parameters to be fitted.\n In case both lower and upper bounds are specified, this is achieved by a tangens and arc tangens\n transformation.\n This is, parameter values, p0 , generated by the optimisation routine, and which are located in the\n range [-Inf, Inf] are transformed, before they are passed to f as:\n p = (upper + lower)/2 + (upper − lower) · arctan(p0 )/π\n .\n which maps them into the interval [lower, upper].\n Before the optimisation routine is called, the original parameter values, as given by argument p are\n mapped from [lower,upper] to [-Inf, Inf] by:\n p0 = tan(π/2 · (2p − upper − lower)/(upper − lower))\n In case only lower or upper bounds are specified, this is achieved by a log transformation and a\n corresponding exponential back transformation.\n In case parameters are transformed (all methods) or in case the method Port, Pseudo, Marq or\n bobyqa is selected, the Hessian is approximated as 2 · J T · J, where J is the Jacobian, estimated by\n finite differences.\n This ignores the second derivative terms, but this is reasonable if the method has truly converged to\n the minimum.\n Note that finite differences are not extremely precise.\n In case the Levenberg-Marquard method (Marq) is used, and parameters are not transformed, 0.5\n times the Hessian of the least squares problem is returned by nls.lm, the original Marquardt algo-\n rithm. To make it compatible, this value is multiplied with 2 and the TRUE Hessian is thus returned\n by modFit.\nValue\n a list of class modFit containing the results as returned from the called optimisation routines.\n This includes the following:\n par the best set of parameters found.\n ssr the sum of squared residuals, evaluated at the best set of parameters.\n Hessian A symmetric matrix giving an estimate of the Hessian at the solution found - see\n note.\n residuals the result of the last f evaluation; that is, the residuals.\n ms the mean squared residuals, i.e. ssr/length(residuals).\n var_ms the weighted and scaled variable mean squared residuals, one value per observed\n variable; only when f returns an element of class modCost; NA otherwise.\n var_ms_unscaled\n the weighted, but not scaled variable mean squared residuals\n var_ms_unweighted\n the raw variable mean squared residuals, unscaled and unweighted.\n ... any other arguments returned by the called optimisation routine.\n Note: this means that some return arguments of the original optimisation functions are renamed.\n More specifically, \"objective\" and \"counts\" from routine nlminb (method = \"Port\") are renamed;\n \"value\" and \"counts\"; \"niter\" and \"minimum\" from routine nls.lm (method=Marq) are renamed;\n \"counts\" and \"value\"; \"minimum\" and \"estimate\" from routine nlm (method = \"Newton\") are re-\n named.\n The list returned by modFit has a method for the summary, deviance, coef, residuals, df.residual\n and print.summary – see note.\nNote\n The summary method is based on an estimate of the parameter covariance matrix. In computing the\n covariance matrix of the fitted parameters, the problem is treated as if it were a linear least squares\n problem, linearizing around the parameter values that minimize Chi2 .\n The covariance matrix is estimated as 1/(0.5 · Hessian).\n This computation relies on several things, i.e.:\n 1. the parameter values are located at the minimum (i.e. the fitting algorithm has converged).\n 2. the observations yj are subject to independent errors whose variances are well estimated by\n 1/(n − p) times the residual sum of squares (where n = number of data points, p = number of\n parameters).\n 3. the model is not too nonlinear.\n This means that the estimated covariance (correlation) matrix and the confidence intervals derived\n from it may be worthless if the assumptions behind the covariance computation are invalid.\n If in doubt about the validity of the summary computations, use Monte Carlo fitting instead, or run\n a modMCMC.\n Other methods included are:\n • deviance, which returns the model deviance,\n • coef, which extracts the values of the fitted parameters,\n • residuals,which extracts the model residuals,\n • df.residual which returns the residual degrees of freedom\n • print.summary, producing a nice printout of the summary.\n Specifying a function to estimate the Jacobian matrix via argument jac may increase speed. The\n Jacobian is used in the methods \"Marq\", \"BFGS\", \"CG\", \"L-BFGS\", \"Port\", and is also used at the\n end, to estimate the Hessian at the optimum.\n Specification of the gradient in routines \"BFGS\", \"CG\", \"L-BFGS\" from optim and \"port\" from\n nlminb is not allowed here. Within modFit, the gradient is rather estimated from the Jacobian jac\n and the function f.\nAuthor(s)\n <NAME> <<EMAIL>>,\n <NAME> <<EMAIL>>\nReferences\n <NAME>., <NAME>. and Varadhan, R. 2014. minqa: Derivative-free optimization\n algorithms by quadratic approximation. R package. https://cran.r-project.org/package=\n minqa\n <NAME>., 1990. Usage Summary for Selected Optimization Routines. Computing Science Tech-\n nical Report No. 153. AT&T Bell Laboratories, Murray Hill, NJ 07974.\n <NAME>. (2009). The BOBYQA algorithm for bound constrained optimization without\n derivatives. Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of\n Cambridge, UK. https://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf\n Press, <NAME>., <NAME>., <NAME>. and <NAME>., 2007. Numerical Recipes in C.\n Cambridge University Press.\n Price, W.L., 1977. A Controlled Random Search Procedure for Global Optimisation. The Computer\n Journal, 20: 367-370. doi:10.1093/comjnl/20.4.367\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\n Please see also additional publications on the help pages of the individual algorithms.\nSee Also\n constrOptim for constrained optimization.\nExamples\n ## =======================================================================\n ## logistic growth model\n ## =======================================================================\n TT <- seq(1, 60, 5)\n N0 <- 0.1\n r <- 0.5\n K <- 100\n ## perturbed analytical solution\n Data <- data.frame(\n time = TT,\n N = K / (1+(K/N0-1) * exp(-r*TT)) * (1 + rnorm(length(TT), sd = 0.01))\n )\n plot(TT, Data[,\"N\"], ylim = c(0, 120), pch = 16, col = \"red\",\n main = \"logistic growth\", xlab = \"time\", ylab = \"N\")\n ##===================================\n ## Fitted with analytical solution #\n ##===================================\n ## initial \"guess\"\n parms <- c(r = 2, K = 10, N0 = 5)\n ## analytical solution\n model <- function(parms,time)\n with (as.list(parms), return(K/(1+(K/N0-1)*exp(-r*time))))\n ## run the model with initial guess and plot results\n lines(TT, model(parms, TT), lwd = 2, col = \"green\")\n ## FITTING algorithm 1\n ModelCost <- function(P) {\n out <- model(P, TT)\n return(Data$N-out) # residuals\n }\n (Fita <- modFit(f = ModelCost, p = parms))\n times <- 0:60\n lines(times, model(Fita$par, times), lwd = 2, col = \"blue\")\n summary(Fita)\n ##===================================\n ## Fitted with numerical solution #\n ##===================================\n ## numeric solution\n logist <- function(t, x, parms) {\n with(as.list(parms), {\n dx <- r * x[1] * (1 - x[1]/K)\n list(dx)\n })\n }\n ## model cost,\n ModelCost2 <- function(P) {\n out <- ode(y = c(N = P[[\"N0\"]]), func = logist, parms = P, times = c(0, TT))\n return(modCost(out, Data)) # object of class modCost\n }\n Fit <- modFit(f = ModelCost2, p = parms, lower = rep(0, 3),\n upper = c(5, 150, 10))\n out <- ode(y = c(N = Fit$par[[\"N0\"]]), func = logist, parms = Fit$par,\n times = times)\n lines(out, col = \"red\", lty = 2)\n legend(\"right\", c(\"data\", \"original\", \"fitted analytical\", \"fitted numerical\"),\n lty = c(NA, 1, 1, 2), lwd = c(NA, 2, 2, 1),\n col = c(\"red\", \"green\", \"blue\", \"red\"), pch = c(16, NA, NA, NA))\n summary(Fit)\n plot(residuals(Fit))\n ## =======================================================================\n ## the use of the Jacobian\n ## =======================================================================\n ## We use modFit to solve a set of linear equations\n A <- matrix(nr = 30, nc = 30, runif(900))\n X <- runif(30)\n B <- A %*% X\n ## try to find vector \"X\"; the Jacobian is matrix A\n ## Function that returns the vector of residuals\n FUN <- function(x)\n as.vector(A %*% x - B)\n ## Function that returns the Jacobian\n JAC <- function(x) A\n ## The port algorithm\n print(system.time(\n mf <- modFit(f = FUN, p = runif(30), method = \"Port\")\n ))\n print(system.time(\n mf <- modFit(f = FUN, p = runif(30), method = \"Port\", jac = JAC)\n ))\n max(abs(mf$par - X)) # should be very small\n ## BFGS\n print(system.time(\n mf <- modFit(f = FUN, p = runif(30), method = \"BFGS\")\n ))\n print(system.time(\n mf <- modFit(f = FUN, p = runif(30), method = \"BFGS\", jac = JAC)\n ))\n max(abs(mf$par - X))\n ## Levenberg-Marquardt\n print(system.time(\n mf <- modFit(f = FUN, p = runif(30), jac = JAC)\n ))\n max(abs(mf$par - X))\n modMCMC Constrained Markov Chain Monte Carlo\nDescription\n Performs a Markov Chain Monte Carlo simulation, using an adaptive Metropolis (AM) algorithm\n and including a delayed rejection (DR) procedure.\nUsage\n modMCMC(f, p, ..., jump = NULL, lower = -Inf, upper = +Inf,\n prior = NULL, var0 = NULL, wvar0 = NULL, n0 = NULL,\n niter = 1000, outputlength = niter, burninlength = 0,\n updatecov = niter, covscale = 2.4^2/length(p),\n ntrydr = 1, drscale = NULL, verbose = TRUE)\n ## S3 method for class 'modMCMC'\n summary(object, remove = NULL, ...)\n ## S3 method for class 'modMCMC'\n pairs(x, Full = FALSE, which = 1:ncol(x$pars),\n remove = NULL, nsample = NULL, ...)\n ## S3 method for class 'modMCMC'\n hist(x, Full = FALSE, which = 1:ncol(x$pars),\n remove = NULL, ask = NULL, ...)\n ## S3 method for class 'modMCMC'\n plot(x, Full = FALSE, which = 1:ncol(x$pars),\n trace = TRUE, remove = NULL, ask = NULL, ...)\nArguments\n f the function to be evaluated, with first argument the vector of parameters which\n should be varied. It should return either the model residuals, an element of class\n modCost (as returned by a call to modCost) or -2*log(likelihood). The latter\n is equivalent to the sum-of-squares functions when using a Gaussian likelihood\n and prior.\n p initial values for the parameters to be optimized over.\n ... additional arguments passed to function f or to the methods.\n jump jump length, either a number, a vector with length equal to the total number\n of parameters, a covariance matrix, or a function that takes as input the current\n values of the parameters and produces as output the perturbed parameters. See\n details.\n prior -2*log(parameter prior probability), either a function that is called as prior(p)\n or NULL; in the latter case a non-informative prior is used (i.e. all parameters are\n equally likely, depending on lower and upper within min and max bounds).\n var0 initial model variance; if NULL, it is assumed that the model variance is 1, and the\n return element from f is -2*log (likelihood). If it has a value, it is assumed that\n the return element from f contain the model residuals or a list of class modFit.\n See details. Good options for var0 are to use the modelvariance (modVariance)\n as returned by the summary method of modFit. When this option is chosen, and\n the model has several variables, they will all be scaled similarly. See vignette\n FMEdyna. In case the model has several variables with different magnitudes,\n then it may be better to scale each variable independently. In that case, one can\n use as var0, the mean of the unweighted squared residuals from the model fit as\n returned from modFit (var_ms_unweighted). See vignette FME.\n wvar0 \"weight\" for the initial model variance – see details.\n n0 parameter used for weighing the initial model variance - if NULL, it is estimated\n as n0=wvar0*n, where n = number of observations. See details.\n lower lower bounds on the parameters; for unbounded parameters set equal to -Inf.\n upper upper bounds on the parameters; for unbounded parameters set equal to Inf.\n niter number of iterations for the MCMC.\n outputlength number of iterations kept in the output; should be smaller or equal to niter.\n updatecov number of iterations after which the parameter covariance matrix is (re)evaluated\n based on the parameters kept thus far, and used to update the MCMC jumps.\n covscale scale factor for the parameter covariance matrix, used to perform the MCMC\n jumps.\n burninlength number of initial iterations to be removed from output.\n ntrydr maximal number of tries for the delayed rejection procedure. It is generally not\n a good idea to set this to a too large value.\n drscale for each try during delayed rejection, the cholesky decomposition of the pro-\n posal matrix is scaled with this amount; if NULL, it is assumed to be c(0.2,0.25,\n 0.333, 0.333, ...)\n verbose if TRUE or 1: prints extra output, if numeric value i > 1, prints status information\n every i iterations.\n object an object of class modMCMC.\n x an object of class modMCMC.\n Full If TRUE then not only the parameters will be plotted, but also the function value\n and (if appropriate) the model variance(s).\n which the name or the index to the parameters that should be plotted. Default = all pa-\n rameters. If Full=TRUE, setting which = NULL will plot only the function value\n and the model variance.\n trace if TRUE, adds smoothed line to the plot.\n remove a list with indices of the runs that should be removed (e.g. to remove runs during\n burnin).\n nsample the number of xy pairs to be plotted on the upper panel in the pairs plot. When\n NULL all xy pairs plotted. Set to a lower number in case the graph becomes too\n dense (and the exported picture too large). This does not affect the histograms\n on the diagonal plot (which are estimated using all MCMC draws).\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask=.) and dev.interactive.\nDetails\n Note that arguments after ... must be matched exactly.\n R-function f is called as f(p, ...). It should return either -2 times the log likelihood of the model\n (one value), the residuals between model and data or an item of class modFit (as created by function\n modFit.\n In the latter two cases, it is assumed that the prior distribution for θ is either non-informative or\n gaussian. If gaussian, it can be treated as a sum of squares (SS). If the measurement function is\n defined as:\n y = f (θ) + ξξ N (0, σ 2 )\n where ξ is the measurement error, assumed normally distribution, then the posterior for the param-\n eters will be estimated as:\n SS(θ)\n p(θ|y, σ 2 ) ∝ exp(−0.5 · ( + SSpri (θ))\n and where σ 2 is the error variance, SS is the sum of squares function SS(θ) = (yi − f (θ))2 . If\n P\n non-informative priors are used, then SSpri (θ) = 0.\n The error variance σ 2 is considered a nuisance parameter. A prior distribution of it should be\n specified and a posterior distribution is estimated.\n If wvar0 or n0 is >0, then the variances are sampled as conjugate priors from the inverse gamma\n distribution with parameters var0 and n0=wvar0*n. Larger values of wvar0 keep these samples\n closer to var0.\n Thus, at each step, 1/ the error variance (σ −2 ) is sampled from a gamma distribution:\n (n0 + n) (n0 · var0 + SS(θ))\n p(σ −2 |y, θ) ∼ Γ( , )\n where n is the number of data points and where n0 = n · wvar0, and where the second argument\n to the gamma function is the shape parameter.\n The prior parameters (var0 and wvar0) are the prior mean for σ 2 and the prior accuracy.\n By setting wvar0 equal to 1, equal weight is given to the prior and the current value.\n If wvar0 is 0 then the prior is ignored.\n If wvar0 is NULL (the default) then the error variances are assumed to be fixed.\n var0 estimates the variance of the measured components. In case independent estimates are not\n available, these variances can be obtained from the mean squares of fitted residuals. (e.g. as reported\n in modFit). See the examples. (but note that this is not truly independent information)\n var0 is either one value, or a value for each observed variable, or a value for each observed data\n point.\n When var0 is not NULL, then f is assumed to return the model residuals OR an instance of class\n modCost.\n When var0=NULL, then f should return either -2*log(probability of the model), or an instance of\n class modCost.\n modMCMC implements the Metropolis-Hastings method. The proposal distribution, which is used to\n generate new parameter values is the (multidimensional) Gaussian density distribution, with stan-\n dard deviation given by jump.\n jump can be either one value, a vector of length = number of parameters or a parameter covariance\n matrix (nrow = ncol = number parameters).\n The jump parameter, jump thus determines how much the new parameter set will deviate from the\n old one.\n If jump is one value, or a vector, then the new parameter values are generated by sampling a normal\n distribution with standard deviation equal to jump. A larger value will lead to larger jumps in the\n parameter space, but acceptance of new points can get very low. Smaller jump lengths increase the\n acceptance rate, but the algorithm may move too slowly, and too many runs may be needed to scan\n the parameter space.\n If jump is NULL, then the jump length is taken as 10% of the parameter value as given in p.\n jump can also be a proposal covariance matrix. In this case, the new parameter values are generated\n by sampling a multidimensional normal distribution. It can be efficient to initialise jump using the\n parameter covariance as resulting from fitting the model (e.g. using modFit) – see examples.\n Finally, jump can also be an R-function that takes as input the current values of the parameters and\n returns the new parameter values.\n Two methods are implemented to increase the number of accepted runs.\n 1. In the \"adaptive Metropolis\" method, new parameters are generated with a covariance matrix\n that is estimated from the parameters generated (and saved) thus far. The idea behind this is\n that the MCMC method is more efficient if the proposal covariance (to generate new parameter\n values) is somehow tuned to the shape and size of the target distribution.\n Setting updatecov smaller than niter will trigger this functionality. In this case, every\n updatecov iterations, the jump covariance matrix will be estimated from the covariance ma-\n trix of the saved parameter values. The covariance matrix is scaled with (2.42 /npar) where\n npar is the number of parameters, unless covscale has been given a different value. Thus,\n Jump = (cov(θ1 , θ2 , ....θn ) · diag(np, +1e−16 ) · (2.42 /npar) where the small number 1e−16\n is added on the diagonal of the covariance matrix to prevent it from becoming singular.\n Note that a problem of adapting the proposal distribution using the MCMC results so far is\n that standard convergence results do not apply. One solution is to use adaptation only for the\n burn-in period and discard the part of the chain where adaptation has been used.\n Thus, when using updatecov with a positive value of burninlength, the proposal distribution\n is only updated during burnin. If burninlength = 0 though, the updates occur throughout the\n entire simulation.\n When using the adaptive Metropolis method, it is best to start with a small value of the jump\n length.\n 2. In the \"delayed rejection\" method, new parameter values are tried upon rejection. The process\n of delaying rejection can be iterated for at most ntrydr trials. Setting ntrydr equal to 1 (the\n default) toggles off delayed rejection.\n During the delayed rejection procedure, new parameters are generated from the last accepted\n value by scaling the jump covariance matrix with a factor as specified in drscale. The accep-\n tance probability of this new set depends on the candidates so far proposed and rejected, in\n such a way that reversibility of the Markov chain is preserved. See Haario et al. (2005, 2006)\n for more details.\n Convergence of the MCMC chain can be checked via plot, which plots for each iteration the values\n of all parameters, and if Full is TRUE, of the function value (SS) and (if appropriate) the modeled\n variance. If converged, there should be no visible drift.\n In addition, the methods from package coda become available by making the object returned by\n modMCMC of class mcmc, as used in the methods of coda. For instance, if object MCMCres is returned\n by modMCMC then as.mcmc(MCMCres$pars) will make an instance of class mcmc, usable by coda.\n The burninlength is the number of initial steps that is not included in the output. It can be useful\n if the initial value of the parameters is far from the optimal value. Starting the MCMC with the best\n fit parameter set will alleviate the need for using burninlength.\nValue\n a list of class modMCMC containing the results as returned from the Markov chain.\n This includes the following:\n pars an array with dimension (outputlength, length(p)), containing the parameters\n of the MCMC at each iteration that is kept.\n SS vector with the sum of squares function, one for each row in pars.\n naccepted the number of accepted runs.\n sig the sampled error variance σ 2 , a matrix with one row for each row in pars.\n bestpar the parameter set that gave the highest probability.\n bestfunp the function value corresponding to bestpar.\n prior the parameter prior, one value for each row in pars.\n count information about the MCMC chain: number of delayed rejection steps (dr_steps),\n the number of alfa steps Alfasteps, the number of accepted runs (num_accepted)\n and the number of times the proposal covariance matrix has been updated (num_covupdate.)\n settings the settings for error covariance calculation, i.e. arguments var0, n0 and N the\n number of data points.\n The list returned by modMCMC has methods for the generic functions summary, plot, pairs – see\n note.\nNote\n The following S3 methods are provided:\n • summary, produces summary statistics of the MCMC results\n • plot, plots the MCMC results, for all parameters. Use it to check convergence.\n • pairs, produces a pairs plot of the MCMC results; overrides the default gap = 0, upper.panel\n = NA, and diag.panel.\n It is also possible to use the methods from the coda package, e.g. densplot.\n To do that, first the modMCMC object has to be converted to an mcmc object. See the examples for an\n application.\nAuthor(s)\n <NAME> <<EMAIL>>\n <NAME> <<EMAIL>>\nReferences\n <NAME>., 2008. Adaptive MCMC Methods With Applications in Environmental and Geophysi-\n cal Models. Finnish Meteorological Institute contributions 69, ISBN 978-951-697-662-7, Finnish\n Meteorological Institute, Helsinki.\n <NAME>., <NAME>. and <NAME>., 2001. An Adaptive Metropolis Algorithm. Bernoulli 7,\n pp. 223–242. doi:10.2307/3318737\n <NAME>., <NAME>., <NAME>. and <NAME>., 2006. DRAM: Efficient Adaptive MCMC. Statis-\n tics and Computing, 16(4), 339–354. doi:10.1007/s1122200694380\n <NAME>., <NAME>. and <NAME>., 2005. Componentwise Adaptation for High Dimen-\n sional MCMC. Computational Statistics 20(2), 265–274. doi:10.1007/BF02789703\n <NAME>. <NAME>., <NAME>. and <NAME>., 2004. Bayesian Data Analysis. Second\n edition. Chapman and Hall, Boca Raton.\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nSee Also\n modFit for constrained model fitting\nExamples\n ## =======================================================================\n ## Sampling a 3-dimensional normal distribution,\n ## =======================================================================\n # mean = 1:3, sd = 0.1\n # f returns -2*log(probability) of the parameter values\n NN <- function(p) {\n mu <- c(1,2,3)\n -2*sum(log(dnorm(p, mean = mu, sd = 0.1))) #-2*log(probability)\n }\n # simple Metropolis-Hastings\n MCMC <- modMCMC(f = NN, p = 0:2, niter = 5000,\n outputlength = 1000, jump = 0.5)\n # More accepted values by updating the jump covariance matrix...\n MCMC <- modMCMC(f = NN, p = 0:2, niter = 5000, updatecov = 100,\n outputlength = 1000, jump = 0.5)\n summary(MCMC)\n plot(MCMC) # check convergence\n pairs(MCMC)\n ## =======================================================================\n ## test 2: sampling a 3-D normal distribution, larger standard deviation...\n ## noninformative priors, lower and upper bounds imposed on parameters\n ## =======================================================================\n NN <- function(p) {\n mu <- c(1,2,2.5)\n -2*sum(log(dnorm(p, mean = mu, sd = 0.5))) #-2*log(probability)\n }\n MCMC2 <- modMCMC(f = NN, p = 1:3, niter = 2000, burninlength = 500,\n updatecov = 10, jump = 0.5, lower = c(0, 2, 1), upper = c(1, 3, 3))\n plot(MCMC2)\n hist(MCMC2, breaks = 20)\n ## Compare output of p3 with theoretical distribution\n hist(MCMC2, which = \"p3\", breaks = 20)\n lines(seq(1, 3, 0.1), dnorm(seq(1, 3, 0.1), mean = 2.5,\n sd = 0.5)/pnorm(3, 2.5, 0.5))\n summary(MCMC2)\n # functions from package coda...\n cumuplot(as.mcmc(MCMC2$pars))\n summary(as.mcmc(MCMC2$pars))\n raftery.diag(MCMC2$pars)\n ## =======================================================================\n ## test 3: sampling a log-normal distribution, log mean=1:4, log sd = 1\n ## =======================================================================\n NL <- function(p) {\n mu <- 1:4\n -2*sum(log(dlnorm(p, mean = mu, sd = 1))) #-2*log(probability)\n }\n MCMCl <- modMCMC(f = NL, p = log(1:4), niter = 3000,\n outputlength = 1000, jump = 5)\n plot(MCMCl) # bad convergence\n cumuplot(as.mcmc(MCMCl$pars))\n MCMCl <- modMCMC (f = NL, p = log(1:4), niter = 3000,\n outputlength = 1000, jump = 2^(2:5))\n plot(MCMCl) # better convergence but CHECK it!\n pairs(MCMCl)\n colMeans(log(MCMCl$pars))\n apply(log(MCMCl$pars), 2, sd)\n MCMCl <- modMCMC (f = NL, p = rep(1, 4), niter = 3000,\n outputlength = 1000, jump = 5, updatecov = 100)\n plot(MCMCl)\n colMeans(log(MCMCl$pars))\n apply(log(MCMCl$pars), 2, sd)\n ## =======================================================================\n ## Fitting a Monod (Michaelis-Menten) function to data\n ## =======================================================================\n # the observations\n #---------------------\n Obs <- data.frame(x=c( 28, 55, 83, 110, 138, 225, 375), # mg COD/l\n y=c(0.053,0.06,0.112,0.105,0.099,0.122,0.125)) # 1/hour\n plot(Obs, pch = 16, cex = 2, xlim = c(0, 400), ylim = c(0, 0.15),\n xlab = \"mg COD/l\", ylab = \"1/hr\", main = \"Monod\")\n # the Monod model\n #---------------------\n Model <- function(p, x) data.frame(x = x, N = p[1]*x/(x+p[2]))\n # Fitting the model to the data\n #---------------------\n # define the residual function\n Residuals <- function(p) (Obs$y - Model(p, Obs$x)$N)\n # use modFit to find parameters\n P <- modFit(f = Residuals, p = c(0.1, 1))\n # plot best-fit model\n x <-0:375\n lines(Model(P$par, x))\n # summary of fit\n sP <- summary(P)\n sP[]\n print(sP)\n # Running an MCMC\n #---------------------\n # estimate parameter covariances\n # (to efficiently generate new parameter values)\n Covar <- sP$cov.scaled * 2.4^2/2\n # the model variance\n s2prior <- sP$modVariance\n # set nprior = 0 to avoid updating model variance\n MCMC <- modMCMC(f = Residuals, p = P$par,jump = Covar, niter = 1000,\n var0 = s2prior, wvar0 = NULL, updatecov = 100)\n plot(MCMC, Full = TRUE)\n pairs(MCMC)\n # function from the coda package.\n raftery.diag(as.mcmc(MCMC$pars))\n cor(MCMC$pars)\n cov(MCMC$pars) # covariances by MCMC\n sP$cov.scaled # covariances by Hessian of fit\n x <- 1:400\n SR <- summary(sensRange(parInput = MCMC$pars, func = Model, x = x))\n plot(SR, xlab=\"mg COD/l\", ylab = \"1/hr\", main = \"Monod\")\n points(Obs, pch = 16, cex = 1.5)\n Norm Normal Random Distribution\nDescription\n Generates random parameter sets that are (multi)normally distributed.\nUsage\n Norm(parMean, parCovar, parRange = NULL, num)\nArguments\n parMean a vector, with the mean value of each parameter.\n parCovar the parameter variance-covariance matrix.\n parRange the range (min, max) of the parameters, a matrix or a data.frame with one row\n for each parameter, and two columns with the minimum (1st) and maximum\n (2nd) column.\n num the number of random parameter sets to generate.\nDetails\n Function Norm, draws parameter sets from a multivariate normal distribution, as specified through\n the mean value and the variance-covariance matrix of the parameters. In addition, it is possible to\n impose a minimum and maximum of each parameter, via parRange. This will generate a truncated\n distribution. Use this for instance if certain parameters cannot become negative.\nValue\n a matrix with one row for each generated parameter set, and one column per parameter.\nNote\n For function Norm to work, parCovar must be a valid variance-covariance matrix. (i.e. positive\n definite). If this is not the case, then the function will fail.\nAuthor(s)\n <NAME> <<EMAIL>>\nSee Also\n Unif for uniformly distributed random parameter sets.\n Latinhyper to generates parameter sets using latin hypercube sampling.\n Grid to generate random parameter sets arranged on a regular grid\n rnorm the R-default for generating normally distributed random numbers.\nExamples\n ## multinormal parameters: variance-covariance matrix and parameter mean\n parCovar <- matrix(data = c(0.5, -0.2, 0.3, 0.4, -0.2, 1.0, 0.1, 0.3,\n 0.3, 0.1, 1.5, -0.7, 1.0, 0.3, -0.7, 4.5), nrow = 4)\n parCovar\n parMean <- 4:1\n ## Generated sample\n Ndist <- Norm(parCovar = parCovar, parMean = parMean, num = 500)\n cov(Ndist) # check\n pairs(Ndist, main = \"normal\")\n ## truncated multinormal\n Ranges <- data.frame(min = rep(0, 4), max = rep(Inf, 4))\n pairs(Norm(parCovar = parCovar, parMean = parMean, parRange = Ranges,\n num = 500), main = \"truncated normal\")\n obsplot Plot Method for observed data\nDescription\n Plot all observed variables in matrix formalt\nUsage\n obsplot(x, ..., which = NULL, xyswap = FALSE, ask = NULL)\nArguments\n x a matrix or data.frame, containing the observed data to be plotted. The ’x’-\n values (first axis) should be the first column.\n Several other matrices or data.frames can be passed in the ..., after x (unnamed)\n - see second example.\n If the first column of x consists of factors, or characters (strings), then it is\n assumed that the data are presented in long (database) format, where the first\n three columns contain (name, x, y). See last example.\n which the name(s) or the index to the variables that should be plotted. Default = all\n variables, except the first column.\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask=.) and dev.interactive.\n xyswap if TRUE, then x-and y-values are swapped and the y-axis is from top to bottom.\n Useful for drawing vertical profiles.\n ... additional arguments.\n The graphical arguments are passed to plot.default and points.\n The dots may contain other matrices and data.frames with observed data to be\n plotted on the same graphs as x - see second example.\n The arguments after . . . must be matched exactly.\nDetails\n The number of panels per page is automatically determined up to 3 x 3 (par(mfrow = c(3, 3))).\n This default can be overwritten by specifying user-defined settings for mfrow or mfcol. Set mfrow\n equal to NULL to avoid the plotting function to change user-defined mfrow or mfcol settings.\n Other graphical parameters can be passed as well. Parameters are vectorized, either according to the\n number of plots (xlab, ylab, main, sub, xlim, ylim, log, asp, ann, axes, frame.plot,panel.first,panel.last,\n cex.lab,cex.axis,cex.main) or according to the number of lines within one plot (other parame-\n ters e.g. col, lty, lwd etc.) so it is possible to assign specific axis labels to individual plots, resp.\n different plotting style. Plotting parameter ylim, or xlim can also be a list to assign different axis\n limits to individual plots.\nSee Also\n print.deSolve, ode, deSolve\nExamples\n ## 'observed' data\n AIRquality <- cbind(DAY = 1:153, airquality[, 1:4])\n head(AIRquality)\n obsplot(AIRquality, type=\"l\", xlab=\"Day since May\")\n ## second set of observed data\n AIR2 <- cbind( 1:100, Solar.R = 250 * runif(100), Temp = 90-30*cos(2*pi*1:100/365) )\n obsplot(AIRquality, AIR2, type = \"l\", xlab = \"Day since May\" , lwd = 1:2)\n obsplot(AIRquality, AIR2, type = \"l\", xlab = \"Day since May\" ,\n lwd = 1 : 2, which =c(\"Solar.R\", \"Temp\"),\n xlim = list(c(0, 150), c(0, 100)))\n obsplot(AIRquality, AIR2, type = \"l\", xlab = \"Day since May\" ,\n lwd = 1 : 2, which =c(\"Solar.R\", \"Temp\"), log = c(\"y\", \"\"))\n obsplot(AIRquality, AIR2, which = 1:3, xyswap = c(TRUE,FALSE,TRUE))\n ## ' a data.frame, with 'treatments', presented in long database format\n Data <- ToothGrowth[,c(2,3,1)]\n head (Data)\n obsplot(Data, ylab = \"len\", xlab = \"dose\")\n # same, plotted as two observed data sets\n obsplot(subset(ToothGrowth, supp == \"VC\", select = c(dose, len)),\n subset(ToothGrowth, supp == \"OJ\", select = c(dose, len)))\n pseudoOptim Pseudo-random Search Optimisation Algorithm of Price (1977)\nDescription\n Fits a model to data, using the pseudo-random search algorithm of Price (1977), a random-based\n fitting technique.\nUsage\n pseudoOptim(f, p,..., lower, upper, control = list())\nArguments\n f function to be minimised, its first argument should be the vector of parameters\n over which minimization is to take place. It should return a scalar result, the\n model cost, e.g the sum of squared residuals.\n p initial values of the parameters to be optimised.\n ... arguments passed to function f.\n lower minimal values of the parameters to be optimised; these must be specified; they\n cannot be -Inf.\n upper maximal values of the parameters to be optimised; these must be specified; they\n cannot be +Inf.\n control a list of control parameters - see details.\nDetails\n The control argument is a list that can supply any of the following components:\n • npop, number of elements in the population. Defaults to max(5*length(p),50).\n • numiter, maximal number of iterations to be performed. Defaults to 10000. The algorithm\n either stops when numiter iterations has been performed or when the remaining variation is\n less than varleft.\n • centroid, number of elements from which to estimate a new parameter vector, defaults to 3.\n • varleft, relative variation remaining; if below this value the algorithm stops; defaults to 1e-8.\n • verbose, if TRUE, more verbose output will contain the parameters in the final population,\n their respective population costs and the cost at each succesful interation. Defaults to FALSE.\n see the book of Soetaert and Herman (2009) for a description of the algorithm AND for a line to\n line explanation of the function code.\nValue\n a list containing:\n par the optimised parameter values.\n cost the model cost, or function evaluation associated to the optimised parameter\n values, i.e. the minimal cost.\n iterations the number of iterations performed.\n and if control$verbose is TRUE:\n poppar all parameter vectors remaining in the population, matrix of dimension (npop,length(par)).\n popcost model costs associated with all population parameter vectors, vector of length\n npop.\n rsstrace a 2-columned matrix with the iteration number and the model cost at each suc-\n cesful iteration.\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n <NAME>. and <NAME>. J., 2009. A Practical Guide to Ecological Modelling. Using R as a\n Simulation Platform. Springer, 372 pp.\n Price, W.L., 1977. A Controlled Random Search Procedure for Global Optimisation. The Computer\n Journal, 20: 367-370.\nExamples\n amp <- 6\n period <- 5\n phase <- 0.5\n x <- runif(20)*13\n y <- amp*sin(2*pi*x/period+phase) + rnorm(20, mean = 0, sd = 0.05)\n plot(x, y, pch = 16)\n cost <- function(par)\n sum((par[1] * sin(2*pi*x/par[2]+par[3])-y)^2)\n p1 <- optim(par = c(amplitude = 1, phase = 1, period = 1), fn = cost)\n p2 <- optim(par = c(amplitude = 1, phase = 1, period = 1), fn = cost,\n method = \"SANN\")\n p3 <- pseudoOptim(p = c(amplitude = 1, phase = 1, period = 1),\n lower = c(0, 1e-8, 0), upper = c(100, 2*pi, 100),\n f = cost, control = c(numiter = 3000, verbose = TRUE))\n curve(p1$par[1]*sin(2*pi*x/p1$par[2]+p1$par[3]), lty = 2, add = TRUE)\n curve(p2$par[1]*sin(2*pi*x/p2$par[2]+p2$par[3]), lty = 3, add = TRUE)\n curve(p3$par[1]*sin(2*pi*x/p3$par[2]+p3$par[3]), lty = 1, add = TRUE)\n legend (\"bottomright\", lty = c(1, 2, 3),\n c(\"Price\", \"Mathematical\", \"Simulated annealing\"))\n sensFun Local Sensitivity Analysis\nDescription\n Given a model consisting of differential equations, estimates the local effect of certain parameters\n on selected sensitivity variables by calculating a matrix of so-called sensitivity functions. In this\n matrix the (i,j)-th element contains\n ∂yi ∆Θj\n ·\n ∂Θj ∆yi\n and where yi is an output variable (at a certain time instance), Θj is a parameter, and ∆yi is the\n scaling of variable yi , ∆Θj is the scaling of parameter Θj .\nUsage\n sensFun(func, parms, sensvar = NULL, senspar = names(parms),\n varscale = NULL, parscale = NULL, tiny = 1e-8, map = 1, ...)\n ## S3 method for class 'sensFun'\n summary(object, vars = FALSE, ...)\n ## S3 method for class 'sensFun'\n pairs(x, which = NULL, ...)\n ## S3 method for class 'sensFun'\n plot(x, which = NULL, legpos=\"topleft\", ask = NULL, ...)\n ## S3 method for class 'summary.sensFun'\n plot(x, which = 1:nrow(x), ...)\nArguments\n func an R-function that has as first argument parms and that returns a matrix or\n data.frame with the values of the output variables (columns) at certain output\n intervals (rows), and – optionally – a mapping variable (by default the first col-\n umn).\n parms parameters passed to func; should be either a vector, or a list with named ele-\n ments. If NULL, then the first element of parInput is taken.\n sensvar the output variables for which the sensitivity needs to be estimated. Either NULL,\n the default, which selects all variables, or a vector with variable names (which\n should be present in the matrix returned by func), or a vector with indices to\n variables as present in the output matrix (note that the column of this matrix\n with the mapping variable should not be selected).\n senspar the parameters whose sensitivity needs to be estimated, the default=all parame-\n ters. Either a vector with parameter names, or a vector with indices to positions\n of parameters in parms.\n varscale the scaling (weighing) factor for sensitivity variables, NULL indicates that the\n variable value is used.\n parscale the scaling (weighing) factor for sensitivity parameters, NULL indicates that the\n parameter value is used.\n tiny the perturbation, or numerical difference, factor, see details.\n map the column number with the (independent) mapping variable in the output ma-\n trix returned by func. For dynamic models solved by integration, this will be\n the (first) column with time. For 1-D spatial output, this column will be some\n distance variable. Set to NULL if there is no mapping variable. Mapping vari-\n ables should not be selected for estimating sensitivity functions; they are used\n for plotting.\n ... additional arguments passed to func or to the methods.\n object an object of class sensFun.\n x an object of class sensFun.\n vars if FALSE: summaries per parameter are returned; if TRUE, summaries per pa-\n rameter and per variable are returned.\n which the name or the index to the variables that should be plotted. Default = all\n variables.\n legpos position of the legend; set to NULL to avoid plotting a legend.\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask = ...) and dev.interactive.\nDetails\n There are essentially two ways in which to use function sensFun.\n • When func returns a matrix or data frame with output values, sensFun can be used for sensi-\n tivity analysis, estimating the impact of parameters on output variables.\n • When func returns an instance of class modCost (as returned by a call to function modCost),\n then sensFun can be used for parameter identifiability. In this case the results from sensFun\n are used as input to function collin. See the help file for collin.\n For each sensitivity parameter, the number of sensitivity functions estimated is: length(sensvar) *\n length(mapping variable), i.e. one for each element returned by func (except the mapping variable).\n The sensitivity functions are estimated numerically. This means that each parameter value Θj is\n perturbed as max (tiny, Θj · (1 + tiny))\nValue\n a data.frame of class sensFun containing the sensitivity functions this is one row for each sensitivity\n variable at each independent (time or position) value and the following columns:\n x, the value of the independent (mapping) variable, usually time (solver= \"ode..\"), or distance\n (solver= \"steady.1D\")\n var, the name of the observed variable,\n ..., a number of columns, one for each sensitivity parameter\n The data.frame returned by sensFun has methods for the generic functions summary, plot, pairs\n – see note.\nNote\n Sensitivity functions are generated by perturbing one by one the parameters with a very small\n amount, and quantifying the differences in the output.\n It is important that the output is generated with high precision, else it is possible, that the sensitivity\n functions are just noise. For instance, when used with a dynamic model (using solver from deSolve)\n set the tolerances atol and rtol to a lower value, to see if the sensitivity results make sense.\n The following methods are provided:\n • summary. Produces summary statistics of the sensitivity functions, a data.frame with: one\n row for each parameter and the following columns:\n – L1: the L1-norm n1 · |Sij |,\n P\n q P\n – L2: the L2-norm · n1 Sij · Sij ,\n – Mean: the mean of the sensitivity functions,\n – Min: the minimal value of the sensitivity functions,\n – Max: the maximal value of the sensitivity functions.\n • var the summary of the variables sensitivity functions, a data.frame with the same columns as\n model and one row for each parameter + variable combination. This is only outputted if the\n variable names are effectively known\n • plot plots the sensitivity functions for each parameter; each parameter has its own color.\n By default, the sensitivity functions for all variables are plotted in one figure, unless which\n gives a selection of variables; in that case, each variable will be plotted in a separate figure,\n and the figures aligned in a rectangular grid, unless par mfrow is passed as an argument.\n • pairs produces a pairs plot of the sensitivity results; per parameter.\n By default, the sensitivity functions for all variables are plotted in one figure, unless which\n gives a selection of variables.\n Overrides the default gap = 0, upper.panel = NA, and diag.panel.\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n <NAME>. and <NAME>., 2009. A Practical Guide to Ecological Modelling – Using R as a\n Simulation Platform. Springer, 390 pp.\n <NAME>., <NAME>. and <NAME>., 2001. Practical Identificability Analysis of Large Environ-\n mental Simulation Models. Water Resour. Res. 37(4): 1015–1030. doi:10.1029/2000WR900350\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Bacterial growth model as in Soetaert and Herman, 2009\n ## =======================================================================\n pars <- list(gmax = 0.5, eff = 0.5,\n ks = 0.5, rB = 0.01, dB = 0.01)\n solveBact <- function(pars) {\n derivs <- function(t, state, pars) { # returns rate of change\n with (as.list(c(state, pars)), {\n dBact <- gmax * eff * Sub/(Sub + ks) * Bact - dB * Bact - rB * Bact\n dSub <- -gmax * Sub/(Sub + ks) * Bact + dB * Bact\n return(list(c(dBact, dSub)))\n })\n }\n state <- c(Bact = 0.1, Sub = 100)\n tout <- seq(0, 50, by = 0.5)\n ## ode solves the model by integration ...\n return(as.data.frame(ode(y = state, times = tout, func = derivs,\n parms = pars)))\n }\n out <- solveBact(pars)\n plot(out$time, out$Bact, ylim = range(c(out$Bact, out$Sub)),\n xlab = \"time, hour\", ylab = \"molC/m3\", type = \"l\", lwd = 2)\n lines(out$time, out$Sub, lty = 2, lwd = 2)\n lines(out$time, out$Sub + out$Bact)\n legend(\"topright\", c(\"Bacteria\", \"Glucose\", \"TOC\"),\n lty = c(1, 2, 1), lwd = c(2, 2, 1))\n ## sensitivity functions\n SnsBact <- sensFun(func = solveBact, parms = pars,\n sensvar = \"Bact\", varscale = 1)\n head(SnsBact)\n plot(SnsBact)\n plot(SnsBact, type = \"b\", pch = 15:19, col = 2:6,\n main = \"Sensitivity all vars\")\n summary(SnsBact)\n plot(summary(SnsBact))\n SF <- sensFun(func = solveBact, parms = pars,\n sensvar = c(\"Bact\", \"Sub\"), varscale = 1)\n head(SF)\n tail(SF)\n summary(SF, var = TRUE)\n plot(SF)\n plot(SF, which = c(\"Sub\",\"Bact\"))\n pm <- par(mfrow = c(1,3))\n plot(SF, which = c(\"Sub\", \"Bact\"), mfrow = NULL)\n plot(SF, mfrow = NULL)\n par(mfrow = pm)\n ## Bivariate sensitivity\n pairs(SF) # same color\n pairs(SF, which = \"Bact\", col = \"green\", pch = 15)\n pairs(SF, which = c(\"Bact\", \"Sub\"), col = c(\"green\", \"blue\"))\n mtext(outer = TRUE, side = 3, line = -2,\n \"Sensitivity functions\", cex = 1.5)\n ## pairwise correlation\n cor(SnsBact[,-(1:2)])\n sensRange Sensitivity Ranges of a Timeseries or 1-D Variables\nDescription\n Given a model consisting of differential equations, estimates the global effect of certain (sensitivity)\n parameters on a time series or on 1-D spatial series of selected sensitivity variables.\n This is done by drawing parameter values according to some predefined distribution, running the\n model with each of these parameter combinations, and calculating the values of the selected output\n variables at each output interval.\n This function thus produces ’envelopes’ around the sensitivity variables.\nUsage\n sensRange(func, parms = NULL, sensvar = NULL, dist = \"unif\",\n parInput = NULL, parRange = NULL, parMean = NULL,\n parCovar = NULL, map = 1, num = 100, ...)\n ## S3 method for class 'sensRange'\n summary(object, ...)\n ## S3 method for class 'summary.sensRange'\n plot(x, xyswap = FALSE,\n which = NULL, legpos = \"topleft\",\n col = c(grey(0.8), grey(0.7)),\n quant = FALSE, ask = NULL, obs = NULL,\n obspar = list(), ...)\n ## S3 method for class 'sensRange'\n plot(x, xyswap = FALSE,\n which = NULL, ask = NULL, ...)\nArguments\n func an R-function that has as first argument parms and that returns a matrix or\n data.frame with the values of the output variables (columns) at certain output\n intervals (rows), and – optionally – a mapping variable (by default the first col-\n umn).\n parms parameters passed to func; should be either a vector, or a list with named ele-\n ments. If NULL, then the first element of parInput is taken.\n sensvar the output variables for which the sensitivity needs to be estimated. Either NULL,\n the default, which selects all variables, or a vector with variable names (which\n should be present in the matrix returned by func), or a vector with indices to\n variables as present in the output matrix (note that the column of this matrix\n with the mapping variable should not be selected).\n dist the distribution according to which the parameters should be generated, one\n of \"unif\" (uniformly random samples), \"norm\", (normally distributed random\n samples), \"latin\" (latin hypercube distribution), \"grid\" (parameters arranged\n on a grid). The input parameters for the distribution are specified by parRange\n (min,max), except for the normally distributed parameters, in which case the\n distribution is specified by the parameter means parMean and the variance-\n covariance matrix, parCovar. Note that, if the distribution is \"norm\" and parRange\n is given, then a truncated distribution will be generated. (This is useful to pre-\n vent for instance that certain parameters become negative). Ignored if parInput\n is specified.\n parRange the range (min, max) of the sensitivity parameters, a matrix or (preferred) a\n data.frame with one row for each parameter, and two columns with the mini-\n mum (1st) and maximum (2nd) value. The rownames of parRange should be\n parameter names that are known in argument parms. Ignored if parInput is\n specified.\n parInput a matrix with dimension (*, npar) with the values of the sensitivity parameters.\n parMean only when dist is \"norm\": the mean value of each parameter. Ignored if\n parInput is specified.\n parCovar only when dist is \"norm\": the parameter’s variance-covariance matrix.\n num the number of times the model has to be run. Set large enough. If parInput is\n specified, then num parameters are selected randomly (from the rows of parInput.\n map the column number with the (independent) mapping variable in the output ma-\n trix returned by func. For dynamic models solved by integration, this will be\n the (first) column with time. For 1-D spatial output, this column will be some\n distance variable. Set to NULL if there is no mapping variable. Mapping vari-\n ables should not be selected for estimating sensitivity ranges; they are used for\n plotting.\n object an object of class sensRange.\n x an object of class sensRange.\n legpos position of the legend; set to NULL to avoid plotting a legend.\n xyswap if TRUE, then x-and y-values are swapped and the y-axis is from top to bottom.\n Useful for drawing vertical profiles.\n which the name or the index to the variables that should be plotted. Default = all\n variables.\n col the two colors of the polygons that should be plotted.\n quant if TRUE, then the median surrounded by the quantiles q25-q75 and q95-q95 are\n plotted, else the min-max and mean +- sd are plotted.\n ask logical; if TRUE, the user is asked before each plot, if NULL the user is only asked\n if more than one page of plots is necessary and the current graphics device is set\n interactive, see par(ask=...) and dev.interactive.\n obs a data.frame or matrix with \"observed data\" that will be added as points\n to the plots. obs can also be a list with multiple data.frames and/or matrices\n containing observed data. The first column of obs should contain the time or\n space-variable. If obs is not NULL and which is NULL, then the variables, com-\n mon to both obs and x will be plotted.\n obspar additional graphics arguments passed to points, for plotting the observed data.\n If obs is a list containing multiple observed data sets, then the graphics argu-\n ments can be a vector or a list (e.g. for xlim, ylim), specifying each data set\n separately.\n ... additional arguments passed to func or to the methods.\nDetails\n Models solved by integration (i.e. by using one of 'ode', 'ode.1D', 'ode.band', 'ode.2D'),\n have the output already in a form usable by sensRange.\nValue\n a data.frame of type sensRange containing the parameter set and the corresponding values of the\n sensitivity output variables.\n The list returned by sensRange has a method for the generic functions summary,plot and plot.summary\n – see note.\nNote\n The following methods are included:\n • summary, estimates summary statistics for the sensitivity variables, a data.frame with as many\n rows as there are mapping variables (or rows in the matrix returned by func) and the following\n columns: x, the mapping value, Mean, the mean, sd, the standard deviation, Min, the minimal\n value, Max, the maximal value, q25, q50, q75, the 25th, 50 and 75% quantile\n • plot, produces a \"matplot\" of the sensRange output, one plot for each sensitivity variable and\n with the mapping variable on the x-axis.\n Each variable will be plotted in a separate figure, and the figures aligned in a rectangular grid,\n unless par mfrow is passed as an argument.\n • summary.plot, produces a plot of the summary of the sensRange output, one plot for each\n sensitivity variable and with the ranges and mean +- standard deviation or the quantiles as\n coloured polygons.\n Each variable will be plotted in a separate figure, and the figures aligned in a rectangular grid,\n unless par mfrow is passed as an argument.\n The output for models solved by a steady-state solver (i.e. one of 'steady', 'steady.1D',\n 'steady.band', 'steady.2D', needs to be rearranged – see examples.\n For plot.summary.sensRange and plot.sensRange, the number of panels per page is automati-\n cally determined up to 3 x 3 (par(mfrow = c(3, 3))). This default can be overwritten by specifying\n user-defined settings for mfrow or mfcol. Set mfrow equal to NULL to avoid the plotting function to\n change user-defined mfrow or mfcol settings.\n Other graphical parameters can be passed as well. Parameters are vectorized, either according to the\n number of plots (xlab, ylab, main, sub, xlim, ylim, log, asp, ann, axes, frame.plot,panel.first,panel.last,\n cex.lab,cex.axis,cex.main) or according to the number of lines within one plot (other parame-\n ters e.g. col, lty, lwd etc.) so it is possible to assign specific axis labels to individual plots, resp.\n different plotting style. Plotting parameter ylim, or xlim can also be a list to assign different axis\n limits to individual plots.\n Similarly, the graphical parameters for observed data, as passed by obspar can be vectorized, ac-\n cording to the number of observed data sets (when obs is a list).\n The data.frame of type sensRange has several attributes, which remain hidden, and which are\n generally not of practical use (they are needed for the S3 methods).\n There is one exception, i.e. if parameter values are imposed via argument parInput, and these\n parameters are generated by a Markov chain (modMCMC). If the number of draws, num, is less than\n the number of rows in parInput, then num random draws will be taken. Attribute, \"pset\" then\n contains the index to the parameters that have been selected.\n The sensRange method only represents the distribution of the model response variables as a func-\n tion of the parameter values. But an additional source of noise is due to the model error, as repre-\n sented by the sampled values of sigma in the Markov chain. In order to represent also this source of\n error, gaussian noise should be added to each sensitivity output variables, with a standard deviation\n that corresponds to the original parameter draw – see vignette \"FMEother\".\nAuthor(s)\n <NAME> <<EMAIL>>\nReferences\n <NAME>. and <NAME>. 2010. Inverse Modelling, Sensitivity and Monte Carlo Analysis in R\n Using Package FME. Journal of Statistical Software 33(3) 1–28. doi:10.18637/jss.v033.i03\nExamples\n ## =======================================================================\n ## Bacterial growth model from Soetaert and Herman, 2009\n ## =======================================================================\n pars <- list(gmax = 0.5,eff = 0.5,\n ks = 0.5, rB = 0.01, dB = 0.01)\n solveBact <- function(pars) {\n derivs <- function(t,state,pars) { # returns rate of change\n with (as.list(c(state,pars)), {\n dBact <- gmax*eff * Sub/(Sub + ks)*Bact - dB*Bact - rB*Bact\n dSub <- -gmax * Sub/(Sub + ks)*Bact + dB*Bact\n return(list(c(dBact,dSub)))\n })\n }\n state <- c(Bact = 0.1,Sub = 100)\n tout <- seq(0, 50, by = 0.5)\n ## ode solves the model by integration ...\n return(as.data.frame(ode(y = state, times = tout, func = derivs,\n parms = pars)))\n }\n out <- solveBact(pars)\n mf <-par(mfrow = c(2,2))\n plot(out$time, out$Bact, main = \"Bacteria\",\n xlab = \"time, hour\", ylab = \"molC/m3\", type = \"l\", lwd = 2)\n ## the sensitivity parameters\n parRanges <- data.frame(min = c(0.4, 0.4, 0.0), max = c(0.6, 0.6, 0.02))\n rownames(parRanges)<- c(\"gmax\", \"eff\", \"rB\")\n parRanges\n tout <- 0:50\n ## sensitivity to rB; equally-spaced parameters (\"grid\")\n SensR <- sensRange(func = solveBact, parms = pars, dist = \"grid\",\n sensvar = \"Bact\", parRange = parRanges[3,], num = 50)\n Sens <-summary(SensR)\n plot(Sens, legpos = \"topleft\", xlab = \"time, hour\", ylab = \"molC/m3\",\n main = \"Sensitivity to rB\", mfrow = NULL)\n ## sensitivity to all; latin hypercube\n Sens2 <- summary(sensRange(func = solveBact, parms = pars, dist = \"latin\",\n sensvar = c(\"Bact\", \"Sub\"), parRange = parRanges, num = 50))\n ## Plot all variables; plot mean +- sd, min max\n plot(Sens2, xlab = \"time, hour\", ylab = \"molC/m3\",\n main = \"Sensitivity to gmax,eff,rB\", mfrow = NULL)\n par(mfrow = mf)\n ## Select one variable for plotting; plot the quantiles\n plot(Sens2, xlab = \"time, hour\", ylab = \"molC/m3\", which = \"Bact\", quant = TRUE)\n ## Add data\n data <- cbind(time = c(0,10,20,30), Bact = c(0,1,10,45))\n plot(Sens2, xlab = \"time, hour\", ylab = \"molC/m3\", quant = TRUE,\n obs = data, obspar = list(col = \"darkblue\", pch = 16, cex = 2))\n Unif Uniform Random Distribution\nDescription\n Generates uniformly distributed random parameter sets.\nUsage\n Unif(parRange, num)\nArguments\n parRange the range (min, max) of the parameters, a matrix or a data.frame with one row\n for each parameter, and two columns with the minimum (1st) and maximum\n (2nd) value.\n num the number of random parameter sets to generate.\nDetails\n In the uniform sampling, each parameter is uniformly random distributed over its range.\nValue\n a matrix with one row for each generated parameter set, and one column per parameter.\nNote\n For small sample sizes, the latin hypercube distributed parameter sets (Latinhyper) may give better\n coverage in parameter space than the uniform random design.\nAuthor(s)\n <NAME> <<EMAIL>>\nSee Also\n Norm for (multi)normally distributed random parameter sets.\n Latinhyper to generates parameter sets using latin hypercube sampling.\n Grid to generate random parameter sets arranged on a regular grid\n runif the R-default for generating uniformally distributed random numbers.\nExamples\n ## 4 parameters\n parRange <- data.frame(min = c(0, 1, 2, 3), max = c(10, 9, 8, 7))\n rownames(parRange) <- c(\"par1\", \"par2\", \"par3\", \"par4\")\n ## uniform\n pairs(Unif(parRange, 100), main = \"Uniformly random\")"}}},{"rowIdx":59485,"cells":{"project":{"kind":"string","value":"CodableAlamofire"},"source":{"kind":"string","value":"cocoapods"},"language":{"kind":"string","value":"Objective-C"},"content":{"kind":"string","value":"codablealamofire\n===\n\n**CodableAlamofire**\n---\n\n**CodableAlamofire** is a powerful and user-friendly library that integrates **Alamofire** with **Codable** to effortlessly parse JSON responses into Swift objects. This library makes working with web services and APIs seamless and efficient by handling all the data serialization and deserialization for you.\n\n### **Key Features**\n\n* Integrates Alamofire and Codable seamlessly\n* Effortlessly parse JSON responses into Swift objects\n* Handle data serialization and deserialization with ease\n* Improve code readability and maintainability\n\n### **Installation**\n\n1. Open your project in Xcode and navigate to the **File** menu.\n2. Click on **Swift Packages** and then select **Add Package Dependency**.\n3. In the search bar, enter **CodableAlamofire**.\n4. Select the latest version and click **Add Package**.\n5. Finally, import the library in your Swift file using **import CodableAlamofire**.\n\n### **Usage**\n\nTo use CodableAlamofire, follow the steps below:\n```\nimport CodableAlamofire\n\n// Make a request using Alamofire and CodableAlamofire AF.request(\"https://api.example.com/data\").responseDecodable(of: MyModel.self) { response in\n guard let data = response.value else { return }\n // Use 'data' which is an instance of MyModel\n}\n```\nIn the above example, we use Alamofire’s **request** method to make a network request to the specified URL. We then use CodableAlamofire’s **responseDecodable** method to automatically parse the JSON response into an instance of **MyModel**. Finally, we can access the parsed data within the completion block using **response.value**.\n\n### **Conclusion**\n\nCodableAlamofire is a fantastic library that simplifies the integration of Alamofire and Codable. By handling the serialization and deserialization of JSON responses for you, it saves you time and effort, while also improving the readability and maintainability of your code.\n\n**Example Heading**\n---\n\nLorem ipsum dolor sit amet, consectetur adipiscing elit. Nullam faucibus tempor augue, vitae vestibulum nulla molestie gravida. Sed hendrerit mauris id scelerisque facilisis. In eget tristique ante. Curabitur finibus, mauris quis bibendum ornare, lectus mauris volutpat nisl, vulputate ullamcorper dolor arcu nec orci. Suspendisse a molestie enim. Sed at pharetra nisl. Donec ut augue nisi. Pellentesque blandit elementum ante ornare semper.\n\n**Another Example Heading**\n---\n\nInteger et tempus lorem. Curabitur non sollicitudin diam. Ut gravida est ut enim tincidunt sagittis. Quisque varius nisi nec sem aliquam, ut posuere eros auctor. Sed mollis volutpat mollis. Nunc eget tortor porttitor, dignissim erat ut, facilisis felis. Proin posuere consectetur ante, et congue neque fringilla ut. Fusce commodo sagittis urna, nec lobortis dolor semper vitae. Etiam dui ex, hendrerit id nisl quis, sodales congue nisl. Integer faucibus sagittis ligula, vitae vulputate nisl aliquet ac. Ut blandit nunc eu libero tempus finibus."}}},{"rowIdx":59486,"cells":{"project":{"kind":"string","value":"mtsta"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘mtsta’\n September 19, 2023\nTitle Accessing the Red List of Montane Tree Species of the Tropical\n Andes\nVersion 0.0.0.1\nDescription Access the 'Red List of Montane Tree Species of the Tropical Andes' Tejedor Gar-\n avito et al.(2014, ISBN:978-1-905164-60-8). This package allows users to search for glob-\n ally threatened tree species within the andean montane forests, including cloud forests and sea-\n sonal (wet) forests above 1500 m a.s.l.\nLicense MIT + file LICENSE\nSuggests dplyr, forcats, ggplot2, janitor, knitr, rmarkdown, stringr,\n testthat, tibble, tidyr\nConfig/testthat/edition 3\nEncoding UTF-8\nLazyData true\nLazyDataCompression xz\nDate 2023-09-16\nRoxygenNote 7.2.3\nMaintainer <NAME> <<EMAIL>>\nURL https://github.com/PaulESantos/mtsta\nBugReports https://github.com/PaulESantos/mtsta/issues\nVignetteBuilder knitr\nDepends R (>= 2.10)\nNeedsCompilation no\nAuthor <NAME> [aut, cre]\n (<https://orcid.org/0000-0002-6635-0375>)\nRepository CRAN\nDate/Publication 2023-09-19 14:20:02 UTC\nR topics documented:\nmtsta_distributio... 2\nmtsta_ta... 3\nsearch_mtst... 4\nsearch_mtsta_distributio... 5\n mtsta_distribution mtsta_distribution: Distribution Data for Species in mtsta_tab\nDescription\n This dataset contains distribution data for species included in A Regional Red List of Montane\n Tree Species of the Tropical Andes - 2014. It provides information on the current accepted names,\n distribution range, and taxonomic status for each species. The data is original diatribution data and\n the updated distribution information for the included species.\nUsage\n mtsta_distribution\nFormat\n A tibble\n accepted_name Character vector with the current accepted name of the species.\n distribution Character vector indicating the distribution range of the species.\n distribution_wcvp Character vector indicating the distribution according to the World Checklist\n of Vascular Plants (WCVP).\n taxonomic_status Character vector indicating the taxonomic status of the species of the submitted\n name (e.g., \"Accepted\").\nDetails\n The dataset contains information on the distribution of species in A Regional Red List of Montane\n Tree Species of the Tropical Andes - 2014. The distribution data includes the geographical range of\n each species, including countries where the species can be found.\nExamples\n # Load the mtsta_distribution dataset\n data(\"mtsta_distribution\")\n mtsta_tab Montane Tree Species of the Tropical Andes - Base Data\nDescription\n This is the curated base data of montane tree species found in the Tropical Andes region. The data\n is stored as a tibble with 132 rows and 11 columns. Each row represents a species and contains\n information such as the species name, accepted name, accepted family, accepted genus, IUCN\n status, distribution, elevation range, assessor, description, and taxonomic status.\nUsage\n mtsta_tab\nFormat\n A tibble with 132 rows and 11 columns.\nDetails\n The columns in the base data tibble are as follows:\n • species_name: The scientific name of the species.\n • accepted_name: The currently accepted name for the species.\n • accepted_family: The family to which the species belongs.\n • accepted_genus: The genus to which the species belongs.\n • taxonomic_status: The taxonomic status of the species.\n • iucn: The conservation status of the species according to the IUCN Red List Categories.\n • distribution: The distribution range of the species.\n • unsure_distribution: Information about the uncertainty in the distribution data.\n • elevation: The elevation range where the species is found.\n • assessor: The person or group responsible for assessing the species.\n • description: Additional information or description of the species.\n The base species list used in the mtsta package has been carefully reviewed and validated with\n the assistance of the Taxonomic Name Resolution Service (TNRS). By utilizing the TNRS, the\n base species list in the mtsta package guarantees accuracy and consistency in the representation of\n species names, enhancing the reliability of the package’s functionalities.\nSource\n The data for this package was obtained from A Regional Red List of Montane Tree Species of the\n Tropical Andes - 2014.\nSee Also\n Use search_mtsta() function to search and match species names using this base data.\nExamples\n data(\"mtsta_tab\")\n search_mtsta Search for Matching Species Names in the Red List of Montane Tree\n Species of the Tropical Andes\nDescription\n This function searches for matching species names in the Red List of Montane Tree Species of the\n Tropical Andes (mtsta package) based on a provided list of species names. The function performs\n approximate matching using the Levenshtein distance algorithm to find similar names within a\n specified maximum distance.\nUsage\n search_mtsta(splist, max_distance = 0.1, ...)\nArguments\n splist A character vector containing the species names to be matched.\n max_distance The distance used is a generalized Levenshtein distance that indicates the to-\n tal number of insertions, deletions, and substitutions allowed to match the two\n names. It can be expressed as an integer or as the fraction of the binomial name.\n A value between 0 and 1 will be treated as a percentage of the string length. A\n value greater than 1 will be treated as an absolute number of allowed changes.\n For example, a name with length 10, and a max_distance = 0.1, allow only one\n change (insertion, deletion, or substitution). A max_distance = 2, allows two\n changes.\n ... Additional arguments (currently unused).\nValue\n A data frame with the following columns:\n • name_submitted: The submitted species names.\n • name_matched: The matched species names from the mtsta data.\n • accepted_name: The accepted scientific name of the matched species.\n • accepted_family: The accepted family name of the matched species.\n • accepted_genus: The accepted genus name of the matched species.\n • taxonomic_status: The taxonomic status of the matched species.\n • iucn: The conservation status of the matched species according to the IUCN Red List Cate-\n gories.\n • distribution: The distribution range of the matched species.\n • unsure_distribution: Information about the uncertainty in the distribution data.\n • elevation: The elevation range where the species is found.\n • assessor: The person or group responsible for assessing the species.\n • description: Additional information or description of the species.\n • distance: The Levenshtein distance between the submitted name and the matched name.\n If no match is found, the name_matched column will contain \"nill\", and the other columns will be\n empty.\nSee Also\n mtsta::mtsta_tab\nExamples\n # Assuming you have the mtsta package loaded with the necessary data\n search_result <- search_mtsta(c(\"<NAME>\",\n \"<NAME>\",\n \"<NAME>\",\n \"<NAME>\",\n \"Ilex colombiana\",\n \"Ilex rimbachii\",\n \"Ilex scopulorum\"),\n max_distance = 0.1)\n search_mtsta_distribution\n Search Species Distribution of A Regional Red List of Montane Tree\n Species of the Tropical Andes\nDescription\n This function searches the Montane Tree Species of the Tropical Andes distribution database for\n a list of submitted species names and returns their distribution information. The search allows for\n approximate string matching within a given maximum distance.\nUsage\n search_mtsta_distribution(splist, max_distance = 0.1, typedf = \"main\")\nArguments\n splist Character vector of submitted plant species names for which distribution data is\n to be searched.\n max_distance Numeric value representing the maximum allowed distance for approximate\n string matching. The default value is 0.1.\n typedf \"main\" return a selected columns in from mtsta_distribution \"full\" return all data\nDetails\n The function uses approximate string matching with a maximum distance specified by the max_distance\n argument. It searches the mtsta distribution database for submitted species names that match the\n provided names within the given distance. The function then retrieves distribution information, in-\n cluding the accepted name, distribution region, unsure distribution (if available), distribution from\n the World Check-list of Vascular Plants (WCVP), taxonomic status, and the Levenshtein distance\n between submitted and matched species names.\nValue\n A data frame with the following columns:\n name_submitted Character vector with the submitted species names.\n name_matched Character vector with the matched species names in the database.\n accepted_name Character vector with the accepted names of the matched species.\n distribution Character vector with the distribution of the matched species.\n unsure_distribution Character vector with information about unsure distribution (if available).\n distribution_wcvp Character vector with the distribution from the World Check-list of Vascular\n Plants (WCVP) database for the matched species.\n taxonomic_status Character vector indicating the taxonomic status of the matched species.\n distance Numeric vector with the Levenshtein distance between submitted and matched species\n names.\nSee Also\n mtsta_distribution\nExamples\n # Example usage of search_mtsta_distribution function\n species_list <- c(\"<NAME>\", \"<NAME>\", \"<NAME>\")\n distribution_data <- search_mtsta_distribution(species_list, max_distance = 0.2)\n print(distribution_data)"}}},{"rowIdx":59487,"cells":{"project":{"kind":"string","value":"django-user-accounts"},"source":{"kind":"string","value":"readthedoc"},"language":{"kind":"string","value":"Python"},"content":{"kind":"string","value":"django-user-accounts 2.0.3 documentation\n\n[django-user-accounts](index.html#document-index)\n\n---\n\ndjango-user-accounts[¶](#django-user-accounts)\n===\n\nProvides user accounts to a Django project.\n\nDevelopment[¶](#development)\n---\n\nThe source repository can be found at <https://github.com/pinax/django-user-accounts/### Contents[¶](#contents)\n\n#### Installation[¶](#installation)\n\nInstall the development version:\n```\npip install django-user-accounts\n```\nAdd `account` to your `INSTALLED_APPS` setting:\n```\nINSTALLED_APPS = (\n # ...\n \"account\",\n # ...\n)\n```\nSee the list of [Settings](index.html#settings) to modify the default behavior of django-user-accounts and make adjustments for your website.\n\nAdd `account.urls` to your URLs definition:\n```\nurlpatterns = patterns(\"\",\n ...\n url(r\"^account/\", include(\"account.urls\")),\n ...\n)\n```\nAdd `account.context_processors.account` to `TEMPLATE_CONTEXT_PROCESSORS`:\n```\nTEMPLATE_CONTEXT_PROCESSORS = [\n ...\n \"account.context_processors.account\",\n ...\n]\n```\nAdd `account.middleware.LocaleMiddleware` and\n`account.middleware.TimezoneMiddleware` to `MIDDLEWARE_CLASSES`:\n```\nMIDDLEWARE_CLASSES = [\n ...\n \"account.middleware.LocaleMiddleware\",\n \"account.middleware.TimezoneMiddleware\",\n ...\n]\n```\nOptionally include `account.middleware.ExpiredPasswordMiddleware` in\n`MIDDLEWARE_CLASSES` if you need password expiration support:\n```\nMIDDLEWARE_CLASSES = [\n ...\n \"account.middleware.ExpiredPasswordMiddleware\",\n ...\n]\n```\nOnce everything is in place make sure you run `migrate` to modify the database with the `account` app models.\n\n##### Dependencies[¶](#dependencies)\n\n###### `django.contrib.auth`[¶](#django-contrib-auth)\n\nThis is bundled with Django. It is enabled by default with all new Django projects, but if you adding django-user-accounts to an existing project you need to make sure `django.contrib.auth` is installed.\n\n###### `django.contrib.sites`[¶](#django-contrib-sites)\n\nThis is bundled with Django. It is enabled by default with all new Django projects. It is used to provide links back to the site in emails or various places in templates that need an absolute URL.\n\n###### [django-appconf](https://github.com/jezdez/django-appconf)[¶](#django-appconf)\n\nWe use django-appconf for app settings. It is listed in `install_requires`\nand will be installed when pip installs.\n\n###### [pytz](http://pypi.python.org/pypi/pytz/)[¶](#pytz)\n\npytz is used for handling timezones for accounts. This dependency is critical due to its extensive dataset for timezones.\n\n#### Usage[¶](#usage)\n\nThis document covers the usage of django-user-accounts. It assumes you’ve read [Installation](index.html#installation).\n\ndjango-user-accounts has very good default behavior when handling user accounts. It has been designed to be customizable in many aspects. By default this app will:\n\n* enable username authentication\n* provide default views and forms for sign up, log in, password reset and account management\n* handle log out with POST\n* require unique email addresses globally\n* require email verification for performing password resets\n\nThe rest of this document will cover how you can tweak the default behavior of django-user-accounts.\n\n##### Limiting access to views[¶](#limiting-access-to-views)\n\nTo limit view access to logged in users, normally you would use the Django decorator `django.contrib.auth.decorators.login_required`. Instead you should use `account.decorators.login_required`.\n\n##### Customizing the sign up process[¶](#customizing-the-sign-up-process)\n\nIn many cases you need to tweak the sign up process to do some domain specific tasks. Perhaps you need to update a profile for the new user or something else.\nThe built-in `SignupView` has hooks to enable just about any sort of customization during sign up. Here’s an example of a custom `SignupView`\ndefined in your project:\n```\nimport account.views\n\nclass SignupView(account.views.SignupView):\n\n def after_signup(self, form):\n self.update_profile(form)\n super(SignupView, self).after_signup(form)\n\n def update_profile(self, form):\n profile = self.created_user.profile # replace with your reverse one-to-one profile attribute\n profile.some_attr = \"some value\"\n profile.save()\n```\nThis example assumes you had a receiver hooked up to the post_save signal for the sender, User like so:\n```\nfrom django.dispatch import receiver from django.db.models.signals import post_save\n\nfrom django.contrib.auth.models import User\n\nfrom mysite.profiles.models import UserProfile\n\n@receiver(post_save, sender=User)\ndef handle_user_save(sender, instance, created, **kwargs):\n if created:\n UserProfile.objects.create(user=instance)\n```\nYou can define your own form class to add fields to the sign up process:\n```\n# forms.py\n\nfrom django import forms from django.forms.extras.widgets import SelectDateWidget\n\nimport account.forms\n\nclass SignupForm(account.forms.SignupForm):\n\n birthdate = forms.DateField(widget=SelectDateWidget(years=range(1910, 1991)))\n\n# views.py\n\nimport account.views\n\nimport myproject.forms\n\nclass SignupView(account.views.SignupView):\n\n form_class = myproject.forms.SignupForm\n\n def after_signup(self, form):\n self.create_profile(form)\n super(SignupView, self).after_signup(form)\n\n def create_profile(self, form):\n profile = self.created_user.profile # replace with your reverse one-to-one profile attribute\n profile.birthdate = form.cleaned_data[\"birthdate\"]\n profile.save()\n```\nTo hook this up for your project you need to override the URL for sign up:\n```\nfrom django.conf.urls import patterns, include, url\n\nimport myproject.views\n\nurlpatterns = patterns(\"\",\n url(r\"^account/signup/$\", myproject.views.SignupView.as_view(), name=\"account_signup\"),\n url(r\"^account/\", include(\"account.urls\")),\n)\n```\nNote\n\nMake sure your `url` for `/account/signup/` comes *before* the\n`include` of `account.urls`. Django will short-circuit on yours.\n\n##### Using email address for authentication[¶](#using-email-address-for-authentication)\n\ndjango-user-accounts allows you to use email addresses for authentication instead of usernames. You still have the option to continue using usernames or get rid of them entirely.\n\nTo enable email authentication do the following:\n\n1. check your settings for the following values:\n```\nACCOUNT_EMAIL_UNIQUE = True ACCOUNT_EMAIL_CONFIRMATION_REQUIRED = True\n```\nNote\n\nIf you need to change the value of `ACCOUNT_EMAIL_UNIQUE` make sure your database schema is modified to support a unique email column in\n`account_emailaddress`.\n\n`ACCOUNT_EMAIL_CONFIRMATION_REQUIRED` is optional, but highly recommended to be `True`.\n2. define your own `LoginView` in your project:\n```\nimport account.forms import account.views\n\nclass LoginView(account.views.LoginView):\n\n form_class = account.forms.LoginEmailForm\n```\n3. ensure `\"account.auth_backends.EmailAuthenticationBackend\"` is in `AUTHENTICATION_BACKENDS`\n\nIf you want to get rid of username you’ll need to do some extra work:\n\n1. define your own `SignupForm` and `SignupView` in your project:\n```\n# forms.py\n\nimport account.forms\n\nclass SignupForm(account.forms.SignupForm):\n\n def __init__(self, *args, **kwargs):\n super(SignupForm, self).__init__(*args, **kwargs)\n del self.fields[\"username\"]\n\n# views.py\n\nimport account.views\n\nimport myproject.forms\n\nclass SignupView(account.views.SignupView):\n\n form_class = myproject.forms.SignupForm\n identifier_field = 'email'\n\n def generate_username(self, form):\n # do something to generate a unique username (required by the\n # Django User model, unfortunately)\n username = \"<magic>\"\n return username\n```\n2. many places will rely on a username for a User instance.\ndjango-user-accounts provides a mechanism to add a level of indirection when representing the user in the user interface. Keep in mind not everything you include in your project will do what you expect when removing usernames entirely.\n\nSet `ACCOUNT_USER_DISPLAY` in settings to a callable suitable for your site:\n```\nACCOUNT_USER_DISPLAY = lambda user: user.email\n```\nYour Python code can use `user_display` to handle user representation:\n```\nfrom account.utils import user_display user_display(user)\n```\nYour templates can use `{% user_display request.user %}`:\n```\n{% load account_tags %}\n{% user_display request.user %}\n```\n##### Allow non-unique email addresses[¶](#allow-non-unique-email-addresses)\n\nIf your site requires that you support non-unique email addresses globally you can tweak the behavior to allow this.\n\nSet `ACCOUNT_EMAIL_UNIQUE` to `False`. If you have already setup the tables for django-user-accounts you will need to migrate the\n`account_emailaddress` table:\n```\nALTER TABLE \"account_emailaddress\" ADD CONSTRAINT \"account_emailaddress_user_id_email_key\" UNIQUE (\"user_id\", \"email\");\nALTER TABLE \"account_emailaddress\" DROP CONSTRAINT \"account_emailaddress_email_key\";\n```\n`ACCOUNT_EMAIL_UNIQUE = False` will allow duplicate email addresses per user, but not across users.\n\n##### Including accounts in fixtures[¶](#including-accounts-in-fixtures)\n\nIf you want to include account_account in your fixture, you may notice that when you load that fixture there is a conflict because django-user-accounts defaults to creating a new account for each new user.\n\nExample:\n```\nIntegrityError: Problem installing fixture \\\n ...'/app/fixtures/some_users_and_accounts.json': \\\n Could not load account.Account(pk=1): duplicate key value violates unique constraint \\\n \"account_account_user_id_key\"\nDETAIL: Key (user_id)=(1) already exists.\n```\nTo prevent this from happening, subclass DiscoverRunner and in setup_test_environment set CREATE_ON_SAVE to False. For example in a file called lib/tests.py:\n```\nfrom django.test.runner import DiscoverRunner from account.conf import AccountAppConf\n\nclass MyTestDiscoverRunner(DiscoverRunner):\n\n def setup_test_environment(self, **kwargs):\n super(MyTestDiscoverRunner, self).setup_test_environment(**kwargs)\n aac = AccountAppConf()\n aac.CREATE_ON_SAVE = False\n```\nAnd in your settings:\n```\nTEST_RUNNER = \"lib.tests.MyTestDiscoverRunner\"\n```\n##### Enabling password expiration[¶](#enabling-password-expiration)\n\nPassword expiration is disabled by default. In order to enable password expiration you must add entries to your settings file:\n```\nACCOUNT_PASSWORD_EXPIRY = 60*60*24*5 # seconds until pw expires, this example shows five days ACCOUNT_PASSWORD_USE_HISTORY = True\n```\nand include ExpiredPasswordMiddleware with your middleware settings:\n```\nMIDDLEWARE_CLASSES = {\n ...\n \"account.middleware.ExpiredPasswordMiddleware\",\n}\n```\n`ACCOUNT_PASSWORD_EXPIRY` indicates the duration a password will stay valid. After that period the password must be reset in order to view any page. If `ACCOUNT_PASSWORD_EXPIRY` is zero (0)\nthen passwords never expire.\n\nIf `ACCOUNT_PASSWORD_USE_HISTORY` is False, no history will be generated and password expiration WILL NOT be checked.\n\nIf `ACCOUNT_PASSWORD_USE_HISTORY` is True, a password history entry is created each time the user changes their password. This entry links the user with their most recent\n(encrypted) password and a timestamp. Unless deleted manually, PasswordHistory items are saved forever, allowing password history checking for new passwords.\n\nFor an authenticated user, `ExpiredPasswordMiddleware` prevents retrieving or posting to any page except the password change page and log out page when the user password is expired.\nHowever, if the user is “staff” (can access the Django admin site), the password check is skipped.\n\n#### Settings[¶](#settings)\n\n##### `ACCOUNT_OPEN_SIGNUP`[¶](#account-open-signup)\n\nDefault: `True`\n\n##### `ACCOUNT_LOGIN_URL`[¶](#account-login-url)\n\nDefault: `\"account_login\"`\n\n##### `ACCOUNT_SIGNUP_REDIRECT_URL`[¶](#account-signup-redirect-url)\n\nDefault: `\"/\"`\n\n##### `ACCOUNT_LOGIN_REDIRECT_URL`[¶](#account-login-redirect-url)\n\nDefault: `\"/\"`\n\n##### `ACCOUNT_LOGOUT_REDIRECT_URL`[¶](#account-logout-redirect-url)\n\nDefault: `\"/\"`\n\n##### `ACCOUNT_PASSWORD_CHANGE_REDIRECT_URL`[¶](#account-password-change-redirect-url)\n\nDefault: `\"account_password\"`\n\n##### `ACCOUNT_PASSWORD_RESET_REDIRECT_URL`[¶](#account-password-reset-redirect-url)\n\nDefault: `\"account_login\"`\n\n##### `ACCOUNT_PASSWORD_EXPIRY`[¶](#account-password-expiry)\n\nDefault: `0`\n\n##### `ACCOUNT_PASSWORD_USE_HISTORY`[¶](#account-password-use-history)\n\nDefault: `False`\n\n##### `ACCOUNT_REMEMBER_ME_EXPIRY`[¶](#account-remember-me-expiry)\n\nDefault: `60 * 60 * 24 * 365 * 10`\n\n##### `ACCOUNT_USER_DISPLAY`[¶](#account-user-display)\n\nDefault: `lambda user: user.username`\n\n##### `ACCOUNT_CREATE_ON_SAVE`[¶](#account-create-on-save)\n\nDefault: `True`\n\n##### `ACCOUNT_EMAIL_UNIQUE`[¶](#account-email-unique)\n\nDefault: `True`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_REQUIRED`[¶](#account-email-confirmation-required)\n\nDefault: `False`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_EMAIL`[¶](#account-email-confirmation-email)\n\nDefault: `True`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_EXPIRE_DAYS`[¶](#account-email-confirmation-expire-days)\n\nDefault: `3`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_ANONYMOUS_REDIRECT_URL`[¶](#account-email-confirmation-anonymous-redirect-url)\n\nDefault: `\"account_login\"`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_AUTHENTICATED_REDIRECT_URL`[¶](#account-email-confirmation-authenticated-redirect-url)\n\nDefault: `None`\n\n##### `ACCOUNT_EMAIL_CONFIRMATION_URL`[¶](#account-email-confirmation-url)\n\nDefault: `\"account_confirm_email\"`\n\n##### `ACCOUNT_SETTINGS_REDIRECT_URL`[¶](#account-settings-redirect-url)\n\nDefault: `\"account_settings\"`\n\n##### `ACCOUNT_NOTIFY_ON_PASSWORD_CHANGE`[¶](#account-notify-on-password-change)\n\nDefault: `True`\n\n##### `ACCOUNT_DELETION_MARK_CALLBACK`[¶](#account-deletion-mark-callback)\n\nDefault: `\"account.callbacks.account_delete_mark\"`\n\n##### `ACCOUNT_DELETION_EXPUNGE_CALLBACK`[¶](#account-deletion-expunge-callback)\n\nDefault: `\"account.callbacks.account_delete_expunge\"`\n\n##### `ACCOUNT_DELETION_EXPUNGE_HOURS`[¶](#account-deletion-expunge-hours)\n\nDefault: `48`\n\n##### `ACCOUNT_HOOKSET`[¶](#account-hookset)\n\nDefault: `\"account.hooks.AccountDefaultHookSet\"`\n\nThis setting allows you define your own hooks for specific functionality that django-user-accounts exposes. Point this to a class using a string and you can override the following methods:\n\n* `send_invitation_email(to, ctx)`\n* `send_confirmation_email(to, ctx)`\n* `send_password_change_email(to, ctx)`\n* `send_password_reset_email(to, ctx)`\n\n##### `ACCOUNT_TIMEZONES`[¶](#account-timezones)\n\nDefault: `list(zip(pytz.all_timezones, pytz.all_timezones))`\n\n##### `ACCOUNT_LANGUAGES`[¶](#account-languages)\n\nSee full list in: <https://github.com/pinax/django-user-accounts/blob/master/account/language_list.py#### Templates[¶](#templates)\n\nThis document covers the implementation of django-user-accounts within Django templates. The [pinax-theme-bootstrap](https://github.com/pinax/pinax-theme-bootstrap) package provides a good [starting point](https://github.com/pinax/pinax-theme-bootstrap/tree/master/pinax_theme_bootstrap/templates/account)\nto build from. Note, this document assumes you have read the installation docs.\n\n##### Template Files[¶](#template-files)\n\nBy default, django-user-accounts expects the following templates. If you don’t use `pinax-theme-bootstrap`, then you will have to create these templates yourself.\n\nLogin/Registration/Signup Templates:\n```\naccount/login.html account/logout.html account/signup.html account/signup_closed.html\n```\nEmail Confirmation Templates:\n```\naccount/email_confirm.html account/email_confirmation_sent.html account/email_confirmed.html\n```\nPassword Management Templates:\n```\naccount/password_change.html account/password_reset.html account/password_reset_sent.html account/password_reset_token.html account/password_reset_token_fail.html\n```\nAccount Settings:\n```\naccount/settings.html\n```\nEmails (actual emails themselves):\n```\naccount/email/email_confirmation_message.txt account/email/email_confirmation_subject.txt account/email/invite_user.txt account/email/invite_user_subject.txt account/email/password_change.txt account/email/password_change_subject.txt account/email/password_reset.txt account/email/password_reset_subject.txt\n```\n##### Template Tags[¶](#template-tags)\n\nTo use the built in template tags you must first load them within the templates:\n```\n{% load account_tags %}\n```\nTo display the current logged-in user:\n```\n{% user_display request.user %}\n```\n#### Signals[¶](#signals)\n\n##### user_signed_up[¶](#user-signed-up)\n\nTriggered when a user signs up successfully. Providing arguments `user`\n(User instance) and `form` (form instance) as arguments.\n\n##### user_sign_up_attempt[¶](#user-sign-up-attempt)\n\nTriggered when a user tried but failed to sign up. Providing arguments\n`username` (string), `email` (string) and `result` (boolean, False if the form did not validate).\n\n##### user_logged_in[¶](#user-logged-in)\n\nTriggered when a user logs in successfully. Providing arguments `user`\n(User instance) and `form` (form instance).\n\n##### user_login_attempt[¶](#user-login-attempt)\n\nTriggered when a user tries and fails to log in. Providing arguments\n`username` (string) and `result` (boolean, False if the form did not validate).\n\n##### signup_code_sent[¶](#signup-code-sent)\n\nTriggered when a signup code was sent. Providing argument `signup_code`\n(SignupCode instance).\n\n##### signup_code_used[¶](#signup-code-used)\n\nTriggered when a user used a signup code. Providing argument\n`signup_code_result` (SignupCodeResult instance).\n\n##### email_confirmed[¶](#email-confirmed)\n\nTriggered when a user confirmed an email. Providing argument\n[``](#id2)email_address``(EmailAddress instance).\n\n##### email_confirmation_sent[¶](#email-confirmation-sent)\n\nTriggered when an email confirmation was sent. Providing argument\n`confirmation` (EmailConfirmation instance).\n\n##### password_changed[¶](#password-changed)\n\nTriggered when a user changes his password. Providing argument `user`\n(User instance).\n\n##### password_expired[¶](#password-expired)\n\nTriggered when a user password is expired. Providing argument `user`\n(User instance).\n\n#### Management Commands[¶](#management-commands)\n\n##### user_password_history[¶](#user-password-history)\n\nCreates an initial password history for all users who don’t already have a password history.\n\nAccepts two optional arguments:\n```\n-d --days <days> - Sets the age of the current password. Default is 10 days.\n-f --force - Sets a new password history for ALL users, regardless of prior history.\n```\n##### user_password_expiry[¶](#user-password-expiry)\n\nCreates a password expiry specific to one user.\n\nPassword expiration checks use a global value (`ACCOUNT_PASSWORD_EXPIRY`)\nfor the expiration time period. This value can be superseded on a per-user basis by creating a user password expiry.\n\nRequires one argument:\n```\n<username> [<username>] - username(s) of the user(s) who needs specific password expiry.\n```\nAccepts one optional argument:\n```\n-e --expire <seconds> - Sets the number of seconds for password expiration.\n Default is the current global ACCOUNT_PASSWORD_EXPIRY value.\n```\nAfter creation, you can modify user password expiration from the Django admin. Find the desired user at `/admin/account/passwordexpiry/` and change the `expiry` value.\n\n#### Migration from Pinax[¶](#migration-from-pinax)\n\ndjango-user-accounts is based on `pinax.apps.account` combining some of the supporting apps. django-email-confirmation, `pinax.apps.signup_codes`\nand bits of django-timezones have been merged to create django-user-accounts.\n\nThis document will outline the changes needed to migrate from Pinax to using this app in your Django project. If you are new to django-user-accounts then this guide will not be useful to you.\n\n##### Database changes[¶](#database-changes)\n\nDue to combining apps the table layout when converting from Pinax has changed.\nWe’ve also taken the opportunity to update the schema to take advantage of much saner defaults. Here is SQL to convert from Pinax to django-user-accounts.\n\n###### PostgreSQL[¶](#postgresql)\n```\nALTER TABLE \"signup_codes_signupcode\" RENAME TO \"account_signupcode\";\nALTER TABLE \"signup_codes_signupcoderesult\" RENAME TO \"account_signupcoderesult\";\nALTER TABLE \"emailconfirmation_emailaddress\" RENAME TO \"account_emailaddress\";\nALTER TABLE \"emailconfirmation_emailconfirmation\" RENAME TO \"account_emailconfirmation\";\nDROP TABLE \"account_passwordreset\";\nALTER TABLE \"account_signupcode\" ALTER COLUMN \"code\" TYPE varchar(64);\nALTER TABLE \"account_signupcode\" ADD CONSTRAINT \"account_signupcode_code_key\" UNIQUE (\"code\");\nALTER TABLE \"account_emailconfirmation\" RENAME COLUMN \"confirmation_key\" TO \"key\";\nALTER TABLE \"account_emailconfirmation\" ALTER COLUMN \"key\" TYPE varchar(64);\nALTER TABLE account_emailconfirmation ADD COLUMN created timestamp with time zone;\nUPDATE account_emailconfirmation SET created = sent;\nALTER TABLE account_emailconfirmation ALTER COLUMN created SET NOT NULL;\nALTER TABLE account_emailconfirmation ALTER COLUMN sent DROP NOT NULL;\n```\nIf `ACCOUNT_EMAIL_UNIQUE` is set to `True` (the default value) you need:\n```\nALTER TABLE \"account_emailaddress\" ADD CONSTRAINT \"account_emailaddress_email_key\" UNIQUE (\"email\");\nALTER TABLE \"account_emailaddress\" DROP CONSTRAINT \"emailconfirmation_emailaddress_user_id_email_key\";\n```\n###### MySQL[¶](#mysql)\n```\nRENAME TABLE `emailconfirmation_emailaddress` TO `account_emailaddress` ;\nRENAME TABLE `emailconfirmation_emailconfirmation` TO `account_emailconfirmation` ;\nDROP TABLE account_passwordreset;\nALTER TABLE `account_emailconfirmation` CHANGE `confirmation_key` `key` VARCHAR(64) NOT NULL;\nALTER TABLE `account_emailconfirmation` ADD UNIQUE (`key`);\nALTER TABLE account_emailconfirmation ADD COLUMN created datetime NOT NULL;\nUPDATE account_emailconfirmation SET created = sent;\nALTER TABLE `account_emailconfirmation` CHANGE `sent` `sent` DATETIME NULL;\n```\nIf `ACCOUNT_EMAIL_UNIQUE` is set to `True` (the default value) you need:\n```\nALTER TABLE `account_emailaddress` ADD UNIQUE (`email`);\nALTER TABLE account_emailaddress DROP INDEX user_id;\n```\nIf you have installed `pinax.apps.signup_codes`:\n```\nRENAME TABLE `signup_codes_signupcode` TO `account_signupcode` ;\nRENAME TABLE `signup_codes_signupcoderesult` TO `account_signupcoderesult` ;\n```\n##### URL changes[¶](#url-changes)\n\nHere is a list of all URLs provided by django-user-accounts and how they map from Pinax. This assumes `account.urls` is mounted at `/account/` as it was in Pinax.\n\n| Pinax | django-user-accounts |\n| --- | --- |\n| `/account/login/` | `/account/login/` |\n| `/account/signup/` | `/account/signup/` |\n| `/account/confirm_email/` | `/account/confirm_email/` |\n| `/account/password_change/` | `/account/password/` [[1]](#id2) |\n| `/account/password_reset/` | `/account/password/reset/` |\n| `/account/password_reset_done/` | *removed* |\n| `/account/password_reset_key/<key>/` | `/account/password/reset/<token>/` |\n\n| [[1]](#id1) | When user is anonymous and requests a GET the user is redirected to\n`/account/password/reset/`. |\n\n##### View changes[¶](#view-changes)\n\nAll views have been converted to class-based views. This is a big departure from the traditional function-based, but has the benefit of being much more flexible.\n\n@@@ todo: table of changes\n\n##### Settings changes[¶](#settings-changes)\n\nWe have cleaned up settings and set saner defaults used by django-user-accounts.\n\n| Pinax | django-user-accounts |\n| --- | --- |\n| `ACCOUNT_OPEN_SIGNUP = True` | `ACCOUNT_OPEN_SIGNUP = True` |\n| `ACCOUNT_UNIQUE_EMAIL = False` | `ACCOUNT_EMAIL_UNIQUE = True` |\n| `EMAIL_CONFIRMATION_UNIQUE_EMAIL = False` | *removed* |\n\n##### General changes[¶](#general-changes)\n\ndjango-user-accounts requires Django 1.4. This means we can take advantage of many of the new features offered by Django. This app implements all of the best practices of Django 1.4. If there is something missing you should let us know!\n\n#### FAQ[¶](#faq)\n\nThis document is a collection of frequently asked questions about django-user-accounts.\n\n##### What is the difference between django-user-accounts and django.contrib.auth?[¶](#what-is-the-difference-between-django-user-accounts-and-django-contrib-auth)\n\ndjango-user-accounts is designed to supplement `django.contrib.auth`. This app provides improved views for log in, password reset, log out and adds sign up functionality. We try not to duplicate code when Django provides a good implementation. For example, we did not re-implement password reset, but simply provide an improved view which calls into the secure Django password reset code. `django.contrib.auth` is still providing many of supporting elements such as `User` model, default authentication backends, helper functions and authorization.\n\ndjango-user-accounts takes your Django project from having simple log in,\nlog out and password reset to a full blown account management system that you will end up building anyways.\n\n##### Why can email addresses get out of sync?[¶](#why-can-email-addresses-get-out-of-sync)\n\ndjango-user-accounts stores email addresses in two locations. The default\n`User` model contains an `email` field and django-user-accounts provides an\n`EmailAddress` model. This latter is provided to support multiple email addresses per user.\n\nIf you use a custom user model you can prevent the double storage. This is because you can choose not to do any email address storage.\n\nIf you don’t use a custom user model then make sure you take extra precaution.\nWhen editing email addresses either in the shell or admin make sure you update in both places. Only the primary email address is stored on the `User` model."}}},{"rowIdx":59488,"cells":{"project":{"kind":"string","value":"CorrBin"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘CorrBin’\n September 29, 2023\nTitle Nonparametrics with Clustered Binary and Multinomial Data\nVersion 1.6.1\nDate 2023-09-28\nEncoding UTF-8\nDepends R(>= 2.6.0)\nImports boot, combinat, geepack, dirmult, mvtnorm\nSuggests lattice\nDescription Implements non-parametric analyses for clustered\n binary and multinomial data. The elements of the cluster are assumed\n exchangeable, and identical joint distribution (also known as marginal\n compatibility, or reproducibility) is assumed for clusters of different\n sizes. A trend test based on stochastic ordering is implemented.\n <NAME>, <NAME>. (2010) <doi:10.1093/biomet/asp077>;\n <NAME>, <NAME>, <NAME>, <NAME> (2016) <doi:10.1093/biomet/asw009>.\nLicense GPL (>= 2)\nLazyLoad yes\nRoxygenNote 7.2.3\nNeedsCompilation yes\nAuthor <NAME> [aut, cre]\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-09-29 07:40:05 UTC\nR topics documented:\nCorrBin-packag... 2\nCBDat... 3\nCMDat... 4\ndeh... 5\negd... 6\nExtrac... 7\nGEE.trend.tes... 8\njointprob... 9\nmc.est.CMDat... 10\nmc.test.chisq.CMDat... 12\nmulti.cor... 13\nmultinom.ge... 14\nNOSTASO... 15\npd... 17\nran.CBDat... 18\nran.CMDat... 19\nread.CBDat... 21\nread.CMDat... 22\nRS.trend.tes... 23\nshellto... 24\nSO.LR... 25\nSO.mc.es... 26\nSO.trend.tes... 27\nsoContro... 29\ntrend.tes... 30\nuniprob... 31\nunwrap.CBDat... 32\n CorrBin-package Nonparametrics for Correlated Binary and Multinomial Data\nDescription\n This package implements nonparametric methods for analyzing exchangeable binary and multino-\n mial data with variable cluster sizes with emphasis on trend testing. The input should specify the\n treatment group, cluster-size, and the number of responses (i.e. the number of cluster elements with\n the outcome of interest) for each cluster.\nDetails\n • The CBData/CMData and read.CBData/read.CMData functions create a ‘CBData’ or ‘CM-\n Data’ object used by the analysis functions.\n • ran.CBData and ran.CMData can be used to generate random binary or multinomial data\n using a variety of distributions.\n • mc.test.chisq tests the assumption of marginal compatibility underlying all the methods,\n while mc.est estimates the distribution of the number of responses under marginal compati-\n bility.\n • Finally, trend.test performs three different tests for trend along the treatment groups for\n binomial data.\nAuthor(s)\n <NAME>\n Maintainer: <NAME> <<EMAIL>>\nReferences\n Szabo A, Ge<NAME>. (2009) On the Use of Stochastic Ordering to Test for Trend with Clustered\n Binary Data. Biometrika\n Stefanescu, C. & <NAME>. (2003) Likelihood inference for exchangeable binary data with\n varying cluster sizes. Biometrics, 59, 18-24\n Pang, Z. & Kuk, A. (2007) Test of marginal compatibility and smoothing methods for exchangeable\n binary data with unequal cluster sizes. Biometrics, 63, 218-227\n CBData Create a ‘CBdata’ object from a data frame.\nDescription\n The CBData function creates an object of class CBData that is used in further analyses. It identifies\n the variables that define treatment group, clustersize and the number of responses.\nUsage\n CBData(x, trt, clustersize, nresp, freq = NULL)\nArguments\n x a data frame with one row representing a cluster or potentially a set of clusters\n of the same size and number of responses\n trt the name of the variable that defines treatment group\n clustersize the name of the variable that defines cluster size\n nresp the name of the variable that defines the number of responses in the cluster\n freq the name of the variable that defines the number of clusters represented by the\n data row. If NULL, then each row is assumed to correspond to one cluster.\nValue\n A data frame with each row representing all the clusters with the same trt/size/number of responses,\n and standardized variable names:\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n NResp numeric, the number of responses\n Freq numeric, number of clusters with the same values\nAuthor(s)\n <NAME>\nSee Also\n read.CBData for creating a CBData object directly from a file.\nExamples\n data(shelltox)\n sh <- CBData(shelltox, trt=\"Trt\", clustersize=\"ClusterSize\", nresp=\"NResp\")\n str(sh)\n CMData Create a ‘CMdata’ object from a data frame.\nDescription\n The CMData function creates an object of class CMData that is used in further analyses. It identifies\n the variables that define treatment group, clustersize and the number of responses for each outcome\n type.\nUsage\n CMData(x, trt, nresp, clustersize = NULL, freq = NULL)\nArguments\n x a data frame with one row representing a cluster or potentially a set of clusters\n of the same size and number of responses for each outcome\n trt the name of the variable that defines treatment group\n nresp either a character vector with the names or a numeric vector with indices of\n the variables that define the number of responses in the cluster for each outcome\n type. If clustersize is NULL, then it will be calculated assuming that the nresp\n vector contains all the possible outcomes. If clustersize is given, then an\n additional category is created for the excess cluster members.\n clustersize the name or index of the variable that defines cluster size, or NULL. If NULL, its\n value will be calculated by adding the counts from the nresp variables. If de-\n fined, an additional response type will be created for the excess cluster members.\n freq the name or index of the variable that defines the number of clusters represented\n by the data row. If NULL, then each row is assumed to correspond to one cluster.\nValue\n A data frame with each row representing all the clusters with the same trt/size/number of responses,\n and standardized variable names:\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n NResp.1--NResp.K+1\n numeric, the number of responses for each of the K+1 outcome types\n Freq numeric, number of clusters with the same values\nAuthor(s)\n <NAME>\nSee Also\n read.CMData for creating a CMData object directly from a file.\nExamples\n data(dehp)\n dehp <- CMData(dehp, trt=\"Trt\", nresp=c(\"NResp.1\",\"NResp.2\",\"NResp.3\"))\n str(dehp)\n dehp Developmental toxicology study of DEHP in mice\nDescription\n This data set is based on a National Toxicology Program study on diethylhexyl phthalate, DEHP.\n Pregnant CD-1 mice were randomly assigned to receive 0, 250, 500, 1000, or 1500 ppm of DEHP\n in their feed during gestational days 0-17. The uterine contents of the mice were examined for\n toxicity endpoints prior to normal delivery. The possible outcomes are 1) malformation, 2) death or\n resorption, 3) no adverse event.\nUsage\n data(dehp)\nFormat\n A ’CMData’ object, that is a data frame with the following variables\n Trt factor giving treatment group\n ClusterSize the size of the litter\n NResp.1 the number of fetuses with a type 1 outcome (malformation)\n NResp.2 the number of fetuses with a type 2 outcome (death or resorption)\n NResp.3 the number of fetuses with a type 3 outcome (normal)\n Freq the number of litters with the given ClusterSize/NResp.1-NResp.3 combination\nSource\n National Toxicology Program, NTP Study TER84064.\nReferences\n <NAME>., <NAME>., <NAME>., and <NAME>. (1988). Developmental toxicity evaluation\n of dietary di(2-ethylhexy)phthalate in Fischer 344 rats and CD-1 mice. Fundamental and Applied\n Toxicology 10, 395-412.\nExamples\n data(dehp)\n library(lattice)\n pl <- xyplot(NResp.1/ClusterSize + NResp.2/ClusterSize + NResp.3/ClusterSize ~ Trt,\n data=dehp, outer=TRUE, type=c(\"p\",\"a\"), jitter.x=TRUE)\n pl$condlevels[[1]] <- c(\"Malformed\", \"Dead\", \"Normal\")\n print(pl)\n egde EGDE data\nDescription\n The data set is based on a developmental toxicity experiment on the effect of ethylene glycol di-\n ethyl ether (EGDE) on fetal development of New Zealand white rabbits. In the study, four groups\n of pregnant does were randomly assigned to dose levels $0, 25, 50$, and $100$ milligrams per\n kilogram body weight of EGDE. For each litter and at each dose level, the adverse response used is\n the combined number of fetal malformation and fetal death.\nUsage\n data(egde)\nFormat\n A ’CBData’ object, that is a data frame with the following variables\n Trt factor giving treatment group\n ClusterSize the size of the litter\n NResp the number of affected fetuses\n Freq the number of litters with the given ClusterSize/NResp combination\nSource\n <NAME>., <NAME>., and <NAME>. (1995). Statistical analysis of overdispersed multinomial data\n from developmental toxicity studies. In Statistics in Toxicology, <NAME>, pp.\\ 151–179. New\n York: Oxford University Press.\nExamples\n data(egde)\n stripchart(I(NResp/ClusterSize)~Trt, cex=sqrt(egde$Freq), data=egde, pch=1,\n method=\"jitter\", vertical=TRUE, ylab=\"Proportion affected\")\n Extract Extract from a CBData or CMData object\nDescription\n The extracting syntax works as for [.data.frame, and in general the returned object is not a CBData\n or CMData object. However if the columns are not modified, then the result is still a CBData or\n CMData object with appropriate attributes preserved, and the unused levels of treatment groups\n dropped.\nUsage\n ## S3 method for class 'CBData'\n x[i, j, drop]\n ## S3 method for class 'CMData'\n x[i, j, drop]\nArguments\n x CMData object.\n i numeric, row index of extracted values\n j numeric, column index of extracted values\n drop logical. If TRUE the result is coerced to the lowest possible dimension. The\n default is the same as for [.data.frame: to drop if only one column is left, but\n not to drop if only one row is left.\nValue\n a CBData or CMData object\nAuthor(s)\n <NAME>\nSee Also\n CBData, CMData\nExamples\n data(shelltox)\n str(shelltox[1:5,])\n str(shelltox[1:5, 2:4])\n data(dehp)\n str(dehp[1:5,])\n str(dehp[1:5, 2:4])\n GEE.trend.test GEE-based trend test\nDescription\n GEE.trend.test implements a GEE based test for linear increasing trend for correlated binary\n data.\nUsage\n GEE.trend.test(cbdata, scale.method = c(\"fixed\", \"trend\", \"all\"))\nArguments\n cbdata a CBData object\n scale.method character string specifying the assumption about the change in the overdisper-\n sion (scale) parameter across the treatment groups: \"fixed\" - constant scale pa-\n rameter (default); \"trend\" - linear trend for the log of the scale parameter; \"all\" -\n separate scale parameter for each group.\nDetails\n The actual work is performed by the geese function of the geepack library. This function only\n provides a convenient wrapper to obtain the results in the same format as RS.trend.test and\n SO.trend.test.\n The implementation aims for testing for increasing trend, and a one-sided p-value is reported. The\n test statistic is asymptotically normally distributed, and a two-sided p-value can be easily computed\n if needed.\nValue\n A list with components\n statistic numeric, the value of the test statistic\n p.val numeric, asymptotic one-sided p-value of the test\nAuthor(s)\n <NAME>, <EMAIL>\nSee Also\n RS.trend.test, SO.trend.test for alternative tests; CBData for constructing a CBData object.\nExamples\n data(shelltox)\n GEE.trend.test(shelltox, \"trend\")\n jointprobs Estimate joint event probabilities for multinomial data\nDescription\n An exchangeable multinomial distribution with K + 1 categories O1 , . . . , OK+1 , can be parame-\n terized by the joint probabilities of events\n \u0002 \u0003\n τr1 ,...,rK |n = P X1 = · · · = Xr1 = O1 , . . . , XPK−1 ri +1 = · · · = XPK ri = OK\n where ri ≥ 0 and r1 + · · · + rK ≤ n. The jointprobs function estimates these probabilities under\n various settings. Note that when some of the ri ’s equal zero, then no restriction on the number of\n outcomes of the corresponding type are imposed, so the resulting probabilities are marginal.\nUsage\n jointprobs(cmdata, type = c(\"averaged\", \"cluster\", \"mc\"))\nArguments\n cmdata a CMData object\n type character string describing the desired type of estimate:\n • \"averaged\" - averaged over the observed cluster-size distribution within\n each treatment\n • \"cluster\" - separately for each cluster size within each treatment\n • \"mc\" - assuming marginal compatibility, ie that τ does not depend on the\n cluster-size\nValue\n a list with an array of estimates for each treatment. For a multinomial distribution with K + 1\n categories the arrays will have either K + 1 or K dimensions, depending on whether cluster-size\n specific estimates (type=\"cluster\") or pooled estimates (type=\"averaged\" or type=\"mc\") are\n requested. For the cluster-size specific estimates the first dimension is the cluster-size. Each addi-\n tional dimension is a possible outcome.\nSee Also\n mc.est for estimating the distribution under marginal compatibility, uniprobs and multi.corr for\n extracting the univariate marginal event probabilities, and the within-multinomial correlations from\n the joint probabilities.\nExamples\n data(dehp)\n # averaged over cluster-sizes\n tau.ave <- jointprobs(dehp, type=\"ave\")\n # averaged P(X1=X2=O1, X3=O2) in the 1500 dose group\n tau.ave[[\"1500\"]][\"2\",\"1\"] # there are two type-1, and one type-2 outcome\n #plot P(X1=O1) - the marginal probability of a type-1 event over cluster-sizes\n tau <- jointprobs(dehp, type=\"cluster\")\n ests <- as.data.frame(lapply(tau, function(x)x[,\"1\",\"0\"]))\n matplot(ests, type=\"b\")\n mc.est.CMData Distribution of the number of responses assuming marginal compati-\n bility.\nDescription\n The mc.est function estimates the distribution of the number of responses in a cluster under the\n assumption of marginal compatibility: information from all cluster sizes is pooled. The estimation\n is performed independently for each treatment group.\nUsage\n ## S3 method for class 'CMData'\n mc.est(object, eps = 1e-06, ...)\n ## S3 method for class 'CBData'\n mc.est(object, ...)\n mc.est(object, ...)\nArguments\n object a CBData or CMData object\n eps numeric; EM iterations proceed until the sum of squared changes fall below eps\n ... other potential arguments; not currently used\nDetails\n The EM algorithm given by Stefanescu and Turnbull (2003) is used for the binary data.\nValue\n For CMData: A data frame giving the estimated pdf for each treatment and clustersize. The proba-\n bilities add up to 1 for each Trt/ClusterSize combination. It has the following columns:\n Prob numeric, the probability of NResp responses in a cluster of size ClusterSize in\n group Trt\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n NResp.1 - NResp.K\n numeric, the number of responses of each type\n For CBData: A data frame giving the estimated pdf for each treatment and clustersize. The proba-\n bilities add up to 1 for each Trt/ClusterSize combination. It has the following columns:\n Prob numeric, the probability of NResp responses in a cluster of size ClusterSize in\n group Trt\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n NResp numeric, the number of responses\nNote\n For multinomial data, the implementation is currently written in R, so it is not very fast.\nAuthor(s)\n <NAME>\nReferences\n <NAME>, <NAME>, <NAME>, <NAME> (2016) On Exchangeable Multinomial Distributions. #’Biometrika\n 103(2), 397-408.\n <NAME>. & <NAME>. (2003) Likelihood inference for exchangeable binary data with\n varying cluster sizes. Biometrics, 59, 18-24\nExamples\n data(dehp)\n dehp.mc <- mc.est(subset(dehp, Trt==\"0\"))\n subset(dehp.mc, ClusterSize==2)\n data(shelltox)\n sh.mc <- mc.est(shelltox)\n library(lattice)\n xyplot(Prob~NResp|factor(ClusterSize), groups=Trt, data=sh.mc, subset=ClusterSize>0,\n type=\"l\", as.table=TRUE, auto.key=list(columns=4, lines=TRUE, points=FALSE),\n xlab=\"Number of responses\", ylab=\"Probability P(R=r|N=n)\")\n mc.test.chisq.CMData Test the assumption of marginal compatibility\nDescription\n mc.test.chisq tests whether the assumption of marginal compatibility is violated in the data.\nUsage\n ## S3 method for class 'CMData'\n mc.test.chisq(object, ...)\n ## S3 method for class 'CBData'\n mc.test.chisq(object, ...)\n mc.test.chisq(object, ...)\nArguments\n object a CBData or CMData object\n ... other potential arguments; not currently used\nDetails\n The assumption of marginal compatibility (AKA reproducibility or interpretability) implies that the\n marginal probability of response does not depend on clustersize. Stefanescu and Turnbull (2003),\n and Pang and Kuk (2007) developed a Cochran-Armitage type test for trend in the marginal prob-\n ability of success as a function of the clustersize. mc.test.chisq implements a generalization of\n that test extending it to multiple treatment groups.\nValue\n A list with the following components:\n overall.chi the test statistic; sum of the statistics for each group\n overall.p p-value of the test\n individual a list of the results of the test applied to each group separately:\n • chi.sq the test statistic for the group\n • p p-value for the group\nAuthor(s)\n <NAME>\nReferences\n <NAME>. & <NAME>. (2003) Likelihood inference for exchangeable binary data with\n varying cluster sizes. Biometrics, 59, 18-24\n Pang, Z. & <NAME>. (2007) Test of marginal compatibility and smoothing methods for exchangeable\n binary data with unequal cluster sizes. Biometrics, 63, 218-227\nSee Also\n mc.est for estimating the distribution under marginal compatibility.\nExamples\n data(dehp)\n mc.test.chisq(dehp)\n data(shelltox)\n mc.test.chisq(shelltox)\n multi.corr Extract correlation coefficients from joint probability arrays\nDescription\n Calculates the within- and between-outcome correlation coefficients for exchangeable correlated\n multinomial data based on joint probability estimates calculated by the jointprobs function. These\n determine the variance inflation due the cluster structure.\nUsage\n multi.corr(jp, type = attr(jp, \"type\"))\nArguments\n jp the output of jointprobs - a list of joint probability arrays by treatment\n type one of c(\"averaged\",\"cluster\",\"mc\") - the type of joint probability. By default,\n the type attribute of jp is used.\nDetails\n If Ri and Rj is the number of events of type i and j, respectively, in a cluster of size n, then\n V ar(Ri ) = npi (1 − pi )(1 + (n − 1)φii )\n Cov(Ri , Rj ) = −npi pj (1 + (n − 1)φij )\n where pi and pj are the marginal event probabilities and φij are the correlation coefficients com-\n puted by multi.corr.\nValue\n a list of estimated correlation matrices by treatment group. If cluster-size specific estimates were\n requested ((type=\"cluster\")), then each list elements are a list of these matrices for each cluster\n size.\nSee Also\n jointprobs for calculating the joint probability arrays\nExamples\n data(dehp)\n tau <- jointprobs(dehp, type=\"averaged\")\n multi.corr(tau)\n multinom.gen Functions for generating multinomial outcomes\nDescription\n These are built-in functions to be used by ran.CMData for generating random multinomial data.\nUsage\n mg.Resample(n, clustersizes, param)\n mg.DirMult(n, clustersizes, param)\n mg.LogitNorm(n, clustersizes, param)\n mg.MixMult(n, clustersizes, param)\nArguments\n n number of independent clusters to generate\n clustersizes an integer vector specifying the sizes of the clusters\n param a list of parameters for each specific generator\nDetails\n For mg.Resample: the param list should be list(param=...), in which the CMData object to be\n resampled is passed.\n For mg.DirMult: the param list should be list(shape=...), in which the parameter vector of the\n Dirichlet distribution is passed (see rdirichlet).\n For mg.LogitNorm: the param list should be list(mu=...,sigma=...), in which the mean vector\n and covariance matrix of the underlying Normal distribution are passed. If sigma is NULL (or\n missing), then an identity matrix is assumed. They should have K-1 dimensions for a K-variate\n multinomial.\n For mg.MixMult: the param list should be list(q=...,m=...), in which the vector of mixture\n probabilities q and the matrix m of logit-transformed means of each component are passed. For a\n K-variate multinomial, the matrixm should have K-1 columns and length(q) rows.\n NOSTASOT Finding the NOSTASOT dose\nDescription\n The NOSTASOT dose is the No-Statistical-Significance-Of-Trend dose – the largest dose at which\n no trend in the rate of response has been observed. It is often used to determine a safe dosage level\n for a potentially toxic compound.\nUsage\n NOSTASOT(\n cbdata,\n test = c(\"RS\", \"GEE\", \"GEEtrend\", \"GEEall\", \"SO\"),\n exact = test == \"SO\",\n R = 100,\n sig.level = 0.05,\n control = soControl()\n )\nArguments\n cbdata a CBData object\n test character string defining the desired test statistic. See trend.test for details.\n exact logical, should an exact permutation test be performed. See trend.test for\n details.\n R integer, number of permutations for the exact test\n sig.level numeric between 0 and 1, significance level of the test\n control an optional list of control settings for the stochastic order (\"SO\") test, usually\n a call to soControl. See there for the names of the settable control values and\n their effect.\nDetails\n A series of hypotheses about the presence of an increasing trend overall, with all but the last group,\n all but the last two groups, etc. are tested. Since this set of hypotheses forms a closed family, one\n can test these hypotheses in a step-down manner with the same sig.level type I error rate at each\n step and still control the family-wise error rate.\n The NOSTASOT dose is the largest dose at which the trend is not statistically significant. If the\n trend test is not significant with all the groups included, the largest dose is the NOSTASOT dose. If\n the testing sequence goes down all the way to two groups, and a significant trend is still detected,\n the lowest dose is the NOSTASOT dose. This assumes that the lowest dose is a control group, and\n this convention might not be meaningful otherwise.\nValue\n a list with two components\n NOSTASOT character string identifying the NOSTASOT dose.\n p numeric vector of the p-values of the tests actually performed.\n The last element corresponds to all doses included, and will not be missing. p-values for tests that\n were not actually performed due to the procedure stopping are set to NA.\nAuthor(s)\n <NAME>, <EMAIL>\nReferences\n <NAME>.; <NAME>. & <NAME>. (1985) Testing the statistical certainty of a response to\n increasing doses of a drug. Biometrics 41, 295-301.\nSee Also\n trend.test for details about the available trend tests.\nExamples\n data(shelltox)\n NOSTASOT(shelltox, test=\"RS\")\n pdf Parametric distributions for correlated binary data\nDescription\n qpower.pdf and betabin.pdf calculate the probability distribution function for the number of\n responses in a cluster of the q-power and beta-binomial distributions, respectively.\nUsage\n betabin.pdf(p, rho, n)\n qpower.pdf(p, rho, n)\nArguments\n p numeric, the probability of success.\n rho numeric between 0 and 1 inclusive, the within-cluster correlation.\n n integer, cluster size.\nDetails\n The pdf of the q-power distribution is\n \u0012 \u0013X x \u0012 \u0013\n n k x γ\n P (X = x) = (−1) q (n−x+k) ,\n x k\n x = 0, . . . , n, where q = 1 − p, and the intra-cluster correlation\n γ\n ρ= .\n The pdf of the beta-binomial distribution is\n \u0012 \u0013\n n B(α + x, n + β − x)\n P (X = x) = ,\n x B(α, β)\n x = 0, . . . , n, where α = p 1−ρ 1−ρ\n ρ , and α = (1 − p) ρ .\nValue\n a numeric vector of length n + 1 giving the value of P (X = x) for x = 0, . . . , n.\nAuthor(s)\n <NAME>, <EMAIL>\nReferences\n <NAME> (2004) Litter-based approach to risk assessment in developmental toxicity studies via a\n power family of completely monotone functions Applied Statistics, 52, 51-61.\n <NAME>. (1975) The Analysis of Binary Responses from Toxicological Experiments Involv-\n ing Reproduction and Teratogenicity Biometrics, 31, 949-952.\nSee Also\n ran.CBData for generating an entire dataset using these functions\nExamples\n #the distributions have quite different shapes\n #with q-power assigning more weight to the \"all affected\" event than other distributions\n plot(0:10, betabin.pdf(0.3, 0.4, 10), type=\"o\", ylim=c(0,0.34),\n ylab=\"Density\", xlab=\"Number of responses out of 10\")\n lines(0:10, qpower.pdf(0.3, 0.4, 10), type=\"o\", col=\"red\")\n ran.CBData Generate random correlated binary data\nDescription\n ran.mc.CBData generates a random CBData object from a given two-parameter distribution.\nUsage\n ran.CBData(\n sample.sizes,\n p.gen.fun = function(g) 0.3,\n rho.gen.fun = function(g) 0.2,\n pdf.fun = qpower.pdf\n )\nArguments\n sample.sizes a dataset with variables Trt, ClusterSize and Freq giving the number of clusters\n to be generated for each Trt/ClusterSize combination.\n p.gen.fun a function of one parameter that generates the value of the first parameter of\n pdf.fun (p) given the group number.\n rho.gen.fun a function of one parameter that generates the value of the second parameter of\n pdf.fun (rho) given the group number.\n pdf.fun a function of three parameters (p, rho, n) giving the PDF of the number of re-\n sponses in a cluster given the two parameters (p, rho), and the cluster size (n).\n Functions implementing two common distributions: the beta-binomial (betabin.pdf)\n and q-power (qpower.pdf) are provided in the package.\nDetails\n p.gen.fun and rho.gen.fun are functions that generate the parameter values for each treatment group;\n pdf.fun is a function generating the pdf of the number of responses given the two parameters p and\n rho, and the cluster size n.\n p.gen.fun and rho.gen.fun expect the parameter value of 1 to represent the first group, 2 - the\n second group, etc.\nValue\n a CBData object with randomly generated number of responses with sample sizes specified in the\n call.\nAuthor(s)\n <NAME>, <EMAIL>\nSee Also\n betabin.pdf and qpower.pdf\nExamples\n set.seed(3486)\n ss <- expand.grid(Trt=0:3, ClusterSize=5, Freq=4)\n #Trt is converted to a factor\n rd <- ran.CBData(ss, p.gen.fun=function(g)0.2+0.1*g)\n rd\n ran.CMData Generate a random CMData object\nDescription\n Generates random exchangeably correlated multinomial data based on a parametric distribution or\n using resampling. The Dirichlet-Multinomial, Logistic-Normal multinomial, and discrete mixture\n multinomial parametric distributions are implemented. All observations will be assigned to the\n same treatment group, and there is no guarantee of a specific order of the observations in the output.\nUsage\n ran.CMData(n, ncat, clustersize.gen, distribution)\nArguments\n n number of independent clusters to generate\n ncat number of response categories\n clustersize.gen\n either an integer vector specifying the sizes of the clusters, which will be recy-\n cled to achieve the target number of clusters n; or a function with one parameter\n that returns an integer vector of cluster sizes when the target number of clusters\n n is passed to it as a parameter\n distribution a list with two components: \"multinom.gen\" and \"param\" that specifies the gen-\n eration process for each cluster. The \"multinom.gen\" component should be a\n function of three parameters: number of clusters, vector of cluster sizes, and\n parameter list, that a matrix of response counts where each row is a cluster and\n each column is the number of responses of a given type. The \"param\" compo-\n nent should specify the list of parameters needed by the multinom.gen function.\nValue\n a CMData object with randomly generated number of responses with sample sizes specified in the\n call\nAuthor(s)\n <NAME>\nSee Also\n CMData for details about CMData objects; multinom.gen for built-in generating functions\nExamples\n # Resample from the dehp dataset\n data(dehp)\n ran.dehp <- ran.CMData(20, 3, 10, list(multinom.gen=mg.Resample, param=list(data=dehp)))\n # Dirichlet-Multinomial distribution with two treatment groups and random cluster sizes\n binom.cs <- function(n){rbinom(n, p=0.3, size=10)+1}\n dm1 <- ran.CMData(15, 4, binom.cs,\n list(multinom.gen=mg.DirMult, param=list(shape=c(2,3,2,1))))\n dm2 <- ran.CMData(15, 4, binom.cs,\n list(multinom.gen=mg.DirMult, param=list(shape=c(1,1,4,1))))\n ran.dm <- rbind(dm1, dm2)\n # Logit-Normal multinomial distribution\n ran.ln <- ran.CMData(13, 3, 3,\n list(multinom.gen=mg.LogitNorm,\n param=list(mu=c(-1, 1), sigma=matrix(c(1,0.8,0.8,2), nr=2))))\n # Mixture of two multinomial distributions\n unif.cs <- function(n){sample(5:9, size=n, replace=TRUE)}\n ran.mm <- ran.CMData(6, 3, unif.cs,\n list(multinom.gen=mg.MixMult,\n param=list(q=c(0.8,0.2), m=rbind(c(-1,0), c(0,2)))))\n read.CBData Read data from external file into a CBData object\nDescription\n A convenience function to read data from specially structured file directly into a CBData object.\nUsage\n read.CBData(file, with.freq = TRUE, ...)\nArguments\n file name of file with data. The first column should contain the treatment group, the\n second the size of the cluster, the third the number of responses in the cluster.\n Optionally, a fourth column could give the number of times the given combina-\n tion occurs in the data.\n with.freq logical indicator of whether a frequency variable is present in the file\n ... additional arguments passed to read.table\nValue\n a CBData object\nAuthor(s)\n <NAME>\nSee Also\n CBData\n read.CMData Read data from external file into a CMData object\nDescription\n A convenience function to read data from specially structured file directly into a CMData object.\n There are two basic data format options: etiher the counts of responses of all categories are given\n (and the cluster size is the sum of these counts), or the total cluster size is given with the counts\n of all but one category. The first column should always give the treatment group, then either the\n counts for each category (first option, chosen by setting with.clustersize = FALSE), or the size\n of the cluster followed by the counts for all but one category (second option, chosen by setting\n with.clustersize = TRUE). Optionally, a last column could give the number of times the given\n combination occurs in the data.\nUsage\n read.CMData(file, with.clustersize = TRUE, with.freq = TRUE, ...)\nArguments\n file name of file with data. The data in the file should be structured as described\n above.\n with.clustersize\n logical indicator of whether a cluster size variable is present in the file\n with.freq logical indicator of whether a frequency variable is present in the file\n ... additional arguments passed to read.table\nValue\n a CMData object\nAuthor(s)\n <NAME>\nSee Also\n CMData\n RS.trend.test Rao-Scott trend test\nDescription\n RS.trend.test implements the Rao-Scott adjusted Cochran-Armitage test for linear increasing\n trend with correlated data.\nUsage\n RS.trend.test(cbdata)\nArguments\n cbdata a CBData object\nDetails\n The test is based on calculating a design effect for each cluster by dividing the observed variability\n by the one expected under independence. The number of responses and the cluster size are then\n divided by the design effect, and a Cochran-Armitage type test statistic is computed based on these\n adjusted values.\n The implementation aims for testing for increasing trend, and a one-sided p-value is reported. The\n test statistic is asymptotically normally distributed, and a two-sided p-value can be easily computed\n if needed.\nValue\n A list with components\n statistic numeric, the value of the test statistic\n p.val numeric, asymptotic one-sided p-value of the test\nAuthor(s)\n <NAME>, <EMAIL>\nReferences\n Rao, <NAME>. & <NAME>. A (1992) Simple Method for the Analysis of Clustered Data Biometrics,\n 48, 577-586.\nSee Also\n SO.trend.test, GEE.trend.test for alternative tests; CBData for constructing a CBData object.\nExamples\n data(shelltox)\n RS.trend.test(shelltox)\n shelltox Shell Toxicology data\nDescription\n This is a classical developmental toxicology data set. Pregnant banded Dutch rabbits were treated\n with one of four levels of a chemical. The actual doses are not known, instead the groups are\n designated as Control, Low, Medium, and High. Before term the animals were sacrificed, and the\n total number of fetuses, as well as the number affected by the treatment was recorded.\nUsage\n data(shelltox)\nFormat\n A ’CBData’ object, that is a data frame with the following variables\n Trt factor giving treatment group\n ClusterSize the size of the litter\n NResp the number of affected fetuses\n Freq the number of litters with the given ClusterSize/NResp combination\nSource\n <NAME>. (1982) Analysis of proportions of affected foetuses in teratological experiments. Bio-\n metrics, 38, 361-370.\n This data set has been analyzed (and listed) in numerous papers, including\n <NAME>. & <NAME>. (1992) A Simple Method for the Analysis of Clustered Data. Biometrics,\n 48, 577-586.\n <NAME>. & <NAME>. (1996) Tests of Independence, Treatment Heterogeneity, and Dose-\n Related Trend With Exchangeable Binary Data. Journal of the American Statistical Association,\n 91, 1602-1610.\n <NAME>. (2003) Analysis of the Binary Littermate Data in the One-Way Layout. Biometrical Journal,\n 45, 195-206.\nExamples\n data(shelltox)\n stripchart(I(NResp/ClusterSize)~Trt, cex=sqrt(shelltox$Freq), data=shelltox, pch=1,\n method=\"jitter\", vertical=TRUE, ylab=\"Proportion affected\")\n SO.LRT Likelihood-ratio test statistic\nDescription\n SO.LRT computes the likelihood ratio test statistic for stochastic ordering against equality assuming\n marginal compatibility for both alternatives. Note that this statistic does not have a χ2 distribution,\n so the p-value computation is not straightforward. The SO.trend.test function implements a\n permutation-based evaluation of the p-value for the likelihood-ratio test.\nUsage\n SO.LRT(cbdata, control = soControl())\nArguments\n cbdata a CBData object\n control an optional list of control settings, usually a call to soControl. See there for the\n names of the settable control values and their effect.\nValue\n The value of the likelihood ratio test statistic is returned with two attributes:\n ll0 the log-likelihood under H0 (equality)\n ll1 the log-likelihood under Ha (stochastic order)\nAuthor(s)\n <NAME>\nSee Also\n SO.trend.test, soControl\nExamples\n data(shelltox)\n LRT <- SO.LRT(shelltox, control=soControl(max.iter = 100, max.directions = 50))\n LRT\n SO.mc.est Order-restricted MLE assuming marginal compatibility\nDescription\n SO.mc.est computes the nonparametric maximum likelihood estimate of the distribution of the\n number of responses in a cluster P (R = r|n) under a stochastic ordering constraint. Umbrella\n ordering can be specified using the turn parameter.\nUsage\n SO.mc.est(cbdata, turn = 1, control = soControl())\nArguments\n cbdata an object of class CBData.\n turn integer specifying the peak of the umbrella ordering (see Details). The default\n corresponds to a non-decreasing order.\n control an optional list of control settings, usually a call to soControl. See there for the\n names of the settable control values and their effect.\nDetails\n Two different algorithms: EM and ISDM are implemented. In general, ISDM (the default) should\n be faster, though its performance depends on the tuning parameter max.directions: values that\n are too low or too high slow the algorithm down.\n SO.mc.est allows extension to an umbrella ordering: D1 ≥st · · · ≥st Dk ≤st · · · ≤st Dn by\n specifying the value of k as the turn parameter. This is an experimental feature, and at this point\n none of the other functions can handle umbrella orderings.\nValue\n A list with components:\n Components Q and D are unlikely to be needed by the user.\n MLest data frame with the maximum likelihood estimates of P (Ri = r|n)\n Q numeric matrix; estimated weights for the mixing distribution\n D numeric matrix; directional derivative of the log-likelihood\n loglik the achieved value of the log-likelihood\n converge a 2-element vector with the achieved relative error and the performed number of\n iterations\nAuthor(s)\n <NAME>, <EMAIL>\nReferences\n Szabo A, George EO. (2010) On the Use of Stochastic Ordering to Test for Trend with Clustered\n Binary Data. Biometrika 97(1), 95-108.\nSee Also\n soControl\nExamples\n data(shelltox)\n ml <- SO.mc.est(shelltox, control=soControl(eps=0.01, method=\"ISDM\"))\n attr(ml, \"converge\")\n require(lattice)\n panel.cumsum <- function(x,y,...){\n x.ord <- order(x)\n panel.xyplot(x[x.ord], cumsum(y[x.ord]), ...)}\n xyplot(Prob~NResp|factor(ClusterSize), groups=Trt, data=ml, type=\"s\",\n panel=panel.superpose, panel.groups=panel.cumsum,\n as.table=TRUE, auto.key=list(columns=4, lines=TRUE, points=FALSE),\n xlab=\"Number of responses\", ylab=\"Cumulative Probability R(R>=r|N=n)\",\n ylim=c(0,1.1), main=\"Stochastically ordered estimates\\n with marginal compatibility\")\n SO.trend.test Likelihood ratio test of stochastic ordering\nDescription\n Performs a likelihood ratio test of stochastic ordering versus equality using permutations to estimate\n the null-distribution and the p-value. If only the value of the test statistic is needed, use SO.LRT\n instead.\nUsage\n SO.trend.test(cbdata, R = 100, control = soControl())\nArguments\n cbdata a CBData object.\n R an integer – the number of random permutations for estimating the null distribu-\n tion.\n control an optional list of control settings, usually a call to soControl. See there for the\n names of the settable control values and their effect.\nDetails\n The test is valid only under the assumption that the cluster-size distribution does not depend on\n group. During the estimation of the null-distribution the group assignments of the clusters are\n permuted keeping the group sizes constant; the within-group distribution of the cluster-sizes will\n vary randomly during the permutation test.\n The default value of R is probably too low for the final data analysis, and should be increased.\nValue\n A list with the following components\n LRT the value of the likelihood ratio test statistic. It has two attributes: ll0 and ll1\n - the values of the log-likelihood under H0 and Ha respectively.\n p.val the estimated one-sided p-value.\n boot.res an object of class \"boot\" with the detailed results of the permutations. See boot\n for details.\nAuthor(s)\n <NAME>, <EMAIL>\nReferences\n <NAME>, <NAME>. (2010) On the Use of Stochastic Ordering to Test for Trend with Clustered\n Binary Data. Biometrika 97(1), 95-108.\nSee Also\n SO.LRT for calculating only the test statistic, soControl\nExamples\n data(shelltox)\n set.seed(45742)\n sh.test <- SO.trend.test(shelltox, R=10, control=soControl(eps=0.1, max.directions=25))\n sh.test\n #a plot of the resampled LRT values\n #would look better with a reasonable value of R\n null.vals <- sh.test$boot.res$t[,1]\n hist(null.vals, breaks=10, freq=FALSE, xlab=\"Test statistic\", ylab=\"Density\",\n main=\"Simulated null-distribution\", xlim=range(c(0,20,null.vals)))\n points(sh.test$LRT, 0, pch=\"*\",col=\"red\", cex=3)\n soControl Control values for order-constrained fit\nDescription\n The values supplied in the function call replace the defaults and a list with all possible argu-\n ments is returned. The returned list is used as the control argument to the mc.est, SO.LRT, and\n SO.trend.test functions.\nUsage\n soControl(\n method = c(\"ISDM\", \"EM\"),\n eps = 0.005,\n max.iter = 5000,\n max.directions = 0,\n start = ifelse(method == \"ISDM\", \"H0\", \"uniform\"),\n verbose = FALSE\n )\nArguments\n method a string specifying the maximization method\n eps a numeric value giving the maximum absolute error in the log-likelihood\n max.iter an integer specifying the maximal number of iterations\n max.directions an integer giving the maximal number of directions considered at one step of the\n ISDM method. If zero or negative, it is set to the number of non-empty cells. A\n value of 1 corresponds to the VDM algorithm.\n start a string specifying the starting setup of the mixing distribution; \"H0\" puts weight\n only on constant vectors (corresponding to the null hypothesis of no change),\n \"uniform\" puts equal weight on all elements. Only a \"uniform\" start can be used\n for the \"EM\" algorithm.\n verbose a logical value; if TRUE details of the optimization are shown.\nValue\n a list with components for each of the possible arguments.\nAuthor(s)\n <NAME> <EMAIL>\nSee Also\n mc.est, SO.LRT, SO.trend.test\nExamples\n # decrease the maximum number iterations and\n # request the \"EM\" algorithm\n soControl(method=\"EM\", max.iter=100)\n trend.test Test for increasing trend with correlated binary data\nDescription\n The trend.test function provides a common interface to the trend tests implemented in this pack-\n age: SO.trend.test, RS.trend.test, and GEE.trend.test. The details of each test can be found\n on their help page.\nUsage\n trend.test(\n cbdata,\n test = c(\"RS\", \"GEE\", \"GEEtrend\", \"GEEall\", \"SO\"),\n exact = test == \"SO\",\n R = 100,\n control = soControl()\n )\nArguments\n cbdata a CBData object\n test character string defining the desired test statistic. \"RS\" performs the Rao-Scott\n test (RS.trend.test), \"SO\" performs the stochastic ordering test (SO.trend.test),\n \"GEE\", \"GEEtrend\", \"GEEall\" perform the GEE-based test (GEE.trend.test)\n with constant, linearly modeled, and freely varying scale parameters, respec-\n tively.\n exact logical, should an exact permutation test be performed. Only an exact test can\n be performed for \"SO\". The default is to use the asymptotic p-values except for\n \"SO\".\n R integer, number of permutations for the exact test\n control an optional list of control settings for the stochastic order (\"SO\") test, usually\n a call to soControl. See there for the names of the settable control values and\n their effect.\nValue\n A list with two components and an optional \"boot\" attribute that contains the detailed results of the\n permutation test as an object of class boot if an exact test was performed.\n statistic numeric, the value of the test statistic\n p.val numeric, asymptotic one-sided p-value of the test\nAuthor(s)\n <NAME>, <EMAIL>\nSee Also\n SO.trend.test, RS.trend.test, and GEE.trend.test for details about the available tests.\nExamples\n data(shelltox)\n trend.test(shelltox, test=\"RS\")\n set.seed(5724)\n #R=50 is too low to get a good estimate of the p-value\n trend.test(shelltox, test=\"RS\", R=50, exact=TRUE)\n uniprobs Extract univariate marginal probabilities from joint probability arrays\nDescription\n Calculates the marginal probability of each event type for exchangeable correlated multinomial data\n based on joint probability estimates calculated by the jointprobs function.\nUsage\n uniprobs(jp, type = attr(jp, \"type\"))\nArguments\n jp the output of jointprobs - a list of joint probability arrays by treatment\n type one of c(\"averaged\",\"cluster\",\"mc\") - the type of joint probability. By default,\n the type attribute of jp is used.\nValue\n a list of estimated probability of each outcome by treatment group. The elements are either matrices\n or vectors depending on whether cluster-size specific estimates were requested (type=\"cluster\")\n or not.\nSee Also\n jointprobs for calculating the joint probability arrays\nExamples\n data(dehp)\n tau <- jointprobs(dehp, type=\"averaged\")\n uniprobs(tau)\n #separately for each cluster size\n tau2 <- jointprobs(dehp, type=\"cluster\")\n uniprobs(tau2)\n unwrap.CBData Unwrap a clustered object\nDescription\n unwrap is a utility function that reformats a CBData or CMData object so that each row is one\n observation (instead of one or more clusters). A new ‘ID’ variable is added to indicate clusters.\n This form can be useful for setting up the data for a different package.\nUsage\n ## S3 method for class 'CBData'\n unwrap(object, ...)\n ## S3 method for class 'CMData'\n unwrap(object, ...)\n unwrap(object, ...)\nArguments\n object a CBData object\n ... other potential arguments; not currently used\nValue\n For unwrap.CMData: a data frame with one row for each cluster element (having a multinomial\n outcome) with the following standardized column names\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n ID factor, each level representing a different cluster\n Resp numeric with integer values giving the response type of the cluster element\n For unwrap.CBData: a data frame with one row for each cluster element (having a binary outcome)\n with the following standardized column names\n Trt factor, the treatment group\n ClusterSize numeric, the cluster size\n ID factor, each level representing a different cluster\n Resp numeric with 0/1 values, giving the response of the cluster element\nAuthor(s)\n <NAME>\nExamples\n data(dehp)\n dehp.long <- unwrap(dehp)\n head(dehp.long)\n data(shelltox)\n ush <- unwrap(shelltox)\n head(ush)"}}},{"rowIdx":59489,"cells":{"project":{"kind":"string","value":"r2redux"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘r2redux’\n September 19, 2023\nTitle R2 Statistic\nVersion 1.0.16\nDescription R2 statistic for significance test. Variance and covariance of R2 values used to as-\n sess the 95% CI and p-value of the R2 difference.\nLicense GPL (>= 3)\nURL https://github.com/mommy003/r2redux\nEncoding UTF-8\nRoxygenNote 7.1.2\nNeedsCompilation no\nDepends R (>= 2.10)\nLazyData true\nSuggests testthat (>= 3.0.0)\nConfig/testthat/edition 3\nAuthor <NAME> [aut, cph],\n <NAME> [aut, cre, cph]\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-09-19 06:50:02 UTC\nR topics documented:\ncc_tr... 2\ndat... 3\ndat... 4\nolkin12_... 4\nolkin12_1... 5\nolkin12_... 5\nolkin12_3... 6\nolkin1_... 6\nolkin_beta1_... 7\nolkin_beta_in... 8\nolkin_beta_rati... 9\nr2_beta_va... 10\nr2_dif... 12\nr2_enrich_bet... 18\nr2_va... 20\nr_dif... 23\n cc_trf cc_trf function\nDescription\n This function transforms the predictive ability (R2) and its standard error (se) between the observed\n scale and liability scale\nUsage\n cc_trf(R2, se, K, P)\nArguments\n R2 R2 or coefficient of determination on the observed or liability scale\n se Standard error of R2\n K Population prevalence\n P The ratio of cases in the study samples\nValue\n This function will transform the R2 and its s.e between observed scale and liability scale.Output\n from the command is the lists of outcomes.\n R2l Transformed R2 on the liability scale\n sel Transformed se on the liability scale\n R2O Transformed R2 on the observed scale\n seO Transformed se on the observed scale\nReferences\n <NAME>., <NAME>., <NAME>., and <NAME>. A better coefficient of determination\n for genetic profile analysis. Genetic epidemiology,(2012). 36(3): p. 214-224.\nExamples\n #To get the transformed R2\n output=cc_trf(0.06, 0.002, 0.05, 0.05)\n output\n #output$R2l (transformed R2 on the liability scale)\n #0.2679337\n #output$sel (transformed se on the liability scale)\n #0.008931123\n #output$R2O (transformed R2 on the observed scale)\n #0.01343616\n #output$seO (transformed se on the observed scale)\n #0.000447872\n dat1 Phenotypes and 10 sets of PGSs\nDescription\n A dataset containing phenotypes and multiple PGSs estimated from 10 sets of SNPs according to\n GWAS p-value thresholds\nUsage\n dat1\nFormat\n A data frame with 1000 rows and 11 variables:\n V1 Phenotype, value\n V2 PGS1, for p value threshold <=1\n V3 PGS2, for p value threshold <=0.5\n V4 PGS3, for p value threshold <=0.4\n V5 PGS4, for p value threshold <=0.3\n V6 PGS5, for p value threshold <=0.2\n V7 PGS6, for p value threshold <=0.1\n V8 PGS7, for p value threshold <=0.05\n V9 PGS8, for p value threshold <=0.01\n V10 PGS9, for p value threshold <=0.001\n V11 PGS10, for p value threshold <=0.0001\n dat2 Phenotypes and 2 sets of PGSs\nDescription\n A dataset containing phenotypes and 2 sets of PGSs estimated from 2 sets of SNPs from regulatroy\n and non-regulatory genomic regions\nUsage\n dat2\nFormat\n A data frame with 1000 rows and 3 variables:\n V1 Phenotype\n V2 PGS1, regulatory region\n V3 PGS2, non-regulatory region\n olkin12_1 olkin12_1 function\nDescription\n olkin12_1 function\nUsage\n olkin12_1(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will be used as source code\n olkin12_13 olkin12_13 function\nDescription\n olkin12_13 function\nUsage\n olkin12_13(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will be used as source code\n olkin12_3 olkin12_3 function\nDescription\n olkin12_3 function\nUsage\n olkin12_3(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will be used as source code\n olkin12_34 olkin12_34 function\nDescription\n olkin12_34 function\nUsage\n olkin12_34(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will be used as source code\n olkin1_2 olkin1_2 function\nDescription\n olkin1_2 function\nUsage\n olkin1_2(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will be used as source code\n olkin_beta1_2 olkin_beta1_2 function\nDescription\n This function derives Information matrix for beta1^2 and beta2^2 where beta1 and 2 are regression\n coefficients from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 + e, where y, x1\n and x2 are column-standardised, (i.e. in the context of correlation coefficients,see Olkin and Finn\n 1995).\nUsage\n olkin_beta1_2(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will give information (variance-covariance) matrix of beta1^2 and beta2^2.To get\n information (variance-covariance) matrix of beta1^2 and beta2^2. Where beta1 and beta2 are re-\n gression coefficients from a multiple regression model. The outputs are listed as follows.\n info 2x2 information (variance-covariance) matrix\n var1 Variance of beta1_2\n var2 Variance of beta2_2\n var1_2 Variance of difference between beta1_2 and beta2_2\nReferences\n <NAME>. and <NAME>. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.\nExamples\n #To get information (variance-covariance) matrix of beta1_2 and beta2_2 where\n #beta1 and 2 are regression coefficients from a multiple regression model.\n dat=dat1\n omat=cor(dat)[1:3,1:3]\n #omat\n #1.0000000 0.1958636 0.1970060\n #0.1958636 1.0000000 0.9981003\n #0.1970060 0.9981003 1.0000000\n nv=length(dat$V1)\n output=olkin_beta1_2(omat,nv)\n output\n #output$info (2x2 information (variance-covariance) matrix)\n #0.04146276 0.08158261\n #0.08158261 0.16111124\n #output$var1 (variance of beta1_2)\n #0.04146276\n #output$var2 (variance of beta2_2)\n #0.1611112\n #output$var1_2 (variance of difference between beta1_2 and beta2_2)\n #0.03940878\n olkin_beta_inf olkin_beta_inf function\nDescription\n This function derives Information matrix for beta1 and beta2 where beta1 and 2 are regression\n coefficients from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 + e, where y, x1 and\n x2 are column-standardised (see Olkin and Finn 1995).\nUsage\n olkin_beta_inf(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv Sample size\nValue\n This function will generate information (variance-covariance) matrix of beta1 and beta2.The outputs\n are listed as follows.\n info 2x2 information (variance-covariance) matrix\n var1 Variance of beta1\n var2 Variance of beta2\n var1_2 Variance of difference between beta1 and beta2\nReferences\n <NAME>. and <NAME>. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.\nExamples\n #To get information (variance-covariance) matrix of beta1 and beta2 where\n #beta1 and 2 are regression coefficients from a multiple regression model.\n dat=dat1\n omat=cor(dat)[1:3,1:3]\n #omat\n #1.0000000 0.1958636 0.1970060\n #0.1958636 1.0000000 0.9981003\n #0.1970060 0.9981003 1.0000000\n nv=length(dat$V1)\n output=olkin_beta_inf(omat,nv)\n output\n #output$info (2x2 information (variance-covariance) matrix)\n #0.2531406 -0.2526212\n #-0.2526212 0.2530269\n #output$var1 (variance of beta1)\n #0.2531406\n #output$var2 (variance of beta2)\n #0.2530269\n #output$var1_2 (variance of difference between beta1 and beta2)\n #1.01141\n olkin_beta_ratio olkin_beta_ratio function\nDescription\n This function derives variance of beta1^2 / R^2 where beta1 and 2 are regression coefficients from\n a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 + e, where y, x1 and x2 are column-\n standardised (see Olkin and Finn 1995).\nUsage\n olkin_beta_ratio(omat, nv)\nArguments\n omat 3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e.\n omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind\n (y,x1,x2)\n nv sampel size\nValue\n This function will generate the variance of the proportion, i.e. beta1_2/R^2.The outputs are listed\n as follows.\n ratio_var Variance of ratio\nReferences\n <NAME>. and <NAME>. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.\nExamples\n #To get information (variance-covariance) matrix of beta1 and beta2 where\n #beta1 and 2 are regression coefficients from a multiple regression model.\n dat=dat2\n omat=cor(dat)[1:3,1:3]\n #omat\n #1.0000000 0.1497007 0.136431\n #0.1497007 1.0000000 0.622790\n #0.1364310 0.6227900 1.000000\n nv=length(dat$V1)\n output=olkin_beta_ratio(omat,nv)\n output\n #r2redux output\n #output$ratio_var (Variance of ratio)\n #0.08042288\n r2_beta_var r2_beta_var\nDescription\n This function estimates var(beta1^2) and (beta2^2), and beta1 and 2 are regression coefficients\n from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 +e, y, x1 and x2 are column-\n standardised (see Olkin and Finn 1995). y is N by 1 matrix having the dependent variable, x1 is\n N by 1 matrix having the ith explanatory variable. x2 is N by 1 matrix having the jth explanatory\n variable. v1 and v2 indicates the ith and jth column in the data (v1 or v2 should be a single interger\n between 1 - M, see Arguments below).\nUsage\n r2_beta_var(dat, v1, v2, nv)\nArguments\n dat N by (M+1) matrix having variables in the order of cbind(y,x)\n v1 This can be set as v1=1, v1=2, v1=3 or any value between 1 - M based on\n combination\n v2 This can be set as v2=1, v2=2, v2=3, or any value between 1 - M based on\n combination\n nv Sample size\nValue\n This function will estiamte the variance of beta1^2 and beta2^2, and the covariance between beta1^2\n and beta2^2, i.e. the information matrix of squared regression coefficients. beta1 and beta2 are\n regression coefficients from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 +e, where\n y, x1 and x2 are column-standardised. The outputs are listed as follows.\n beta1_sq beta1_sq\n beta2_sq beta2_sq\n var1 Variance of beta1_sq\n var2 Variance of beta2_sq\n var1_2 Variance of difference between beta1_sq and beta2_sq\n cov Covariance between beta1_sq and beta2_sq\n upper_beta1_sq upper limit of 95% CI for beta1_sq\n lower_beta1_sq lower limit of 95% CI for beta1_sq\n upper_beta2_sq upper limit of 95% CI for beta2_sq\n lower_beta2_sq lower limit of 95% CI for beta2_sq\nReferences\n <NAME> <NAME>. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.\nExamples\n #To get the 95% CI of beta1_sq and beta2_sq\n #beta1 and beta2 are regression coefficients from a multiple regression model,\n #i.e. y = x1 * beta1 + x2 * beta2 +e, where y, x1 and x2 are column-standardised.\n dat=dat2\n nv=length(dat$V1)\n v1=c(1)\n v2=c(2)\n output=r2_beta_var(dat,v1,v2,nv)\n output\n #r2redux output\n #output$beta1_sq (beta1_sq)\n #0.01118301\n #output$beta2_sq (beta2_sq)\n #0.004980285\n #output$var1 (variance of beta1_sq)\n #7.072931e-05\n #output$var2 (variance of beta2_sq)\n #3.161929e-05\n #output$var1_2 (variance of difference between beta1_sq and beta2_sq)\n #0.000162113\n #output$cov (covariance between beta1_sq and beta2_sq)\n #-2.988221e-05\n #output$upper_beta1_sq (upper limit of 95% CI for beta1_sq)\n #0.03037793\n #output$lower_beta1_sq (lower limit of 95% CI for beta1_sq)\n #-0.00123582\n #output$upper_beta2_sq (upper limit of 95% CI for beta2_sq)\n #0.02490076\n #output$lower_beta2_sq (lower limit of 95% CI for beta2_sq)\n #-0.005127546\n r2_diff r2_diff function\nDescription\n This function estimates var(R2(y~x[,v1]) - R2(y~x[,v2])) where R2 is the R squared value of the\n model, y is N by 1 matrix having the dependent variable, and x is N by M matrix having M explana-\n tory variables. v1 or v2 indicates the ith column in the x matrix (v1 or v2 can be multiple values\n between 1 - M, see Arguments below)\nUsage\n r2_diff(dat, v1, v2, nv)\nArguments\n dat N by (M+1) matrix having variables in the order of cbind(y,x)\n v1 This can be set as v1=c(1) or v1=c(1,2)\n v2 This can be set as v2=c(2), v2=c(3), v2=c(1,3) or v2=c(3,4)\n nv Sample size\nValue\n This function will estimate significant difference between two PGS (either dependent or indepen-\n dent and joint or single). To get the test statistics for the difference between R2(y~x[,v1]) and\n R2(y~x[,v2]). (here we define R2_1=R2(y~x[,v1])) and R2_2=R2(y~x[,v2]))). The outputs are\n listed as follows.\n rsq1 R2_1\n rsq2 R2_2\n var1 Variance of R2_1\n var2 variance of R2_2\n var_diff Variance of difference between R2_1 and R2_2\n r2_based_p two tailed P-value for significant difference between R2_1 and R2_2\n r2_based_p_one_tail\n one tailed P-value for significant difference\n mean_diff Differences between R2_1 and R2_2\n upper_diff Upper limit of 95% CI for the difference\n lower_diff Lower limit of 95% CI for the difference\nExamples\n #To get the test statistics for the difference between R2(y~x[,1]) and\n #R2(y~x[,2]). (here we define R2_1=R2(y~x[,1])) and R2_2=R2(y~x[,2])))\n dat=dat1\n nv=length(dat$V1)\n v1=c(1)\n v2=c(2)\n output=r2_diff(dat,v1,v2,nv)\n output\n #r2redux output\n #output$rsq1 (R2_1)\n #0.03836254\n #output$rsq2 (R2_2)\n #0.03881135\n #output$var1 (variance of R2_1)\n #0.0001436128\n #output$var2 (variance of R2_2)\n #0.0001451358\n #output$var_diff (variance of difference between R2_1 and R2_2)\n #5.678517e-07\n #output$r2_based_p (two tailed p-value for significant difference)\n #0.5514562\n #output$r2_based_p_one_tail(one tailed p-value for significant difference)\n #0.2757281\n #output$mean_diff (differences between R2_1 and R2_2)\n #-0.0004488044\n #output$upper_diff (upper limit of 95% CI for the difference)\n #0.001028172\n #output$lower_diff (lower limit of 95% CI for the difference)\n #-0.001925781\n #output$$p$nested\n #1\n #output$$p$nonnested\n #0.5514562\n #output$$p$LRT\n #1\n #To get the test statistics for the difference between R2(y~x[,1]+x[,2]) and\n #R2(y~x[,2]). (here R2_1=R2(y~x[,1]+x[,2]) and R2_2=R2(y~x[,1]))\n dat=dat1\n nv=length(dat$V1)\n v1=c(1,2)\n v2=c(1)\n output=r2_diff(dat,v1,v2,nv)\n #r2redux output\n #output$rsq1 (R2_1)\n #0.03896678\n #output$rsq2 (R2_2)\n #0.03836254\n #output$var1 (variance of R2_1)\n #0.0001473686\n #output$var2 (variance of R2_2)\n #0.0001436128\n #output$var_diff (variance of difference between R2_1 and R2_2)\n #2.321425e-06\n #output$r2_based_p (p-value for significant difference between R2_1 and R2_2)\n #0.4366883\n #output$mean_diff (differences between R2_1 and R2_2)\n #0.0006042383\n #output$upper_diff (upper limit of 95% CI for the difference)\n #0.00488788\n #output$lower_diff (lower limit of 95% CI for the difference)\n #-0.0005576171\n #When faced with multiple predictors common between two models, for example,\n #y = any_cov1 + any_cov2 + ... + any_covN + e vs.\n #y = PRS + any_cov1 + any_cov2 +...+ any_covN + e\n #A more streamlined approach can be adopted by consolidating the various\n #predictors into a single predictor (see R code below).\n #R\n #dat=dat1\n #here let's assume, we wanted to test one PRS (dat$V2)\n #with 5 covariates (dat$V7 to dat$V11)\n #mod1 <- lm(dat$V1~dat$V2 + dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #merged_predictor1 <- mod1$fitted.values\n #mod2 <- lm(dat$V1~ dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #merged_predictor2 <- mod2$fitted.values\n #dat=data.frame(dat$V1,merged_predictor1,merged_predictor2)\n #the comparison can be equivalently expressed as:\n #y = merged_predictor1 + e vs.\n #y = merged_predictor2 + e\n #This comparison can be simply achieved using the r2_diff function, e.g.\n #To get the test statistics for the difference between R2(y~x[,1]) and\n #R2(y~x[,2]). (here x[,1]= merged_predictor2 (from full model),\n #and x[,2]= merged_predictor1(from reduced model))\n #v1=c(1)\n #v2=c(2)\n #output=r2_diff(dat,v1,v2,nv)\n #note that the merged predictor from the full model (v1) should be the first.\n #str(output)\n #List of 11\n #$ rsq1 : num 0.0428\n #$ rsq2 : num 0.042\n #$ var1 : num 0.0.000158\n #$ var2 : num 0.0.000156\n #$ var_diff : num 2.87e-06\n #$ r2_based_p : num 0.658\n #$ r2_based_p_one_tail: num 0.329\n #$ mean_diff : num 0.000751\n #$ upper_diff : num 0.00407\n #$ lower_diff : num -0.00257\n #$ p :List of 3\n #..$ nested : num 0.386\n #..$ nonnested: num 0.658\n #..$ LRT : num 0.376\n #Importantly note that in this case, merged_predictor1 is nested within\n #merged_predictor2 (see mod1 vs. mod2 above). Therefore, this is\n #nested model comparison. So, output$p$nested (0.386) should be used\n #instead of output$p$nonnested (0.658).\n #Note that r2_based_p is the same as output$p$nonnested (0.658) here.\n ##For this scenario, alternatively, the outcome variable (y) can be preadjusted\n #with covariate(s), following the procedure in R:\n #mod <- lm(y ~ any_cov1 + any_cov2 + ... + any_covN)\n #y_adj=scale(mod$residuals)\n #then, the comparative significance test can be approximated by using\n #the following model y_adj = PRS (r2_var(dat, v1, nv))\n #R\n #dat=dat1\n #mod <- lm(dat$V1~dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #y_adj=scale(mod$residuals)\n #dat=data.frame(y_adj,dat$V2)\n #v1=c(1)\n #output=r2_var(dat, v1, nv)\n #str(output)\n #$ var : num 2e-06\n #$ LRT_p :Class 'logLik' : 0.98 (df=2)\n #$ r2_based_p: num 0.977\n #$ rsq : num 8.21e-07\n #$ upper_r2 : num 0.00403\n #$ lower_r2 : num -0.000999\n #In another scenario where the same covariates, but different\n #PRS1 and PRS2 are compared,\n #y = PRS1 + any_cov1 + any_cov2 + ... + any_covN + e vs.\n #y = PRS2 + any_cov1 + any_cov2 + ... + any_covN + e\n #following approach can be employed (see R code below).\n #R\n #dat=dat1\n #here let's assume dat$V2 as PRS1, dat$V3 as PRS2 and dat$V7 to dat$V11 as covariates\n #mod1 <- lm(dat$V1~dat$V2 + dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #merged_predictor1 <- mod1$fitted.values\n #mod2 <- lm(dat$V1~dat$V3 + dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #merged_predictor2 <- mod2$fitted.values\n #dat=data.frame(dat$V1,merged_predictor2,merged_predictor1)\n #the comparison can be equivalently expressed as:\n #y = merged_predictor1 + e vs.\n #y = merged_predictor2 + e\n #This comparison can be simply achieved using the r2_diff function, e.g.\n #To get the test statistics for the difference between R2(y~x[,1]) and\n #R2(y~x[,2]). (here x[,1]= merged_predictor2, and x[,2]= merged_predictor1)\n #v1=c(1)\n #v2=c(2)\n #output=r2_diff(dat,v1,v2,nv)\n #str(output)\n #List of 11\n #$ rsq1 : num 0.043\n #$ rsq2 : num 0.0428\n #$ var1 : num 0.000159\n #$ var2 : num 0.000158\n #$ var_diff : num 2.6e-07\n #$ r2_based_p : num 0.657\n #$ r2_based_p_one_tail: num 0.328\n #$ mean_diff : num 0.000227\n #$ upper_diff : num 0.00123\n #$ lower_diff : num 0.000773\n #$ p :List of 3\n #..$ nested : num 0.634\n #..$ nonnested: num 0.657\n #..$ LRT : num 0.627\n #Importantly note that in this case, merged_predictor1 and merged_predictor2\n #are not nested to each other (see mod1 vs. mod2 above).\n #Therefore, this is nonnested model comparison.\n #So, output$p$nonnested (0.657) should be used instead of\n #output$p$nested (0.634). Note that r2_based_p is the same\n #as output$p$nonnested (0.657) here.\n #For the above non-nested scenario, alternatively, the outcome variable (y)\n #can be preadjusted with covariate(s), following the procedure in R:\n #mod <- lm(y ~ any_cov1 + any_cov2 + ... + any_covN)\n #y_adj=scale(mod$residuals)\n #R\n #dat=dat1\n #mod <- lm(dat$V1~dat$V7+ dat$V8+ dat$V9+ dat$V10+ dat$V11)\n #y_adj=scale(mod$residuals)\n #dat=data.frame(y_adj,dat$V3,dat$V2)\n #the comparison can be equivalently expressed as:\n #y_adj = PRS1 + e vs.\n #y_adj = PRS2 + e\n #then, the comparative significance test can be approximated by using r2_diff function\n #To get the test statistics for the difference between R2(y~x[,1]) and\n #R2(y~x[,2]). (here x[,1]= PRS1 and x[,2]= PRS2)\n #v1=c(1)\n #v2=c(2)\n #output=r2_diff(dat,v1,v2,nv)\n #str(output)\n #List of 11\n #$ rsq1 : num 5.16e-05\n #$ rsq2 : num 4.63e-05\n #$ var1 : num 2.21e-06\n #$ var2 : num 2.18e-06\n #$ var_diff : num 1.31e-09\n #$ r2_based_p : num 0.884\n #$ r2_based_p_one_tail: num 0.442\n #$ mean_diff : num 5.28e-06\n #$ upper_diff : num 7.63e-05\n #$ lower_diff : num -6.57e-05\n #$ p :List of 3\n #..$ nested : num 0.942\n #..$ nonnested: num 0.884\n #..$ LRT : num 0.942\n r2_enrich_beta r2_enrich_beta\nDescription\n This function estimates var(beta1^2/R^2), beta1 and R^2 are regression coefficient and the coeffi-\n cient of determination from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 +e, where\n y, x1 and x2 are column-standardised (see Olkin and Finn 1995). y is N by 1 matrix having the\n dependent variable, and x1 is N by 1 matrix having the ith explanatory variables. x2 is N by 1\n matrix having the jth explanatory variables. v1 and v2 indicates the ith and jth column in the data\n (v1 or v2 should be a single interger between 1 - M, see Arguments below).\nUsage\n r2_enrich_beta(dat, v1, v2, nv, exp1)\nArguments\n dat N by (M+1) matrix having variables in the order of cbind(y,x)\n v1 These can be set as v1=1, v1=2, v1=3 or any value between 1 - M based on\n combination\n v2 These can be set as v2=1, v2=2, v2=3, or any value between 1 - M based on\n combination\n nv Sample size\n exp1 The expectation of the ratio (e.g. ratio of # SNPs in genomic partitioning)\nValue\n This function will estimate var(beta1^2/R^2), beta1 and R^2 are regression coefficient and the co-\n efficient of determination from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 +e,\n where y, x1 and x2 are column-standardised. The outputs are listed as follows.\n beta1_sq beta1_sq\n beta2_sq beta2_sq\n ratio1 beta1_sq/R^2\n ratio2 beta2_sq/R^2\n ratio_var1 variance of ratio 1\n ratio_var2 variance of ratio 2\n upper_ratio1 upper limit of 95% CI for ratio 1\n lower_ratio1 lower limit of 95% CI for ratio 1\n upper_ratio2 upper limit of 95% CI for ratio 2\n lower_ratio2 lower limit of 95% CI for ratio 2\n enrich_p1 two tailed P-value for beta1_sq/R^2 is significantly different from exp1\n enrich_p1_one_tail\n one tailed P-value for beta1_sq/R^2 is significantly different from exp1\n enrich_p2 P-value for beta2_sq/R2 is significantly different from (1-exp1)\n enrich_p2_one_tail\n one tailed P-value for beta2_sq/R2 is significantly different from (1-exp1)\nReferences\n <NAME>. and <NAME>. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.\nExamples\n #To get the test statistic for the ratio which is significantly\n #different from the expectation, this function estiamtes\n #var (beta1^2/R^2), where\n #beta1^2 and R^2 are regression coefficients and the\n #coefficient of dterminationfrom a multiple regression model,\n #i.e. y = x1 * beta1 + x2 * beta2 +e, where y, x1 and x2 are\n #column-standardised.\n dat=dat2\n nv=length(dat$V1)\n v1=c(1)\n v2=c(2)\n expected_ratio=0.04\n output=r2_enrich_beta(dat,v1,v2,nv,expected_ratio)\n output\n #r2redux output\n #output$beta1_sq (beta1_sq)\n #0.01118301\n #output$beta2_sq (beta2_sq)\n #0.004980285\n #output$ratio1 (beta1_sq/R^2)\n #0.4392572\n #output$ratio2 (beta2_sq/R^2)\n #0.1956205\n #output$ratio_var1 (variance of ratio 1)\n #0.08042288\n #output$ratio_var2 (variance of ratio 2)\n #0.0431134\n #output$upper_ratio1 (upper limit of 95% CI for ratio 1)\n #0.9950922\n #output$lower_ratio1 (lower limit of 95% CI for ratio 1)\n #-0.1165778\n #output$upper_ratio2 upper limit of 95% CI for ratio 2)\n #0.6025904\n #output$lower_ratio2 (lower limit of 95% CI for ratio 2)\n #-0.2113493\n #output$enrich_p1 (two tailed P-value for beta1_sq/R^2 is\n #significantly different from exp1)\n #0.1591692\n #output$enrich_p1_one_tail (one tailed P-value for beta1_sq/R^2\n #is significantly different from exp1)\n #0.07958459\n #output$enrich_p2 (two tailed P-value for beta2_sq/R2 is\n #significantly different from (1-exp1))\n #0.000232035\n #output$enrich_p2_one_tail (one tailed P-value for beta2_sq/R2\n #is significantly different from (1-exp1))\n #0.0001160175\n r2_var r2_var function\nDescription\n This function estimates var(R2(y~x[,v1])) where R2 is the R squared value of the model, where R2\n is the R squared value of the model, y is N by 1 matrix having the dependent variable, and x is N\n by M matrix having M explanatory variables. v1 indicates the ith column in the x matrix (v1 can be\n multiple values between 1 - M, see Arguments below)\nUsage\n r2_var(dat, v1, nv)\nArguments\n dat N by (M+1) matrix having variables in the order of cbind(y,x)\n v1 This can be set as v1=c(1), v1=c(1,2) or possibly with more values\n nv Sample size\nValue\n This function will test the null hypothesis for R2. To get the test statistics for R2(y~x[,v1]). The\n outputs are listed as follows.\n rsq R2\n var Variance of R2\n r2_based_p P-value under the null hypothesis, i.e. R2=0\n upper_r2 Upper limit of 95% CI for R2\n lower_r2 Lower limit of 95% CI for R2\nExamples\n #To get the test statistics for R2(y~x[,1])\n dat=dat1\n nv=length(dat$V1)\n v1=c(1)\n output=r2_var(dat,v1,nv)\n output\n #r2redux output\n #output$rsq (R2)\n #0.03836254\n #output$var (variance of R2)\n #0.0001436128\n #output$r2_based_p (P-value under the null hypothesis, i.e. R2=0)\n #1.188162e-10\n #output$upper_r2 (upper limit of 95% CI for R2)\n #0.06433782\n #output$lower_r2 (lower limit of 95% CI for R2)\n #0.01764252\n #To get the test statistic for R2(y~x[,1]+x[,2]+x[,3])\n dat=dat1\n nv=length(dat$V1)\n v1=c(1,2,3)\n r2_var(dat,v1,nv)\n #r2redux output\n #output$rsq (R2)\n #0.03836254\n #output$var (variance of R2)\n #0.0001436128\n #output$r2_based_p (R2 based P-value)\n #1.188162e-10\n #output$upper_r2 (upper limit of 95% CI for R2)\n #0.06433782\n #output$lower_r2 (lower limit of 95% CI for R2)\n #0.0176425\n #When comparing two independent sets of PGSs\n #Let’s assume dat1$V1 and dat2$V2 are independent for this example\n #(e.g. male PGS vs. female PGS)\n nv=length(dat1$V1)\n v1=c(1)\n output1=r2_var(dat1,v1,nv)\n nv=length(dat2$V1)\n v1=c(1)\n output2=r2_var(dat2,v1,nv)\n #To get the difference between two independent sets of PGSs\n r2_diff_independent=abs(output1$rsq-output2$rsq)\n #To get the variance of the difference between two independent sets of PGSs\n var_r2_diff_independent= output1$var+output2$var\n sd_r2_diff_independent=sqrt(var_r2_diff_independent)\n #To get p-value (following eq. 15 in the paper)\n chi=r2_diff_independent^2/var_r2_diff_independent\n p_value=pchisq(chi,1,lower.tail=FALSE)\n #to get 95% CI (following eq. 15 in the paper)\n uci=r2_diff_independent+1.96*sd_r2_diff_independent\n lci=r2_diff_independent-1.96*sd_r2_diff_independent\n r_diff r_diff function\nDescription\n This function estimates var(R(y~x[,v1]) - R(y~x[,v2])) where R is the correlation between y and x,\n y is N by 1 matrix having the dependent variable, and x is N by M matrix having M explanatory\n variables. v1 or v2 indicates the ith column in the x matrix (v1 or v2 can be multiple values between\n 1 - M, see Arguments below)\nUsage\n r_diff(dat, v1, v2, nv)\nArguments\n dat N by (M+1) matrix having variables in the order of cbind(y,x)\n v1 This can be set as v1=c(1) or v1=c(1,2)\n v2 This can be set as v2=c(2), v2=c(3), v2=c(1,3) or v2=c(3,4)\n nv Sample size\nValue\n This function will estimate significant difference between two PGS (either dependent or indepen-\n dent and joint or single). To get the test statistics for the difference between R(y~x[,v1]) and\n R(y~x[,v2]). (here we define R_1=R(y~x[,v1])) and R_2=R(y~x[,v2]))). The outputs are listed\n as follows.\n r1 R_1\n r2 R_2\n var1 Variance of R_1\n var2 variance of R_2\n var_diff Variance of difference between R_1 and R_2\n r2_based_p P-value for significant difference between R_1 and R_2 for two tailed test\n r_based_p_one_tail\n P-value for significant difference between R_1 and R_2 for one tailed test\n mean_diff Differences between R_1 and R_2\n upper_diff Upper limit of 95% CI for the difference\n lower_diff Lower limit of 95% CI for the difference\nExamples\n #To get the test statistics for the difference between R(y~x[,1]) and\n #R(y~x[,2]). (here we define R_1=R(y~x[,1])) and R_2=R(y~x[,2])))\n dat=dat1\n nv=length(dat$V1)\n v1=c(1)\n v2=c(2)\n output=r_diff(dat,v1,v2,nv)\n output\n #r2redux output\n #output$r1 (R_1)\n #0.1958636\n #output$r2 (R_2)\n #0.197006\n #output$var1 (variance of R_1)\n #0.0009247466\n #output$var2 (variance of R_1)\n #0.0001451358\n #output$var_diff (variance of difference between R_1 and R_2)\n #3.65286e-06\n #output$r_based_p (two tailed p-value for significant difference between R_1 and R_2)\n #0.5500319\n #output$r_based_p_one_tail (one tailed p-value\n #0.2750159\n #output$mean_diff\n #-0.001142375 (differences between R2_1 and R2_2)\n #output$upper_diff (upper limit of 95% CI for the difference)\n #0.002603666\n #output$lower_diff (lower limit of 95% CI for the difference)\n #-0.004888417\n #To get the test statistics for the difference between R(y~x[,1]+[,2]) and\n #R(y~x[,2]). (here R_1=R(y~x[,1]+x[,2]) and R_2=R(y~x[,1]))\n nv=length(dat$V1)\n v1=c(1,2)\n v2=c(2)\n output=r_diff(dat,v1,v2,nv)\n output\nr_diff 25\n #output$r1\n #0.1974001\n #output$r2\n #0.197006\n #output$var1\n #0.0009235848\n #output$var2\n #0.0009238836\n #output$var_diff\n #3.837451e-06\n #output$r2_based_p\n #0.8405593\n #output$mean_diff\n #0.0003940961\n #output$upper_diff\n #0.004233621\n #output$lower_diff\n #-0.003445429"}}},{"rowIdx":59490,"cells":{"project":{"kind":"string","value":"flashClust"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘flashClust’\n October 13, 2022\nVersion 1.01-2\nDate 2012-08-21\nTitle Implementation of optimal hierarchical clustering\nAuthor code by <NAME> and R development team, modifications and\n packaging by <NAME>\nMaintainer <NAME> <<EMAIL>>\nDepends R (>= 2.3.0)\nZipData no\nLicense GPL (>= 2)\nDescription Fast implementation of hierarchical clustering\nRepository CRAN\nDate/Publication 2012-08-21 18:23:43\nNeedsCompilation yes\nR topics documented:\nflashClus... 1\n flashClust Faster alternative to hclust\nDescription\n This function implements optimal hierarchical clustering with the same interface as hclust.\nUsage\n hclust(d, method = \"complete\", members=NULL)\n flashClust(d, method = \"complete\", members=NULL)\nArguments\n d a dissimilarity structure as produced by ’dist’.\n method the agglomeration method to be used. This should be (an unambiguous abbre-\n viation of) one of \"ward\", \"single\", \"complete\", \"average\", \"mcquitty\",\n \"median\" or \"centroid\".\n members NULL or a vector with length size of d. See the ‘Details’ section.\nDetails\n See the description of hclust for details on available clustering methods.\n If members!=NULL, then d is taken to be a dissimilarity matrix between clusters instead of dissim-\n ilarities between singletons and members gives the number of observations per cluster. This way\n the hierarchical cluster algorithm can be ‘started in the middle of the dendrogram’, e.g., in order\n to reconstruct the part of the tree above a cut (see examples). Dissimilarities between clusters can\n be efficiently computed (i.e., without hclust itself) only for a limited number of distance/linkage\n combinations, the simplest one being squared Euclidean distance and centroid linkage. In this case\n the dissimilarities between the clusters are the squared Euclidean distances between cluster means.\n flashClust is a wrapper for compatibility with older code.\nValue\n Returned value is the same as that of hclust: An object of class hclust which describes the tree\n produced by the clustering process. The object is a list with components:\n merge an n − 1 by 2 matrix. Row i of merge describes the merging of clusters at step i\n of the clustering. If an element j in the row is negative, then observation −j was\n merged at this stage. If j is positive then the merge was with the cluster formed\n at the (earlier) stage j of the algorithm. Thus negative entries in merge indicate\n agglomerations of singletons, and positive entries indicate agglomerations of\n non-singletons.\n height a set of n − 1 non-decreasing real values. The clustering height: that is, the\n value of the criterion associated with the clustering method for the particular\n agglomeration.\n order a vector giving the permutation of the original observations suitable for plotting,\n in the sense that a cluster plot using this ordering and matrix merge will not have\n crossings of the branches.\n labels labels for each of the objects being clustered.\n call the call which produced the result.\n method the cluster method that has been used.\n dist.method the distance that has been used to create d (only returned if the distance object\n has a \"method\" attribute).\nAuthor(s)\n <NAME>, adapted and packaged by <NAME>der\nReferences\n This implementation is mentioned in\n Peter Langfelder, <NAME> (2012) Fast R Functions for Robust Correlations and Hierarchical\n Clustering. Journal of Statistical Software, 46(11), 1-17. http://www.jstatsoft.org/v46/i11/\n F.Murtagh’s software web site: http://www.classification-society.org/csna/mda-sw/ , section 6\n <NAME>., <NAME>. and <NAME>. (1988) The New S Language. Wadsworth \\&\n Brooks/Cole. (S version.)\n <NAME>. (1974). Cluster Analysis. London: Heinemann Educ. Books.\n <NAME>. (1975). Clustering Algorithms. New York: Wiley.\n Sneath, <NAME>. and <NAME> (1973). Numerical Taxonomy. San Francisco: Freeman.\n Anderberg, <NAME>. (1973). Cluster Analysis for Applications. Academic Press: New York.\n <NAME>. (1999). Classification. Second Edition. London: Chapman and Hall / CRC\n Murtagh, F. (1985). “Multidimensional Clustering Algorithms”, in COMPSTAT Lectures 4. Wuerzburg:\n Physica-Verlag (for algorithmic details of algorithms used).\n <NAME>. (1966). Similarity Analysis by Reciprocal Pairs for Discrete and Continuous Data.\n Educational and Psychological Measurement, 26, 825–831.\nSee Also\n hclust\nExamples\n # generate some data to cluster\n set.seed(1);\n nNodes = 2000;\n # Random \"distance\" matrix\n dst = matrix(runif(n = nNodes^2, min = 0, max = 1), nNodes, nNodes);\n # Time the flashClust clustering\n system.time( {\n h1 = hclust(as.dist(dst), method= \"average\");\n } );\n # Time the standard R clustering\n system.time( {\n h2 = stats::hclust(as.dist(dst), method = \"average\");\n } );\n all.equal(h1, h2)\n # What is different:\n h1[[6]]\n h2[[6]]\n # Everything but the 'call' component is the same; in particular, the trees are exactly equal."}}},{"rowIdx":59491,"cells":{"project":{"kind":"string","value":"bartCause"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘bartCause’\n January 23, 2023\nVersion 1.0-6\nDate 2023-01-23\nTitle Causal Inference using Bayesian Additive Regression Trees\nDepends R (>= 3.1-0)\nImports dbarts (>= 0.9-16), methods, stats, graphics, parallel, utils,\n grDevices\nSuggests testthat (>= 0.9-0), lme4, rpart, tmle, stan4bart\nDescription Contains a variety of methods to generate typical causal inference estimates us-\n ing Bayesian Additive Regression Trees (BART) as the underlying regres-\n sion model (Hill (2012) <doi:10.1198/jcgs.2010.08162>).\nLicense GPL (>= 2)\nNeedsCompilation no\nURL https://github.com/vdorie/bartCause\nBugReports https://github.com/vdorie/bartCause/issues\nAuthor <NAME> [aut, cre] (<https://orcid.org/0000-0002-9576-3064>),\n <NAME> [aut] (<https://orcid.org/0000-0003-4983-2206>)\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-01-23 19:40:08 UTC\nR topics documented:\nbart... 2\nbartc-generic... 8\nbartc-plo... 11\nsummary.bartcFi... 14\n bartc Causal Inference using Bayesian Additive Regression Trees\nDescription\n Fits a collection of treatment and response models using the Bayesian Additive Regression Trees\n (BART) algorithm, producing estimates of treatment effects.\nUsage\n bartc(response, treatment, confounders, parametric, data, subset, weights,\n method.rsp = c(\"bart\", \"tmle\", \"p.weight\"),\n method.trt = c(\"bart\", \"glm\", \"none\"),\n estimand = c(\"ate\", \"att\", \"atc\"),\n group.by = NULL,\n commonSup.rule = c(\"none\", \"sd\", \"chisq\"),\n commonSup.cut = c(NA_real_, 1, 0.05),\n args.rsp = list(), args.trt = list(),\n p.scoreAsCovariate = TRUE, use.ranef = TRUE, group.effects = FALSE,\n crossvalidate = FALSE,\n keepCall = TRUE, verbose = TRUE,\n seed = NA_integer_,\n ...)\nArguments\n response A vector of the outcome variable, or a reference to such in the data argument.\n Can be continuous or binary.\n treatment A vector of the binary treatment variable, or a reference to data.\n confounders A matrix or data frame of covariates to be used in estimating the treatment and\n response model. Can also be the right-hand-side of a formula (e.g. x1 + x2 +\n ...). The data argument will be searched if supplied.\n parametric The right-hand-side of a formula (e.g. x1 + x2 + (1 | g) ...) giving the equa-\n tion of a parametric form to be used for estimating the mean structure. See the\n details section below.\n data An optional data frame or named list containing the response, treatment, and\n confounders.\n subset An optional vector using to subset the data. Can refer to data if provided.\n weights An optional vector of population weights used in model fitting and estimating\n the treatment effect. Can refer to data if provided.\n method.rsp A character string specifying which method to use when fitting the response sur-\n face and estimating the treatment effect. Options are: \"bart\" - fit the response\n surface with BART and take the average of the individual treatment effect esti-\n mates, \"p.weight\" - fit the response surface with BART but compute the treat-\n ment effect estimate by using a propensity score weighted sum of individual\n effects, and \"tmle\" - as above, but further adjust the individual estimates using\n the Targeted Minimum Loss based Estimation (TMLE) adjustment.\n method.trt A character string specifying which method to use when fitting the treatment\n assignment mechanism, or a vector/matrix of propensity scores. Character string\n options are: \"bart\" - fit BART directly to the treatment variable, \"glm\" - fit a\n generalized linear model with a binomial response and all confounders added\n linearly, and \"none\" - do no propensity score estimation. Cannot be \"none\" if\n the response model requires propensity scores. When supplied as a matrix, it\n should be of dimensions equal to the number of observations times the number\n of samples used in any response model.\n estimand A character string specifying which causal effect to target. Options are \"ate\"\n - average treatment effect, \"att\" - average treatment effect on the treated, and\n \"atc\" - average treatment effect on the controls.\n group.by An optional factor that, when present, causes the treatment effect estimate to be\n calculated within each group.\n commonSup.rule Rule for exclusion of observations lacking in common support. Options are\n \"none\" - no suppression, \"sd\" - exclude units whose predicted counterfactual\n standard deviation is extreme compared to the maximum standard deviation un-\n der those units’ observed treatment condition, where extreme refers to the dis-\n tribution of all standard deviations of observed treatment conditions, \"chisq\"\n - exclude observations according to ratio of the variance of posterior predicted\n counterfactual to the posterior variance of the observed condition, having a Chi\n Squared distribution with one degree of freedom under the null hypothesis of\n have equal distributions.\n commonSup.cut Cutoffs for commonSup.rule. Ignored for \"none\", when commonSup.rule is\n \"sd\", refers to how many standard deviations of the distribution of posterior\n variance for counterfactuals an observation can be above the maximum of poste-\n rior variances for that treatment condition. When commonSup.rule is \"chisq\",\n is the p value used for rejection of the hypothesis of equal variances.\n p.scoreAsCovariate\n A logical such that when TRUE, the propensity score is added to the response\n model as a covariate. When used, this is equivalent to the ’ps-BART’ method\n described by described by Hahn, Murray, and Carvalho.\n use.ranef Logical specifying if group.by variable - when present - should be included as a\n \"random\" or \"fixed\" effect. If true, rbart will be used for BART models. Using\n random effects for treatment assignment mechanisms of type \"glm\" require that\n the lme4 package be available.\n group.effects Logical specifying if effects should be calculated within groups if the group.by\n variable is provided. Response methods of \"tmle\" and \"p.weight\" are such\n that if group effects are calculated, then the population effect is not provided.\n keepCall A logical such that when FALSE, the call to bartc is not kept. This can reduce\n the amount of information printed by summary when passing in data as literals.\n crossvalidate One of TRUE, FALSE, \"trt\", or \"rsp\". Enables code to attempt to estimate\n the optimal end-node sensitivity parameter. This uses a rudimentary Bayesian\n optimization routine and can be extremely slow.\n verbose A logical that when TRUE prints information as the model is fit.\n seed Optional integer specifying the desired pRNG seed. It should not be needed\n when running single-threaded - set.seed will suffice, and can be used to obtain\n reproducible results when multi-threaded. See Reproducibility section of bart2.\n args.rsp, args.trt, ...\n Further arguments to the treatment and response model fitting algorithms. Argu-\n ments passed to the main function as . . . will be used in both models. args.rsp\n and args.trt can be used to set parameters in a single fit, and will override\n other values. See glm and bart2 for reference.\nDetails\n bartc represents a collection of methods that primarily use the Bayesian Additive Regression Trees\n (BART) algorithm to estimate causal treatment effects with binary treatment variables and contin-\n uous or binary outcomes. This requires models to be fit to the response surface (distribution of the\n response as a function of treatment and confounders, p(Y (1), Y (0)|X) and optionally for treatment\n assignment mechanism (probability of receiving treatment, i.e. propensity score, P r(Z = 1|X)).\n The response surface model is used to impute counterfactuals, which may then be adjusted together\n with the propensity score to produce estimates of effects.\n Similar to lm, models can be specified symbolically. When the data term is present, it will be added\n to the search path for the response, treatment, and confounders variables. The confounders must\n be specified devoid of any \"left hand side\", as they appear in both of the models.\n Response Surface\n The response surface methods included are:\n • \"bart\" - use BART to fit the response surface and produce individual estimates Ŷ (1)i and\n Ŷ (0)i . Treatment effect estimates are obtained by averaging the difference of these across the\n population of interest.\n • \"p.weight\" - individual effects are estimated as in \"bart\", but treatment effect estimates are\n obtained by using a propensity score weighted\n P average. For the average treatment effect on\n the treated, these weights are p(zi |xi )/( z/n). For ATC, replace z with 1 − z. For ATE,\n \"p.weight\" is equal to \"bart\".\n • \"tmle\" - individual effects are estimated as in \"bart\" and a weighted average is taken as in\n \"p.weight\", however the response surface estimates and propensity scores are corrected by\n using the Targeted Minimum Loss based Estimation method.\n Treatment Assignment\n The treatment assignment models are:\n • \"bart\" - fit a binary BART directly to the treatment using all the confounders.\n • \"none\" - no modeling is done. Only applies when using response method \"bart\" and p.scoreAsCovariate\n is FALSE.\n • \"glm\" - fit a binomial generalized linear model with logistic link and confounders included as\n linear terms.\n • Finally, a vector or matrix of propensity scores can be supplied. Propensity score matrices\n should have a number of rows equal to the number of observations in the data and a number\n of columns equal to the number of posterior samples.\n Parametrics\n bartc uses the stan4bart package, when available, to fit semi- parametric surfaces. Equations can\n be given as to lm. Grouping structures are also permitted, and use the syntax of lmer.\n Generics\n For a fitted model, the easiest way to analyze the resulting fit is to use the generics fitted, extract,\n and predict to analyze specific quantities and summary to aggregate those values into targets (e.g.\n ATE, ATT, or ATC).\n Common Support Rules\n Common support, or that the probability of receiving all treatment conditions is non-zero within\n every area of the covariate space (P (Z = 1|X = x) > 0 for all x in the inferential sample), can be\n enforced by excluding observations with high posterior uncertainty. bartc supports two common\n support rules through commonSup.rule argument:\n • \"sd\" - observations are cut from the inferential sample if: si > mz +a×sd(sj , where\n f (1−z)\n si is the posteriors standard deviation of the predicted counterfactual for observation i,\n f\n sj (z) is the posterior standard deviation of the prediction for the observed treatment condition\n f (z)\n of observation j, sd(sj is the empirical standard deviation of those quantities, and mz =\n f (z)\n maxj {sj } for all j in the same treatment group, i.e. Zj = z. a is a constant to be passed\n in using commonSup.cut and its default is 1.\n • \"chisq\" - observations are cut from the inferential sample if: (si /si )2 > qα , where\n si are as above and qα , is the upper α percentile of a χ distribution with one degree of\n freedom, corresponding to a null hypothesis of equal variance. The default for α is 0.05, and\n it is specified using the commonSup.cut parameter.\n Special Arguments\n Some default arguments are unconventional or are passed in a unique fashion.\n • If n.chains is missing, unlike in bart2 a default of 10 is used.\n • For method.rsp == \"tmle\", a special arg.trt of posteriorOfTMLE determines if the TMLE\n correction should be applied to each posterior sample (TRUE), or just the posterior mean\n (FALSE).\n Missing Data\n Missingness is allowed only in the response. If some response values are NA, the BART models\n will be trained just for where data are available and those values will be used to make predictions\n for the missing observations. Missing observations are not used when calculating statistics for\n assessing common support, although they may still be excluded on those grounds. Further, missing\n observations may not be compatible with response method \"tmle\".\nValue\n bartc returns an object of class bartcFit. Information about the object can be derived by using\n methods summary, plot_sigma, plot_est, plot_indiv, and plot_support. Numerical quantities\n are recovered with the fitted and extract generics. Predictions for new observations are obtained\n with predict.\n Objects of class bartcFit are lists containing items:\n method.rsp character string specifying the method used to fit the response surface\n method.trt character string specifying the method used to fit the treatment assignment mech-\n anism\n estimand character string specifying the targeted causal effect\n fit.rsp object containing the fitted response model\n data.rsp dbartsData object used when fitting the response model\n fit.trt object containing the fitted treatment model\n group.by optional factor vector containing the groups in which treatment effects are esti-\n mated\n est matrix or array of posterior samples of the treatment effect estimate\n p.score the vector of propensity scores used as a covariate in the response model, when\n applicable\n samples.p.score\n matrix or array of posterior samples of the propensity score, when applicable\n mu.hat.obs samples from the posterior of the expected value for individual responses under\n the observed treatment regime\n mu.hat.cf samples from the posterior of the expected value for individual responses under\n the counterfactual treatment\n name.trt character string giving the name of the treatment variable in the data of fit.rsp\n trt vector of treatment assignments\n call how bartc was called\n n.chains number of independent posterior sampler chains in response model\n commonSup.rule common support rule used for suppressing observations\n commonSup.cut common support parameter used to set cutoff when suppressing observations\n sd.obs vector of standard deviations of individual posterior predictors for observed\n treatment conditions\n sd.cf vector of standard deviations of individual posterior predictors for counterfactu-\n als\n commonSup.sub logical vector expressing which observations are used when estimating treat-\n ment effects\n use.ranef logical for whether ranef models were used; only added when true\n group.effects logical for whether group-level estimates are made; only added when true\n seed a random seed for use when drawing from the posterior predictive distribution\nAuthor(s)\n <NAME>: <<EMAIL>>.\nReferences\n <NAME>., <NAME>. and <NAME>. (2010) BART: Bayesian additive regression trees. The\n Annals of Applied Statistics 4(1), 266–298. The Institute of Mathematical Statistics. doi:10.1214/\n 09AOAS285.\n <NAME>. (2011) Bayesian Nonparametric Modeling for Causal Inference. Journal of Computa-\n tional and Graphical Statistics 20(1), 217–240. Taylor & Francis. doi:10.1198/jcgs.2010.08162.\n <NAME>. and <NAME>. (2013) Assessing Lack of Common Support in Causal Inference Using\n Bayesian Nonparametrics: Implications for Evaluating the Effect of Breastfeeding on Children’s\n Cognitive Outcomes The Annals of Applied Statistics 7(3), 1386–1420. The Institute of Mathemat-\n ical Statistics. doi:10.1214/13AOAS630.\n <NAME>. (2019) Comment: Contributions of Model Features to BART Causal Inference\n Performance Using ACIC 2016 Competition Data Statistical Science 34(1), 90–93. The Institute of\n Mathematical Statistics. doi:10.1214/18STS682\n <NAME>., <NAME>., and <NAME>. (2020) Bayesian Regression Tree Models for Causal\n Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion). Bayesian\n Analysis 15(3), 965–1056. International Society for Bayesian Analysis. doi:10.1214/19BA1195.\nSee Also\n bart2\nExamples\n ## fit a simple linear model\n n <- 100L\n beta.z <- c(.75, -0.5, 0.25)\n beta.y <- c(.5, 1.0, -1.5)\n sigma <- 2\n set.seed(725)\n x <- matrix(rnorm(3 * n), n, 3)\n tau <- rgamma(1L, 0.25 * 16 * rgamma(1L, 1 * 32, 32), 16)\n p.score <- pnorm(x %*% beta.z)\n z <- rbinom(n, 1, p.score)\n mu.0 <- x %*% beta.y\n mu.1 <- x %*% beta.y + tau\n y <- mu.0 * (1 - z) + mu.1 * z + rnorm(n, 0, sigma)\n # low parameters only for example\n fit <- bartc(y, z, x, n.samples = 100L, n.burn = 15L, n.chains = 2L)\n summary(fit)\n ## example to show refitting under the common support rule\n fit2 <- refit(fit, commonSup.rule = \"sd\")\n fit3 <- bartc(y, z, x, subset = fit2$commonSup.sub,\n n.samples = 100L, n.burn = 15L, n.chains = 2L)\n bartc-generics Generic Methods for bartcFit Objects\nDescription\n Visual exploratory data analysis and model fitting diagnostics for causal inference models fit using\n the bartc function.\nUsage\n ## S3 method for class 'bartcFit'\n fitted(object,\n type = c(\"pate\", \"sate\", \"cate\", \"mu.obs\", \"mu.cf\", \"mu.0\",\n \"mu.1\", \"y.cf\", \"y.0\", \"y.1\", \"icate\", \"ite\",\n \"p.score\", \"p.weights\"),\n sample = c(\"inferential\", \"all\"),\n ...)\n extract(object, ...)\n ## S3 method for class 'bartcFit'\n extract(object,\n type = c(\"pate\", \"sate\", \"cate\", \"mu.obs\", \"mu.cf\", \"mu.0\",\n \"mu.1\", \"y.cf\", \"y.0\", \"y.1\", \"icate\", \"ite\",\n \"p.score\", \"p.weights\", \"sigma\"),\n sample = c(\"inferential\", \"all\"),\n combineChains = TRUE,\n ...)\n ## S3 method for class 'bartcFit'\n predict(object, newdata,\n group.by,\n type = c(\"mu\", \"y\", \"mu.0\", \"mu.1\", \"y.0\", \"y.1\", \"icate\", \"ite\",\n \"p.score\"),\n combineChains = TRUE,\n ...)\n refit(object, newresp, ...)\n ## S3 method for class 'bartcFit'\n refit(object,\n newresp = NULL,\n commonSup.rule = c(\"none\", \"sd\", \"chisq\"),\n commonSup.cut = c(NA_real_, 1, 0.05),\n ...)\nArguments\n object Object of class bartcFit.\n type Which quantity to return. See details for a description of possible values.\n sample Return information for either the \"inferential\" (e.g. treated observations\n when the estimand is att) or \"all\" observations.\n combineChains If the models were fit with more than one chain, results retain the chain structure\n unless combineChains is TRUE.\n newresp Not presently used, but provided for compatibility with other definitions of the\n refit generic.\n newdata Data corresponding to the confounders in a bartc fit.\n group.by Optional grouping variable. See definition of group.by in bartc.\n commonSup.rule, commonSup.cut\n As in bartc.\n ... Additional parameters passed up the generic method chain.\nDetails\n fitted returns the values that would serve as predictions for an object returned by the bartc func-\n tion, while extract instead returns the full matrix or array of posterior samples. The possible\n options are:\n • \"pate\", \"sate\", \"cate\" - various target quantities; see summary\n • \"mu\" - predict only: expected value; requires user-supplied treatment variable in newdata\n • \"y\" - predict only: sample of the response; requires user-supplied treatment variable in newdata\n • \"mu.obs\" - (samples from the posterior of) the expected value under the observed treatment\n condition, i.e. muˆ i (1) ∗ zi + mu\n ˆ i (0) ∗ (1 − zi )\n • \"mu.cf\" - the expected value under the counterfactual treatment condition, i.e. mu ˆ i (1) ∗ (1 −\n zi ) + muˆ i (0) ∗ zi )\n • \"mu.0\" - the expected value under the control condition\n • \"mu.1\" - the expected value under the treated condition\n • \"y.cf\" - samples of the response under the the counterfactual treatment condition, i.e. ŷi (1 −\n zi )); values are obtained by adding noise to mu.cf using the posterior predictive distribution\n • \"y.0\" - observed responses under the control together with predicted under the treated, i.e.\n ŷi (1) ∗ zi + y(0) ∗ (1 − zi )\n • \"y.1\" - observed responses under the treatment together with predicted under the control, i.e.\n yi (1) ∗ zi + ŷ(0) ∗ (1 − zi )\n • \"ite\" - (sample) individual treatment effect estimates, i.e. (yi (zi ) − yi (1 − zi )) ∗ (2zi − 1);\n uses observed responses and posterior predicted counterfactuals\n • \"icate\" - individual conditional average treatment effect estimates, i.e. mu ˆ i (1) − mu ˆ i (0)\n • \"p.score\" - probability that each observation is assigned to the treatment group\n • \"p.weights\" - weights assigned to each individual difference if the response method is\n \"p.weight\"\n • \"sigma\" - residual standard deviation from continuous response models\n refit exists to allow the same regressions to be used to calculate estimates under different common\n support rules. To refit those models on a subset, see the examples in bartc.\n predict allows the fitted model to be used to make predictions on an out-of-sample set. Requires\n model to be fit with keepTrees equal to TRUE. As ‘y’ values are all considered out of sample, the\n posterior predictive distribution is always used when relevant.\nValue\n For fitted, extract, and predict, a matrix, array, or vector depending on the dimensions of the\n result and the number of chains. For the following, when n.chains is one the dimension is dropped.\n • \"pate\", \"sate\", or \"cate\" - with fitted, a scalar; with extract, n.chains x n.samples\n • \"p.score\" - depending on the fitting method, samples may or not be present; when samples\n are absent, a vector is returned for both functions; when present, the same as \"y\".\n • all other types - with fitted, a vector of length equal to the number of observations (n.obs);\n with extract or predict, a matrix or array of dimensions n.chains x n.samples x n.obs.\n For refit, an object of class bartcFit.\nAuthor(s)\n <NAME>: <<EMAIL>>.\nSee Also\n bartc\nExamples\n ## fit a simple linear model\n n <- 100L\n beta.z <- c(.75, -0.5, 0.25)\n beta.y <- c(.5, 1.0, -1.5)\n sigma <- 2\n set.seed(725)\n x <- matrix(rnorm(3 * n), n, 3)\n tau <- rgamma(1L, 0.25 * 16 * rgamma(1L, 1 * 32, 32), 16)\n p.score <- pnorm(x %*% beta.z)\n z <- rbinom(n, 1, p.score)\n mu.0 <- x %*% beta.y\n mu.1 <- x %*% beta.y + tau\n y <- mu.0 * (1 - z) + mu.1 * z + rnorm(n, 0, sigma)\n # low parameters only for example\n fit <- bartc(y, z, x, n.samples = 100L, n.burn = 15L, n.chains = 2L)\n # compare fit to linear model\n lm.fit <- lm(y ~ z + x)\n plot(fitted(fit, type = \"mu.obs\"), fitted(lm.fit))\n # rank order sample individual treatment effect estimates and plot\n ites <- extract(fit, type = \"ite\")\n ite.m <- apply(ites, 2, mean)\n ite.sd <- apply(ites, 2, sd)\n ite.lb <- ite.m - 2 * ite.sd\n ite.ub <- ite.m + 2 * ite.sd\n ite.o <- order(ite.m)\n plot(NULL, type = \"n\",\n xlim = c(1, length(ite.m)), ylim = range(ite.lb, ite.ub),\n xlab = \"effect order\", ylab = \"individual treatment effect\")\n lines(rbind(seq_along(ite.m), seq_along(ite.m), NA),\n rbind(ite.lb[ite.o], ite.ub[ite.o], NA), lwd = 0.5)\n points(seq_along(ite.m), ite.m[ite.o], pch = 20)\n bartc-plot Plot methods for bartc\nDescription\n Visual exploratory data analysis and model fitting diagnostics for causal inference models fit using\n the bartc function.\nUsage\n plot_sigma(x, main = \"Traceplot sigma\",\n xlab = \"iteration\", ylab = \"sigma\",\n lty = 1:x$n.chains,\n ...)\n plot_est(x, main = paste(\"Traceplot\", x$estimand),\n xlab = \"iteration\", ylab = x$estimand,\n lty = 1:x$n.chains, col = NULL,\n ...)\n plot_indiv(x, main = \"Histogram Individual Quantities\",\n type = c(\"icate\", \"mu.obs\", \"mu.cf\", \"mu.0\",\n \"mu.1\", \"y.cf\", \"y.0\", \"y.1\", \"ite\"),\n xlab = \"treatment effect\",\n breaks = 20,\n ...)\n plot_support(x, main = \"Common Support Scatterplot\",\n xvar = \"tree.1\", yvar = \"tree.2\",\n sample = c(\"inferential\", \"all\"),\n xlab = NULL, ylab = NULL,\n pch.trt = 21, bg.trt = \"black\",\n pch.ctl = pch.trt, bg.ctl = NA,\n pch.sup = pch.trt, bg.sup = NA, col.sup = \"red\", cex.sup = 1.5,\n legend.x = \"topleft\", legend.y = NULL,\n ...)\nArguments\n x Object of class bartcFit.\n main Character title of plot.\n xlab Character label of x axis. For plot_support, if NULL a default will be used.\n ylab Character label of y axis. For plot_support, if NULL a default will be used.\n lty For line plots (plot_sigma, plot_est), models use the values of lty to visually\n distinguish each chain.\n col For line plots, use col vector to distinguish between groups (if any).\n breaks Argument to codehist.\n type The individual quantity to be plotted. See fitted.\n xvar Variable for use on x axis. Can be one of \"tree.XX\", \"pca.XX\", \"css\", any\n individual level quantity accepted by fitted, the number or name of a column\n used to fit the response model, or a given vector. See below for details.\n sample Return information for either the \"inferential\" (e.g. treated observations\n when the estimand is att) or \"all\" observations.\n yvar Variable for use on the y axis, of the same form as xvar.\n pch.trt pch point value used when plotting treatment observations.\n bg.trt bg background value used when plotting treatment observations.\n pch.ctl pch point value used when plotting control observations.\n bg.ctl bg background value used when plotting treatment observations.\n pch.sup pch point value used when plotting suppressed observations.\n bg.sup bg background value used when plotting suppressed observations.\n col.sup col color value used when plotting suppressed observations.\n cex.sup cex size value used when plotting suppressed observations.\n legend.x x value passed to legend. If NULL, legend plotting is skipped.\n legend.y Optional y value passed to legend\n ... Optional graphical parameters.\nDetails\n Produces various plots using objects fit by bartc. plot_sigma and plot_est are traditional pa-\n rameter trace plots that can be used to diagnose the convergence of the posterior sampler. If the\n bartc model is fit with n.chains greater than one, by default each chain will be plotted with its\n own line type.\n plot_indiv produces a simple histogram of the distribution of the estimates of the individual ef-\n fects, taken as the average of their posterior samples.\n plot_support is used to visualize the common support diagnostic in the form of a scatterplot.\n Points that the diagnostic excludes are outlined in red. The contents of the x and y axes are con-\n trolled by the xvar and yvar arguments respectively and can be of the form:\n • \"tree.XX\" - Variable number \"XX\" as selected by variable importance in predicting individual\n treatment effects using a tree fit by rpart. \"XX\" must be a number not exceeding the number\n of continuous variables used to fit the response model.\n • \"pca.XX\" - \"XX\"th principal component axis.\n • \"css\" - The common support statistic.\n • \"y\" - Observed response variable.\n • \"y0\" - Predicted values for the response under the control as obtained by fitted.\n • \"y1\" - Predicted values for the response under the treatment fitted.\n • \"indiv.diff\" - Individual treatment effect estimates, or ŷ(1) − ŷ(0).\n • \"p.score\" - Propensity score used to fit the response model (if applicable).\n • \"p.weights\" - Weights used when taking average of individual differences for response\n method \"p.weight\".\n • predictor columns - Given by name or number.\n • supplied vector - Any vector of length equal to the number of observations.\nValue\n None, although plotting occurs as a side-effect.\nAuthor(s)\n <NAME>: <<EMAIL>>.\nSee Also\n bartc\nExamples\n # generate fake data using a simple linear model\n n <- 100L\n beta.z <- c(.75, -0.5, 0.25)\n beta.y <- c(.5, 1.0, -1.5)\n sigma <- 2\n set.seed(725)\n x <- matrix(rnorm(3 * n), n, 3)\n tau <- rgamma(1L, 0.25 * 16 * rgamma(1L, 1 * 32, 32), 16)\n p.score <- pnorm(x %*% beta.z)\n z <- rbinom(n, 1, p.score)\n mu.0 <- x %*% beta.y\n mu.1 <- x %*% beta.y + tau\n y <- mu.0 * (1 - z) + mu.1 * z + rnorm(n, 0, sigma)\n # run with low parameters only for example\n fit <- bartc(y, z, x, n.samples = 100L, n.burn = 15L, n.chains = 2L,\n n.threads = 1L,\n commonSup.rule = \"sd\")\n ## plot specific functions\n # sigma plot can be used to access convergence of chains\n plot_sigma(fit)\n # show points lacking common support\n plot_support(fit, xvar = \"tree.1\", yvar = \"css\", legend.x = NULL)\n # see example in ?\"bartc-generics\" for rank-ordered individual effects plot\n summary.bartcFit Summary for bartcFit Objects\nDescription\n Summarizes bartc fits by calculating target quantities and uncertainty estimates.\nUsage\n ## S3 method for class 'bartcFit'\n summary(object,\n target = c(\"pate\", \"sate\", \"cate\"),\n ci.style = c(\"norm\", \"quant\", \"hpd\"), ci.level = 0.95,\n pate.style = c(\"ppd\", \"var.exp\"),\n ...)\nArguments\n object Object of class bartcFit.\n target Treatment effect to calculate. One of \"pate\" - population average treatment ef-\n fect, \"sate\" - sample average treatment effect, and \"cate\" - conditional average\n treatment effect.\n ci.style Means of calculating confidence intervals (posterior credible regions). Options\n include \"norm\" - use a normal approximation, \"quant\" - the empirical quantites\n of the posterior samples, and \"hpd\" - region of highest posterior density.\n ci.level Level of confidence for intervals.\n pate.style For target \"pate\", calculate uncertainty by using \"ppd\" - the posterior predictive\n distribution or \"var.exp\" a variance expansion formula.\n ... Not used at moment, but present to match summary generic signature.\nDetails\n summary produces a numeric and qualitative summary of a bartc fit.\n Target Types\n The SATE and PATE involve calculating predicted response values under different treatment con-\n ditions. When using extract or fitted, these values are simulated directly from the posterior\n predictive distribution. However, since these quantities all have the same expected value, in order\n to provide consistent results summary only uses those simulations to derive credible intervals. Thus\n the estimates for CATE, SATE, and PATE all should be reported as the same but with increasing\n degrees of uncertainty.\n Grouped Data\n If a model is fit with a supplied grouping variable and group.effects = TRUE, the estimates will\n also be reported within groups. When possible, the last line corresponds to the population. Within\n group estimates for resposne methods such as \"tmle\" cannot easily be extrapolated to the popula-\n tion at large - the means will combine based on the sample sizes but the uncertainty estimates will\n lack correlations.\nValue\n An object of class bartcFit.summary equivalent to a list with named items:\n call how bartc was called\n method.rsp character string specifying the method used to fit the response surface\n method.trt character string specifying the method used to fit the treatment assignment mech-\n anism\n ci.info a named list with items target, ci.style, ci.level, and pate.style as\n passed to summary\n n.obs total number of observations\n n.samples number of samples within any one chain\n n.chains total number of chains\n commonSup.rule common support rule used when fitting object to produce estimates\n estimates a data.frame with columns \"estimate\" - the target, \"sd\" - standard devi-\n ation of posterior of estimate, \"ci.lower\" - lower bound of credible region,\n \"ci.upper\" - upper bound of credible region, and optionally \"n.cut\" - how\n many observations were dropped using common support rule\n16 summary.bartcFit\nAuthor(s)\n <NAME>: <<EMAIL>>."}}},{"rowIdx":59492,"cells":{"project":{"kind":"string","value":"velociraptr"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘velociraptr’\n October 12, 2022\nType Package\nTitle Fossil Analysis\nVersion 1.1.0\nAuthor <NAME>\nMaintainer <NAME> <<EMAIL>>\nDescription Functions for downloading, reshaping, culling, cleaning, and analyzing fos-\n sil data from the Paleobiology Database <https://paleobiodb.org>.\nImports sf\nLicense GPL-3\nEncoding UTF-8\nLazyData true\nRoxygenNote 6.1.1\nNeedsCompilation no\nRepository CRAN\nDate/Publication 2019-07-31 19:20:02 UTC\nR topics documented:\nabundanceMatri... 2\nageRange... 3\ncleanTaxonom... 4\nconstrainAge... 5\ncullMatri... 6\ndownloadPaleogeograph... 7\ndownloadPBD... 8\ndownloadPlace... 9\ndownloadTim... 10\nfixedLatitud... 11\nmultiplicativeBet... 12\npresenceMatri... 13\ntaxonAlph... 14\n abundanceMatrix Create a community matrix of taxon abundances\nDescription\n Creates a community matrix of taxon abundances, with samples as rows and species as columns,\n from a data frame.\nUsage\n abundanceMatrix(Data, Rows = \"geoplate\", Columns = \"genus\")\nArguments\n Data A data.frame of taxonomic occurrences. Must have at least two columns. One\n column representing the samples, and one column representing the taxa.\n Rows A characer string\n Columns A character string\nDetails\n Note that older versions of this function automatically checked for and removed hanging factors.\n However, this is something that should really be dictated by the user, and that step is no longer a\n part of the function. This is unlikely to introduce any breaking changes in older scripts, but we note\n it here for documentation purposes..\nValue\n A numeric matrix of taxon abundances. Samples as the rownames and species as the column names.\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of pleistocene bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\", StartInterval=\"Pleistocene\", StopInterval=\"Pleistocene\")\n # Clean the genus column\n # DataPBDB<-cleanTaxonomy(DataPBDB,\"genus\")\n # Create a community matrix of genera by tectonic plate id#\n # CommunityMatrix<-abundanceMatrix(Data=DataPBDB, Rows=\"geoplate\", Columns=\"genus\")\n ageRanges Find the age range for each taxon in a dataframe\nDescription\n Find the age range (first occurrence and last occurrence) for each taxon in a PBDB dataset. Can be\n run for any level of the taxonomic hierarchy (e.g., family, genus).\nUsage\n ageRanges(Data, Taxonomy = \"genus\")\nArguments\n Data A data frame downloaded from the paleobiology database API.\n Taxonomy A characer string identifying the desired level of the taxonomic hierarchy.\nDetails\n Returns a data frame of that states gives the time of origination and extinction for each taxon as\n numeric values. Note that older versions of this function automatically dropped hanging factors and\n NA’s, but that cleaning step should ideally be dictated by the user up-front. So that functionality has\n been dropped. This may introduce breaking chanes in legacy scripts, but is easily fixed by standard\n data cleaning steps.\nValue\n A numeric matrix of first and last ages for each taxon, with tax as rownames.\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of Cenozoic bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Cenozoic\",StopInterval=\"Cenozoic\")\n # Find the first occurrence and last occurrence for all Cenozoic bivalves in DataPBDB\n # AgeRanges<-ageRanges(DataPBDB,\"genus\")\n cleanTaxonomy Clean taxonomic names\nDescription\n Removes NAs and subgenera from the genus column.\nUsage\n cleanTaxonomy(Data, Taxonomy = \"genus\")\nArguments\n Data A data frame of taxonomic ocurrences downloaded from the paleobiology database\n API.\n Taxonomy A character string\nDetails\n Will remove NA’s and subgenera from the genus column of a PBDB dataset. It can also be used on\n other datasets of similar structure to convert species names to genus, or remove NAs.\nValue\n Will return a data frame identical to the original, but with the genus column cleaned.\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of Cenozoic bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Cenozoic\",StopInterval=\"Cenozoic\")\n # Clean up the genus column.\n # CleanedPBDB<-cleanTaxonomy(DataPBDB,\"genus\")\n constrainAges Constrain a dataset to only occurrences within a certain age-range\nDescription\n Assign fossil occurrences to different intervals within a geologic timescale, then remove occur-\n rences that are not temporally constrained to a single interval within that timescale.\nUsage\n constrainAges(Data, Timescale)\n multiplyAges(Data, Timescale)\nArguments\n Data A data frame\n Timescale A data frame\nDetails\n Cull a paleobiology database data frame to only occurrences temporally constrained to be within a\n certain level of the geologic timescale (e.g., period, epoch). The geologic timescale should come\n from the Macrostrat database, but custom time-scales can be used if structured in the same way. See\n downloadTime for how to download a timescale.\nValue\n A data frame\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of Cenozoic bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Cenozoic\",StopInterval=\"Cenozoic\")\n # Download the international epochs timescale from macrostrat.org\n # Epochs<-downloadTime(\"international epochs\")\n # Find only occurrences that are temporally constrained to a single international epoch\n # ConstrainedPBDB<-constrainAges(DataPBDB,Timescale=Epochs)\n # Create mutliple instances of a single occurrence for each epoch it occurs in\n # MultipliedPBDB<-multiplyAges(DataPBDB,Timescale=Epochs)\n cullMatrix Cull rare taxa and depauperate samples\nDescription\n Functions for recursively culling community matrices of rare taxa and depauperate samples.\nUsage\n cullMatrix(CommunityMatrix, Rarity = 2, Richness = 2, Silent = FALSE)\nArguments\n CommunityMatrix\n a matrix\n Rarity a whole number\n Richness a whole number\n Silent logical\nDetails\n Takes a community matrix (see presenceMatrix or abundanceMatrix) and removes all samples\n with fewer than a certain number of taxa and all taxa that occur below a certain threshold of samples.\n The function operates recursively, and will check to see if removing a rare taxon drops a sampe\n below the input minimum richness and vice-versa. This means that it is possible to eliminate all\n taxa and samples if the rarity and richness minimums are too high. If the Silent argument is set\n to FALSE the function will throw an error and print a warning if no taxa or samples are left after\n culling. If Silent is set to TRUE the function will simply return NULL. The latter case is useful if\n many matrices are being culled as a part of a loop, and you do not want to break the loop with an\n error.\n These functions originally appeared in the R script appendix of Holland, S.M. and <NAME> (2011)\n \"Niche conservatism along an onshore-offshore gradient\". Paleobiology 37:270-286.\nValue\n A community matrix with depauperate samples and rare taxa removed.\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of pleistocene bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Pleistocene\",StopInterval=\"Pleistocene\")\n # Create a community matrix with tectonic plates as \"samples\".\n # CommunityMatrix<-abundanceMatrix(DataPBDB,\"geoplate\")\n # Remove taxa that occur in less than 5 samples and samples with fewer than 25 taxa.\n # cullMatrix(CommunityMatrix,Rarity=5,Richness=25,Silent=FALSE)\n downloadPaleogeography\n Downloads paleogeographic maps\nDescription\n Download a paleogeographic map for an age expressed in millions of years ago.\nUsage\n downloadPaleogeography(Age = 0)\nArguments\n Age A whole number up to 550\nDetails\n Downloads a map of paleocontinents for a specific age from Macrostrat.org as a shapefile. The\n given age must be expressed as a whole number. Note that the function makes use of the rgdal and\n RCurl packages.\nValue\n A simple features object\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of Maastrichtian bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Maastrichtian\",StopInterval=\"Maastrichtian\")\n # Download a paleogeographic map.\n # KTBoundary<-downloadPaleogeography(Age=66)\n # Plot the paleogeographic map (uses rgdal) and the PBDB points.\n # plot(KTBoundary,col=\"grey\")\n # points(x=DataPBDB[,\"paleolng\"],y=DataPBDB[,\"paleolat\"],pch=16,cex=2)\n downloadPBDB Download Occurrences from the Paleobiology Database\nDescription\n Downloads a data frame of Paleobiology Database fossil occurrences.\nUsage\n downloadPBDB(Taxa, StartInterval = \"Pliocene\",\n StopInterval = \"Pleistocene\")\nArguments\n Taxa a character vector\n StartInterval a character vector\n StopInterval a character vector\nDetails\n Downloads a data frame of Paleobiology Database fossil occurrences matching certain taxonomic\n groups and age range. This is simply a convenience function for rapid data download, and only\n returns the most generically useful fields. Go directly to the Paleobiology Database to make more\n complex searches or access additional fields. This function makes use of the RCurl package.\n • ocurrence_no: The Paleobiology Database occurrence number.\n • collection_no: The Paleobiology Database collection number.\n • reference_no: The Paleobiology Database reference number.\n • Classifications: The stated Linnean classification of the occurence from phylum through\n genus. See cleanTaxonomy for how to simplify these fields.\n • accepted_name: The highest resolution taxonomic name assigned to the occurrence.\n • Geologic Intervals: The earliest possible age of the occurrence and latest possible age of the\n occurrence, expressed in terms of geologic intervals. See constrainAge for how to simplify\n these fields.\n • Numeric Ages: The earliest possible age of the occurrence and latest possible age of the\n occurrence, expressed as millions of years ago.\n • Geolocation: Both present-day and rotated paleocoordinates of the occurrence. The geoplate\n id used by the rotation model is also included. The key for geoplate ids can be found in the\n Paleobiology Database API documentation.\nValue\n a data frame\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of Ypresian bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Ypresian\",StopInterval=\"Ypresian\")\n # Download a test dataset of Ordovician-Silurian trilobites and brachiopods.\n # DataPBDB<-downloadPBDB(c(\"Trilobita\",\"Brachiopoda\"),\"Ordovician\",\"Silurian\")\n downloadPlaces Download Shapefile of Places\nDescription\n Download a shapefile of a geolocation from the Macrostrat API’s implementation of the Who’s on\n First database by MapZen.\nUsage\n downloadPlaces(Place = \"Wisconsin\", Type = \"region\")\nArguments\n Place A character string; the name of a place\n Type A character string; a type of place\nDetails\n Download a shapefile of a geolocation from the Macrostrat API. The Macrostrat database provides a\n GeoJSON of a particular location given the location’s name and type. Type can be of the categories:\n \"continent\", \"country\", \"region\", \"county\", and \"locality\".\n If multiple locations of the same type share the same name (e.g., Alexandria), the route will return\n a feature collection of all matching polygons.\nValue\n An rgdal compatible shapefile\nAuthor(s)\n <NAME>\nExamples\n # Download a polygon of Dane County, Wisconsin, United States, North America\n # DaneCounty<-downloadPlaces(Place=\"Dane\",Type=\"county\")\n # Download a polygon of Wisconsin, United States, North America\n # Wisconsin<-downloadPlaces(Place=\"Wisconsin\",Type=\"region\")\n # Download a polygon of North America\n # NorthAmerica<-downloadPlaces(Place=\"North America\",Type=\"continent\")\n downloadTime Download geologic timescale\nDescription\n Downloads a geologic timescale from the Macrostrat.org database.\nUsage\n downloadTime(Timescale = \"interational epochs\")\nArguments\n Timescale character string; a recognized timescale in the Macrostrat.org database\nDetails\n Downloads a recognized timescale from the Macrostrat.org database. This includes the name, mini-\n mum age, maximum age, midpoint age, and official International Commission on Stratigraphy color\n hexcode if applicable of each interval in the timescale. Go to https://macrostrat.org/api/defs/timescales?all\n for a list of recognized timescales.\nValue\n A data frame\nAuthor(s)\n <NAME>\nExamples\n # Download the ICS recognized periods timescale\n Timescale<-downloadTime(Timescale=\"international periods\")\n fixedLatitude Download fixed-latitude equal-area grid\nDescription\n Download an equal-area grid of the world with fixed latitudinal spacing and variable longitudinal\n spacing.\nUsage\n fixedLatitude(LatSpacing = 5, CellArea = \"500000\")\nArguments\n LatSpacing Number of degrees desired between latitudinal bands\n CellArea Desired target area of the cells in km^2 as a character string\nDetails\n Downloads an equal-area grid with fixed latitudinal spacing and variable longitudinal spacing. The\n distance between longitudinal borders of grids will adjust to the target area size within each band of\n latitude. The algorithm will adjust the area of the grids to ensure that the total surface of the globe\n is covered.\nValue\n A simple features object\nAuthor(s)\n <NAME>\nExamples\n # Download an equal area grid with 10 degree latitudinal spacing and 1,000,000 km^2 grids\n # EqualArea<-fixedLatitude(LatSpacing=10,CellArea=\"1000000\")\n multiplicativeBeta Multiplicative Diversity Partitioning\nDescription\n Calculates beta diversity under various Multiplicative Diversity Partitioning paradigms.\nUsage\n multiplicativeBeta(CommunityMatrix)\n completeTurnovers(CommunityMatrix)\n notEndemic(CommunityMatrix)\nArguments\n CommunityMatrix\n a matrix\nDetails\n Takes a community matrix (see presenceMatrix or abundanceMatrix) and returns one of three\n types of multiplicative beta diversity.\n Refer to Tuomisto, H (2010) \"A diversity of beta diversities: straightening up a concept gone awry.\n Part 1. Defining beta diversity as a function of alpha and gamma diversity\". Ecography 33:2-22.\n • multiplicativeBeta(CommunityMatrix): Calculates the original beta diversity ratio - Gamma/Alpha.\n It quantifies how many times as rich gamma is than alpha.\n • completeTurnovers(CommunityMatrix): The number of complete effective species turnovers\n observed among compositonal units in the dataset - (Gamma-Alpha)/Alpha.\n • notEndemic(CommunityMatrix): The proportion of taxa in the dataset not limited to a single\n sample - (Gamma-Alpha)/Gamma\nValue\n A numeric vector\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of pleistocene bivalves from the Paleobiology Database.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",\"Pleistocene\",\"Pleistocene\")\n # Create a community matrix with tectonic plates as \"samples\".\n # CommunityMatrix<-abundanceMatrix(DataPBDB,\"geoplate\")\n # \"True local diversity ratio\"\n # multiplicativeBeta(CommunityMatrix)\n # Whittaker's effective species turnover\n # completeTurnovers(CommunityMatrix)\n # Proportional effective species turnover\n # notEndemic(CommunityMatrix)\n presenceMatrix Create a matrix of presences and absences\nDescription\n Creates a community matrix of taxon presences and absences from a data frame with a column of\n sites and a column of species.\nUsage\n presenceMatrix(Data, Rows = \"geoplate\", Columns = \"genus\")\nArguments\n Data A dataframe or matrix\n Rows A characer string\n Columns A character string\nValue\n A presence-absence matrix\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of pleistocene bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",\"Pleistocene\",\"Pleistocene\")\n # Create a community matrix of genera by plates.\n # CommunityMatrix<-presenceMatrix(DataPBDB,Rows=\"geoplate\",Columns=\"genus\")\n # Create a community matrix of families by geologic interval.\n # CommunityMatrix<-presenceMatrix(DataPBDB,Rows=\"early_interval\",Columns=\"family\")\n taxonAlpha Additive Diversity Partitioning functions\nDescription\n Functions for calculating alpha, beta, and gamma richness of a community matrix under the Addi-\n tive Diversity partitioning paradigm of R. Lande.\nUsage\n taxonAlpha(CommunityMatrix)\n meanAlpha(CommunityMatrix)\n taxonBeta(CommunityMatrix)\n sampleBeta(CommunityMatrix)\n totalBeta(CommunityMatrix)\n totalGamma(CommunityMatrix)\nArguments\n CommunityMatrix\n a matrix\nDetails\n Takes a community matrix (see presenceMatrix or abundanceMatrix) and returns the either the\n alpha, beta, or gamma richness of a community matrix.\n These functions were originally presented in Holland, SM (2010) \"Additive diversity partitioning\n in palaeobiology: revisiting Sepkoski’s question\" Paleontology 53:1237-1254.\n • taxonAlpha(CommunityMatrix) Calculates the contribution to alpha diversity of each taxon.\n • meanAlpha(CommunityMatrix) Calculates the average alpha diversity of all samples.\n • taxonBeta(CommunityMatrix) Calculates the contribution to beta diversity of each taxon.\n • sampleBeta(CommunityMatrix) Calculates the contribution to beta diversity of each sample.\n • totalBeta(CommunityMatrix) Calculates the total beta diversity.\n • totalGamma(CommunityMatrix) Calculates the richness of all samples in the community\n matrix.\nValue\n A vector of the alpha, beta, or gamma richness of a taxon, sample, or entire community matrix.\nAuthor(s)\n <NAME>\nExamples\n # Download a test dataset of pleistocene bivalves.\n # DataPBDB<-downloadPBDB(Taxa=\"Bivalvia\",StartInterval=\"Pleistocene\",StopInterval=\"Pleistocene\")\n # Create a community matrix with tectonic plates as \"samples\"\n # CommunityMatrix<-abundanceMatrix(DataPBDB,\"geoplate\")\n # Calculate the average richness of all samples in a community.\n # meanAlpha(CommunityMatrix)\n # The beta diversity of all samples in a community.\n # totalBeta(CommunityMatrix)\n # This is, by definition, equivalent to the gamma diversity - mean alpha diversity.\n # totalBeta(CommunityMatrix)==(totalGamma(CommunityMatrix)-meanAlpha(CommunityMatrix))"}}},{"rowIdx":59493,"cells":{"project":{"kind":"string","value":"mcbette"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘mcbette’\n September 27, 2023\nTitle Model Comparison Using 'babette'\nVersion 1.15.2\nMaintainer <NAME> <<EMAIL>>\nDescription 'BEAST2' (<https://www.beast2.org>) is a widely used\n Bayesian phylogenetic tool, that uses DNA/RNA/protein data\n and many model priors to create a posterior of jointly estimated\n phylogenies and parameters.\n 'mcbette' allows to do a Bayesian model comparison over some\n site and clock models,\n using 'babette' (<https://github.com/ropensci/babette/>).\nLicense GPL-3\nRoxygenNote 7.2.3\nVignetteBuilder knitr\nURL https://github.com/ropensci/mcbette/\nBugReports https://github.com/ropensci/mcbette/issues\nImports babette (>= 2.3), beautier (>= 2.6.2), beastier (>= 2.4.6),\n curl, devtools, mauricer (>= 2.5), Rmpfr, testit, txtplot\nSuggests ape, ggplot2, hunspell, knitr, lintr, markdown, nLTT,\n phangorn, rappdirs, rmarkdown, spelling, stringr, testthat (>=\n 2.1.0), tracerer\nLanguage en-US\nEncoding UTF-8\nSystemRequirements BEAST2 (https://www.beast2.org/)\nNeedsCompilation no\nAuthor <NAME> [aut, cre]\n (<https://orcid.org/0000-0003-1107-7049>),\n <NAME> [rev] (Joëlle reviewed the package for rOpenSci,\n see https://github.com/ropensci/software-review/issues/360),\n <NAME> [rev] (Vikram reviewed the package for rOpenSci, see\n https://github.com/ropensci/software-review/issues/360,\n <https://orcid.org/0000-0002-9367-8974>)\nRepository CRAN\nDate/Publication 2023-09-27 09:00:02 UTC\nR topics documented:\ncalc_weight... 2\ncan_run_mcbett... 3\ncheck_beast2_ns_pk... 4\ncheck_marg_lik... 4\ncheck_mcbette_stat... 5\ndefault_params_do... 5\nest_marg_li... 7\nest_marg_lik... 9\nget_mcbette_stat... 11\nget_test_marg_lik... 12\ninterpret_bayes_facto... 12\ninterpret_marg_lik_estimate... 13\nis_marg_lik... 14\nmcbette_repor... 14\nmcbette_self_tes... 15\nplot_marg_lik... 16\nset_mcbette_stat... 17\n calc_weights Calculate the weights for each marginal likelihood\nDescription\n Calculate the weights for each marginal likelihood\nUsage\n calc_weights(marg_liks)\nArguments\n marg_liks (non-log) marginal likelihood estimates\nValue\n the weight of each marginal likelihood estimate, which will sum up to 1.0\nAuthor(s)\n <NAME>\nExamples\n # Evidences (aka marginal likelihoods) can be very small\n evidences <- c(0.0001, 0.0002, 0.0003, 0.0004)\n # Sum will be 1.0\n calc_weights(evidences)\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n can_run_mcbette Can ’mcbette’ run?\nDescription\n Can ’mcbette’ run? Will return TRUE if:\n • (1) Running on Linux or MacOS\n • (2) BEAST2 is installed\n • (3) The BEAST2 NS package is installed\nUsage\n can_run_mcbette(beast2_folder = beastier::get_default_beast2_folder())\nArguments\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\nAuthor(s)\n <NAME>\nExamples\n can_run_mcbette()\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n check_beast2_ns_pkg Checks if the BEAST2 ’NS’ package is installed.\nDescription\n Checks if the BEAST2 ’NS’ package is installed. Will stop if not\nUsage\n check_beast2_ns_pkg(beast2_bin_path = beastier::get_default_beast2_bin_path())\nArguments\n beast2_bin_path\n path to the the BEAST2 binary file\n check_marg_liks Check if the marg_liks are of the same type as returned by\n est_marg_liks.\nDescription\n stop if not.\nUsage\n check_marg_liks(marg_liks)\nArguments\n marg_liks a table of (estimated) marginal likelihoods, as, for example, created by est_marg_liks.\n This data.frame has the following columns:\n • site_model_name: name of the site model, must be an element of get_site_model_names\n • clock_model_name: name of the clock model, must be an element of\n get_clock_model_names\n • tree_prior_name: name of the tree prior, must be an element of get_tree_prior_names\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of\n this model combination) to 0.0 (no evidence in favor of this model combi-\n nation)\n • ess: effective sample size of the marginal likelihood estimation\n Use get_test_marg_liks to get a test marg_liks. Use is_marg_liks to determine\n if a marg_liks is valid. Use check_marg_liks to check that a marg_liks is\n valid.\n check_mcbette_state Check if the mcbette_state is valid.\nDescription\n Check if the mcbette_state is valid. Will stop otherwise.\nUsage\n check_mcbette_state(mcbette_state)\nArguments\n mcbette_state the mcbette state, which is a list with the following elements:\n • beast2_installed TRUE if BEAST2 is installed, FALSE otherwise\n • ns_installed NA if BEAST2 is not installed. TRUE if the BEAST2 NS\n package is installed FALSE if the BEAST2 NS package is not installed\nAuthor(s)\n <NAME>\n default_params_doc Documentation of general function arguments. This function does\n nothing. It is intended to inherit function argument documentation.\nDescription\n Documentation of general function arguments. This function does nothing. It is intended to inherit\n function argument documentation.\nUsage\n default_params_doc(\n beast2_bin_path,\n beast2_folder,\n beast2_working_dir,\n beast2_options,\n beast2_optionses,\n clock_model,\n clock_models,\n epsilon,\n fasta_filename,\n inference_model,\n inference_models,\n marg_liks,\n mcbette_state,\n mcmc,\n os,\n rng_seed,\n site_model,\n site_models,\n tree_prior,\n tree_priors,\n verbose\n )\nArguments\n beast2_bin_path\n path to the the BEAST2 binary file\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\n beast2_working_dir\n folder in which BEAST2 will run and produce intermediate files. By default,\n this is a temporary folder\n beast2_options a beast2_options structure, as can be created by create_mcbette_beast2_options.\n beast2_optionses\n list of one or more beast2_options structures, as can be created by create_mcbette_beast2_options.\n Use of reduplicated plural to achieve difference with beast2_options\n clock_model a clock model, as can be created by create_clock_model\n clock_models a list of one or more clock models, as can be created by create_clock_models\n epsilon measure of relative accuracy. Smaller values result in longer, more precise esti-\n mations\n fasta_filename name of the FASTA file\n inference_model\n an inference model, as can be created by create_inference_model\n inference_models\n a list of one or more inference models, as can be created by create_inference_model\n marg_liks a table of (estimated) marginal likelihoods, as, for example, created by est_marg_liks.\n This data.frame has the following columns:\n • site_model_name: name of the site model, must be an element of get_site_model_names\n • clock_model_name: name of the clock model, must be an element of\n get_clock_model_names\n • tree_prior_name: name of the tree prior, must be an element of get_tree_prior_names\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of\n this model combination) to 0.0 (no evidence in favor of this model combi-\n nation)\n • ess: effective sample size of the marginal likelihood estimation\n Use get_test_marg_liks to get a test marg_liks. Use is_marg_liks to determine\n if a marg_liks is valid. Use check_marg_liks to check that a marg_liks is\n valid.\n mcbette_state the mcbette state, which is a list with the following elements:\n • beast2_installed TRUE if BEAST2 is installed, FALSE otherwise\n • ns_installed NA if BEAST2 is not installed. TRUE if the BEAST2 NS\n package is installed FALSE if the BEAST2 NS package is not installed\n mcmc an MCMC for the Nested Sampling run, as can be created by create_mcmc_nested_sampling\n os name of the operating system, must be unix (Linux, Mac) or win (Windows)\n rng_seed a random number generator seed used for the BEAST2 inference\n site_model a site model, as can be created by create_site_model\n site_models a list of one or more site models, as can be created by create_site_models\n tree_prior a tree prior, as can be created by create_tree_prior\n tree_priors a list of one or more tree priors, as can be created by create_tree_priors\n verbose if TRUE show debug output\nNote\n This is an internal function, so it should be marked with @noRd. This is not done, as this will\n disallow all functions to find the documentation parameters\nAuthor(s)\n <NAME>\n est_marg_lik Estimate the marginal likelihood for an inference model.\nDescription\n Estimate the marginal likelihood for an inference model.\nUsage\n est_marg_lik(\n fasta_filename,\n inference_model = beautier::create_ns_inference_model(),\n beast2_options = beastier::create_mcbette_beast2_options(),\n os = rappdirs::app_dir()$os\n )\nArguments\n fasta_filename name of the FASTA file\n inference_model\n an inference model, as can be created by create_inference_model\n beast2_options a beast2_options structure, as can be created by create_mcbette_beast2_options.\n os name of the operating system, must be unix (Linux, Mac) or win (Windows)\nValue\n a list showing the estimated marginal likelihoods (and its estimated error), its items are::\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • esses the Effective Sample Size\nAuthor(s)\n <NAME>\nSee Also\n • can_run_mcbette: see if ’mcbette’ can run\n • est_marg_liks: estimate multiple marginal likelihoods\nExamples\n if (can_run_mcbette()) {\n # An example FASTA file\n fasta_filename <- system.file(\"extdata\", \"simple.fas\", package = \"mcbette\")\n # A testing inference model with inaccurate (thus fast) marginal\n # likelihood estimation\n inference_model <- beautier::create_ns_inference_model()\n # Shorten the run, by doing a short (dirty, unreliable) MCMC\n inference_model$mcmc <- beautier::create_test_ns_mcmc()\n # Setup the options for BEAST2 to be able to call BEAST2 packages\n beast2_options <- beastier::create_mcbette_beast2_options()\n # Estimate the marginal likelihood\n est_marg_lik(\n fasta_filename = fasta_filename,\n inference_model = inference_model,\n beast2_options = beast2_options\n )\n beastier::remove_beaustier_folders()\n }\n est_marg_liks Estimate the marginal likelihoods for one or more inference models\nDescription\n Estimate the marginal likelihoods (aka evidence) for one or more inference models, based on a\n single alignment. Also, the marginal likelihoods are compared, resulting in a relative weight for\n each model, where a relative weight of a model close to 1.0 means that that model is way likelier\n than the others.\nUsage\n est_marg_liks(\n fasta_filename,\n inference_models = list(beautier::create_inference_model(mcmc =\n beautier::create_ns_mcmc())),\n beast2_optionses = rep(list(beastier::create_mcbette_beast2_options()), times =\n length(inference_models)),\n verbose = FALSE,\n os = rappdirs::app_dir()$os\n )\nArguments\n fasta_filename name of the FASTA file\n inference_models\n a list of one or more inference models, as can be created by create_inference_model\n beast2_optionses\n list of one or more beast2_options structures, as can be created by create_mcbette_beast2_options.\n Use of reduplicated plural to achieve difference with beast2_options\n verbose if TRUE show debug output\n os name of the operating system, must be unix (Linux, Mac) or win (Windows)\nDetails\n In the process, multiple (temporary) files are created (where [x] denotes the index in a list)\n • beast2_optionses[x]$input_filename path to the the BEAST2 XML input file\n • beast2_optionses[x]$output_state_filename path to the BEAST2 XML state file\n • inference_models[x]$mcmc$tracelog$filename path to the BEAST2 trace file with pa-\n rameter estimates\n • inference_models[x]$mcmc$treelog$filename path to the BEAST2 trees file with the\n posterior trees\n • inference_models[x]$mcmc$screenlog$filename path to the BEAST2 screen output file\n These file can be deleted manually by bbt_delete_temp_files, else these will be deleted automati-\n cally by the operating system.\nValue\n a data.frame showing the estimated marginal likelihoods (and its estimated error) per combination\n of models. Columns are:\n • site_model_name: name of the site model\n • clock_model_name: name of the clock model\n • tree_prior_name: name of the tree prior\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of this model combi-\n nation) to 0.0 (no evidence in favor of this model combination)\n • ess: effective sample size of the marginal likelihood estimation\nAuthor(s)\n <NAME>\nSee Also\n • can_run_mcbette: see if ’mcbette’ can run\n • est_marg_liks: estimate multiple marginal likelihood of a single inference mode\nExamples\n if (can_run_mcbette()) {\n # Use an example FASTA file\n fasta_filename <- system.file(\"extdata\", \"simple.fas\", package = \"mcbette\")\n # Create two inference models\n inference_model_1 <- beautier::create_ns_inference_model(\n site_model = beautier::create_jc69_site_model()\n )\n inference_model_2 <- beautier::create_ns_inference_model(\n site_model = beautier::create_hky_site_model()\n )\n # Shorten the run, by doing a short (dirty, unreliable) MCMC\n inference_model_1$mcmc <- beautier::create_test_ns_mcmc()\n inference_model_2$mcmc <- beautier::create_test_ns_mcmc()\n # Combine the inference models\n inference_models <- list(inference_model_1, inference_model_2)\n # Create the BEAST2 options, that will write the output\n # to different (temporary) filanems\n beast2_options_1 <- beastier::create_mcbette_beast2_options()\n beast2_options_2 <- beastier::create_mcbette_beast2_options()\n # Combine the two BEAST2 options sets,\n # use reduplicated plural\n beast2_optionses <- list(beast2_options_1, beast2_options_2)\n # Compare the models\n marg_liks <- est_marg_liks(\n fasta_filename,\n inference_models = inference_models,\n beast2_optionses = beast2_optionses\n )\n # Interpret the results\n interpret_marg_lik_estimates(marg_liks)\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n }\n get_mcbette_state Get the current state of mcbette\nDescription\n Get the current state of mcbette\nUsage\n get_mcbette_state(beast2_folder = beastier::get_default_beast2_folder())\nArguments\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\nValue\n a list with the following elements:\n • beast2_installed TRUE if BEAST2 is installed, FALSE otherwise\n • ns_installed TRUE if the BEAST2 NS package is installed FALSE if the BEAST2 or the\n BEAST2 NS package is not installed\nExamples\n get_mcbette_state()\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n get_test_marg_liks Get testing marg_liks\nDescription\n Get testing marg_liks\nUsage\n get_test_marg_liks()\nExamples\n get_test_marg_liks()\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n interpret_bayes_factor\n Interpret a Bayes factor\nDescription\n Interpret a Bayes factor, using the interpretation from [1].\nUsage\n interpret_bayes_factor(bayes_factor)\nArguments\n bayes_factor Bayes factor to be interpreted\nDetails\n • [1] <NAME> (1961). The Theory of Probability (3rd ed.). Oxford. p. 432\nValue\n a string with the interpretation in English\nAuthor(s)\n <NAME>\nExamples\n interpret_bayes_factor(0.5)\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n interpret_marg_lik_estimates\n Interpret the marginal likelihood estimates\nDescription\n Interpret the marginal likelihood estimates as created by est_marg_liks.\nUsage\n interpret_marg_lik_estimates(marg_liks)\nArguments\n marg_liks a table of (estimated) marginal likelihoods, as, for example, created by est_marg_liks.\n This data.frame has the following columns:\n • site_model_name: name of the site model, must be an element of get_site_model_names\n • clock_model_name: name of the clock model, must be an element of\n get_clock_model_names\n • tree_prior_name: name of the tree prior, must be an element of get_tree_prior_names\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of\n this model combination) to 0.0 (no evidence in favor of this model combi-\n nation)\n • ess: effective sample size of the marginal likelihood estimation\n Use get_test_marg_liks to get a test marg_liks. Use is_marg_liks to determine\n if a marg_liks is valid. Use check_marg_liks to check that a marg_liks is\n valid.\nAuthor(s)\n <NAME>\n is_marg_liks Determine if the marg_liks is valid\nDescription\n Determine if the marg_liks is valid\nUsage\n is_marg_liks(marg_liks, verbose = FALSE)\nArguments\n marg_liks a table of (estimated) marginal likelihoods, as, for example, created by est_marg_liks.\n This data.frame has the following columns:\n • site_model_name: name of the site model, must be an element of get_site_model_names\n • clock_model_name: name of the clock model, must be an element of\n get_clock_model_names\n • tree_prior_name: name of the tree prior, must be an element of get_tree_prior_names\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of\n this model combination) to 0.0 (no evidence in favor of this model combi-\n nation)\n • ess: effective sample size of the marginal likelihood estimation\n Use get_test_marg_liks to get a test marg_liks. Use is_marg_liks to determine\n if a marg_liks is valid. Use check_marg_liks to check that a marg_liks is\n valid.\n verbose if TRUE show debug output\nValue\n TRUE if the argument is a valid marg_liks, FALSE otherwise\n mcbette_report Create a mcbette report, to be used when reporting bugs\nDescription\n Create a mcbette report, to be used when reporting bugs\nUsage\n mcbette_report(beast2_folder = beastier::get_default_beast2_folder())\nArguments\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\nValue\n nothing. It is intended that the output (not the return value) is copy-pasted from screen.\nAuthor(s)\n <NAME>\nExamples\n if(beautier::is_on_ci()) {\n mcbette_report()\n }\n mcbette_self_test Performs a minimal mcbette run\nDescription\n Performs a minimal mcbette run\nUsage\n mcbette_self_test(beast2_folder = beastier::get_default_beast2_folder())\nArguments\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\n plot_marg_liks Plot the marg_liks\nDescription\n Plot the marg_liks\nUsage\n plot_marg_liks(marg_liks)\nArguments\n marg_liks a table of (estimated) marginal likelihoods, as, for example, created by est_marg_liks.\n This data.frame has the following columns:\n • site_model_name: name of the site model, must be an element of get_site_model_names\n • clock_model_name: name of the clock model, must be an element of\n get_clock_model_names\n • tree_prior_name: name of the tree prior, must be an element of get_tree_prior_names\n • marg_log_lik: estimated marginal (natural) log likelihood\n • marg_log_lik_sd: estimated error of marg_log_lik\n • weight: relative model weight, a value from 1.0 (all evidence is in favor of\n this model combination) to 0.0 (no evidence in favor of this model combi-\n nation)\n • ess: effective sample size of the marginal likelihood estimation\n Use get_test_marg_liks to get a test marg_liks. Use is_marg_liks to determine\n if a marg_liks is valid. Use check_marg_liks to check that a marg_liks is\n valid.\nValue\n a ggplot\nExamples\n plot_marg_liks(get_test_marg_liks())\n beastier::remove_beaustier_folders()\n beastier::check_empty_beaustier_folders()\n set_mcbette_state Set the mcbette state.\nDescription\n Set the mcbette state to having BEAST2 installed with or without installing the BEAST2 NS pack-\n age.\nUsage\n set_mcbette_state(\n mcbette_state,\n beast2_folder = beastier::get_default_beast2_folder(),\n verbose = FALSE\n )\nArguments\n mcbette_state the mcbette state, which is a list with the following elements:\n • beast2_installed TRUE if BEAST2 is installed, FALSE otherwise\n • ns_installed NA if BEAST2 is not installed. TRUE if the BEAST2 NS\n package is installed FALSE if the BEAST2 NS package is not installed\n beast2_folder the folder where the BEAST2 is installed. Note that this is not the folder\n where the BEAST2 executable is installed: the BEAST2 executable is in a\n subfolder. Use get_default_beast2_folder to get the default BEAST2 folder.\n Use get_default_beast2_bin_path to get the full path to the default BEAST2\n executable. Use get_default_beast2_jar_path to get the full path to the default\n BEAST2 jar file.\n verbose if TRUE show debug output\nNote\n In newer versions of BEAST2, BEAST2 comes pre-installed with the BEAST2 NS package. For\n such a version, one cannot install BEAST2 without NS. A warning will be issues if one intends to\n only install BEAST2 (i.e. without the BEAST2 NS package) and gets the BEAST2 NS package\n installed as a side effect as well.\n Also, installing or uninstalling a BEAST2 package from a BEAST2 installation will affect all in-\n stallations.\nSee Also\n • Use get_mcbette_state to get the current mcbette state\n • Use check_mcbette_state to check the current mcbette state"}}},{"rowIdx":59494,"cells":{"project":{"kind":"string","value":"asphalt-influxdb"},"source":{"kind":"string","value":"readthedoc"},"language":{"kind":"string","value":"Python"},"content":{"kind":"string","value":"asphalt-influxdb 2.1.0.post3 documentation\n\n[asphalt-influxdb](index.html#document-index)\n\n---\n\nThis Asphalt framework component provides connectivity to [InfluxDB](https://www.influxdata.com/) database servers.\n\nTable of contents[¶](#table-of-contents)\n===\n\nConfiguration[¶](#configuration)\n---\n\nThe typical InfluxDB configuration using a single database at `localhost` on the default port would look like this:\n```\ncomponents:\n influxdb:\n db: mydb\n```\nThe above configuration creates an [`asphalt.influxdb.client.InfluxDBClient`](index.html#asphalt.influxdb.client.InfluxDBClient) instance in the context, available as `ctx.influxdb` (resource name: `default`).\n\nIf you wanted to connect to `influx.example.org` on port 8886, you would do:\n```\ncomponents:\n influxdb:\n base_urls: http://influx.example.org:8886\n db: mydb\n```\nTo connect to an InfluxEnterprise cluster, list all the nodes under `base_urls`:\n```\ncomponents:\n influxdb:\n base_urls:\n - http://influx1.example.org:8086\n - http://influx2.example.org:8086\n - http://influx3.example.org:8086\n db: mydb\n```\nTo connect to two unrelated InfluxDB servers, you could use a configuration like:\n```\ncomponents:\n influxdb:\n clients:\n influx1:\n base_urls: http://influx.example.org:8886\n db: mydb\n influx2:\n context_attr: influxalter\n base_urls: https://influxalter.example.org/influxdb\n db: anotherdb\n username: testuser\n password: testpass\n```\nThis configuration creates two [`asphalt.influxdb.client.InfluxDBClient`](index.html#asphalt.influxdb.client.InfluxDBClient) resources,\n`influx1` and `influx2` (`ctx.influx1` and `ctx.influxalter`) respectively.\n\nNote\n\nSee the documentation of the [`asphalt.influxdb.client.InfluxDBClient`](index.html#asphalt.influxdb.client.InfluxDBClient) class for a comprehensive listing of all connection options.\n\nUsing the InfluxDB client[¶](#using-the-influxdb-client)\n---\n\n### Getting the server version[¶](#getting-the-server-version)\n\nYou can find out which version of InfluxDB you’re running in the following manner:\n```\nasync def handler(ctx):\n version = await ctx.influxdb.ping()\n print('Running InfluxDB version ' + version)\n```\n### Writing data points[¶](#writing-data-points)\n\nEach data point being written into an InfluxDB database contains the following information:\n* name of the measurement (corresponds to a table in a relational database)\n* one or more tags (corresponds to indexed, non-nullable string columns in a RDBMS)\n* zero or more fields (corresponds to nullable columns in a RDBMS)\n* a timestamp (supplied by the server if omitted)\n\nData points can be written one at a time ([`write()`](index.html#asphalt.influxdb.client.InfluxDBClient.write))\nor many at once ([`write_many()`](index.html#asphalt.influxdb.client.InfluxDBClient.write_many)). It should be noted that the former is merely a wrapper for the latter.\n\nTo write a single data point:\n```\nasync def handler(ctx):\n await ctx.influxdb.write('cpu_load_short', dict(host=server02), dict(value=0.67))\n print('Running InfluxDB version ' + version)\n```\nTo write multiple data points, you need use use the [`DataPoint`](index.html#asphalt.influxdb.client.DataPoint)\nclass:\n```\nasync def handler(ctx):\n await ctx.influxdb.write_many([\n DataPoint('cpu_load_short', dict(host=server02), dict(value=0.67)),\n DataPoint('cpu_load_short', dict(host=server01), dict(value=0.21))\n ])\n```\nThe data points don’t have to be within the same measurement.\n\n### Querying the database[¶](#querying-the-database)\n\nThis library offers the ability to query data via both raw InfluxQL queries and a programmatic query builder. To learn how the query builder works, see the next section.\n\nSending raw queries is done using [`raw_query()`](index.html#asphalt.influxdb.client.InfluxDBClient.raw_query):\n```\nasync def handler(ctx):\n series = await ctx.influxdb.raw_query('SHOW DATABASES')\n print([row[0] for row in series])\n```\nIf you include more than one measurement in the `FROM` clause of a `SELECT` query, you will get a list of [`Series`](index.html#asphalt.influxdb.query.Series) as a result:\n```\nasync def handler(ctx):\n cpu_load, temperature = await ctx.influxdb.raw_query('SELECT * FROM cpu_load,temperature')\n print([row[0] for row in series])\n```\nIt is possible to send multiple queries by delimiting them with a semicolon (`;`).\nIf you do that, the call will return a list of results for each query, each of which may be a\n[`Series`](index.html#asphalt.influxdb.query.Series) or a list thereof:\n```\nasync def handler(ctx):\n db_series, m_series = await ctx.influxdb.raw_query('SHOW DATABASES; SHOW MEASUREMENTS')\n print('Databases:')\n print([row[0] for row in db_series])\n print('Measurements:')\n print([row[0] for row in m_series])\n```\nWarning\n\nDue to [this bug](https://github.com/aio-libs/yarl/issues/34), multiple queries with the same call do not currently work.\n\nNote\n\nIf you want to send a query like `SELECT ... INTO ...`, you must call\n[`raw_query()`](index.html#asphalt.influxdb.client.InfluxDBClient.raw_query) `with http_verb='POST'`.\nThe proper HTTP verb should be automatically detected from the query string for all other queries.\n\n### Using the query builder[¶](#using-the-query-builder)\n\nThe query builder allows one to dynamically build queries without having to do error prone manual string concatenation. The query builder is considered immutable, so every one of its methods returns a new builder with the modifications made to it, just like with [SQLAlchemy](http://sqlalchemy.org/) ORM queries.\n\nFor example, to select `field1` and `field2` from measurements `m1` and `m2`:\n```\nasync def handler(ctx):\n query = ctx.influxdb.query(['field1', 'field2'], ['m1', 'm2'])\n return await query.execute()\n```\nThis will produce a query like `SELECT \"field1\",\"field2\" FROM \"m1\",\"m2\"`.\n\nMore complex expressions can be given but field or tag names are not automatically quoted:\n```\nasync def handler(ctx):\n query = ctx.influxdb.query('field1 + field2', 'm1')\n return await query.execute()\n```\nThe query will look like `SELECT field1 + field2 FROM \"m1\"`.\n\nFilters can be added by using [`where()`](index.html#asphalt.influxdb.query.SelectQuery.where) with positional and/or keyword arguments:\n```\nasync def handler(ctx):\n query = ctx.influxdb.query(['field1', 'field2'], 'm1').\\\n where('field1 > 3.5', 'field2 < 6.2', location='Helsinki')\n return await query.execute()\n```\nThis will produce a query like\n`SELECT field1,field2 FROM \"m1\" WHERE field1 > 3.5 AND field2 < 6.2 AND location='Helsinki'`.\n\nTo use `OR`, you have to manually include it in one of the `WHERE` expressions.\n\nFurther calls to `.where()` will add conditions to the `WHERE` clause of the query.\nA call to `.where()` with no arguments will clear the `WHERE` clause.\n\nGrouping by tags works largely the same way:\n```\nasync def handler(ctx):\n query = ctx.influxdb.query(['field1', 'SUM(field2)'], 'm1').group_by('tag1')\n return await query.execute()\n```\nThe SQL: `SELECT field1,SUM(field2) FROM \"m1\" GROUP BY \"tag1\"`\n\nVersion history[¶](#version-history)\n---\n\nThis library adheres to [Semantic Versioning](http://semver.org/).\n\n**2.1.0** (2017-09-20)\n\n* Exposed the `Series.values` attribute to enable faster processing of query results\n\n**2.0.1** (2017-06-04)\n\n* Added compatibility with Asphalt 4.0\n* Fixed `DeprecationWarning: ClientSession.close() is not coroutine` warnings\n* Added Docker configuration for easier local testing\n\n**2.0.0** (2017-04-11)\n\n* **BACKWARD INCOMPATIBLE** Migrated to Asphalt 3.0\n* **BACKWARD INCOMPATIBLE** Migrated to aiohttp 2.0\n\n**1.1.1** (2017-02-09)\n\n* Fixed handling of long responses (on InfluxDB 1.2+)\n\n**1.1.0** (2016-12-15)\n\n* Added the `KeyedTuple._asdict()` method\n* Fixed wrong quoting of string values (should use single quotes, not double quotes)\n\n**1.0.0** (2016-12-12)\n\n* Initial release\n\n* [API reference](py-modindex.html)"}}},{"rowIdx":59495,"cells":{"project":{"kind":"string","value":"phpmyadmin-japanese"},"source":{"kind":"string","value":"readthedoc"},"language":{"kind":"string","value":"PHP"},"content":{"kind":"string","value":"phpMyAdmin 6.0.0-dev ドキュメント\n\n### ナビゲーション\n\n* [phpMyAdmin 6.0.0-dev ドキュメント](index.html#document-index) »\n\nphpMyAdmin 日本語ドキュメント[¶](#welcome-to-phpmyadmin-s-documentation)\n===\n\n目次:\n\nはじめに[¶](#introduction)\n---\n\nphpMyAdmin は、 MySQL または MariaDB データベースサーバの管理を扱うことを目的とした、 PHP で記述されたフリーソフトウェアのツールです。 phpMyAdmin を使用して、データベースの作成、クエリの実行、ユーザアカウントの追加など、ほとんどの管理タスクを実行できます。\n\n### 対応している機能[¶](#supported-features)\n\nphpMyAdmin は現在次のことができます。\n\n* データベース、テーブル、ビュー、カラム、インデックスの作成、表示、削除\n* ストアドプロシージャやクエリを通しての複数の結果セットの表示\n* データベース、テーブル、カラム、インデックスの作成、複製、削除、名前や定義の変更\n* サーバ、データベース、テーブルの保守、そのためのサーバの設定を提案\n* あらゆる [SQL](index.html#term-sql) 文の実行、編集、ブックマークができ、バッチクエリも可\n* テキストファイルをテーブルに読み込み\n* テーブルダンプの作成 [[1]](#f1) と読み込み\n* 様々な形式のデータのエクスポート [[1]](#f1)。 [CSV](index.html#term-csv), [XML](index.html#term-xml), [PDF](index.html#term-pdf), [ISO](index.html#term-iso)/[IEC](index.html#term-iec) 26300 - [OpenDocument](index.html#term-opendocument) テキストおよびスプレッドシート, Microsoft Word 2000, LATEX 形式\n* データと [MySQL](index.html#term-47) 構造のインポート。 [OpenDocument](index.html#term-opendocument) スプレッドシート、 [XML](index.html#term-xml)、 [CSV](index.html#term-csv)、 [SQL](index.html#term-sql) の各ファイルより\n* 複数のサーバの管理\n* MySQL ユーザアカウントと権限の追加、編集、削除\n* MyISAM テーブルにおける参照完全性のチェック\n* データベースレイアウトの [PDF](index.html#term-pdf) 画像の作成\n* データベースないしそのサブセットのグローバル検索\n* 事前に定義された一連の関数を使用した、格納されたデータの任意の形式への変換。 BLOB データを画像やダウンロードリンクとして表示するなど\n* データベース、テーブル、ビューの変更の追跡\n* InnoDB テーブルと外部キーの対応\n* 改良版の MySQL 拡張モジュールである mysqli の対応、[1.17 phpMyAdmin が対応しているデータベースのバージョンは？](index.html#faq1-17) を参照\n* ストアドプロシージャや関数の作成、編集、呼び出し、エクスポート、削除\n* イベントやトリガの作成、編集、エクスポート、削除\n* [80 の異なる言語](https://www.phpmyadmin.net/translations/) に対応\n\n### ショートカットキー[¶](#shortcut-keys)\n\n現在、phpMyAdmin は以下のショートカットに対応しています。\n\n* k - コンソールの表示/非表示\n* h - ホームページへ移動\n* s - 設定を開く\n* d + s - データベースの構造へ移動 (データベース関連のページにいる場合)\n* d + f - データベースを検索 (データベース関連のページにいる場合)\n* t + s - テーブルの構造へ移動 (テーブル関連のページにいる場合)\n* t + f - テーブルを検索 (テーブル関連のページにいる場合)\n* backspace - ひとつ前のページへ移動。\n\n### ユーザについて一言[¶](#a-word-about-users)\n\n多くの人々が phpMyAdmin におけるユーザ管理の概念を理解するのが難しいと感じています。ユーザが phpMyAdmin にログインすると、その時のユーザ名とパスワードは MySQL に直接渡されます。phpMyAdmin は、独自にアカウント管理を (MySQL のユーザアカウント情報を操作するために１つ許可している以外は) 行っていません。すべてのユーザは、有効な MySQL ユーザである必要があります。\n\n脚注\n\n| [1] | *([1](#footnote-reference-1), [2](#footnote-reference-2))* [Zlib](index.html#term-zlib) に対応 (`--with-zlib`) した PHP を使用すると、 phpMyAdmin は圧縮ダンプ ([ZIP](index.html#term-zip)、 [GZip](index.html#term-gzip)、 [RFC 1952](index.html#term-rfc-1952) 形式) や [CSV](index.html#term-csv) エクスポートが利用できるようになります。適切な対応には `php.ini` の変更が必要になる場合があります。 |\n\n要件[¶](#requirements)\n---\n\n### ウェブサーバ[¶](#web-server)\n\nphpMyAdmin のインタフェースは完全にブラウザに基づいているため、 phpMyAdmin のファイルをインストールするにはウェブサーバ (Apache、 nginx、 [IIS](index.html#term-iis) など) が必要です。\n\n### PHP[¶](#php)\n\n* You need PHP 8.1.2 or newer, with `session` support, the Standard PHP Library\n(SPL) extension, hash, ctype, and JSON support.\n* `mbstring` 拡張機能 ([mbstring](index.html#term-mbstring) を参照) を性能上の理由から強く推奨します。\n* ZIP ファイルのアップロードに対応するには、PHP の `zip` 拡張モジュールが必要です。\n* JPEG 画像のインラインサムネイル (\"image/jpeg: inline\") を正しい縦横比で表示する場合は、 PHP が GD2 に対応している必要があります。\n* クッキー認証を使用する場合は (既定)、 [openssl](https://www.php.net/openssl) 拡張モジュールを強く推奨します。\n* アップロードの進捗バーに対応するには、 [2.9 アップロード進行状況バーが見えるようにする](index.html#faq2-9) を参照してください。\n* XML と Open Document スプレッドシートのインポートに対応するには、 [libxml](https://www.php.net/libxml) 拡張モジュールが必要です。\n* ログインページで reCAPTCHA に対応するには、 [openssl](https://www.php.net/openssl) 拡張モジュールが必要です。\n* phpMyAdmin の最新のバージョンの表示に対応するには、 `php.ini` の中の `allow_url_open` を有効にするか、 [curl](https://www.php.net/curl) 拡張モジュールを使用する必要があります。\n\n参考\n\n[1.17 phpMyAdmin が対応している MySQL のバージョンは？](index.html#faq1-31)、 [認証モードの使い方](index.html#authentication-modes)\n\n### データベース[¶](#database)\n\nphpMyAdmin は MySQL と互換性のあるデータベースに対応しています。\n\n* MySQL 5.5 以降\n* MariaDB 5.0 以降\n\n参考\n\n[1.17 phpMyAdmin が対応しているデータベースのバージョンは？](index.html#faq1-17)\n\n### ウェブブラウザ[¶](#web-browser)\n\nphpMyAdmin にアクセスするには、クッキーと JavaScript を有効にしたウェブブラウザが必要です。\n\nBootstrap 4.5 が対応しているブラウザが必要です。 <<https://getbootstrap.com/docs/4.5/getting-started/browsers-devices/>> を参照してください。\n\nバージョン 5.2.0 で変更: Bootstrap 5.0 に対応したブラウザが必要です。 <<https://getbootstrap.com/docs/5.0/getting-started/browsers-devices/>> を参照してください。\n\nインストール[¶](#installation)\n---\n\nphpMyAdmin は MySQL データベースサーバに特別なセキュリティをほどこすものではありません。phpMyAdmin を使ったとしても、MySQL データベースに適切なパーミッションを付与するのは、やはりシステム管理者の仕事です。ただし、その目的で phpMyAdmin の ユーザアカウント ページを使うことはできます。\n\n### Linux ディストリビューション[¶](#linux-distributions)\n\nphpMyAdmin は多くの Linux ディストリビューションに含まれています。できればディストリビューションのパッケージを使用することをお勧めします。そちらはふつう、ディストリビューションとの統合が提供され、ディストリビューションからのセキュリティ更新を自動的に受けることができるからです。\n\n#### Debian と Ubuntu[¶](#debian-and-ubuntu)\n\nDebian と Ubuntu のほとんどのバージョンは phpMyAdmin パッケージを含んでいますが、設定ファイルは `/etc/phpmyadmin` の中で管理されており、公式の phpMyAdmin のドキュメントといくつかの点で異なることがあります。特に、以下のような点です。\n\n* ウェブサーバの設定 (Apache および lighttpd で動作)。\n* dbconfig-common を使用して [phpMyAdmin 環境保管領域](#linked-tables) を作成すること。\n* セットアップスクリプトの保護。 [Debian、Ubuntu とその派生製品のセットアップスクリプト](#debian-setup) を参照してください。\n\nDebian または Ubuntu パッケージのインストールに関する詳細は [Wiki 内](https://github.com/phpmyadmin/phpmyadmin/wiki/DebianUbuntu) にあります。\n\n参考\n\n詳しい情報は [README.Debian](https://salsa.debian.org/phpmyadmin-team/phpmyadmin/blob/debian/latest/debian/README.Debian) にあります (パッケージの `/usr/share/doc/phpmyadmin/README.Debian` としてインストールされます)。\n\n#### OpenSUSE[¶](#opensuse)\n\nOpenSUSE ではすでに phpMyAdmin パッケージがあり、 [openSUSE Build Service](https://software.opensuse.org/package/phpMyAdmin) からパッケージをインストールするだけです。\n\n#### Gentoo[¶](#gentoo)\n\nGentoo は、ストックに近い設定と `webapp-config` 設定の両方で phpMyAdmin パッケージを提供しています。インストールするには `emerge dev-db/phpmyadmin` を使用してください。\n\n#### Mandriva[¶](#mandriva)\n\nMandriva は phpMyAdmin パッケージを `contrib` ブランチで提供しており、通常の Control Center からインストールすることができます。\n\n#### Fedora[¶](#fedora)\n\nFedora は phpMyAdmin パッケージを提供していますが、設定ファイルは `/etc/phpMyAdmin/` に保持されており、公式の phpMyAdmin ドキュメントとは異なる場合があることに注意してください。\n\n#### Red Hat Enterprise Linux[¶](#red-hat-enterprise-linux)\n\nRed Hat Enterprise Linux itself and thus derivatives like CentOS don't ship phpMyAdmin, but the Fedora-driven repository\n[Extra Packages for Enterprise Linux (EPEL)](https://docs.fedoraproject.org/en-US/epel/)\nis doing so, if it's\n[enabled](https://fedoraproject.org/wiki/EPEL/FAQ#howtouse).\nBut be aware that the configuration file is maintained in\n`/etc/phpMyAdmin/` and may differ in some ways from the official phpMyAdmin documentation.\n\n### Windows へのインストール[¶](#installing-on-windows)\n\nphpMyAdmin を Windows 上で利用できるようにするもっとも簡単な方法は、 [XAMPP](https://www.apachefriends.org/index.html) のような phpMyAdmin とデータベース、ウェブサーバを一緒に含むサードパーティ製品をインストールすることです。\n\nそれ以外の同様の選択肢は [Wikipedia](https://en.wikipedia.org/wiki/List_of_AMP_packages) を参照してください。\n\n### Git からのインストール[¶](#installing-from-git)\n\nGit からインストールするためには、いくつかのサポートアプリケーションが必要になります。\n\n* Git <https://git-scm.com/downloads> _ でソースをダウンロードします。または最新のソースを Github <https://codeload.github.com/phpmyadmin/phpmyadmin/zip/master> _ から直接ダウンロードすることができます\n* [Composer](https://getcomposer.org/download/)\n* [Node.js](https://nodejs.org/en/download/) (version 14 or higher)\n* [Yarn](https://classic.yarnpkg.com/en/docs/install)\n\n現在の phpMyAdmin のソースを `https://github.com/phpmyadmin/phpmyadmin.git` からクローンすることができます。\n```\ngit clone https://github.com/phpmyadmin/phpmyadmin.git\n```\n加えて、 [Composer](https://getcomposer.org) を使用して依存するものをインストールする必要があります。\n```\ncomposer update\n```\n開発目的でなければ、次のように実行すると開発者ツールのインストールをスキップすることができます。\n```\ncomposer update --no-dev\n```\n最後に、 [Yarn](https://classic.yarnpkg.com/en/docs/install) を使用して JavaScript の依存モジュールをいくつかインストールする必要があります。\n```\nyarn install --production\n```\n### Composer を使用したインストール[¶](#installing-using-composer)\n\nphpMyAdmin は [Composer tool](https://getcomposer.org/) を用いてインストールすることもでき、 4.7.0 からはデフォルトの [Packagist](https://packagist.org/) リポジトリに自動的に反映されます。\n\n注釈\n\nComposer のリポジトリの内容は、リリースとは独立して自動的に生成されるため、必ずしもダウンロード版と 100% 同じとは限りません。しかし、機能的な違いはないでしょう。\n\nphpMyAdmin をインストールするには、次のように実行するだけです。\n```\ncomposer create-project phpmyadmin/phpmyadmin\n```\n他にもリリース版を含む独自の Composer リポジトリを使用することもできます。 <<https://www.phpmyadmin.net/packages.json>> から利用することができます。\n```\ncomposer create-project phpmyadmin/phpmyadmin --repository-url=https://www.phpmyadmin.net/packages.json --no-dev\n```\n### Docker を使用したインストール[¶](#installing-using-docker)\n\nphpMyAdmin には簡単に配布することができる [Docker official image](https://hub.docker.com/_/phpmyadmin) が付属しており、次のようにダウンロードすることができます。\n```\ndocker pull phpmyadmin\n```\nphpMyAdmin サーバはポート80を待ち受けします。データベースサーバへのリンクを設定する方法は複数あり、データベースコンテナを phpMyAdmin の `db` にリンクするDockerのリンク機能を使用したり (`--link your_db_host:db` を指定)、環境変数で指定したりします (この場合、 phpMyAdmin コンテナがネットワーク経由でデータベースコンテナにアクセスできるように Docker でネットワークを設定する必要があります)。\n\n#### Docker の環境変数[¶](#docker-environment-variables)\n\n以下の環境変数を使用して phpMyAdmin のいくつかの機能を設定することができます。\n\n`PMA_ARBITRARY`[¶](#envvar-PMA_ARBITRARY)\nログインフォームでデータベースサーバのホスト名を入力できるようにします。\n\n参考\n\n[`$cfg['AllowArbitraryServer']`](index.html#cfg_AllowArbitraryServer)\n\n`PMA_HOST`[¶](#envvar-PMA_HOST)\n使用するデータベースサーバのホスト名と IP アドレスです。\n\n参考\n\n[`$cfg['Servers'][$i]['host']`](index.html#cfg_Servers_host)\n\n`PMA_HOSTS`[¶](#envvar-PMA_HOSTS)\nカンマ区切りの使用するデータベースサーバのホスト名と IP アドレスです。\n\n注釈\n\n[`PMA_HOST`](#envvar-PMA_HOST) が空の場合のみ使用されます。\n\n`PMA_VERBOSE`[¶](#envvar-PMA_VERBOSE)\nこのデータベースサーバの詳細な名前です。\n\n参考\n\n[`$cfg['Servers'][$i]['verbose']`](index.html#cfg_Servers_verbose)\n\n`PMA_VERBOSES`[¶](#envvar-PMA_VERBOSES)\nカンマ区切りのデータベースサーバの詳細な名前です。\n\n注釈\n\n[`PMA_VERBOSE`](#envvar-PMA_VERBOSE) が空の場合のみ使用されます。\n\n`PMA_USER`[¶](#envvar-PMA_USER)\n[config 認証モード](#auth-config) で使用するユーザ名です。\n\n`PMA_PASSWORD`[¶](#envvar-PMA_PASSWORD)\n[config 認証モード](#auth-config) で使用するパスワードです。\n\n`PMA_PORT`[¶](#envvar-PMA_PORT)\n使用するデータベースサーバのポート番号です。\n\n`PMA_PORTS`[¶](#envvar-PMA_PORTS)\nカンマ区切りで使用するデータベースサーバのポート番号です。\n\n注釈\n\n[`PMA_PORT`](#envvar-PMA_PORT) が空の場合のみ使用されます。\n\n`PMA_SOCKET`[¶](#envvar-PMA_SOCKET)\nSocket file for the database connection.\n\n`PMA_SOCKETS`[¶](#envvar-PMA_SOCKETS)\nComma-separated list of socket files for the database connections.\n\n注釈\n\nUsed only if [`PMA_SOCKET`](#envvar-PMA_SOCKET) is empty.\n\n`PMA_ABSOLUTE_URI`[¶](#envvar-PMA_ABSOLUTE_URI)\nphpMyAdmin を利用できるようにするリバースプロキシの完全修飾パス (`https://pma.example.net/`) です。\n\n参考\n\n[`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri)\n\n`PMA_QUERYHISTORYDB`[¶](#envvar-PMA_QUERYHISTORYDB)\ntrue に設定すると、 SQL 履歴が [`$cfg['Servers'][$i]['pmadb']`](index.html#cfg_Servers_pmadb) に保存できるようになります。 false の場合、履歴はブラウザに保存され、ログアウト時に消去されます。\n\n参考\n\n[`$cfg['Servers'][$i]['history']`](index.html#cfg_Servers_history)\n\n参考\n\n[`$cfg['QueryHistoryDB']`](index.html#cfg_QueryHistoryDB)\n\n`PMA_QUERYHISTORYMAX`[¶](#envvar-PMA_QUERYHISTORYMAX)\n整数に設定すると、履歴項目の数を制御します。\n\n参考\n\n[`$cfg['QueryHistoryMax']`](index.html#cfg_QueryHistoryMax)\n\n`PMA_CONTROLHOST`[¶](#envvar-PMA_CONTROLHOST)\nすると、 \"[phpMyAdmin 環境保管領域](#linked-tables)\" データベースを格納するために使用される代替データベースホストを指します。\n\n参考\n\n[`$cfg['Servers'][$i]['controlhost']`](index.html#cfg_Servers_controlhost)\n\n`PMA_CONTROLUSER`[¶](#envvar-PMA_CONTROLUSER)\nphpMyAdmin が \"[phpMyAdmin 環境保管領域](#linked-tables)\" データベースで使用するユーザ名を定義します。\n\n参考\n\n[`$cfg['Servers'][$i]['controluser']`](index.html#cfg_Servers_controluser)\n\n`PMA_CONTROLPASS`[¶](#envvar-PMA_CONTROLPASS)\nphpMyAdmin が \"[phpMyAdmin 環境保管領域](#linked-tables)\" データベースで使用するためのパスワードを定義します。\n\n参考\n\n[`$cfg['Servers'][$i]['controlpass']`](index.html#cfg_Servers_controlpass)\n\n`PMA_CONTROLPORT`[¶](#envvar-PMA_CONTROLPORT)\n設定された場合、制御ホストに接続するための既定値 (3306) を上書きします。\n\n参考\n\n[`$cfg['Servers'][$i]['controlport']`](index.html#cfg_Servers_controlport)\n\n`PMA_PMADB`[¶](#envvar-PMA_PMADB)\n設定された場合、 \"[phpMyAdmin 環境保管領域](#linked-tables)\" データベースで使用するデータベース名を定義します。設定しない場合、高度な機能はデフォルトで有効になりません。 [ゼロ設定](#zeroconf) 機能でログインした場合には、ユーザが潜在的に有効化することができます。\n\n注釈\n\n推奨値: phpmyadmin または pmadb\n\n参考\n\n[`$cfg['Servers'][$i]['pmadb']`](index.html#cfg_Servers_pmadb)\n\n`HIDE_PHP_VERSION`[¶](#envvar-HIDE_PHP_VERSION)\n定義すると、 PHP のバージョンを非表示にします (expose_php = Off)。任意の値を設定してください (HIDE_PHP_VERSION=true など)。\n\n`UPLOAD_LIMIT`[¶](#envvar-UPLOAD_LIMIT)\n設定されている場合、このオプションは apache および php-fpm のデフォルト値を上書きします (これにより、 `upload_max_filesize` および `post_max_size` の値が変更されます)。\n\n注釈\n\n[0-9+](K,M,G) という書式で、デフォルト値は`2048K` です\n\n`MEMORY_LIMIT`[¶](#envvar-MEMORY_LIMIT)\n設定すると、phpMyAdmin のメモリ制限 [`$cfg['MemoryLimit']`](index.html#cfg_MemoryLimit) と PHP の memory_limit を上書きするようになります。\n\n注釈\n\n書式は`[0-9+](K,M,G)` で、K はキロバイト、M はメガバイト、G はギガバイトを表し、 1K = 1024 バイトです。デフォルト値は 512M です。\n\n`MAX_EXECUTION_TIME`[¶](#envvar-MAX_EXECUTION_TIME)\n設定された場合、このオプションは phpMyAdmin の [`$cfg['ExecTimeLimit']`](index.html#cfg_ExecTimeLimit) と PHP の max_execution_time の最大実行時間 (秒) を上書きすることになります。\n\n注釈\n\n書式は [0-9+] です。デフォルト値は`600` です。\n\n`PMA_CONFIG_BASE64`[¶](#envvar-PMA_CONFIG_BASE64)\n設定されている場合、このオプションは変数を base64 デコードした内容でデフォルトの config.inc.php を上書きします。\n\n`PMA_USER_CONFIG_BASE64`[¶](#envvar-PMA_USER_CONFIG_BASE64)\n設定されている場合、このオプションは変数を base64 デコードした内容でデフォルトの config.user.inc.php を上書きします。\n\n`PMA_UPLOADDIR`[¶](#envvar-PMA_UPLOADDIR)\n設定された場合、このオプションは、インポートするためにファイルを保存できるパスを設定します ([`$cfg['UploadDir']`](index.html#cfg_UploadDir))\n\n`PMA_SAVEDIR`[¶](#envvar-PMA_SAVEDIR)\n設定された場合、このオプションはエクスポートされたファイルを保存するためのパスを設定します ([`$cfg['SaveDir']`](index.html#cfg_SaveDir))\n\n`APACHE_PORT`[¶](#envvar-APACHE_PORT)\nこのオプションを設定すると、権限のないポートのような別のポートで Apache を実行したい場合に、デフォルトの Apache のポートを 80 から変更することができます。任意のポート値 (例: APACHE_PORT=8090) を設定することができます。\n\nデフォルトでは [クッキー認証モード](#cookie) が使用されますが、 [`PMA_USER`](#envvar-PMA_USER) と [`PMA_PASSWORD`](#envvar-PMA_PASSWORD) が設定された場合 [config 認証モード](#auth-config) に切り替わります。\n\n注釈\n\nログインに必要な資格情報は MySQL サーバに保存されます。 Docker イメージの場合、さまざまな方法で設定できます (たとえば、 MySQL コンテナの起動時は `MYSQL_ROOT_PASSWORD`)。 [MariaDB コンテナ](https://hub.docker.com/_/mariadb) または [MySQL コンテナ](https://hub.docker.com/_/mysql) のドキュメントを確認してください。\n\n#### 設定のカスタマイズ[¶](#customizing-configuration)\n\nさらに、設定は `/etc/phpmyadmin/config.user.inc.php` で調整できます。このファイルが存在する場合は、上記の環境変数から設定が生成された後に読み込まれるため、任意の設定変数を上書きできます。この設定は、 -v /some/local/directory/config.user.inc.php:/etc/phpmyadmin/config.user.inc.php 引数を使用して docker を呼び出すときにボリュームとして追加できます。\n\nなお、提供された設定ファイルは [Docker の環境変数](#docker-vars) の後で適用されますが、任意の値を上書きできます。\n\n例えば、 CSV エクスポートのデフォルトの動作を変更する場合は、以下の設定ファイルを使用してください。\n```\n<?php\n$cfg['Export']['csv_columns'] = true;\n```\n[Docker の環境変数](#docker-vars) に書かれている環境変数を使用する代わりに、サーバ設定を定義することで利用することもできます。\n```\n<?php\n/* Override Servers array */\n$cfg['Servers'] = [\n 1 => [\n 'auth_type' => 'cookie',\n 'host' => 'mydb1',\n 'port' => 3306,\n 'verbose' => 'Verbose name 1',\n ],\n 2 => [\n 'auth_type' => 'cookie',\n 'host' => 'mydb2',\n 'port' => 3306,\n 'verbose' => 'Verbose name 2',\n ],\n];\n```\n参考\n\n設定オプションの詳細な説明は [設定](index.html#config) を参照してください。\n\n#### Docker ボリューム[¶](#docker-volumes)\n\n以下のボリュームを使用して、イメージの動作をカスタマイズすることができます。\n\n`/etc/phpmyadmin/config.user.inc.php`\n\n> 追加の設定に使用することができます。詳しくは前の節を参照してください。\n\n`/sessions/`\n\n> セッションが保存されるディレクトリです。例えば [サインオン認証モード](#auth-signon) を使用するときに共有したくなるかもしれません。\n\n`/www/themes/`\n\n> phpMyAdmin がテーマを検索するディレクトリです。デフォルトでは、 phpMyAdmin に付属しているものだけが含まれていますが、 Docker ボリュームを利用して、追加の phpMyAdmin テーマ ([カスタムテーマ](index.html#themes) を参照) を入れることができます。\n\n#### Docker の例[¶](#docker-examples)\n\nphpMyAdmin を指定されたサーバに接続させるには、以下を使用してください。\n```\ndocker run --name phpmyadmin -d -e PMA_HOST=dbhost -p 8080:80 phpmyadmin:latest\n```\nphpMyAdmin を他のサーバにも接続させるには、以下を使用してください。\n```\ndocker run --name phpmyadmin -d -e PMA_HOSTS=dbhost1,dbhost2,dbhost3 -p 8080:80 phpmyadmin:latest\n```\n任意のサーバオプションを使用する場合です。\n```\ndocker run --name phpmyadmin -d --link mysql_db_server:db -p 8080:80 -e PMA_ARBITRARY=1 phpmyadmin:latest\n```\nDocker を用いてデータベースコンテナをリンクすることもできます。\n```\ndocker run --name phpmyadmin -d --link mysql_db_server:db -p 8080:80 phpmyadmin:latest\n```\n追加の設定で実行する方法です。\n```\ndocker run --name phpmyadmin -d --link mysql_db_server:db -p 8080:80 -v /some/local/directory/config.user.inc.php:/etc/phpmyadmin/config.user.inc.php phpmyadmin:latest\n```\n追加のテーマで実行します。\n```\ndocker run --name phpmyadmin -d --link mysql_db_server:db -p 8080:80 -v /some/local/directory/custom/phpmyadmin/themeName/:/var/www/html/themes/themeName/ phpmyadmin:latest\n```\n#### docker-compose の使用[¶](#using-docker-compose)\n\nまたは、 <<https://github.com/phpmyadmin/docker>> の docker-compose.yml で docker-compose を使用することもできます。これにより、 phpMyAdmin を任意のサーバで実行できます。ログインページで MySQL/MariaDB サーバを指定できます。\n```\ndocker compose up -d\n```\n#### docker-compose を使用した設定ファイルのカスタマイズ[¶](#customizing-configuration-file-using-docker-compose)\n\n外部ファイルを使用して phpMyAdmin の設定をカスタマイズし、 volumes 設定項目を使用して渡すことができます。\n```\nphpmyadmin:\n image: phpmyadmin:latest\n container_name: phpmyadmin\n environment:\n - PMA_ARBITRARY=1\n restart: always\n ports:\n - 8080:80\n volumes:\n - /sessions\n - ~/docker/phpmyadmin/config.user.inc.php:/etc/phpmyadmin/config.user.inc.php\n - /custom/phpmyadmin/theme/:/www/themes/theme/\n```\n参考\n\n[設定のカスタマイズ](#docker-custom)\n\n#### サブディレクトリの haproxy の背後で実行[¶](#running-behind-haproxy-in-a-subdirectory)\n\nサブディレクトリの Docker コンテナで実行されている phpMyAdmin を公開する場合は、リクエストを中継するサーバのリクエストパスを書き換える必要があります。\n\nたとえば、 haproxy を使用すると、次のように実行できます。\n```\nfrontend http\n bind *:80\n option forwardfor\n option http-server-close\n\n ### NETWORK restriction\n acl LOCALNET src 10.0.0.0/8 192.168.0.0/16 172.16.0.0/12\n\n # /phpmyadmin\n acl phpmyadmin path_dir /phpmyadmin\n use_backend phpmyadmin if phpmyadmin LOCALNET\n\nbackend phpmyadmin\n mode http\n\n reqirep ^(GET|POST|HEAD)\\ /phpmyadmin/(.*) \\1\\ /\\2\n\n # phpMyAdmin container IP\n server localhost 172.30.21.21:80\n```\ntraefik を使用する場合、次のようなものが機能するはずです。\n```\ndefaultEntryPoints = [\"http\"]\n[entryPoints]\n [entryPoints.http]\n address = \":80\"\n [entryPoints.http.redirect]\n regex = \"(http:\\\\/\\\\/[^\\\\/]+\\\\/([^\\\\?\\\\.]+)[^\\\\/])$\"\n replacement = \"$1/\"\n\n[backends]\n [backends.myadmin]\n [backends.myadmin.servers.myadmin]\n url=\"http://internal.address.to.pma\"\n\n[frontends]\n [frontends.myadmin]\n backend = \"myadmin\"\n passHostHeader = true\n [frontends.myadmin.routes.default]\n rule=\"PathPrefixStrip:/phpmyadmin/;AddPrefix:/\"\n```\n次に、 docker-compose の設定で [`PMA_ABSOLUTE_URI`](#envvar-PMA_ABSOLUTE_URI) を指定してください。\n```\nversion: '2'\n\nservices:\n phpmyadmin:\n restart: always\n image: phpmyadmin:latest\n container_name: phpmyadmin\n hostname: phpmyadmin\n domainname: example.com\n ports:\n - 8000:80\n environment:\n - PMA_HOSTS=172.26.36.7,172.26.36.8,172.26.36.9,172.26.36.10\n - PMA_VERBOSES=production-db1,production-db2,dev-db1,dev-db2\n - PMA_USER=root\n - PMA_PASSWORD=\n - PMA_ABSOLUTE_URI=http://example.com/phpmyadmin/\n```\n### IBM クラウド[¶](#ibm-cloud)\n\nユーザの1人が、 phpMyAdmin を [IBM Cloud プラットフォーム](https://github.com/KissConsult/phpmyadmin_tutorial#readme) にインストールするための役立つガイドを作成してくれました。\n\n### クイックインストール[¶](#quick-install-1)\n\n1. Choose an appropriate distribution kit from the phpmyadmin.net Downloads page. Some kits contain only the English messages, others contain all languages. We'll assume you chose a kit whose name looks like `phpMyAdmin-x.x.x-all-languages.tar.gz`.\n2. 正しいアーカイブをダウンロードしたことを確認してください。 [phpMyAdmin リリースの検証](#verify) を参照してください。\n3. tar または zip の配布ファイルを展開します (unzip の場合はサブディレクトリ付きで)。ウェブサーバのドキュメントルートで `tar -xzvf phpMyAdmin_x.x.x-all-languages.tar.gz` を実行します。ドキュメントルートへの直接アクセス権がない場合は、ローカルマシンのディレクトリにファイルを解凍し、ステップ 4 まで済んだらそのディレクトリを FTP などでウェブサーバに転送してください。\n4. 必ずすべてのスクリプトの所有者を適切に設定してください (PHP がセーフモードで実行されている場合、スクリプトによって所有者が異なると問題が発生します)。解説については [4.2 phpMyAdmin を悪意のあるアクセスから守るようにするお勧めの方法はありますか？](index.html#faq4-2) や [1.26 phpMyAdmin を IIS のドキュメントルートにインストールしたところなのですが、phpMyAdmin を実行しようとすると「No input file specified（入力ファイルが指定されていません）」というエラーが出ます。](index.html#faq1-26) を参照してください。\n5. まず最初に、インストールを設定する必要があります。やり方は 2 つあります。1 つは、ユーザが `config.inc.php` を手動で編集・コピーする伝統的な方法ですが、グラフィカルなインストールを好む人向けにウィザード形式のセットアップスクリプトも提供するようになりました。現在でも `config.inc.php` を作成する方がすばやく始められる方法であり、一部の高度な機能にはこちらが必要です。\n\n#### 手作業でのファイルの作成[¶](#manually-creating-the-file)\n\n手作業でファイルを作成するには、テキストエディタを使用して `config.inc.php` ファイルを phpMyAdmin のメイン (トップレベル) ディレクトリ (`index.php` があるところ) に作成するだけです (その際、 `config.sample.inc.php` をコピーすることで最小限の設定ファイルを作成することもできます)。最初に phpMyAdmin はデフォルトの設定値をを読み込み、それから `config.inc.php` 内で見つかった値でデフォルト値を上書きします。設定に問題がなければ、デフォルト値は `config.inc.php` に含める必要はありません。稼動させるにはいくつかの設定項目が必要ですが、単純な設定では以下にようになります。\n```\n<?php\n// The string is a hexadecimal representation of a 32-bytes long string of random bytes.\n$cfg['blowfish_secret'] = sodium_hex2bin('f16ce59f45714194371b48fe362072dc3b019da7861558cd4ad29e4d6fb13851');\n\n$i=0;\n$i++;\n$cfg['Servers'][$i]['auth_type'] = 'cookie';\n// if you insist on \"root\" having no password:\n// $cfg['Servers'][$i]['AllowNoPassword'] = true;\n```\nあるいは、ログインするたびにプロンプトを表示させたくないのであれば以下のようにします。\n```\n<?php\n\n$i=0;\n$i++;\n$cfg['Servers'][$i]['user'] = 'root';\n$cfg['Servers'][$i]['password'] = 'changeme'; // use here your password\n$cfg['Servers'][$i]['auth_type'] = 'config';\n```\n警告\n\n設定にパスワードを保存すると、誰でもデータベースを操作できるようになるため安全ではありません。\n\n使用可能な設定値の詳細な解説については、このドキュメントの [設定](index.html#config) を参照してください。\n\n#### セットアップスクリプトの使用[¶](#using-the-setup-script)\n\n`config.inc.php` を手動で編集する代わりに、 phpMyAdmin のセットアップ機能を使用することができます。セットアップを使用してファイルを生成し、サーバにアップロードするためにダウンロードすることができます。\n\n次にブラウザを開き、 phpMyAdmin をインストールした場所の最後に `/setup` を付けてアクセスします。変更はサーバに保存されません。 ダウンロード ボタンを使用して変更をコンピュータに保存してから、サーバにアップロードする必要があります。\n\nこれで、ファイルを使用する準備ができました。セットアップスクリプトが提供していない一部の高度なオプションを設定したい場合は、好きなエディタでファイルを確認したり編集したりすることを選択できます。\n\n1. `auth_type` に ”config\" を使用した場合は、phpMyAdmin をインストールしたディレクトリを保護することをお勧めします。なぜなら、config 認証を使用した場合、インストールされた phpMyAdmin にアクセスするのに、ユーザがパスワードの入力を必要としないからです。 [.htaccess](index.html#term-htaccess) ファイルで HTTP 認証を設定したり、 `auth_type` を cookie または http で使用するなど、その他の認証方法の使うことをお勧めします。詳細については [ISP やマルチユーザのインストール](index.html#faqmultiuser) 、特に [4.4 HTTP 認証を使用すると必ず「Access denied (アクセスは拒否されました)」になります。](index.html#faq4-4) を参照してください。\n2. ブラウザで phpMyAdmin のメインディレクトリを開きます。 [HTTP](index.html#term-http) 認証やクッキー認証モードを使用している場合、 phpMyAdmin はようこそ画面とデータベース、またはログインダイアログが表示されるようになりました。\n\n##### Debian、Ubuntu とその派生製品のセットアップスクリプト[¶](#setup-script-on-debian-ubuntu-and-derivatives)\n\nDebian と Ubuntu では、セットアップスクリプトを有効にしたり無効にしたりする方法が変更されました。これにより、それぞれのために単一のコマンドを実行する必要があります。\n\n設定を編集できるようにするには、次のように呼び出してください。\n```\n/usr/sbin/pma-configure\n```\n設定の編集を防止するには、次のように呼び出してください。\n```\n/usr/sbin/pma-secure\n```\n##### openSUSE のセットアップスクリプト[¶](#setup-script-on-opensuse)\n\nopenSUSE の一部のリリースでは、パッケージにセットアップスクリプトが含まれていません。そのような環境の場合は、 <<https://www.phpmyadmin.net/>> から元のパッケージをダウンロードしたり、デモサーバ <<https://demo.phpmyadmin.net/master/setup/>> のセットアップスクリプトを使用したりすることで、設定を作成することができます。\n\n### phpMyAdmin リリースの検証[¶](#verifying-phpmyadmin-releases)\n\n2015年7月以降、すべての phpMyAdmin のリリースはリリース開発者によって暗号で署名されており、2016年1月までは Marc Delisle でした。彼のキーIDは 0xFE<KEY> であり、彼の PGP フィンガープリントは次のとおりです。\n```\n436F F188 4B1A 0C3F DCBF 0D79 FEFC 65D1 81AF 644A\n```\nまた、他の識別情報は <<https://keybase.io/lem9>> から入手できます。\n\n2016年1月から、リリース管理者は <NAME> です。彼のキー ID は 0xCE<KEY> であり、 PGP フィンガープリントは次の通りです。\n```\n3D06 A59E CE73 0EB7 1B51 1C17 CE75 2F17 8259 BD92\n```\nまた、他の識別情報は <<https://keybase.io/ibennetch>> から入手できます。\n\nその他のいくつかのダウンロード (例えばテーマ) は、 <NAME> が署名していることがあります。彼のキー ID は 0x<KEY> で、 PGP フィンガープリントは次の通りです。\n```\n63CB 1DF1 EF12 CF2A C0EE 5A32 9C27 B313 42B7 511D\n```\nまた、他の識別情報は <<https://keybase.io/nijel>> から入手できます。\n\n署名がダウンロードしたアーカイブと一致することを確認してください。この方法で、リリースされたものと同じコードを使用していることを確認できます。また、署名の日付を確認して、最新バージョンをダウンロードしたことを確認してください。\n\n各アーカイブには、その PGP 署名を含む `.asc` ファイルが付属しています。両方を同じフォルダに入れれば、署名を検証することができます。\n```\n$ gpg --verify phpMyAdmin-4.5.4.1-all-languages.zip.asc gpg: Signature made Fri 29 Jan 2016 08:59:37 AM EST using RSA key ID 8259BD92 gpg: Can't check signature: public key not found\n```\nご覧のとおり、 gpg は公開鍵を知らないと報告します。この時点で、次のいずれかの手順を実行する必要があります。\n\n* [ダウンロードサーバ](https://files.phpmyadmin.net/phpmyadmin.keyring) からキーリングをダウンロードし、次のようにしてインポートしてください。\n```\n$ gpg --import phpmyadmin.keyring\n```\n* 鍵サーバのうちの 1 つから鍵をダウンロードしてインポートしてください。\n```\n$ gpg --keyserver hkp://pgp.mit.edu --recv-keys 3D06A59ECE730EB71B511C17CE752F178259BD92 gpg: requesting key 8259BD92 from hkp server pgp.mit.edu gpg: key 8259BD92: public key \"<NAME> <<EMAIL>>\" imported gpg: no ultimately trusted keys found gpg: Total number processed: 1 gpg: imported: 1 (RSA: 1)\n```\nこれにより、状況が少し改善されます。この時点で、指定された鍵の署名が正しいことを確認できますが、鍵で使用されている名前を信頼することはできません。\n```\n$ gpg --verify phpMyAdmin-4.5.4.1-all-languages.zip.asc gpg: Signature made Fri 29 Jan 2016 08:59:37 AM EST using RSA key ID 8259BD92 gpg: Good signature from \"<NAME> <<EMAIL>>\"\ngpg: aka \"<NAME> <<EMAIL>>\"\ngpg: WARNING: This key is not certified with a trusted signature!\ngpg: There is no indication that the signature belongs to the owner.\nPrimary key fingerprint: 3D06 A59E CE73 0EB7 1B51 1C17 CE75 2F17 8259 BD92\n```\nここでの問題は、誰でもこの名前の鍵を発行できることです。実際に言及された人が鍵を所有していることを確認する必要があります。 GNU プライバシーハンドブックは、 [Validating other keys on your public keyring](https://www.gnupg.org/gph/en/manual.html#AEN335) の章でこのトピックを扱っています。最も信頼できる方法は、開発者に直接会ってキーフィンガープリントを交換することですが、信頼できるウェブに頼ることもできます。このようにして、開発者に直接会った他の人の署名を介して、キーを推移的に信頼することができます。\n\nキーが信頼されると、警告は発生しません。\n```\n$ gpg --verify phpMyAdmin-4.5.4.1-all-languages.zip.asc gpg: Signature made Fri 29 Jan 2016 08:59:37 AM EST using RSA key ID 8259BD92 gpg: Good signature from \"<NAME> <<EMAIL>>\" [full]\n```\n署名が無効な場合 (アーカイブが変更されている場合)、鍵が信頼されているかどうかに関係なく、明確なエラーが発生します。\n```\n$ gpg --verify phpMyAdmin-4.5.4.1-all-languages.zip.asc gpg: Signature made Fri 29 Jan 2016 08:59:37 AM EST using RSA key ID 8259BD92 gpg: BAD signature from \"<NAME> <<EMAIL>>\" [unknown]\n```\n### phpMyAdmin 環境保管領域[¶](#phpmyadmin-configuration-storage)\n\nバージョン 3.4.0 で変更: phpMyAdmin 3.4.0 より前は、これはリンクテーブル基盤と呼ばれていましたが、ストレージの用途が拡大されたため、名前が変更されました。\n\n一連の追加機能 ([ブックマーク](index.html#bookmarks)、コメント、 [SQL](index.html#term-sql) の履歴、コマンド追跡機能、 [PDF](index.html#term-pdf) 生成、 [変換機能](index.html#transformations)、 [リレーション](index.html#relations) など) を使うには専用のテーブル群を作成する必要があります。これらのテーブル群は自分のデータベースに格納することもできますし、マルチユーザのインストールの場合はセントラルデータベースに格納することもできます (このセントラルデータベースは制御ユーザがアクセスするものです。ほかのユーザに権限を持たせないでください)。\n\n#### ゼロ設定[¶](#zero-configuration)\n\nIn many cases, this database structure can be automatically created and configured. This is called “Zero Configuration” mode and can be particularly useful in shared hosting situations. “ZeroConf” mode is on by default, to disable set [`$cfg['ZeroConf']`](index.html#cfg_ZeroConf) to false.\n\nゼロ設定モードは、以下の３種類のシナリオに対応しています。\n\n* 環境保管領域のテーブルが存在しないデータベースに入ると、 phpMyAdmin は [操作] タブから作成することを提案します。\n* テーブルがすでに存在するデータベースに入ると、ソフトウェアはこれを自動的に検出して使用し始めます。これは最も一般的な状況です。テーブルが最初に自動的に作成された後、ユーザを邪魔することなく継続的に使用されます。これは、共有ホスティングでユーザが `config.inc.php` を編集できず、通常、ユーザが1つのデータベースにしかアクセスしない場面で最も有用です。\n* 複数のデータベースにアクセスする場合、ユーザが先に環境保管領域のテーブルを含むデータベースに入ってから、別のデータベースに切り替えた場合、 phpMyAdmin は最初のデータベースのテーブルを使用し続けます。ユーザに対して、新しいデータベースにさらにテーブルを作成するよう求めることはありません。\n\n#### 手作業での設定[¶](#manual-configuration)\n\n`./sql/` ディレクトリを確認してください。 *create_tables.sql* というファイルがあるはずです (Windows サーバを使用している場合は、 [1.23 MySQL を Win32 マシンで稼動させているのですが、新規テーブルを作成するたびにテーブル名とカラム名が小文字に変わってしまいます！](index.html#faq1-23) を注意深く読んでください)。\n\nすでにこの仕組みを使用している場合は、次のことを実行してください。\n\n* MySQL 4.1.2 以降にアップグレードする場合は、 `sql/upgrade_tables_mysql_4_1_2+.sql` を使用してください。\n* phpMyAdmin 2.5.0 以降 (4.2.x 以前) から 4.3.0 以降にアップグレードした場合は、 `sql/upgrade_column_info_4_3_0+.sql` を使用してください。\n* phpMyAdmin 4.3.0 以降から 4.7.0 以降にアップグレードした場合は、 `sql/upgrade_tables_4_7_0+.sql` を使用してください。\n\nそれから `sql/create_tables.sql` をインポートして新しいテーブルを作成してください。\n\nphpMyAdmin を使ってテーブル群を作成することもできますが、いくつか注意することがあります。データベースやテーブルを作成する際には特別な (管理者の) 権限が必要になるかもしれません。また、データベース名によってはスクリプトに多少の修正を加える必要があるかもしれません。\n\n`sql/create_tables.sql` ファイルをインポートしたら、 `config.inc.php` ファイルでテーブル名を指定してください。このとき使う設定項目の説明は [設定](index.html#config) にあります。\n\nこれらのテーブルに対して正しい権限を持った制御ユーザ ([`$cfg['Servers'][$i]['controluser']`](index.html#cfg_Servers_controluser) および [`$cfg['Servers'][$i]['controlpass']`](index.html#cfg_Servers_controlpass) 設定) が必要です。例えば、以下の文を使用して作成することができます。\n\nMariaDB の任意のバージョンの場合:\n```\nCREATE USER 'pma'@'localhost' IDENTIFIED VIA mysql_native_password USING 'pmapass';\nGRANT SELECT, INSERT, UPDATE, DELETE ON `<pma_db>`.* TO 'pma'@'localhost';\n```\nMySQL 8.0 以降の場合:\n```\nCREATE USER 'pma'@'localhost' IDENTIFIED WITH caching_sha2_password BY 'pmapass';\nGRANT SELECT, INSERT, UPDATE, DELETE ON <pma_db>.* TO 'pma'@'localhost';\n```\nMySQL 8.0 以前の場合:\n```\nCREATE USER 'pma'@'localhost' IDENTIFIED WITH mysql_native_password AS 'pmapass';\nGRANT SELECT, INSERT, UPDATE, DELETE ON <pma_db>.* TO 'pma'@'localhost';\n```\nなお、 PHP 7.4 より前と MySQL 8.0 より後の MySQL インストールでは、応急措置として mysql_native_password 認証を使用する必要があるかもしれません。詳しくは [1.45 ログインしようとすると、 caching_sha2_password が不明な認証方法であることに関するエラーメッセージが表示されます](index.html#faq1-45) を参照してください。\n\n### 旧版からのアップグレード[¶](#upgrading-from-an-older-version)\n\n警告\n\n**絶対に** インストール済みの phpMyAdmin の上に新しいバージョンを展開しないでください。必ず先に古いファイルを削除し、設定のみを保持するようにしてください。\n\nこのようにして、セキュリティに深刻な影響を及ぼしたり、さまざまな破損を引き起こしたりする可能性がある古いファイルをディレクトリに残さないようにします。\n\n以前インストールされたものから `config.inc.php` を新しく展開した先にコピーするだけです。古いバージョンにあった設定ファイルは、一部のオプションを変更したり削除したりする若干の調整が必要な場合があります。設定ファイルの末尾付近に `set_magic_quotes_runtime(0);` 文が見つかった場合は、 PHP 5.3 以降との互換性のために削除してください。\n\nいくつかの単純な手順で完全なアップグレードを行うことができます。\n\n1. 最新版の phpMyAdmin を <<https://www.phpmyadmin.net/downloads/>> からダウンロードしてください。\n2. 既存の phpMyAdmin のフォルダの名前を変更します (例えば `phpmyadmin-old` などへ)。\n3. 新しくダウンロードした phpMyAdmin を必要な場所 (例えば `phpmyadmin`) に展開してください。\n4. `config.inc.php` を古い場所 (`phpmyadmin-old`) から新しい場所 (`phpmyadmin`) へコピーします。\n5. すべてが正しく動作することをテストします。\n6. 以前のバージョンのバックアップ (`phpmyadmin-old`) を削除します。\n\nMySQL サーバをバージョン 4.1.2 以前から 5.x 以降へアップグレードして、かつ、 phpMyAdmin 環境保管領域を使用している場合、 `sql/upgrade_tables_mysql_4_1_2+.sql` にある [SQL](index.html#term-sql) スクリプトを実行する必要があります。\n\nphpMyAdmin 2.5.0 以降 (4.2.x 以前) を 4.3.0 以降にアップグレードした場合で、 phpMyAdmin 環境保管領域を使用している場合は、 `sql/upgrade_column_info_4_3_0+.sql` にある [SQL](index.html#term-sql) スクリプトを実行してください。\n\nブラウザのキャッシュをクリアすることと、ログアウトして古いセッションを空にし、ログインし直すことを忘れないでください。\n\n### 認証モードの使い方[¶](#using-authentication-modes)\n\n[HTTP](index.html#term-http) 認証モードとクッキー認証モードは、ユーザに自分のデータベースへのアクセスを許可し、他のデータベースにアクセスしてほしくない **マルチユーザ環境** にお勧めです。それでも、 MS Internet Explorer の少なくともバージョン 6 までは、クッキーについて実にバグが多いことに注意してください。 **シングルユーザ環境** でも、ユーザ名とパスワードのが設定ファイルで明らかにならないので、 [HTTP](index.html#term-http) 認証モードやクッキー認証モードを使用することをお勧めします。\n\n[HTTP](index.html#term-http) 認証モードやクッキー認証モードの方がより安全です。 MySQL のログイン情報を phpMyAdmin の設定ファイルに書く必要がないからです ([`$cfg['Servers'][$i]['controluser']`](index.html#cfg_Servers_controluser))。しかし、 HTTPS プロトコルを使用しない限り、パスワードはプレーンテキストで送信されることに気を付けてください。クッキーモードでは、パスワードは一時的なクッキーに AES アルゴリズムで暗号化した上で保存されます。\n\nそれから、それぞれの *本当の* ユーザには、特定のデータベースのセットに対する一連の権限を与えなければなりません。通常、権限の影響を理解しているユーザでない限り(例えばスーパーユーザを作成している場合など)、通常のユーザにグローバル権限を与えるべきではありません。例えば、 *real_user* にデータベース *user_base* 上のすべての権限を付与するには、以下のようにしてください。\n```\nGRANT ALL PRIVILEGES ON user_base.* TO 'real_user'@localhost IDENTIFIED BY 'real_password';\n```\nユーザが実行できることは、完全に MySQL のユーザ管理システムによって制御されます。 HTTP またはクッキー認証モードでは、 [`$cfg['Servers']`](index.html#cfg_Servers) のユーザ/パスワードフィールドに記入する必要はありません。\n\n参考\n\n[1.32 IIS で HTTP 認証を利用できますか？](index.html#faq1-32)、 [1.35 Apache の CGI で HTTP 認証が使用できますか？](index.html#faq1-35)、 [4.1 当方は ISP です。 phpMyAdmin のセントラルコピーを一つだけセットアップするようにできますか？それとも顧客ごとにインストールする必要がありますか？](index.html#faq4-1)、 [4.2 phpMyAdmin を悪意のあるアクセスから守るようにするお勧めの方法はありますか？](index.html#faq4-2)、 [4.3 /lang や /libraries の中のファイルをインクルードできないというエラーが出ます。](index.html#faq4-3)\n\n#### HTTP 認証モード[¶](#http-authentication-mode)\n\n* [HTTP](index.html#term-http) の Basic 認証を使用して、有効な MySQL ユーザとしてログインできるようになります。\n* ほとんどの PHP 構成が対応しています。 [CGI](index.html#term-cgi) PHP を使用した [IIS](index.html#term-iis) ([ISAPI](index.html#term-isapi)) の対応については、 [1.32 IIS で HTTP 認証を利用できますか？](index.html#faq1-32) を参照し、 Apache [CGI](index.html#term-cgi) の場合は [1.35 Apache の CGI で HTTP 認証が使用できますか？](index.html#faq1-35) を参照してください。\n* PHP が Apache の [mod_proxy_fcgi](index.html#term-mod-proxy-fcgi) の下で (例えば PHP-FPM で) 実行されている場合、 `Authorization` ヘッダが配下の FCGI アプリケーションに渡されず、 FCGI アプリケーションに渡されないため、資格情報がアプリケーションに到達しません。この場合、次の設定項目を追加できます。\n```\nSetEnvIf Authorization \"(.*)\" HTTP_AUTHORIZATION=$1\n```\n* '[HTTP](index.html#term-http)' 認証モードで [.htaccess](index.html#term-htaccess) メカニズムを使用しない方法については、 [4.4 HTTP 認証を使用すると必ず「Access denied (アクセスは拒否されました)」になります。](index.html#faq4-4) も参照してください。\n\n注釈\n\nHTTP 認証で適切なログアウトを行う方法はありません。ほとんどのブラウザでは、他の認証が成功しない限り、資格情報を保持します。このため、この方法ではログアウト後に同じユーザでログインできないという制限があります。\n\n#### クッキー認証モード[¶](#cookie-authentication-mode)\n\n* ユーザ名とパスワードはセッション中はクッキーに保存され、パスワードは終了時に削除されます。\n* このモードでは、ユーザは phpMyAdmin のログアウトが確実に行え、同じユーザ名でログインし直すことができます (これは [HTTP 認証モード](#auth-http) ではできません)。\n* 接続先に (`config.inc.php` で設定したサーバのみでなく) ユーザが任意のホスト名を入力できるようにしたいのであれば、 [`$cfg['AllowArbitraryServer']`](index.html#cfg_AllowArbitraryServer) の設定項目を参照してください。\n* [要件](index.html#require) の章にある通り、 `openssl` 拡張機能を利用するとアクセスが顕著に高速化されますが、必須ではありません。\n\n#### サインオン認証モード[¶](#signon-authentication-mode)\n\n* このモードは、別のアプリケーションからの資格情報を使用して phpMyAdmin に認証を行い、シングルサインオンのソリューションを実装するのに便利な方法です。\n* 別なアプリケーションがセッションデータにログイン情報を格納するか ([`$cfg['Servers'][$i]['SignonSession']`](index.html#cfg_Servers_SignonSession) および [`$cfg['Servers'][$i]['SignonCookieParams']`](index.html#cfg_Servers_SignonCookieParams) を参照)、こちらで資格情報を返すスクリプトを実装する必要があります ([`$cfg['Servers'][$i]['SignonScript']`](index.html#cfg_Servers_SignonScript) を参照)。\n* 資格情報が利用できない場合は、ユーザがログインプロセスを行う [`$cfg['Servers'][$i]['SignonURL']`](index.html#cfg_Servers_SignonURL) にリダイレクトされます。\n\n資格情報をセッションに保存するとても基本的な例が `examples/signon.php` にあります。\n```\n<?php\n/**\n * Single signon for phpMyAdmin\n *\n * This is just example how to use session based single signon with\n * phpMyAdmin, it is not intended to be perfect code and look, only\n * shows how you can integrate this functionality in your application.\n */\n\ndeclare(strict_types=1);\n\n/* Use cookies for session */\nini_set('session.use_cookies', 'true');\n/* Change this to true if using phpMyAdmin over https */\n$secureCookie = false;\n/* Need to have cookie visible from parent directory */\nsession_set_cookie_params(0, '/', '', $secureCookie, true);\n/* Create signon session */\n$sessionName = 'SignonSession';\nsession_name($sessionName);\n// Uncomment and change the following line to match your $cfg['SessionSavePath']\n//session_save_path('/foobar');\n@session_start();\n\n/* Was data posted? */\nif (isset($_POST['user'])) {\n /* Store there credentials */\n $_SESSION['PMA_single_signon_user'] = $_POST['user'];\n $_SESSION['PMA_single_signon_password'] = $_POST['password'];\n $_SESSION['PMA_single_signon_host'] = $_POST['host'];\n $_SESSION['PMA_single_signon_port'] = $_POST['port'];\n /* Update another field of server configuration */\n $_SESSION['PMA_single_signon_cfgupdate'] = ['verbose' => 'Signon test'];\n $_SESSION['PMA_single_signon_HMAC_secret'] = hash('sha1', uniqid(strval(random_int(0, mt_getrandmax())), true));\n $id = session_id();\n /* Close that session */\n @session_write_close();\n /* Redirect to phpMyAdmin (should use absolute URL here!) */\n header('Location: ../index.php');\n} else {\n /* Show simple form */\n header('Content-Type: text/html; charset=utf-8');\n\n echo '<?xml version=\"1.0\" encoding=\"utf-8\"?>' . \"\\n\";\n echo '<!DOCTYPE HTML>\n<html lang=\"en\" dir=\"ltr\">\n<head>\n<link rel=\"icon\" href=\"../favicon.ico\" type=\"image/x-icon\">\n<link rel=\"shortcut icon\" href=\"../favicon.ico\" type=\"image/x-icon\">\n<meta charset=\"utf-8\">\n<title>phpMyAdmin single signon example</title>\n</head>\n<body>';\n\n if (isset($_SESSION['PMA_single_signon_error_message'])) {\n echo '<p class=\"error\">';\n echo $_SESSION['PMA_single_signon_error_message'];\n echo '</p>';\n }\n\n echo '<form action=\"signon.php\" method=\"post\">\nUsername: <input type=\"text\" name=\"user\" autocomplete=\"username\" spellcheck=\"false\"><br>\nPassword: <input type=\"password\" name=\"password\" autocomplete=\"current-password\" spellcheck=\"false\"><br>\nHost: (will use the one from config.inc.php by default)\n<input type=\"text\" name=\"host\"><br>\nPort: (will use the one from config.inc.php by default)\n<input type=\"text\" name=\"port\"><br>\n<input type=\"submit\">\n</form>\n</body>\n</html>';\n}\n```\nまたは、 `examples/openid.php` にあるように、この方法を使用して OpenID と統合することもできます。\n```\n<?php\n/**\n * Single signon for phpMyAdmin using OpenID\n *\n * This is just example how to use single signon with phpMyAdmin, it is\n * not intended to be perfect code and look, only shows how you can\n * integrate this functionality in your application.\n *\n * It uses OpenID pear package, see https://pear.php.net/package/OpenID\n *\n * User first authenticates using OpenID and based on content of $AUTH_MAP\n * the login information is passed to phpMyAdmin in session data.\n */\n\ndeclare(strict_types=1);\n\nif (false === @include_once 'OpenID/RelyingParty.php') {\n exit;\n}\n\n/* Change this to true if using phpMyAdmin over https */\n$secureCookie = false;\n\n/**\n * Map of authenticated users to MySQL user/password pairs.\n */\n$authMap = ['https://launchpad.net/~username' => ['user' => 'root', 'password' => '']];\n\n// phpcs:disable PSR1.Files.SideEffects,Squiz.Functions.GlobalFunction\n\n/**\n * Simple function to show HTML page with given content.\n *\n * @param string $contents Content to include in page\n */\nfunction Show_page(string $contents): void\n{\n header('Content-Type: text/html; charset=utf-8');\n\n echo '<?xml version=\"1.0\" encoding=\"utf-8\"?>' . \"\\n\";\n echo '<!DOCTYPE HTML>\n<html lang=\"en\" dir=\"ltr\">\n<head>\n<link rel=\"icon\" href=\"../favicon.ico\" type=\"image/x-icon\">\n<link rel=\"shortcut icon\" href=\"../favicon.ico\" type=\"image/x-icon\">\n<meta charset=\"utf-8\">\n<title>phpMyAdmin OpenID signon example</title>\n</head>\n<body>';\n\n if (isset($_SESSION['PMA_single_signon_error_message'])) {\n echo '<p class=\"error\">' . $_SESSION['PMA_single_signon_message'] . '</p>';\n unset($_SESSION['PMA_single_signon_message']);\n }\n\n echo $contents;\n echo '</body></html>';\n}\n\n/**\n * Display error and exit\n *\n * @param Exception $e Exception object\n */\nfunction Die_error(Throwable $e): void\n{\n $contents = \"<div class='relyingparty_results'>\\n\";\n $contents .= '<pre>' . htmlspecialchars($e->getMessage()) . \"</pre>\\n\";\n $contents .= \"</div class='relyingparty_results'>\";\n Show_page($contents);\n exit;\n}\n\n// phpcs:enable\n\n/* Need to have cookie visible from parent directory */\nsession_set_cookie_params(0, '/', '', $secureCookie, true);\n/* Create signon session */\n$sessionName = 'SignonSession';\nsession_name($sessionName);\n@session_start();\n\n// Determine realm and return_to\n$base = 'http';\nif (isset($_SERVER['HTTPS']) && $_SERVER['HTTPS'] === 'on') {\n $base .= 's';\n}\n\n$base .= '://' . $_SERVER['SERVER_NAME'] . ':' . $_SERVER['SERVER_PORT'];\n\n$realm = $base . '/';\n$returnTo = $base . dirname($_SERVER['PHP_SELF']);\nif ($returnTo[strlen($returnTo) - 1] !== '/') {\n $returnTo .= '/';\n}\n\n$returnTo .= 'openid.php';\n\n/* Display form */\nif ((! count($_GET) && ! count($_POST)) || isset($_GET['phpMyAdmin'])) {\n /* Show simple form */\n $content = '<form action=\"openid.php\" method=\"post\">\nOpenID: <input type=\"text\" name=\"identifier\"><br>\n<input type=\"submit\" name=\"start\">\n</form>';\n Show_page($content);\n exit;\n}\n\n/* Grab identifier */\n$identifier = null;\nif (isset($_POST['identifier']) && is_string($_POST['identifier'])) {\n $identifier = $_POST['identifier'];\n} elseif (isset($_SESSION['identifier']) && is_string($_SESSION['identifier'])) {\n $identifier = $_SESSION['identifier'];\n}\n\n/* Create OpenID object */\ntry {\n $o = new OpenID_RelyingParty($returnTo, $realm, $identifier);\n} catch (Throwable $e) {\n Die_error($e);\n}\n\n/* Redirect to OpenID provider */\nif (isset($_POST['start'])) {\n try {\n $authRequest = $o->prepare();\n } catch (Throwable $e) {\n Die_error($e);\n }\n\n $url = $authRequest->getAuthorizeURL();\n\n header('Location: ' . $url);\n exit;\n}\n\n/* Grab query string */\nif (! count($_POST)) {\n [, $queryString] = explode('?', $_SERVER['REQUEST_URI']);\n} else {\n // Fetch the raw query body\n $queryString = file_get_contents('php://input');\n}\n\n/* Check reply */\ntry {\n $message = new OpenID_Message($queryString, OpenID_Message::FORMAT_HTTP);\n} catch (Throwable $e) {\n Die_error($e);\n}\n\n$id = $message->get('openid.claimed_id');\n\nif (empty($id) || ! isset($authMap[$id])) {\n Show_page('<p>User not allowed!</p>');\n exit;\n}\n\n$_SESSION['PMA_single_signon_user'] = $authMap[$id]['user'];\n$_SESSION['PMA_single_signon_password'] = $authMap[$id]['password'];\n$_SESSION['PMA_single_signon_HMAC_secret'] = hash('sha1', uniqid(strval(random_int(0, mt_getrandmax())), true));\nsession_write_close();\n/* Redirect to phpMyAdmin (should use absolute URL here!) */\nheader('Location: ../index.php');\n```\n他の方法で認証情報を渡す場合は、 PHP にラッパーを実装してデータを取得し、 [`$cfg['Servers'][$i]['SignonScript']`](index.html#cfg_Servers_SignonScript) に設定しなければなりません。 `examples/signon-script.php` に非常にシンプルな例があります。\n```\n<?php\n/**\n * Single signon for phpMyAdmin\n *\n * This is just example how to use script based single signon with\n * phpMyAdmin, it is not intended to be perfect code and look, only\n * shows how you can integrate this functionality in your application.\n */\n\ndeclare(strict_types=1);\n\n// phpcs:disable Squiz.Functions.GlobalFunction\n\n/**\n * This function returns username and password.\n *\n * It can optionally use configured username as parameter.\n *\n * @param string $user User name\n *\n * @return array<int,string>\n */\nfunction get_login_credentials(string $user): array\n{\n /* Optionally we can use passed username */\n if (! empty($user)) {\n return [$user, 'password'];\n }\n\n /* Here we would retrieve the credentials */\n return ['root', ''];\n}\n```\n参考\n\n[`$cfg['Servers'][$i]['auth_type']`](index.html#cfg_Servers_auth_type)、 [`$cfg['Servers'][$i]['SignonSession']`](index.html#cfg_Servers_SignonSession)、 [`$cfg['Servers'][$i]['SignonCookieParams']`](index.html#cfg_Servers_SignonCookieParams)、 [`$cfg['Servers'][$i]['SignonScript']`](index.html#cfg_Servers_SignonScript)、 [`$cfg['Servers'][$i]['SignonURL']`](index.html#cfg_Servers_SignonURL)、 [サインオン認証モードの例](index.html#example-signon)\n\n#### config 認証モード[¶](#config-authentication-mode)\n\n* このモードはあまり安全ではありません。設定項目の [`$cfg['Servers'][$i]['user']`](index.html#cfg_Servers_user) と [`$cfg['Servers'][$i]['password']`](index.html#cfg_Servers_password) を記入する必要があるからです (そのため、 `config.inc.php` を読める人なら誰でもユーザ名とパスワードを見ることができてしまいます)。\n* [ISP やマルチユーザのインストール](index.html#faqmultiuser) 節の中で、構成ファイルを保護する方法を説明している項目があります。\n* このモードのセキュリティを向上させるには、 [`$cfg['Servers'][$i]['AllowDeny']['order']`](index.html#cfg_Servers_AllowDeny_order) と [`$cfg['Servers'][$i]['AllowDeny']['rules']`](index.html#cfg_Servers_AllowDeny_rules) の設定項目でホスト認証することを検討してみてください。\n* クッキー認証や HTTP 認証とは異なり、最初に phpMyAdmin サイトを読み込んだときに、ユーザがログインする必要がありません。これは仕様によるものですが、インストール先へのアクセスをどのユーザにも許可しているということです。いくつかの制約をかけることを推奨します。 [.htaccess](index.html#term-htaccess) ファイルで HTTP 認証を設定したり、ルータやファイアウォールで入ってくる HTTP リクエストを拒否したりすればおそらく十分でしょう (どちらもこのマニュアルの範疇を超えていますが、Google で容易に検索できます)。\n\n### phpMyAdmin のインストールを安全にする[¶](#securing-your-phpmyadmin-installation)\n\nphpMyAdmin チームは、アプリケーションを安全にするために一生懸命努力していますが、インストールをより安全にする方法は常にあります。\n\n* 私たちの [セキュリティアナウンス](https://www.phpmyadmin.net/security/) をフォローし、新しい脆弱性が公開されるたびに phpMyAdmin をアップグレードしてください。\n* phpMyAdmin を HTTPS のみで提供してください。できれば、プロトコルのダウングレード攻撃から保護するために、 HSTS も使用してください。\n* PHP の設定が本番サイトの推奨事項に従っていることを確認してください。たとえば、 [display_errors](https://www.php.net/manual/ja/errorfunc.configuration.php#ini.display-errors) を無効にしてください。\n* 開発中でテストスイートが必要な場合を除いて、 phpMyAdmin から `test` ディレクトリを削除してください。\n* phpMyAdmin から `setup` ディレクトリを削除してください。おそらく初期セットアップの後は使用しないでしょう。\n* 認証方法を適切に選択してください。 - 共有ホスティングにはおそらく [クッキー認証モード](#cookie) が最良の選択でしょう。\n* ウェブサーバの設定で、サブフォルダ `./libraries/` または `./templates/` にある外部ファイルへのアクセスを拒否してください。このような設定により、そのコードで発生する可能性のあるパスの公開やクロスサイトスクリプティングの脆弱性を防ぐことができます。 Apache ウェブサーバでは、多くの場合、これらのディレクトリにある [.htaccess](index.html#term-htaccess) ファイルで設定します。\n* 一時ファイルへのアクセスを拒否するようにしてください。 [`$cfg['TempDir']`](index.html#cfg_TempDir) を参照してください (ウェブルート内に配置されている場合は、「[ウェブサーバのアップロード/保存/インポートディレクトリ](index.html#web-dirs)」も参照してください)。\n* 一般的に、公開している phpMyAdmin のインストールをロボットからのアクセスから保護することは良い考えです。ウェブサーバのルートにある `robots.txt` ファイルを使用して行ったり、ウェブサーバの構成でアクセスを制限したりすることで実現できます。 [1.42 ロボットから phpMyAdmin へのアクセスを防ぐにはどうすればいいのでしょうか？](index.html#faq1-42) を参照してください。\n* すべての MySQL ユーザが phpMyAdmin にアクセスできるようにしたくない場合は、 [`$cfg['Servers'][$i]['AllowDeny']['rules']`](index.html#cfg_Servers_AllowDeny_rules) を使用して制限したり、 [`$cfg['Servers'][$i]['AllowRoot']`](index.html#cfg_Servers_AllowRoot) を使用して root ユーザのアクセスを拒否したりすることができます。\n* アカウントで [二要素認証](index.html#fa) を有効にしてください。\n* phpMyAdmin を認証プロキシの背後に隠すことを検討してください。そうすればユーザが phpMyAdmin に MySQL の資格情報を入力する前に認証を受けるようになります。これは、ウェブサーバに HTTP 認証を要求するように構成することで実現できます。例えば Apache では、次のようにして実現できます。\n```\nAuthType Basic AuthName \"Restricted Access\"\nAuthUserFile /usr/share/phpmyadmin/passwd Require valid-user\n```\n構成を変更したら、認証するユーザの一覧を作成する必要があります。これは **htpasswd** ユーティリティを使用して行うことができます。\n```\nhtpasswd -c /usr/share/phpmyadmin/passwd username\n```\n* 自動攻撃を恐れているのであれば、 [`$cfg['CaptchaLoginPublicKey']`](index.html#cfg_CaptchaLoginPublicKey) と [`$cfg['CaptchaLoginPrivateKey']`](index.html#cfg_CaptchaLoginPrivateKey) で Captcha を有効にするのも選択肢の一つです。\n* 失敗したログインの試みは syslog に記録されます (利用可能な場合は、 [`$cfg['AuthLog']`](index.html#cfg_AuthLog) を参照してください)。これにより、 fail2ban などのツールを使用して総当たり攻撃をブロックできます。 syslog が使用するログファイルは、 Apache のエラーログやアクセスログファイルと同じではないことに注意してください。\n* phpMyAdmin を他の PHP アプリケーションと一緒に実行している場合は、 phpMyAdmin に対して個別のセッションストレージを使用して、セッションベースの攻撃を回避することをお勧めします。これを実現するには、 [`$cfg['SessionSavePath']`](index.html#cfg_SessionSavePath) が使用できます。\n\n### データベースサーバへの接続で SSL を使用する[¶](#using-ssl-for-connection-to-database-server)\n\nリモートデータベースサーバに接続するときは SSL を使用することをお勧めします。 SSL のセットアップに関連するいくつかの設定オプションがあります。\n\n[`$cfg['Servers'][$i]['ssl']`](index.html#cfg_Servers_ssl)\nSSLを使用するかどうかを定義します。これのみを有効にすると、接続は暗号化されますが、接続の認証は行われません。適切なサーバと通信していることを確認することはできません。\n[`$cfg['Servers'][$i]['ssl_key']`](index.html#cfg_Servers_ssl_key) と [`$cfg['Servers'][$i]['ssl_cert']`](index.html#cfg_Servers_ssl_cert)\nこれはクライアントからサーバの認証に使用されます。\n[`$cfg['Servers'][$i]['ssl_ca']`](index.html#cfg_Servers_ssl_ca) と [`$cfg['Servers'][$i]['ssl_ca_path']`](index.html#cfg_Servers_ssl_ca_path)\nサーバ証明書で信頼する認証局です。これは、信頼できるサーバと通信していることを確認するために使用されます。\n[`$cfg['Servers'][$i]['ssl_verify']`](index.html#cfg_Servers_ssl_verify)\nこの構成はサーバ証明書の検証を無効にします。注意して使用してください。\n\nデータベースサーバがローカル接続やプライベートネットワークを使用していて SSL が構成できない場合は、 [`$cfg['MysqlSslWarningSafeHosts']`](index.html#cfg_MysqlSslWarningSafeHosts) に安全と見なすホスト名を明示的に並べることができます。\n\n参考\n\n[SSL 経由で Google Cloud SQL を使用](index.html#example-google-ssl)、 example-googleaws-ssl、 [`$cfg['Servers'][$i]['ssl']`](index.html#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](index.html#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](index.html#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](index.html#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](index.html#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](index.html#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](index.html#cfg_Servers_ssl_verify)\n\n### 既知の問題[¶](#known-issues)\n\n#### カラム固有の権限を持ったユーザが [表示] を利用できない[¶](#users-with-column-specific-privileges-are-unable-to-browse)\n\nユーザがテーブルの一部の (すべてではない) カラムに特有の権限しか持っていない場合、 [表示] は失敗してエラーメッセージを表示します。\n\n回避策として、テーブルと同じ名前のブックマーククエリを作成することができ、そうすれば [表示] リンクを使用したときに代わりに実行されます。 [課題 11922](https://github.com/phpmyadmin/phpmyadmin/issues/11922)。\n\n#### 'http' 認証を使用してログアウトした後、再度ログインする際の問題[¶](#trouble-logging-back-in-after-logging-out-using-http-authentication)\n\n'http' `auth_type` を使用している場合、(ログアウトが手動で行われたとき、または一定時間非アクティブになった後で) 再度のログインができない場合があります。 [課題 11898](https://github.com/phpmyadmin/phpmyadmin/issues/11898)。\n\n設定[¶](#configuration)\n---\n\n設定可能なデータは、ほとんどが phpMyAdmin の最上位ディレクトリの `config.inc.php` にあります。このファイルが存在しない場合は、 [インストール](index.html#setup) の節を参照して作成してください。このファイルには、既定値から変更したい引数のみ入れておく必要があります。\n\n参考\n\n[設定例](#config-examples) に設定の例があります\n\nある設定項目がファイルにない場合は、そのファイルにもう一行追加してください。このファイルは既定値を上書きするためのものです。デフォルト値を使いたい場合は、ここに行を追加する必要はありません。\n\nデザイン関係の引数 (色など) は `themes/themename/scss/_variables.scss` にあります。また、 `config.footer.inc.php` と `config.header.inc.php` ファイルを修正すれば各ページの先頭と末尾にページ固有のコードを追加できます。\n\n注釈\n\n一部のディストリビューション (例えば Debian や Ubuntu) では、 `config.inc.php` が phpMyAdmin のソース内ではなく `/etc/phpmyadmin` にあります。\n\n### 基本設定[¶](#basic-settings)\n\n`$cfg['PmaAbsoluteUri']`[¶](#cfg_PmaAbsoluteUri)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nバージョン 4.6.5 で変更: この設定は phpMyAdmin 4.6.0 - 4.6.4 では利用できません。\n\nここには、phpMyAdmin がインストールされているディレクトリの完全な [URL](index.html#term-url) を (フルパスで) 設定します。例えば `https://www.example.net/path_to_your_phpMyAdmin_directory/` などです。なお、多くのウェブサーバでは (Windows であっても) この [URL](index.html#term-url) の大文字小文字を区別します。末尾のスラッシュを忘れないようにしてください。\n\nバージョン 2.3.0 からはここを空欄にすることが推奨されています。たいていの場合、phpMyAdmin は自動的に適切な設定を検出します。ポート転送をしているユーザはこれをを設定する必要があるでしょう。\n\n試しに、テーブルを表示して、行を編集して保存してみてください。 phpMyAdmin が正しい値を自動検出できていない場合はエラーメッセージが表示されるはずです。この値を設定してくださいというエラーが出る、あるいは自動検出コードがパスの検出に失敗する場合は、開発陣がコードを改善できるよう、バグレポートをバグトラッカーにお送りください。\n\n参考\n\n[1.40 Apache のリバースプロキシを介して phpMyAdmin にアクセスすると、クッキーログインが機能しません。](index.html#faq1-40)、[2.5 行を挿入や削除をしようとしたり、データベースやテーブルを削除したりしようとするたびに 404 (ページが見つかりません) エラーが表示されます。また、 HTTP またはクッキー認証をしているときはログインし直すように求められます。何が悪いのでしょうか？](index.html#faq2-5)、[4.7 認証ウインドウが複数回表示されます。なぜでしょうか？](index.html#faq4-7)、[5.16 Internet Explorer で「アクセスが拒否されました（Access is denied）」という JavaScript のエラーが出ます。あるいは、 Windows で phpMyAdmin を実行できません。](index.html#faq5-16)\n\n`$cfg['PmaNoRelation_DisableWarning']`[¶](#cfg_PmaNoRelation_DisableWarning)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 2.3.0 以降、マスタ／外部テーブルを操作する機能が多数提供されています ([`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) 参照)。\n\nそのマスタ／外部データベースをセットアップしてみてもうまくいかない場合、その機能を利用したいデータベースの 構造 ページを見れば、無効になっている理由を分析するリンクが見つかるはずです。\n\nそういった機能を使いたくない場合は、この変数を `true` に設定しておけばメッセージが表示されなくなります。\n\n`$cfg['AuthLog']`[¶](#cfg_AuthLog)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'auto'` |\n\nバージョン 4.8.0 で追加: phpMyAdmin 4.8.0 以降で対応しています。\n\n認証ログの記録先を設定します。認証に失敗した (あるいはすべて、 [`$cfg['AuthLogSuccess']`](#cfg_AuthLogSuccess) に依存する) 認証の試みは、この設定項目に従ってログに記録されます。\n\n`auto`\nphpMyAdmin に自動的に `syslog` と `php` を選択させます。\n`syslog`\nsyslog を使用してログを記録し、 AUTH 機能を使用すると、ほとんどのシステムで `/var/log/auth.log` になります。\n`php`\nPHP エラーログにログ出力します。\n`sapi`\nPHP の SAPI ログにログ出力します。\n`/path/to/file`\nそれ以外の値はファイル名として扱われ、ログ項目はそこに書き込まれます。\n\n注釈\n\nファイルにログを記録する際には、ウェブサーバのユーザ向けにパーミッションを正しく設定していることを確認し、設定が [`$cfg['TempDir']`](#cfg_TempDir) に記述されている指示と合っている必要があります。\n\n`$cfg['AuthLogSuccess']`[¶](#cfg_AuthLogSuccess)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.8.0 で追加: phpMyAdmin 4.8.0 以降で対応しています。\n\n認証の成功を [`$cfg['AuthLog']`](#cfg_AuthLog) に記録するかどうか。\n\n`$cfg['SuhosinDisableWarning']`[¶](#cfg_SuhosinDisableWarning)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nSuhosin が検出された場合、警告をメインページに表示します。\n\nこの引数を `true` に設定することで、メッセージの表示を止めることができます。\n\n`$cfg['LoginCookieValidityDisableWarning']`[¶](#cfg_LoginCookieValidityDisableWarning)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nPHP のパラメータ session.gc_maxlifetime が phpMyAdmin で設定したクッキーの有効期限よりも短い場合、メインページに警告が表示されます。\n\nこの引数を `true` に設定することで、メッセージの表示を止めることができます。\n\n`$cfg['ServerLibraryDifference_DisableWarning']`[¶](#cfg_ServerLibraryDifference_DisableWarning)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.7.0 で非推奨: この設定は警告が削除されたので削除しました。\n\nMySQL ライブラリとサーバのバージョンが異なる場合、メインページに警告が表示されます。\n\nこの引数を `true` に設定することで、メッセージの表示を止めることができます。\n\n`$cfg['ReservedWordDisableWarning']`[¶](#cfg_ReservedWordDisableWarning)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nこの警告は、1つ以上のカラム名が MySQL の予約語と一致した場合に、テーブルの構造ページに表示されます。\n\nこの警告を消したい場合は、 `true` に設定すると警告が表示されなくなります。\n\n`$cfg['TranslationWarningThreshold']`[¶](#cfg_TranslationWarningThreshold)\n\n| データ型: | 整数型 |\n| デフォルト値: | 80 |\n\n指定されたしきい値に達していない不完全な翻訳に対して警告を表示します。\n\n`$cfg['SendErrorReports']`[¶](#cfg_SendErrorReports)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'ask'` |\n\n可能な値は次の通りです。\n\n* `ask`\n* `always`\n* `never`\n\nJavaScript エラー報告の既定の動作を設定します。\n\nユーザが同意すれば、 JavaScript の実行中にエラーが検出されるたび、エラーレポートが phpMyAdmin チームに送信されることがあります。\n\nデフォルトの設定では `'ask'` は新しいエラー報告があるたびにユーザに確認を求めます。しかし、このパラメータを `'always'` に設定すると確認を求めずにエラーレポートを送信することができますし、 `'never'` に設定するとエラーレポートを送信しません。\n\nこの設定項目は、設定ファイルとユーザ設定の両方で利用できます。マルチユーザインストールの責任者がこの機能をすべてのユーザに対して無効にしたい場合は、 `'never'` を設定し、 [`$cfg['UserprefsDisallow']`](#cfg_UserprefsDisallow) 設定項目の配列の値の一つに `'SendErrorReports'` を含める必要があります。\n\n`$cfg['ConsoleEnterExecutes']`[¶](#cfg_ConsoleEnterExecutes)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nこれを `true` に設定すると、ユーザが Ctrl+Enter の代わりに Enter キーを押すことでクエリを実行できるようになります。改行は Shift+Enter で挿入することができます。\n\nコンソールの動作は、コンソールの設定インタフェースを使用して一時的に変更することができます。\n\n`$cfg['AllowThirdPartyFraming']`[¶](#cfg_AllowThirdPartyFraming)\n\n| データ型: | 論理型|文字列型 |\n| デフォルト値: | false |\n\nこれを `true` に設定すると、 phpMyAdmin をフレーム内に表示することを許可しますが、クロスフレームスクリプト攻撃やクリックジャックを可能にする潜在的なセキュリティホールにもなりえます。これを 'sameorigin' に設定すると、他の文書であれば文書が同じドメインのものであっても、 phpMyAdmin をフレーム内に表示することを防止します。\n\n### サーバ接続設定[¶](#server-connection-settings)\n\n`$cfg['Servers']`[¶](#cfg_Servers)\n\n| データ型: | 配列型 |\n| デフォルト値: | 以下に示すような設定のサーバの配列 |\n\nバージョン 1.4.2 以降、phpMyAdmin は複数の MySQL サーバを管理できるようになっています。そのために追加されたのが [`$cfg['Servers']`](#cfg_Servers) 配列です。ここにはさまざまなサーバへのログイン情報が格納されます。例えば、最初の [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) には最初のサーバのホスト名が、2 番目の [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) には 2 番目のサーバのホスト名が入ります。 `config.inc.php` には必要なだけの数の定義を追加できますので、ブロックや必要な部分をコピーしいてください (すべての設定を定義する必要はありません。必要な部分のみ変更してください)。\n\n注釈\n\n[`$cfg['Servers']`](#cfg_Servers) の配列は $cfg['Servers'][1] から始まります。 cfg['Servers'][0] は使用しないでください。複数のサーバが必要な場合は、以下の部分を何度かコピーしてください ($iのインクリメントを含む)。サーバの配列を完全に定義する必要はなく、変更したい値を定義するだけです。\n\n`$cfg['Servers'][$i]['host']`[¶](#cfg_Servers_host)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'localhost'` |\n\n$i 番目の MySQL サーバのホスト名または [IP](index.html#term-ip) アドレスが入ります。 例えば `localhost` です。\n\n可能な値は次の通りです。\n\n* ホスト名、例えば `'localhost'` や `'mydb.example.org'`\n* IP アドレス、例えば `'127.0.0.1'` や `'192.168.10.1'`\n* IPv6 アドレス、例えば `2001:cdba:0000:0000:0000:0000:3257:9652`\n* ドット - `'.'`、例えば、 Windows システムで名前付きパイプを使用\n* 空文字列 - `''`、このサーバを無効にする\n\n注釈\n\nホスト名 `localhost` は MySQL によって特別に扱われ、ソケットベースの接続プロトコルを使用します。 TCP/IP ネットワークを利用するには、 `127.0.0.0.1` や `db.example.com` などの IP アドレスやホスト名を使用してください。ソケットへのパスは [`$cfg['Servers'][$i]['socket']`](#cfg_Servers_socket) で設定できます。\n\n参考\n\n[`$cfg['Servers'][$i]['port']`](#cfg_Servers_port)、 <<https://dev.mysql.com/doc/refman/8.0/ja/connecting.html>`$cfg['Servers'][$i]['port']`[¶](#cfg_Servers_port)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n$i 番目の MySQL サーバのポート番号。デフォルトは 3306 (空白のまま)。\n\n注釈\n\nホスト名を `localhost` にすると、 MySQL はポート番号を無視してソケット接続しますので、デフォルトとは別のポートで接続したい場合は `127.0.0.1` または実際のホスト名を [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) に記入してください。\n\n参考\n\n[`$cfg['Servers'][$i]['host']`](#cfg_Servers_host)、<<https://dev.mysql.com/doc/refman/8.0/ja/connecting.html>`$cfg['Servers'][$i]['socket']`[¶](#cfg_Servers_socket)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n適切にソケットを使用するには、MySQL の設定などを確認してください。 **mysql** コマンドラインクライアントを使用して、 `status` コマンドの発行してください。その結果の中に、ソケットが使われているかが表示されます。\n\n注釈\n\n[`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) が `localhost` に設定されているときのみ効果があります。\n\n参考\n\n[`$cfg['Servers'][$i]['host']`](#cfg_Servers_host)、<<https://dev.mysql.com/doc/refman/8.0/ja/connecting.html>`$cfg['Servers'][$i]['ssl']`[¶](#cfg_Servers_ssl)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nphpMyAdmin とMySQL サーバとの間の接続を安全にするために SSL を有効にするかどうか。\n\n`'mysql'` 拡張モジュールを使用している場合、残りの `'ssl...'` 設定オプションはどれも適用されません。\n\nこのオプションを使う場合は `'mysqli'` 拡張モジュールを使うことを強くお勧めします。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、[Amazon RDS Aurora with SSL](#example-aws-ssl)、[`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_key']`[¶](#cfg_Servers_ssl_key)\n\n| データ型: | 文字列型 |\n| デフォルト値: | NULL |\n\nMySQL サーバへの接続に SSL を使用する場合のクライアントキーファイルへのパス。これは、サーバに対してクライアントを認証するために使用されます。\n\n例:\n```\n$cfg['Servers'][$i]['ssl_key'] = '/etc/mysql/server-key.pem';\n```\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_cert']`[¶](#cfg_Servers_ssl_cert)\n\n| データ型: | 文字列型 |\n| デフォルト値: | NULL |\n\nMySQL サーバへ SSL で接続する際のクライアント資格情報ファイルへのパス。これはクライアントからサーバへ認証する際に使用されます。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_ca']`[¶](#cfg_Servers_ssl_ca)\n\n| データ型: | 文字列型 |\n| デフォルト値: | NULL |\n\nMySQL サーバへの接続に SSL を使用する場合の CA ファイルへのパス。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_ca_path']`[¶](#cfg_Servers_ssl_ca_path)\n\n| データ型: | 文字列型 |\n| デフォルト値: | NULL |\n\nPEM 形式の信頼できる SSL CA 証明書を含むディレクトリ。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_ciphers']`[¶](#cfg_Servers_ssl_ciphers)\n\n| データ型: | 文字列型 |\n| デフォルト値: | NULL |\n\nMySQL サーバに対する SSL 接続で利用できる暗号のリスト。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['ssl_verify']`[¶](#cfg_Servers_ssl_verify)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nバージョン 4.6.0 で追加: phpMyAdmin 4.6.0 以降で対応しています。\n\nPHP のインストールで MySQL ネイティブドライバ (mysqlnd) を使用している場合、 MySQL サーバは 5.6 以降であり、SSL 証明書が自己署名されている場合、検証のために SSL 接続が失敗する可能性があります。これを `false` に設定すると、検証チェックが無効になります。\n\nPHP 5.6.0 以降では、サーバ名が証明書の CN と一致するかどうかも確認されます。現在、完全な SSL 検証を無効にせずに、このチェックを無効にする方法はありません。\n\n警告\n\n証明書の検証を無効にすると、 SSL を使用する目的が無効になります。これにより、接続は中間攻撃者に対して脆弱になります。\n\n注釈\n\nこのフラグは PHP 5.6.16 以降でのみ有効です。\n\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [SSL 経由で Google Cloud SQL を使用](#example-google-ssl)、 [Amazon RDS Aurora with SSL](#example-aws-ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n`$cfg['Servers'][$i]['connect_type']`[¶](#cfg_Servers_connect_type)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'tcp'` |\n\nバージョン 4.7.0 で非推奨: この設定は 4.7.0 以降では使用されなくなりました。 MySQL はホスト名に基づいて接続種別を決定するため、想定外の結果を導く可能性があるためです。代わりに、 [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) を設定してください。\n\nMySQL サーバで利用する接続タイプが入ります。選択肢は `'socket'` と `'tcp'` です。デフォルトが tcp になっているのは、どんな MySQL サーバでもほぼ確実に利用できるためです。ソケットの方はプラットフォームによっては対応していません。\n\n`$cfg['Servers'][$i]['compress']`[¶](#cfg_Servers_compress)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nMySQL サーバとの接続に圧縮プロトコルを使うかどうかが入ります（実験段階です）。\n\n`$cfg['Servers'][$i]['controlhost']`[¶](#cfg_Servers_controlhost)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n指定すると、phpMyAdmin 環境保管領域に対して代替ホストが使えるようになります。\n\n参考\n\n[`$cfg['Servers'][$i]['control_*']`](#cfg_Servers_control_*)\n\n`$cfg['Servers'][$i]['controlport']`[¶](#cfg_Servers_controlport)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n環境保管領域を保持するホストに別なポートを使用して接続することを許可します。\n\n参考\n\n[`$cfg['Servers'][$i]['control_*']`](#cfg_Servers_control_*)\n\n`$cfg['Servers'][$i]['controluser']`[¶](#cfg_Servers_controluser)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n`$cfg['Servers'][$i]['controlpass']`[¶](#cfg_Servers_controlpass)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nこの特殊なアカウントは、 [phpMyAdmin 環境保管領域](index.html#linked-tables) にアクセスするために使用されます。単一のユーザの場合は必要ありませんが、 phpMyAdmin が共有されている場合は、このユーザにのみ [phpMyAdmin 環境保管領域](index.html#linked-tables) へのアクセス権を与え、それを使用するように phpMyAdmin を設定することをお勧めします。すべてのユーザが [phpMyAdmin 環境保管領域](index.html#linked-tables) に直接アクセスすることなく、機能が使用できるようになります。\n\nバージョン 2.2.5 で変更: 以前は `stduser` および `stdpass` と呼ばれていました\n\n参考\n\n[インストール](index.html#setup)、 [認証モードの使い方](index.html#authentication-modes)、 [phpMyAdmin 環境保管領域](index.html#linked-tables)、 [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb)、 [`$cfg['Servers'][$i]['controlhost']`](#cfg_Servers_controlhost)、 [`$cfg['Servers'][$i]['controlport']`](#cfg_Servers_controlport)、 [`$cfg['Servers'][$i]['control_*']`](#cfg_Servers_control_*)\n\n`$cfg['Servers'][$i]['control_*']`[¶](#cfg_Servers_control_*)\n\n| データ型: | 混合型 |\n\nバージョン 4.7.0 で追加.\n\n接頭辞 `control_` のついた設定を使用すると、制御リンク ([phpMyAdmin 環境保管領域](index.html#linked-tables) へのアクセスに使用) の MySQL 接続設定を変更できます。\n\nこれを使用することで、デフォルトでユーザと同じ引数を使用する制御接続の任意の側面を変更できます。\n\n例えば、制御接続用に SSL を設定できます。\n```\n// Enable SSL\n$cfg['Servers'][$i]['control_ssl'] = true;\n// Client secret key\n$cfg['Servers'][$i]['control_ssl_key'] = '../client-key.pem';\n// Client certificate\n$cfg['Servers'][$i]['control_ssl_cert'] = '../client-cert.pem';\n// Server certification authority\n$cfg['Servers'][$i]['control_ssl_ca'] = '../server-ca.pem';\n```\n参考\n\n[`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_ca_path']`](#cfg_Servers_ssl_ca_path)、 [`$cfg['Servers'][$i]['ssl_ciphers']`](#cfg_Servers_ssl_ciphers)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify), [`$cfg['Servers'][$i]['socket']`](#cfg_Servers_socket), [`$cfg['Servers'][$i]['compress']`](#cfg_Servers_compress), [`$cfg['Servers'][$i]['hide_connection_errors']`](#cfg_Servers_hide_connection_errors)\n\n`$cfg['Servers'][$i]['auth_type']`[¶](#cfg_Servers_auth_type)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'cookie'` |\n\nこのサーバで認証するのに config、 cookie、 [HTTP](index.html#term-http)、サインオンのいずれを使用するか。\n\n* 'config' 認証 (`$auth_type = 'config'`) は従来からの方法です。ユーザ名とパスワードは `config.inc.php` に保存されます。\n* 'cookie' 認証モード (`$auth_type = 'cookie'`) では、クッキーによって有効な MySQL ユーザとしてログインできます。\n* 'http' 認証では、 HTTP-Auth によって有効な MySQL ユーザとしてログインできます。\n* 'signon' 認証モード (`$auth_type = 'signon'`) では、あらかじめ準備された PHP セッションデータまたは提要された PHP スクリプトを使用してログインできます。\n\n参考\n\n[認証モードの使い方](index.html#authentication-modes)\n\n`$cfg['Servers'][$i]['auth_http_realm']`[¶](#cfg_Servers_auth_http_realm)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nauth_type = `http` を使用した場合、この項目で、ユーザに表示される [HTTP](index.html#term-http) の Basic 認証の領域名を定義することができます。設定で明示的に指定されていない場合には、 \"phpMyAdmin \" と [`$cfg['Servers'][$i]['verbose']`](#cfg_Servers_verbose) または [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) のいずれかを組み合わせた文字列が使用されます。\n\n`$cfg['Servers'][$i]['auth_swekey_config']`[¶](#cfg_Servers_auth_swekey_config)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nバージョン 3.0.0.0 で追加: この設定は $cfg['Servers'][$i]['auth_feebee_config'] に改名されました。改名されたのは 3.0.0.0 より前です。\n\nバージョン 4.6.4 で非推奨: この設定は、サーバーがすでに稼働しておらず、また正しく動作していなかったため、削除されました。\n\nバージョン 4.0.10.17 で非推奨: この設定はメンテナンスリリースで削除されました。サーバーがすでに稼働しておらず、正しく動作していなかったためです。\n\nハードウェア認証用の Swekey ID とログイン名を含むファイルの名前を指定します。空欄にすると、この機能が無効になります。\n\n`$cfg['Servers'][$i]['user']`[¶](#cfg_Servers_user)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'root'` |\n\n`$cfg['Servers'][$i]['password']`[¶](#cfg_Servers_password)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n[`$cfg['Servers'][$i]['auth_type']`](#cfg_Servers_auth_type) が 'config' に設定されている場合は、 MySQL サーバに接続するときに phpMyAdmin が利用するユーザ名／パスワードの組が入ります。このユーザ名／パスワードの組は、 [HTTP](index.html#term-http) またはクッキー認証を利用する場合は必要ありませんので、空欄にしておいてください。\n\n`$cfg['Servers'][$i]['nopassword']`[¶](#cfg_Servers_nopassword)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.7.0 で非推奨: この設定は予期しない結果を生み出す可能性があるため、削除されました。\n\nパスワードを使用してログインが失敗したときにパスワードなしでログインしようとするとを許可します。これは、HTTP 認証と一緒に使用することができます。MySQL に接続する手段の一つとして、ユーザ名と空のパスワードを使用して認証を行います。パスワードログインを行わないというわけではなく、パスワードログインが最初に試され、最後の手段としてパスワードなし方式が試されます。\n\n注釈\n\nIt is possible to allow logging in with no password with the [`$cfg['Servers'][$i]['AllowNoPassword']`](#cfg_Servers_AllowNoPassword) directive.\n\n`$cfg['Servers'][$i]['only_db']`[¶](#cfg_Servers_only_db)\n\n| データ型: | 文字列型または配列型 |\n| デフォルト値: | `''` |\n\nデータベース名 (の配列) を設定すると、ユーザにはそのデータベースしか見えなくなります。phpMyAdmin 2.2.1 以降、このデータベース名には MySQL のワイルドカード文字 (\"_\" と \"%\") を含めることができます。ワイルドカード文字を実際の文字として使う場合はエスケープしてください (すなわち `'my_db'` ではなく、 `'my\\_db'` のようにします)。\n\nこの設定はサーバの負荷を下げるのに効果的です。利用できるデータベースのリストを作成する際に MySQL にリクエストを送る必要がなくなるためです。ただし、 **これは MySQL データベースサーバの権限の規則に代わるものではありません。** つまり、設定すればそのデータベースだけが表示されるようになりますが、 **ほかのすべてのデータベースが使えなくなるわけではありません。**\n\n複数のデータベースを使用した例です。\n```\n$cfg['Servers'][$i]['only_db'] = ['db1', 'db2'];\n```\nバージョン 4.0.0 で変更: 以前のバージョンでは、この設定項目でデータベース名の表示順序を指定できました。\n\n`$cfg['Servers'][$i]['hide_db']`[¶](#cfg_Servers_hide_db)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n権限のないユーザからデータベースを隠すための正規表現です。これはリストから見えなくするだけで、ユーザがそれらに (SQL クエリ領域などを使用して) アクセスすることはます。アクセスを制限するには MySQL 権限システムを使用してください。例えば、すべてのデータベースから \"a\" の文字で始まるデータベースを隠すには、次のようにします。\n```\n$cfg['Servers'][$i]['hide_db'] = '^a';\n```\n”db1\" と \"db2\" の両方を非表示にするには、次のようにします。\n```\n$cfg['Servers'][$i]['hide_db'] = '^(db1|db2)$';\n```\n正規表現の詳細は、PHP リファレンスマニュアルの [PCRE のパターン構文](https://www.php.net/manual/ja/reference.pcre.pattern.syntax.php) の項にあります。\n\n`$cfg['Servers'][$i]['verbose']`[¶](#cfg_Servers_verbose)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n複数のサーバエントリがある場合にのみ有用です。設定しておくと、メインページのプルダウンメニューに、ホスト名ではなく、この文字列が表示されます。例えば、システム上のいくつかのデータベースのみ表示させる場合には便利です。HTTP 認証の場合、 ASCII 文字以外はすべて無視されるかもしれません。\n\n`$cfg['Servers'][$i]['extension']`[¶](#cfg_Servers_extension)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'mysqli'` |\n\nバージョン 4.2.0 で非推奨: この設定は削除されました。 `mysql` 拡張モジュールは `mysqli` 拡張モジュールが利用できない場合にのみ使用されます。 5.0.0 では、 `mysqli` 拡張モジュールのみが利用できます。\n\n使用する PHP の MySQL 拡張モジュールです (`mysql` または `mysqli`)。\n\nすべてのインストールで `mysqli` を使用することを推奨します。\n\n`$cfg['Servers'][$i]['pmadb']`[¶](#cfg_Servers_pmadb)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nphpMyAdmin 環境保管領域を格納するデータベース名が入ります。\n\nこのドキュメントの [phpMyAdmin 環境保管領域](index.html#linked-tables) の節をご覧ください。このテーブル構造の利点や、データベースの簡単な作成法、必要なテーブルが書かれています。\n\nインストールした phpMyAdmin のユーザが 1 人だけの場合は、使用中のデータベースにこれらの特殊なテーブル群を格納することもできます。その場合は使用中のデータベース名を [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) に記述してください。複数のユーザの場合は phpMyAdmin 環境保管領域を格納する中心データベース名を設定します。\n\n`$cfg['Servers'][$i]['bookmarktable']`[¶](#cfg_Servers_bookmarktable)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.2.0 で追加.\n\nバージョン 2.2.0 以降の phpMyAdmin ではブックマーククエリを利用できます。よく利用するクエリがある場合は便利です。この機能の利用を許可するには、次のようにしてください。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['bookmarktable']`](#cfg_Servers_bookmarktable) にテーブル名を入力する\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['relation']`[¶](#cfg_Servers_relation)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.2.4 で追加.\n\nバージョン 2.2.4 以降、専用の「リレーション」テーブルにどのカラムが別のテーブルのキー (外部キー) になっているか記述することができるようになりました。phpMyAdmin は現在この機能を次のような用途で使っています。\n\n* マスタテーブルを閲覧しているときに、外部テーブルを指し示すデータ値をクリックできるようにします。\n* マスタテーブルを閲覧しているときにマウスを外部キーが含まれるカラムに移動すると、表示するカラムのオプションで指定されたツールチップが表示される (「table_info」テーブルも使用される) ([6.7 どうすれば [表示するカラム] 機能が利用できますか？](index.html#faqdisplay) を参照)\n* 編集／挿入モードでは、使用できる外部キーがドロップダウンリストで表示される (キーの値と「表示するカラム」が表示される) ([6.21 編集／挿入モードで、外部のテーブルに基づいた利用可能なカラムの値の一覧を見るにはどうすればよいでしょうか？](index.html#faq6-21) を参照)\n* テーブルのプロパティページでは、記載されているキーごとに参照の整合性をチェックする（リンクの切れた外部キーを表示する）リンクを表示します。\n* 定型問い合わせでは、自動結合を作成します ([6.6 どうすれば定型問い合わせの際にリレーションテーブルを使えるのでしょうか？](index.html#faq6-6) を参照)\n* データベースの [PDF](index.html#term-pdf) スキーマを取得できる (table_coords テーブルも使用)。\n\nキーは数値でも文字でも可です。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['relation']`](#cfg_Servers_relation) にリレーションテーブル名を入れる\n* 一般ユーザとして phpMyAdmin を開き、この機能を使いたいそれぞれテーブルで 構造/リレーションビュー/ をクリックして、外部カラムを選択する。\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n注釈\n\n現在のバージョンでは、 `master_db` は `foreign_db` と一致しなければならないことに注意してください。これらのカラムは将来クロスデータベースリレーションを開発するために用意されています。\n\n`$cfg['Servers'][$i]['table_info']`[¶](#cfg_Servers_table_info)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.3.0 で追加.\n\nバージョン 2.3.0 以降、対応するキーにカーソルを動かしたときどのカラムをツールチップとして表示するか、専用の 'table_info' テーブルに記述できるようになりました。の設定変数には、この特殊テーブルの名前が保持されます。この機能を許可するには次のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* テーブル名を [`$cfg['Servers'][$i]['table_info']`](#cfg_Servers_table_info) に入れます。(例: `pma__table_info`)\n* それから、この機能を利用したいテーブルごとに「構造⇒リレーションビュー⇒表示するカラムの選択」をクリックして、カラムを選択します。\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n参考\n\n[6.7 どうすれば [表示するカラム] 機能が利用できますか？](index.html#faqdisplay)\n\n`$cfg['Servers'][$i]['table_coords']`[¶](#cfg_Servers_table_coords)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nデザイナ機能では、ページレイアウトを保存することができます。拡張デザイナメニューの「ページを保存」または「ページを名前を付けて保存」ボタンを押すことで、レイアウトをカスタマイズし、次回デザイナを使用するときに読み込ませることができます。そのレイアウトはこのテーブルに保存されます。さらに、このテーブルは PDF リレーションのエクスポート機能を使用するためにも必要です。詳しくは [`$cfg['Servers'][$i]['pdf_pages']`](#cfg_Servers_pdf_pages) を参照してください。\n\n`$cfg['Servers'][$i]['pdf_pages']`[¶](#cfg_Servers_pdf_pages)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.3.0 で追加.\n\nバージョン 2.3.0 以降、phpMyAdmin はテーブル間のリレーションを表示する [PDF](index.html#term-pdf) ページを作成できるようになりました。このためには \"pdf_pages\" (作成する [PDF](index.html#term-pdf) ページの情報の保管用) と \"table_coords\" ([PDF](index.html#term-pdf) スキーマ出力の際に各テーブルが配置される座標の保管用) という２つのテーブルが必要となります。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['table_coords']`](#cfg_Servers_table_coords) と [`$cfg['Servers'][$i]['pdf_pages']`](#cfg_Servers_pdf_pages) に正しいテーブル名を入れる\n\nこの機能はどちらかの設定を `false` に設定することで無効化することができます。\n\n参考\n\n[6.8 データベースの PDF スキーマを作るにはどうするのですか？](index.html#faqpdf).\n\n`$cfg['Servers'][$i]['designer_coords']`[¶](#cfg_Servers_designer_coords)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nバージョン 2.10.0 で追加: バージョン 2.10.0 より。デザイナインターフェイスが使用でき、リレーションの視覚的な管理を可能にします。\n\nバージョン 4.3.0 で非推奨: この設定は削除され、デザイナのテーブルの位置データは [`$cfg['Servers'][$i]['table_coords']`](#cfg_Servers_table_coords) に格納されるようになりました。\n\n注釈\n\nテーブル pma__designer_coords を phpMyAdmin の環境保管領域データベースから削除できるようになりました。設定ファイルから [`$cfg['Servers'][$i]['designer_coords']`](#cfg_Servers_designer_coords) を削除してください。\n\n`$cfg['Servers'][$i]['column_info']`[¶](#cfg_Servers_column_info)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.3.0 で追加.\n\nこの部分のコンテンツは更新する必要があります。バージョン 2.3.0 以降、テーブルごとに各カラムを説明するコメントを保管できるようになりました。このコメントは「印刷用画面」の際に表示されます。\n\nバージョン 2.5.0 以降、テーブルのプロパティページやテーブルの表示機能でもコメントを利用するようになりました。カラム名の上に表示されるツールチップ（プロパティページ）や表示機能のテーブルヘッダに埋め込まれます。また、テーブルをダンプする際に表示することもできます。後述の関連する設定項目もご覧ください。\n\nまた、バージョン 2.5.0 の新機能として、MIME 変換システムがありますが、これも以下のテーブル構造をベースにしています。詳しくは [変換機能](index.html#transformations) をご覧ください。MIME 変換システムを利用する際は、 column_info テーブルに「mimetype」、「transformation」、「transformation_options」というカラムを新たに付け加える必要があります。\n\nリリース 4.3.0 以降、新しい入力指向の変換システムが導入されました。また、古い変換システムで使用していた後方互換性のためのコードが削除されました。結果的に、以前の変換と新しい入力指向の変換システムが動作するためには column_info の更新が必要です。 phpMydmin は現在の column_info テーブルの構造を解析して自動的にアップグレードします。ただし、自動アップグレードに失敗した場合は `./sql/upgrade_column_info_4_3_0+.sql` にある SQL スクリプトを使用して手動でアップグレードすることもできます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['column_info']`](#cfg_Servers_column_info) にテーブル名を設定する (例: `pma__column_info`)\n* 2.5.0 以前の Column_comments table テーブルを更新するには次のようにしてください。また、 `config.inc.php` 内の変数を `$cfg['Servers'][$i]['column_comments']` から [`$cfg['Servers'][$i]['column_info']`](#cfg_Servers_column_info) に変更することを忘れないでください。\n```\nALTER TABLE `pma__column_comments`\nADD `mimetype` VARCHAR( 255 ) NOT NULL,\nADD `transformation` VARCHAR( 255 ) NOT NULL,\nADD `transformation_options` VARCHAR( 255 ) NOT NULL;\n```\n* 4.3.0 以前の Column_info テーブルを手作業で更新するには、この `./sql/upgrade_column_info_4_3_0+.sql` SQL スクリプトを使用してください。\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n注釈\n\n自動アップグレード機能を動作させるには [`$cfg['Servers'][$i]['controluser']`](#cfg_Servers_controluser) が `phpmyadmin` データベースに ALTER 権限を持っている必要があります。ユーザに対して権限を `GRANT` で許可する方法は、 [MySQL 文書の GRANT](https://dev.mysql.com/doc/refman/8.0/ja/grant.html) を参照してください。\n\n`$cfg['Servers'][$i]['history']`[¶](#cfg_Servers_history)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 2.5.0 で追加.\n\nバージョン 2.5.0 以降、 [SQL](index.html#term-sql) の履歴 (phpMyAdmin インタフェースに手入力したすべてのクエリ) を保管できるようになりました。テーブルベースの履歴は利用したくない場合、JavaScript ベースの履歴を利用することもできます。\n\n使用すると、ウィンドウを閉じるときにすべての履歴項目が削除されます。 [`$cfg['QueryHistoryMax']`](#cfg_QueryHistoryMax) を使うと、保持しておきたい履歴リストの上限を指定できます。このリストはログインのたびに上限値にまで切り詰められます。\n\nクエリの履歴を利用できるのはブラウザの JavaScript が有効になっている場合のみです。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['history']`](#cfg_Servers_history) にテーブル名を入れます。(例: `pma__history`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['recent']`[¶](#cfg_Servers_recent)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 3.5.0 で追加.\n\nバージョン 3.5.0 以降、左側のナビゲーションフレームで最近使用されたテーブルを表示することができます。データベースを選択することなく、直接テーブルへ移動することができます。 [`$cfg['NumRecentTables']`](#cfg_NumRecentTables) で最近使用したテーブルの表示できる最大数が設定できます。リストからテーブルを選択すると、指定されたページに [`$cfg['NavigationTreeDefaultTabTable']`](#cfg_NavigationTreeDefaultTabTable) 内において移動が行われます。\n\nphpMyAdmin 環境保管領域がなくても、最近使用されたテーブルにアクセスすることができますが、ログアウトすると記録は失われてしまいます。\n\nこの機能を永続的に利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['recent']`](#cfg_Servers_recent) にテーブル名を入れます。(例: `pma__recent`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['favorite']`[¶](#cfg_Servers_favorite)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.2.0 で追加.\n\nバージョン 4.2.0 以降では、ナビゲーションパネルで選択されたテーブルの一覧を表示することができます。これはデータベースを選択してからテーブルを選択するのではなく、直接テーブルにジャンプするのに役立ちます。一覧からテーブルを選択すると、 [`$cfg['NavigationTreeDefaultTabTable']`](#cfg_NavigationTreeDefaultTabTable) で指定されたページに移動します。\n\nテーブルをこのリストに加えたり削除したりするのを、テーブル名の隣にある星印をクリックすることで行えるようになります。 [`$cfg['NumFavoriteTables']`](#cfg_NumFavoriteTables) を使用するとお気に入りのテーブルに表示される最大数を設定することができます。\n\nphpMyAdmin 環境保管領域がなくても、テーブルのブックマークにアクセスすることができますが、ログアウトすると記録は失われてしまいます。\n\nこの機能を永続的に利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['favorite']`](#cfg_Servers_favorite) にテーブル名を入れます。(例: `pma__favorite`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['table_uiprefs']`[¶](#cfg_Servers_table_uiprefs)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 3.5.0 で追加.\n\nバージョン 3.5.0 以降、 phpMyAdmin は表示しているテーブルのさまざまな環境設定 (ソートされた [`$cfg['RememberSorting']`](#cfg_RememberSorting) カラム、テカラムの表示順、カラムの表示有無) を覚えておくことができます。環境保管領域がなくてもこれらの機能は使用することができますが、ログアウトすると値は失われてしまいます。\n\nこれらの機能を永続的に利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['table_uiprefs']`](#cfg_Servers_table_uiprefs) にテーブル名を設定する (例: `pma__table_uiprefs`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['users']`[¶](#cfg_Servers_users)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nphpMyAdmin がユーザ名情報をユーザグループに関連付けるために使用するテーブルです。詳細や推奨設定は [`$cfg['Servers'][$i]['usergroups']`](#cfg_Servers_usergroups) の項目を参照してください。\n\n`$cfg['Servers'][$i]['usergroups']`[¶](#cfg_Servers_usergroups)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.1.0 で追加.\n\nリリース 4.1.0 以降では、メニュー項目が関連付けられた別のユーザグループを作成することができます。ユーザをこれらのグループに割り当てることができ、ログインしているユーザには、自分が割り当てられているユーザグループに対して構成されたメニュー項目のみが表示されます。そのためには、 \"usergroups\" (各ユーザ グループに対して許可されたメニュー項目を格納する) と \"users\" (ユーザとユーザ グループへの割り当てを格納する) の 2 つのテーブルが必要です。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['users']`](#cfg_Servers_users) (例: `pma__users`) および [`$cfg['Servers'][$i]['usergroups']`](#cfg_Servers_usergroups) (例: `pma__usergroups`) に正しいテーブル名を設定する\n\nこの機能はどちらかの設定を `false` に設定することで無効化することができます。\n\n参考\n\n[設定可能なメニューとユーザグループ](index.html#configurablemenus)\n\n`$cfg['Servers'][$i]['navigationhiding']`[¶](#cfg_Servers_navigationhiding)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.1.0 で追加.\n\nリリース 4.1.0 以降、ナビゲーションツリー内の項目を表示/非表示にすることができます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* テーブル名を [`$cfg['Servers'][$i]['navigationhiding']`](#cfg_Servers_navigationhiding) に設定する (例：'pma_tracking')\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['central_columns']`[¶](#cfg_Servers_central_columns)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.3.0 で追加.\n\nリリース 4.3.0 以降では、主要カラムのリストをデータベースごとに持つことができます。必要に応じてカラムをリストに追加/削除することができます。リスト内の主要カラムは、テーブルに新しいカラム作成したり、テーブル自体を作成したりするときに利用することができます。主要カラムのリストから選択して新しいカラムを作成し、同じカラム定義を再利用したり、同様のカラムを異なる名前で書いたりすることができます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* テーブル名を [`$cfg['Servers'][$i]['central_columns']`](#cfg_Servers_central_columns) に設定する (例：`pma__central_columns`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['designer_settings']`[¶](#cfg_Servers_designer_settings)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.5.0 で追加.\n\nリリース 4.5.0 以降、デザイナ設定は記憶されます。「角/直リンク」、「グリッドにあわせる」、「リレーションラインの表示切替」、「すべてを大きく/小さく」、「メニューを移動する」、「ピンテキスト」に関する選択肢は永続的に記憶することができます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['designer_settings']`](#cfg_Servers_designer_settings) にテーブル名を設定する (例: `pma__designer_settings`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['savedsearches']`[¶](#cfg_Servers_savedsearches)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.2.0 で追加.\n\nリリース 4.2.0 以降では、定型問い合わせの検索を「データベース > クエリ」パネルから保存・読み出しできます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['savedsearches']`](#cfg_Servers_savedsearches) にテーブル名を設定する (例: `pma__savedsearches`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['export_templates']`[¶](#cfg_Servers_export_templates)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 4.5.0 で追加.\n\nリリース 4.5.0 以降、エクスポートテンプレートの保存および読み出しができます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* [`$cfg['Servers'][$i]['export_templates']`](#cfg_Servers_export_templates) にテーブル名を設定します (例: `pma__export_templates`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['tracking']`[¶](#cfg_Servers_tracking)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 3.3.x で追加.\n\nリリース 3.3.x 以降では、コマンド追跡機能が利用できます。これは、phpMyAdmin によって実行されたすべての [SQL](index.html#term-sql) コマンドの追跡に役立ちます。この仕組みは、データの操作とデータ定義文のログ記録に対応しています。有効にすると、テーブルの世代を作成することができます。\n\n世代を作成すると、２つの効果があります。\n\n* phpMyAdmin が構造とインデックスを含むテーブルのスナップショットを保存します。\n* phpMyAdmin がテーブルの構造やデータの変更を行うすべてのコマンドをログに記録し、これらのコマンドと版数を結び付けます。\n\nもちろん、変更履歴を表示することもできます。 コマンド追跡 ページにすべての版に対しての詳細なレポートがあります。レポートは表示件数を絞ることができます。例えば、日付範囲などを指定することで条件内のコマンドリストを取得が行えます。ユーザ名で絞る場合は、すべての名前が対象であれば「*」を入力、名前のリストに対しては「,」で区切って入力してください。更に、(絞り込んだ) レポートをファイルまたは一時的なデータベースへエクスポートすることもできます。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* テーブル名を [`$cfg['Servers'][$i]['tracking']`](#cfg_Servers_tracking) に設定します。(例: `pma__tracking`)\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['tracking_version_auto_create']`[¶](#cfg_Servers_tracking_version_auto_create)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nSQL コマンドの追跡機能が、テーブルやビューに対して自動的に版を作成するかどうか。\n\nこれが true に設定されており、以下のようにテーブルやビューを作成したとき\n\n* CREATE TABLE ...\n* CREATE VIEW ...\n\n既存の版が存在しなかった場合、追跡機能は自動的に版を生成します。\n\n`$cfg['Servers'][$i]['tracking_default_statements']`[¶](#cfg_Servers_tracking_default_statements)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'CREATE TABLE,ALTER TABLE,DROP TABLE,RENAME TABLE,CREATE INDEX,DROP INDEX,INSERT,UPDATE,DELETE,TRUNCATE,REPLACE,CREATE VIEW,ALTER VIEW,DROP VIEW,CREATE DATABASE,ALTER DATABASE,DROP DATABASE'` |\n\n使用されたときに新しい版を自動生成する文のリストを定義します。\n\n`$cfg['Servers'][$i]['tracking_add_drop_view']`[¶](#cfg_Servers_tracking_add_drop_view)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nビューを作成するときにログの最初の行に DROP VIEW IF EXISTS 文を追加するかどうか。\n\n`$cfg['Servers'][$i]['tracking_add_drop_table']`[¶](#cfg_Servers_tracking_add_drop_table)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nテーブルを作成するときにログの最初の行に DROP TABLE IF EXISTS 文を追加するかどうか。\n\n`$cfg['Servers'][$i]['tracking_add_drop_database']`[¶](#cfg_Servers_tracking_add_drop_database)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nデータベースを作成するときにログの最初の行に DROP DATABASE IF EXISTS 文を追加するかどうか。\n\n`$cfg['Servers'][$i]['userconfig']`[¶](#cfg_Servers_userconfig)\n\n| データ型: | 文字列型または false |\n| デフォルト値: | `''` |\n\nバージョン 3.4.x で追加.\n\nバージョン 3.4.x より。ユーザが自分自身用の環境設定を行い、それをデータベース (phpMyAdmin 環境保管領域) に格納することを許可します。\n\n[`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) への環境の格納が許可されていなくても、ユーザは phpMyAdmin をカスタマイズすることができますが、ブラウザのローカルストレージに設定を保存することになるか、それもできない場合はセッションの終了時までとなります。\n\nこの機能を利用できるようにするには、以下のようにします。\n\n* [`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) と phpMyAdmin 環境保管領域をセットアップする\n* テーブル名を [`$cfg['Servers'][$i]['userconfig']`](#cfg_Servers_userconfig) に設定する\n\nこの機能はこの設定を `false` に設定することで無効にすることができます。\n\n`$cfg['Servers'][$i]['MaxTableUiprefs']`[¶](#cfg_Servers_MaxTableUiprefs)\n\n| データ型: | 整数型 |\n| デフォルト値: | 100 |\n\n[`$cfg['Servers'][$i]['table_uiprefs']`](#cfg_Servers_table_uiprefs) テーブルに保存できる最大行数です。\n\nテーブルが削除されたり名前が変更されたりした場合、 [`$cfg['Servers'][$i]['table_uiprefs']`](#cfg_Servers_table_uiprefs) のデータが正しくなくなることがあります (もう存在しないテーブルを参照しているため)。 [`$cfg['Servers'][$i]['table_uiprefs']`](#cfg_Servers_table_uiprefs) の行数のみを保存し、それより古い行は自動的に削除します。\n\n`$cfg['Servers'][$i]['SessionTimeZone']`[¶](#cfg_Servers_SessionTimeZone)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nphpMyAdmin で使用されるタイムゾーンを設定します。空欄にすると、データベースサーバのタイムゾーンを使用します。使用可能な値は <https://dev.mysql.com/doc/refman/8.0/ja/time-zone-support.html> で説明しています。\n\nこれはデータベースサーバが使用するタイムゾーンが、 phpMyAdmin で使用したいタイムゾーンとは異なる場合に有用です。\n\n`$cfg['Servers'][$i]['AllowRoot']`[¶](#cfg_Servers_AllowRoot)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nroot のアクセスを許可するかどうか。これは下記の [`$cfg['Servers'][$i]['AllowDeny']['rules']`](#cfg_Servers_AllowDeny_rules) を簡略化しただけのものです。\n\n`$cfg['Servers'][$i]['AllowNoPassword']`[¶](#cfg_Servers_AllowNoPassword)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nパスワードなしでのログインを許可するかどうか。このパラメータがデフォルト値の `false` であれば、 root または匿名 (空欄) ユーザが空のパスワードのままの定義で残っていたとしても、MySQL サーバへの意図しないアクセスを防ぐことができます。\n\n`$cfg['Servers'][$i]['AllowDeny']['order']`[¶](#cfg_Servers_AllowDeny_order)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n規則の適用順が空の場合、 [IP](index.html#term-ip) 認証は無効になります。\n\n規則の適用順が `'deny,allow'` の場合、システムは拒否規則をすべて適用してから許可規則を適用します。アクセスは許可がデフォルトです。拒否コマンドに一致しないクライアント、許可コマンドに一致するクライアントはすべてサーバへのアクセスが許可されます。\n\n規則の適用順が `'allow,deny'` の場合、システムは許可規則をすべて適用してから拒否規則を適用します。アクセスは拒否がデフォルトです。 Allow の設定項目に一致しないクライアント、 Deny の設定項目に一致するクライアントはすべてサーバへのアクセスが拒否されます。\n\n規則の適用順が `'explicit'` の場合、認証は 'deny,allow' と同様に行われますが、追加される制限は、ホスト名／ユーザ名の組が *allow* 規則に含まれる **必要があり** 、かつ、 *deny* 規則に含まれては **いけません** 。これは Allow/Deny 規則を利用するうえでは **最も** 安全な方法です。以前は Apache で順番を指定せずに許可・拒否規則を指定することで実現していたものです。\n\nプロキシを通しての IP アドレスの検出については [`$cfg['TrustedProxies']`](#cfg_TrustedProxies) も参照してください。\n\n`$cfg['Servers'][$i]['AllowDeny']['rules']`[¶](#cfg_Servers_AllowDeny_rules)\n\n| データ型: | 文字列型の配列 |\n| デフォルト値: | array() |\n\nこの規則の一般的な書式は次の通りです。\n```\n<'allow' | 'deny'> <username> [from] <ipmask>\n```\nすべてのユーザに一致させたい場合は、 *username* 欄にワイルドカードとして `'%'` を使うこともできます。\n\nまた、 *ipmask* 欄でもいくつかショートカットが利用できます (SERVER_ADDRESS の部分は、どんなウェブサーバでも利用できるとは限りませんので注意してください)。\n```\n'all' -> 0.0.0.0/0\n'localhost' -> 127.0.0.1/8\n'localnetA' -> SERVER_ADDRESS/8\n'localnetB' -> SERVER_ADDRESS/16\n'localnetC' -> SERVER_ADDRESS/24\n```\n規則のリストを空にすると、規則の適用順が `'deny,allow'` の場合は `'allow % from all'` と、適用順が `'allow,deny'` ないし `'explicit'` の場合は `'deny % from all'` と等価になります。\n\n[IP アドレス](index.html#term-ip-address) のマッチング規則としては、下記のものが利用できます。\n\n* `xxx.xxx.xxx.xxx` (正確な [IP アドレス](index.html#term-ip-address))\n* `xxx.xxx.xxx.[yyy-zzz]` ([IP アドレス](index.html#term-ip-address) の範囲)\n* `xxx.xxx.xxx.xxx/nn` (CIDR (Classless Inter-Domain Routing) タイプの [IP](index.html#term-ip) アドレス)\n\nただし、以下は利用できません。\n\n* `xxx.xxx.xxx.xx[yyy-zzz]` ([IP](index.html#term-ip) アドレスの一部範囲指定)\n\n[IPv6](index.html#term-ipv6) アドレスでは、以下のものが利用できます。\n\n* `xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx` (正確な [IPv6](index.html#term-ipv6) アドレス)\n* `xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:[yyyy-zzzz]` ([IPv6](index.html#term-ipv6) アドレスの範囲)\n* `xxxx:xxxx:xxxx:xxxx/nn` (CIDR (Classless Inter-Domain Routing) タイプの [IPv6](index.html#term-ipv6) アドレス)\n\nただし、以下は利用できません。\n\n* `xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xxxx:xx[yyy-zzz]` ([IPv6](index.html#term-ipv6) アドレスの一部範囲指定)\n\n例:\n```\n$cfg['Servers'][$i]['AllowDeny']['order'] = 'allow,deny';\n$cfg['Servers'][$i]['AllowDeny']['rules'] = ['allow bob from all'];\n// Allow only 'bob' to connect from any host\n\n$cfg['Servers'][$i]['AllowDeny']['order'] = 'allow,deny';\n$cfg['Servers'][$i]['AllowDeny']['rules'] = ['allow mary from 192.168.100.[50-100]'];\n// Allow only 'mary' to connect from host 192.168.100.50 through 192.168.100.100\n\n$cfg['Servers'][$i]['AllowDeny']['order'] = 'allow,deny';\n$cfg['Servers'][$i]['AllowDeny']['rules'] = ['allow % from 192.168.[5-6].10'];\n// Allow any user to connect from host 192.168.5.10 or 192.168.6.10\n\n$cfg['Servers'][$i]['AllowDeny']['order'] = 'allow,deny';\n$cfg['Servers'][$i]['AllowDeny']['rules'] = ['allow root from 192.168.5.50','allow % from 192.168.6.10'];\n// Allow any user to connect from 192.168.6.10, and additionally allow root to connect from 192.168.5.50\n```\n`$cfg['Servers'][$i]['DisableIS']`[¶](#cfg_Servers_DisableIS)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n情報を取得するための `INFORMATION_SCHEMA` の使用を無効にします (代わりに `SHOW` コマンドを使用します)。多くのデータベースが存在している場合に速度的な問題があるためです。\n\n注釈\n\nこのオプションを有効にすると、古い MySQL サーバでは性能が飛躍的に向上する可能性があります。\n\n`$cfg['Servers'][$i]['SignonScript']`[¶](#cfg_Servers_SignonScript)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nバージョン 3.5.0 で追加.\n\nログイン資格情報を取得するために実行される PHP スクリプトの名前。これは、セッションに基づくシングルサインオンに代わる手法です。このスクリプトは、ユーザ名とパスワードの一覧を返す関数 `get_login_credentials` を提供していて、単一のパラメータとして存在するユーザ名 (空欄も可) を受け入れる必要があります。サンプルは、 `examples/signon-script.php` を参照してください。\n```\n<?php\n/**\n * Single signon for phpMyAdmin\n *\n * This is just example how to use script based single signon with\n * phpMyAdmin, it is not intended to be perfect code and look, only\n * shows how you can integrate this functionality in your application.\n */\n\ndeclare(strict_types=1);\n\n// phpcs:disable Squiz.Functions.GlobalFunction\n\n/**\n * This function returns username and password.\n *\n * It can optionally use configured username as parameter.\n *\n * @param string $user User name\n *\n * @return array<int,string>\n */\nfunction get_login_credentials(string $user): array\n{\n /* Optionally we can use passed username */\n if (! empty($user)) {\n return [$user, 'password'];\n }\n\n /* Here we would retrieve the credentials */\n return ['root', ''];\n}\n```\n参考\n\n[サインオン認証モード](index.html#auth-signon)\n\n`$cfg['Servers'][$i]['SignonSession']`[¶](#cfg_Servers_SignonSession)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nサインオン認証方式に使用されるセッションの名前です。`phpMyAdmin` という名前は phpMyAdmin が内部的に使用しているセッションであるため、それとは異なる名前を使用する必要があります。 [`$cfg['Servers'][$i]['SignonScript']`](#cfg_Servers_SignonScript) を解除しないと、こちらは機能しません。\n\n参考\n\n[サインオン認証モード](index.html#auth-signon)\n\n`$cfg['Servers'][$i]['SignonCookieParams']`[¶](#cfg_Servers_SignonCookieParams)\n\n| データ型: | 配列型 |\n| デフォルト値: | `array()` |\n\nバージョン 4.7.0 で追加.\n\n他の認証システムのセッションクッキーパラメータの連想配列。他の認証システムが session_set_cookie_params() を使用していない場合は必要ありません。キーには 'lifetime'、'path'、'domain'、'secure'、'httponly' のいずれかを指定します。有効な値は [session_get_cookie_params](https://www.php.net/manual/ja/function.session-get-cookie-params.php) で説明されています。 [`$cfg['Servers'][$i]['SignonScript']`](#cfg_Servers_SignonScript) が設定されていない場合にのみ有効です。\n\n参考\n\n[サインオン認証モード](index.html#auth-signon)\n\n`$cfg['Servers'][$i]['SignonURL']`[¶](#cfg_Servers_SignonURL)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nサインオン認証方式にログインするためにユーザがリダイレクトされる [URL](index.html#term-url) です。プロトコルを含めた絶対パスである必要があります。\n\n参考\n\n[サインオン認証モード](index.html#auth-signon)\n\n`$cfg['Servers'][$i]['LogoutURL']`[¶](#cfg_Servers_LogoutURL)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nユーザがログアウト後にリダイレクトされる [URL](index.html#term-url) (認証方式の設定には影響しません)。プロトコルを含む絶対パスにする必要があります。\n\n`$cfg['Servers'][$i]['hide_connection_errors']`[¶](#cfg_Servers_hide_connection_errors)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.9.8 で追加.\n\nログインページで MySQL/MariaDB の詳細なエラーを表示するかどうか。\n\n注釈\n\nこのエラーメッセージには、対象となるデータベースサーバーのホスト名や IP アドレスが含まれることがあり、攻撃者にネットワークに関する情報を知られてしまう可能性があります。\n\n### 一般設定[¶](#generic-settings)\n\n`$cfg['DisableShortcutKeys']`[¶](#cfg_DisableShortcutKeys)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n[`$cfg['DisableShortcutKeys']`](#cfg_DisableShortcutKeys) を true に設定することで phpMyAdmin のショートカットキーを無効にすることができます。\n\n`$cfg['ServerDefault']`[¶](#cfg_ServerDefault)\n\n| データ型: | 整数型 |\n| デフォルト値: | 1 |\n\n複数のサーバが設定されている場合、[`$cfg['ServerDefault']`](#cfg_ServerDefault) にサーバ番号を設定しておくと phpMyAdmin を立ち上げたときに自動的にそのサーバに接続するようにできます。0 に設定するとログインしないでサーバのリストを表示します。\n\nサーバが 1 つしか設定されていない場合、[`$cfg['ServerDefault']`](#cfg_ServerDefault) はそのサーバに設定しなければなりません。\n\n`$cfg['VersionCheck']`[¶](#cfg_VersionCheck)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n最新バージョンの確認を、 phpMyAdmin メインページ上で JavaScript を使用したり、 index.php?route=/version-check に直接アクセスしたりすることで行えるようにします。\n\n注釈\n\nこの設定はベンダーが変更する可能性があります。\n\n`$cfg['ProxyUrl']`[¶](#cfg_ProxyUrl)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n最新のバージョン情報を取得したり、エラーレポートを送信したりするときなど、 phpmyadmin が外部のインターネットにアクセスする必要があるときに使用するプロキシの URL です。 phpMyAdmin がインストールされているサーバがインターネットに直接アクセスできない場合に必要です。書式は \"ホスト名:ポート番号\" です。\n\n`$cfg['ProxyUser']`[¶](#cfg_ProxyUser)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nプロキシサーバで認証するユーザ名。デフォルトでは認証は行われません。ユーザ名が与えられた場合は、 Basic 認証が行われます。現在のところ、他の種類の認証には対応していません。\n\n`$cfg['ProxyPass']`[¶](#cfg_ProxyPass)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nプロキシサーバへログインするためのパスワード。\n\n`$cfg['MaxDbList']`[¶](#cfg_MaxDbList)\n\n| データ型: | 整数型 |\n| デフォルト値: | 100 |\n\nメインパネルのデータベース一覧に表示されるデータベース名の最大数。\n\n`$cfg['MaxTableList']`[¶](#cfg_MaxTableList)\n\n| データ型: | 整数型 |\n| デフォルト値: | 250 |\n\nメインパネルのリストに表示されるテーブル名の最大数 (エクスポートページを除く)。\n\n`$cfg['ShowHint']`[¶](#cfg_ShowHint)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nヒントを表示するかどうか (テーブルのヘッダ部などにマウスカーソルを重ねると表示されるものです)。\n\n`$cfg['MaxCharactersInDisplayedSQL']`[¶](#cfg_MaxCharactersInDisplayedSQL)\n\n| データ型: | 整数型 |\n| デフォルト値: | 1000 |\n\n[SQL](index.html#term-sql) クエリ表示時の最大文字数。デフォルトの制限は 1000 ですが、 BLOB を表現するのに多量の 16 進コードで表示されるのを防ぐには、このくらいで正しいでしょう。しかし、ユーザによっては 1000 文字よりも長い実際の [SQL](index.html#term-sql) クエリを使用します。また、クエリの長さがこの制限を超えている場合、そのクエリは履歴に保存されません。\n\n`$cfg['PersistentConnections']`[¶](#cfg_PersistentConnections)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n[持続的な接続](https://www.php.net/manual/ja/features.persistent-connections.php) を使用するかどうか。\n\n参考\n\n[持続的な接続の mysqli 文書](https://www.php.net/manual/en/mysqli.persistconns.php)\n\n`$cfg['ForceSSL']`[¶](#cfg_ForceSSL)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.6.0 で非推奨: この設定は phpMyAdmin 4.6.0 以降は有効ではありません。代わりにウェブサーバを設定してください。\n\nphpMyAdmin にアクセスするときに https を強制するかどうか。リバースプロキシの設定では、これを `true` にすることはサポートされていません。\n\n注釈\n\n設定によっては (分離型の SSL プロキシやロードバランサなど)、正しくリダイレクトするために [`$cfg['PmaAbsoluteUri']`](#cfg_PmaAbsoluteUri) を設定しなければならないかもしれません。\n\n`$cfg['MysqlSslWarningSafeHosts']`[¶](#cfg_MysqlSslWarningSafeHosts)\n\n| データ型: | 配列型 |\n| デフォルト値: | `['127.0.0.1', 'localhost']` |\n\nこの検索は大文字と小文字を区別し、厳密に一致する文字列のみを検索します。 SSLを使用していないが、ローカル接続やプライベートネットワークを使用しているために安全だと分かっている場合は、ホスト名や [IP](index.html#term-ip) アドレスをリストに追加することができます。また、デフォルトの項目を削除して自分のものだけを含めることもできます。\n\nこのチェックは [`$cfg['Servers'][$i]['host']`](#cfg_Servers_host) の値を使用します。\n\nバージョン 5.1.0 で追加.\n\n設定例\n```\n$cfg['MysqlSslWarningSafeHosts'] = ['127.0.0.1', 'localhost', 'mariadb.local'];\n```\n`$cfg['ExecTimeLimit']`[¶](#cfg_ExecTimeLimit)\n\n| データ型: | 整数型 [秒数] |\n| デフォルト値: | 300 |\n\nスクリプトの実行が許可される時間を秒数で設定します。秒数を 0 にすると、時間制限がなくなります。この設定はダンプファイルのインポート／エクスポートの際に使用されますが、 PHP がセーフモードになっているときは効果がありません。\n\n`$cfg['SessionSavePath']`[¶](#cfg_SessionSavePath)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nセッションデータを保存のためのパス ([session_save_path PHP 引数](https://www.php.net/session_save_path))。\n\n警告\n\nこのフォルダはウェブサーバを通して一般からアクセス可能にしてはいけません。セッションからプライベートデータが漏洩するリスクがあります。\n\n`$cfg['MemoryLimit']`[¶](#cfg_MemoryLimit)\n\n| データ型: | 文字列型 [バイト数] |\n| デフォルト値: | `'-1'` |\n\nスクリプトに割り当てることができるバイト数を設定します。 `'-1'` を設定すると、制限は適用されません。 `'0'` を設定すると、メモリの制限の変更が行われず、 `php.ini` の `memory_limit` が使用されます。\n\nこの設定はダンプファイルのインポート／エクスポートをする際に使用されます。この値を極端に低くくする必要は全くありません。PHP がセーフモードになっているときは効果がありません。\n\nまた、 `php.ini` 内で使われているような任意の文字列を使用することができます (例: '16M')。単位の接尾辞を忘れていないか確認してください (「16」は 16 バイトを意味します)\n\n`$cfg['SkipLockedTables']`[¶](#cfg_SkipLockedTables)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n利用しているテーブルに印をつけることで、テーブルがロックされているデータベースを表示できるようにします（3.23.30 以降）。\n\n`$cfg['ShowSQL']`[¶](#cfg_ShowSQL)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nphpMyAdmin が生成する [SQL](index.html#term-sql) クエリを表示するかどうかを定義します。\n\n`$cfg['RetainQueryBox']`[¶](#cfg_RetainQueryBox)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n送信後もそのまま [SQL](index.html#term-sql) クエリボックスを表示させておくかどうかを定義します。\n\n`$cfg['CodemirrorEnable']`[¶](#cfg_CodemirrorEnable)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックスに JavaScript コードエディタを使用するかどうかを定義します。 CodeMirror では構文の強調と行番号の表示ができます。ただし、いくつかの Linux ディストリビューション (Ubuntu など) で提供されている真ん中ボタンによる貼り付けは、すべてのブラウザではサポートされていません。\n\n`$cfg['LintEnable']`[¶](#cfg_LintEnable)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nバージョン 4.5.0 で追加.\n\n実行前にパーサーを使用してクエリ内のエラーを検出するかどうかを定義します。\n\n`$cfg['DefaultForeignKeyChecks']`[¶](#cfg_DefaultForeignKeyChecks)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'default'` |\n\n指定されたクエリの外部キーのチェックを無効/有効にする外部キーチェックのチェックボックスのデフォルト値です。指定可能な値は `'default'`, `'enable'`, `'disable'` です。 `'default'` に設定すると、 MySQL 環境変数の `FOREIGN_KEY_CHECKS` の値が使用されます。\n\n`$cfg['AllowUserDropDatabase']`[¶](#cfg_AllowUserDropDatabase)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n警告\n\nこれは、これを回避する方法が常に存在するので、セキュリティ対策にはなりません。ユーザがデータベースを削除することを禁止したい場合は、対応する DROP 権限を無効にしてください。\n\n通常ユーザ (管理者以外) に自分自身のデータベースの削除を許可するかどうかを定義します。FALSE にすると、 データベースを削除する のリンクは表示されませんし、 `DROP DATABASE mydatabase` すらも拒否されます。多くの顧客をかかえる [ISP](index.html#term-isp) にとってはきわめて実用的です。\n\n[SQL](index.html#term-sql) クエリに対するこの制限は、MySQL の権限を使用した場合ほど厳格ではないことに注意してください。これは [SQL](index.html#term-sql) クエリの性質によるもので、非常に複雑になる可能性があります。この設定は、厳密な権限の制限というよりも、意図しない削除を防止するのに役立つものとして見るべきです。\n\n`$cfg['Confirm']`[¶](#cfg_Confirm)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nデータが消失しそうな操作をしたときに警告 (「本当に〜してもよろしいですか」) を表示するかどうか。\n\n`$cfg['UseDbSearch']`[¶](#cfg_UseDbSearch)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n「データベース内の検索」を有効にするかどうかを定義します。\n\n`$cfg['IgnoreMultiSubmitErrors']`[¶](#cfg_IgnoreMultiSubmitErrors)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n複数のクエリを含む文のクエリのひとつが失敗したときに処理を続けるかどうかを定義します。デフォルトでは処理を中止します。\n\n`$cfg['enable_drag_drop_import']`[¶](#cfg_enable_drag_drop_import)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nドラッグ＆ドロップによるインポート機能が有効になっているかどうか。有効になっている場合、ユーザがファイルをブラウザにドラッグすると、 phpMyAdmin はファイルのインポートを試みます。\n\n`$cfg['URLQueryEncryption']`[¶](#cfg_URLQueryEncryption)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 4.9.8 で追加.\n\nphpMyAdmin が、 URL クエリ文字列から機密データ (データベース名やテーブル名など) を暗号化するかどうかを定義します。デフォルトでは、 URL クエリ文字列を暗号化しません。\n\n`$cfg['URLQueryEncryptionSecretKey']`[¶](#cfg_URLQueryEncryptionSecretKey)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nバージョン 4.9.8 で追加.\n\nURL クエリ文字列の暗号化/復号で使用される秘密鍵。 32 バイトにしてください。\n\n参考\n\n[2.10 ランダムなバイト列を生成するには](index.html#faq2-10)\n\n`$cfg['maxRowPlotLimit']`[¶](#cfg_maxRowPlotLimit)\n\n| データ型: | 整数型 |\n| デフォルト値: | 500 |\n\nズーム検索で取得される行の最大数。\n\n### クッキー認証オプション[¶](#cookie-authentication-options)\n\n`$cfg['blowfish_secret']`[¶](#cfg_blowfish_secret)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n\"cookie\" 認証方式は、クッキーを暗号化するのに [Sodium](index.html#term-sodium) 拡張機能を使用します ([Cookie](index.html#term-cookie) を参照)。 \"cookie\" 認証方式を使用する場合は、暗号化キーとして使用するためにここにランダムなバイト列の文字列を入力してください。これは [Sodium](index.html#term-sodium) 拡張機能で内部的に使用され、この暗号化キーを入力するよう促されることはありません。\n\nバイナリ文字列は通常は表示できないので、([`sodium_bin2hex<https://www.php.net/sodium_bin2hex>`_](#system-message-1) のような関数を使用して) 16進数表現に変換し、設定ファイルで使用することができます。たとえば、\n```\n// The string is a hexadecimal representation of a 32-bytes long string of random bytes.\n$cfg['blowfish_secret'] = sodium_hex2bin('f16ce59f45714194371b48fe362072dc3b019da7861558cd4ad29e4d6fb13851');\n```\nバイナリ文字列を使用することが推奨されます。ただし、文字列の 32 バイトすべてが可視文字である場合は、[`sodium_bin2hex<https://www.php.net/sodium_bin2hex>`_](#system-message-2) のような関数は必要ありません。例:\n```\n// A string of 32 characters.\n$cfg['blowfish_secret'] = 'JOFw435365IScA&Q!cDugr!lSfuAz*OW';\n```\n警告\n\n暗号化キーは 32 バイト長である必要があります。バイト長より長い場合は、最初の 32 バイトだけが使用され、短い場合は、新しい一時的な鍵が自動的に生成されます。ただし、この一時的な鍵は、セッションの間だけ有効です。\n\n注釈\n\nもともと暗号化に Blowfish アルゴリズムが使用されていたという経緯上、この設定は blowfish_secret と呼ばれています。\n\nバージョン 3.1.0 で変更: バージョン 3.1.0 以降、このパスフレーズが（空の場合は）自動で生成されるようになってはいますが、これはセキュリティ上あまり強いものではありません。通常、クッキーからユーザ名を取り出すといったことは不可能ですが、自動生成された（暗号／複合に必要な）パスフレーズがセッションに格納されるからです。\n\nバージョン 5.2.0 で変更: バージョン 5.2.0 以降、phpMyAdmin は PHP 関数の [`sodium_crypto_secretbox<https://www.php.net/sodium_crypto_secretbox>`_](#system-message-3) および`sodium_crypto_secretbox_open<<https://www.php.net/sodium_crypto_secretbox_open>>`_ を使用して Cookie をそれぞれ暗号化および復号しています。\n\n参考\n\n[2.10 ランダムなバイト列を生成するには](index.html#faq2-10)\n\n`$cfg['CookieSameSite']`[¶](#cfg_CookieSameSite)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'Strict'` |\n\nバージョン 5.1.0 で追加.\n\n[HTTP](index.html#term-http) レスポンスヘッダーの Set-Cookie の SameSite 属性を設定します。有効な値は次の通りです。\n\n* `Lax`\n* `Strict`\n* `None`\n\n参考\n\n[rfc6265 bis](https://datatracker.ietf.org/doc/html/draft-ietf-httpbis-rfc6265bis-03#section-5.3.7)\n\n`$cfg['LoginCookieRecall']`[¶](#cfg_LoginCookieRecall)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nクッキー認証モードの場合に、前回ログインしたときの状態に戻すかどうかを定義します。\n\n[`$cfg['blowfish_secret']`](#cfg_blowfish_secret) を設定しなかった場合、自動的に無効になります。\n\n`$cfg['LoginCookieValidity']`[¶](#cfg_LoginCookieValidity)\n\n| データ型: | 整数型 [秒数] |\n| デフォルト値: | 1440 |\n\nログインクッキーの有効期間を定義します。PHP の設定オプション [session.gc_maxlifetime](https://www.php.net/manual/ja/session.configuration.php#ini.session.gc-maxlifetime) は、セッションの有効性を制限する可能性があるので注意してください。セッションが失われている場合、ログインクッキーも無効になります。ですから、 `session.gc_maxlifetime` は [`$cfg['LoginCookieValidity']`](#cfg_LoginCookieValidity) と同じ値以上に設定したほうがいいのです。\n\n`$cfg['LoginCookieStore']`[¶](#cfg_LoginCookieStore)\n\n| データ型: | 整数型 [秒数] |\n| デフォルト値: | 0 |\n\nログインクッキーをブラウザに保存しておく期間を定義します。デフォルト値「0」は、セッションが存在している間だけ保持しておくことを意味します。これは、信頼できない環境に適しています。\n\n`$cfg['LoginCookieDeleteAll']`[¶](#cfg_LoginCookieDeleteAll)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n有効 (デフォルト) にすると、ログアウト時に全てのサーバのクッキーを削除します。無効にした場合は現在サーバにのみ削除します。これを false に設定すると、複数のサーバを使用していた場合、他のサーバからのログアウトを忘れやすくなります。\n\n`$cfg['AllowArbitraryServer']`[¶](#cfg_AllowArbitraryServer)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n有効にすると、クッキー認証を利用して任意のサーバにログインできるようになります。\n\n注釈\n\nこの機能は慎重に使用してください。 [HTTP](index.html#term-http) サーバが置かれているファイアウォール越しにユーザが MySQL サーバにアクセスできてしまうことがあります。 [`$cfg['ArbitraryServerRegexp']`](#cfg_ArbitraryServerRegexp) も参照してください。\n\n`$cfg['ArbitraryServerRegexp']`[¶](#cfg_ArbitraryServerRegexp)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n[`$cfg['AllowArbitraryServer']`](#cfg_AllowArbitraryServer) が有効な場合、 [IP](index.html#term-ip) または MySQL サーバのホスト名を正規表現に一致させることで、ユーザがログインできる MySQL サーバを制限します。正規表現は区切り文字で囲まなければなりません。\n\n文字列が部分一致することを避けるために、正規表現に開始記号と終了記号を設定することをお勧めします。\n\n**例:**\n```\n// Allow connection to three listed servers:\n$cfg['ArbitraryServerRegexp'] = '/^(server|another|yetdifferent)$/';\n\n// Allow connection to range of IP addresses:\n$cfg['ArbitraryServerRegexp'] = '@^192\\.168\\.0\\.[0-9]{1,}$@';\n\n// Allow connection to server name ending with -mysql:\n$cfg['ArbitraryServerRegexp'] = '@^[^:]\\-mysql$@';\n```\n注釈\n\nサーバ名全体をマッチさせるとき、ポートが含まれることがあります。 MySQL は接続パラメータに寛容なので、 ``server:3306-mysql`` のような接続文字列を使うことができます。これは、他のサーバに接続する際に、接尾辞による正規表現をバイパスするために使用されることがあります。\n\n`$cfg['CaptchaMethod']`[¶](#cfg_CaptchaMethod)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'invisible'` |\n\n可能な値は次の通りです。\n\n* `'invisible'` 不可視の CAPTCHA チェック方法を使用する\n* `'checkbox'` ユーザがロボットでないことを確認するチェックボックスを使用する。\n\nバージョン 5.0.3 で追加.\n\n`$cfg['CaptchaApi']`[¶](#cfg_CaptchaApi)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'https://www.google.com/recaptcha/api.js'` |\n\nバージョン 5.1.0 で追加.\n\nGoogle または互換性のある reCaptcha v2 サービス API の URL です。\n\n`$cfg['CaptchaCsp']`[¶](#cfg_CaptchaCsp)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'https://apis.google.com https://www.google.com/recaptcha/ https://www.gstatic.com/recaptcha/ https://ssl.gstatic.com/'` |\n\nバージョン 5.1.0 で追加.\n\nGoogle または互換サービスの reCaptcha v2 サービスの Content-Security-Policy スニペット (埋め込みコンテンツを許可する URL) です。\n\n`$cfg['CaptchaRequestParam']`[¶](#cfg_CaptchaRequestParam)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'g-recaptcha'` |\n\nバージョン 5.1.0 で追加.\n\nreCaptcha v2 サービスで使用されるリクエスト引数です。\n\n`$cfg['CaptchaResponseParam']`[¶](#cfg_CaptchaResponseParam)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'g-recaptcha-response'` |\n\nバージョン 5.1.0 で追加.\n\nreCaptcha v2 で使用されるレスポンス引数です。\n\n`$cfg['CaptchaLoginPublicKey']`[¶](#cfg_CaptchaLoginPublicKey)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nreCaptcha サービスの公開鍵で、 <https://www.google.com/recaptcha/about/> の「管理コンソール」から入手できるものです。\n\n参考\n\n<<https://developers.google.com/recaptcha/docs/v3>reCaptcha は [クッキー認証モード](index.html#cookie) で使用されます。\n\nバージョン 4.1.0 で追加.\n\n`$cfg['CaptchaLoginPrivateKey']`[¶](#cfg_CaptchaLoginPrivateKey)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nreCaptcha サービスの秘密鍵で、 <https://www.google.com/recaptcha/about/> の「管理コンソール」から入手できるものです。\n\n参考\n\n<<https://developers.google.com/recaptcha/docs/v3>reCaptcha は [クッキー認証モード](index.html#cookie) で使用されます。\n\nバージョン 4.1.0 で追加.\n\n`$cfg['CaptchaSiteVerifyURL']`[¶](#cfg_CaptchaSiteVerifyURL)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nsiteverify アクションを行う reCaptcha サービスの URL です。\n\nreCaptcha は [クッキー認証モード](index.html#cookie) で使用されます。\n\nバージョン 5.1.0 で追加.\n\n### ナビゲーションパネルの設定[¶](#navigation-panel-setup)\n\n`$cfg['ShowDatabasesNavigationAsTree']`[¶](#cfg_ShowDatabasesNavigationAsTree)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネル内のデータベースツリーをセレクタで置き換えます\n\n`$cfg['FirstLevelNavigationItems']`[¶](#cfg_FirstLevelNavigationItems)\n\n| データ型: | 整数型 |\n| デフォルト値: | 100 |\n\nナビゲーションツリーの各ページに表示される第一階層のデータベースの数。\n\n`$cfg['MaxNavigationItems']`[¶](#cfg_MaxNavigationItems)\n\n| データ型: | 整数型 |\n| デフォルト値: | 50 |\n\nナビゲーションツリーの各ページに表示する項目 (テーブル、列、インデックス) の数。\n\n`$cfg['NavigationTreeEnableGrouping']`[¶](#cfg_NavigationTreeEnableGrouping)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n名前と [`$cfg['NavigationTreeDbSeparator']`](#cfg_NavigationTreeDbSeparator) による共通の接頭辞に基づいてデータベースをグループ化するかどうかを定義します。\n\n`$cfg['NavigationTreeDbSeparator']`[¶](#cfg_NavigationTreeDbSeparator)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'_'` |\n\nデータベース名をツリー表示するときに、分離する部分に使われる文字列。\n\n`$cfg['NavigationTreeTableSeparator']`[¶](#cfg_NavigationTreeTableSeparator)\n\n| データ型: | 文字列型または配列型 |\n| デフォルト値: | `'__'` |\n\nテーブル空間を入れ子にするために使う文字列を定義します。つまり、 `first__second__third` のようなテーブルがある場合は、first > second > third のような 3 階層構造で表示されます。 false または空に設定すると、この機能は無効になります。注意: テーブル名の最初や最後にこの区切り文字を使ってはいけません。\n\n`$cfg['NavigationTreeTableLevel']`[¶](#cfg_NavigationTreeTableLevel)\n\n| データ型: | 整数型 |\n| デフォルト値: | 1 |\n\nテーブルを上記の区切り文字で分割表示する際に何階層まで表示するかを定義します。\n\n`$cfg['NumRecentTables']`[¶](#cfg_NumRecentTables)\n\n| データ型: | 整数型 |\n| デフォルト値: | 10 |\n\nナビゲーションパネルで表示される最近使用したテーブルの最大数。この値を 0 に設定すると最近使用したテーブルのリストは無効になります。\n\n`$cfg['NumFavoriteTables']`[¶](#cfg_NumFavoriteTables)\n\n| データ型: | 整数型 |\n| デフォルト値: | 10 |\n\nナビゲーションパネルに表示されるお気に入りのテーブルの最大数。この値を 0 に設定するとお気に入りのテーブルの一覧は無効になります。\n\n`$cfg['ZeroConf']`[¶](#cfg_ZeroConf)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nゼロ設定モードを有効にします。このモードでは、現在のデータベースに phpMyAdmin 環境保管領域を作成するか、既存のものを使用するかの選択がユーザに提供されます。\n\nphpMyAdmin 環境保管領域が適切に作成され、関連する設定項目 ([`$cfg['Servers'][$i]['pmadb']`](#cfg_Servers_pmadb) など) が設定されている場合は、この設定は影響を受けません。\n\n`$cfg['NavigationLinkWithMainPanel']`[¶](#cfg_NavigationLinkWithMainPanel)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nメインパネルのリンクで現在のデータベースやテーブルを強調表示するかどうかを定義します。\n\n`$cfg['NavigationDisplayLogo']`[¶](#cfg_NavigationDisplayLogo)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nphpMyAdmin ロゴをナビゲーションパネルの最上部に表示するかどうかを定義します。\n\n`$cfg['NavigationLogoLink']`[¶](#cfg_NavigationLogoLink)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'index.php'` |\n\nナビゲーションパネルのロゴが指す [URL](index.html#term-url) を入力してください。特に、独自のテーマで使用する場合に変更することがあります。相対/内部 URL の場合、 `'./sql.phpindex.php?route=/server/sql?'` のように `./` で始め `?` で終える必要があります。外部 URL の場合は、プロトコルスキーム (`http` または `https`) を絶対 URL に含めてください。\n\nリンクをブラウザの新しいタブで開きたい場合は、 [`$cfg['NavigationLogoLinkWindow']`](#cfg_NavigationLogoLinkWindow) を使う必要があります\n\n`$cfg['NavigationLogoLinkWindow']`[¶](#cfg_NavigationLogoLinkWindow)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'main'` |\n\nリンクされているページをメインウィンドウ (`main`) を新しいウィンドウ (`new`) のどちらで開くか。注: `phpmyadmin.net` にリンクしている場合は、 `new` が使われます。\n\nメインウィンドウでリンクを開く場合は、 [コンテンツセキュリティポリシー](index.html#term-content-security-policy) のヘッダのため、 [`$cfg['NavigationLogoLink']`](#cfg_NavigationLogoLink) の値を [`$cfg['CSPAllow']`](#cfg_CSPAllow) に追加する必要があります。\n\n`$cfg['NavigationTreeDisplayItemFilterMinimum']`[¶](#cfg_NavigationTreeDisplayItemFilterMinimum)\n\n| データ型: | 整数型 |\n| デフォルト値: | 30 |\n\nナビゲーションツリーの項目の一覧の上に JavaScript のフィルタボックスを表示する項目（テーブル、ビュー、ルーチン、イベント）の最小数を定義します。\n\nフィルタを完全に無効にするためには、何か大きい数値を使用します (例: 9999)\n\n`$cfg['NavigationTreeDisplayDbFilterMinimum']`[¶](#cfg_NavigationTreeDisplayDbFilterMinimum)\n\n| データ型: | 整数型 |\n| デフォルト値: | 30 |\n\nナビゲーションツリー内のデータベース一覧の上の JavaScript フィルタボックスに表示するデータベースの最小数を定義します。\n\nフィルタを完全に無効にするためには、何か大きい数値を使用します (例: 9999)\n\n`$cfg['NavigationDisplayServers']`[¶](#cfg_NavigationDisplayServers)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルの最上部にあるサーバの選択を表示するかどうかを定義します。\n\n`$cfg['DisplayServersList']`[¶](#cfg_DisplayServersList)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nこのサーバの選択肢をドロップダウンではなくリンクとして表示するかどうかを定義します。\n\n`$cfg['NavigationTreeDefaultTabTable']`[¶](#cfg_NavigationTreeDefaultTabTable)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'structure'` |\n\nナビゲーションパネルで各テーブル名の隣にある小さなアイコンをクリックしたときにデフォルトで表示されるタブを定義します。可能な値は次のいずれかです。\n\n* `structure`\n* `sql`\n* `search`\n* `insert`\n* `browse`\n\n`$cfg['NavigationTreeDefaultTabTable2']`[¶](#cfg_NavigationTreeDefaultTabTable2)\n\n| データ型: | 文字列型 |\n| デフォルト値: | null |\n\nナビゲーションパネルで各テーブル名の隣にある2番目の小さなアイコンをクリックしたときにデフォルトで表示されるタブを定義します。可能な値は次のいずれかです。\n\n* `(empty)`\n* `structure`\n* `sql`\n* `search`\n* `insert`\n* `browse`\n\n`$cfg['NavigationTreeEnableExpansion']`[¶](#cfg_NavigationTreeEnableExpansion)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルでツリー展開の設定。\n\n`$cfg['NavigationTreeShowTables']`[¶](#cfg_NavigationTreeShowTables)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルのデータベースの下にテーブルを表示するかどうかです。\n\n`$cfg['NavigationTreeShowViews']`[¶](#cfg_NavigationTreeShowViews)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルのデータベースの下にビューを表示するかどうかです。\n\n`$cfg['NavigationTreeShowFunctions']`[¶](#cfg_NavigationTreeShowFunctions)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルのデータベースの下に関数を表示するかどうかです。\n\n`$cfg['NavigationTreeShowProcedures']`[¶](#cfg_NavigationTreeShowProcedures)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルのデータベースの下にプロシージャを表示するかどうかです。\n\n`$cfg['NavigationTreeShowEvents']`[¶](#cfg_NavigationTreeShowEvents)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションパネルのデータベースの下にイベントを表示するかどうかです。\n\n`$cfg['NavigationTreeAutoexpandSingleDb']`[¶](#cfg_NavigationTreeAutoexpandSingleDb)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nナビゲーションツリーで１つデータベースを自動的に展開するかどうか。\n\n`$cfg['NavigationWidth']`[¶](#cfg_NavigationWidth)\n\n| データ型: | 整数型 |\n| デフォルト値: | 240 |\n\nナビゲーションパネルの幅で、 0 に設定するとデフォルトで畳みます。\n\n### メインパネル[¶](#main-panel)\n\n`$cfg['ShowStats']`[¶](#cfg_ShowStats)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nデータベースやテーブルについてのディスク容量の使用状況や統計情報を表示するかどうかを定義します。ただし、統計情報を表示するには MySQL 3.23.3 以上が必要であり、現時点では MySQL は Berkeley DB テーブル向けの情報などを返しません。\n\n`$cfg['ShowServerInfo']`[¶](#cfg_ShowServerInfo)\n\n| データ型: | 論理型|文字列型 |\n| デフォルト値: | true |\n\nメインページに詳細なサーバ情報を表示するかどうかを定義します。取りうる値は次の通りです。\n\n* `true` ならばすべてのサーバ情報を表示\n* `false` ならばサーバ情報を非表示\n* `'database-server'` ならば、データベースサーバ情報のみを表示\n* `'web-server'` ならばウェブサーバ情報のみを表示\n\nさらに、 [`$cfg['Servers'][$i]['verbose']`](#cfg_Servers_verbose) を使用することにより、より多くの情報を隠すことができます。\n\nバージョン 6.0.0 で変更: `'database-server'` および `'web-server'` オプションを追加しました。\n\n`$cfg['ShowPhpInfo']`[¶](#cfg_ShowPhpInfo)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n立ち上げ時のメイン（右）フレームに、 PHP情報を表示する を表示するかどうかを定義します。\n\nスクリプト内で [``](#system-message-1)phpinfo()``の使用を禁止するための注意点。:file:[`](#system-message-2)php.ini`に含めることが必要な記述:\n```\ndisable_functions = phpinfo()\n```\n警告\n\nphpinfo ページを有効化すると、サーバの設定に関する膨大な情報を漏洩することになります。共有インストールではこれを有効にすることはお勧めしません。\n\nこれによって、インストールに対する一部のリモート攻撃が容易になる可能性があるため、必要な場合しかこれを有効化しないようにしてください。\n\n`$cfg['ShowChgPassword']`[¶](#cfg_ShowChgPassword)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n立ち上げ時のメイン（右）フレームに、 パスワードを変更する のリンクを表示するかどうかを定義します。この設定は、直接入力された MySQL コマンドをチェックするものではありません。\n\nなお、 config 認証モードでは、たとえ設定が有効であっても パスワードを変更する リンクは無効になります。設定ファイルに直接書き込まれたパスワードは、ログインユーザが書き換えることができないからです。\n\n`$cfg['ShowCreateDb']`[¶](#cfg_ShowCreateDb)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n立ち上げ時のメイン（右）フレームに、データベースを作成するフォームを表示するかどうかを定義します。この設定は、直接入力された MySQL コマンドに対してチェックするわけではありません。\n\n`$cfg['ShowGitRevision']`[¶](#cfg_ShowGitRevision)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n(もしあれば) 現在の Git リビジョンに関する情報をメインパネルに表示するかどうかを定義します。\n\n`$cfg['MysqlMinVersion']`[¶](#cfg_MysqlMinVersion)\n\n| データ型: | 配列型 |\n\n対応している MySQL の最低バージョンを定義します。デフォルト値は phpMyAdmin チームによって選択されます。ただし、この設定項目は (ほとんどの phpMyAdmin の機能が動作する) 古い MySQL サーバとの統合を容易にするために、 Plesk コントロールパネルの開発者から依頼されたものです。\n\n### データベースの構造[¶](#database-structure)\n\n`$cfg['ShowDbStructureCharset']`[¶](#cfg_ShowDbStructureCharset)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベース構造ページ内のすべてのテーブルの文字セットを表示する列を表示するかどうかを定義します。\n\n`$cfg['ShowDbStructureComment']`[¶](#cfg_ShowDbStructureComment)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベース構造ページ内のすべてのテーブルのコメントを表示する列を表示するかどうかを定義します。\n\n`$cfg['ShowDbStructureCreation']`[¶](#cfg_ShowDbStructureCreation)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベース構造ページ (テーブル一覧) において、「作成日時」カラムでいつテーブルが作成されたかを表示させるかどうかを定義します。\n\n`$cfg['ShowDbStructureLastUpdate']`[¶](#cfg_ShowDbStructureLastUpdate)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベース構造ページ (テーブル一覧) において、「最終更新」カラムでテーブル最後に更新された時期を表示させるかどうかを定義します。\n\n`$cfg['ShowDbStructureLastCheck']`[¶](#cfg_ShowDbStructureLastCheck)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベース構造ページ (テーブル一覧) において、「最終検査」カラムでテーブルを最後に検査した時期を表示させるかどうかを定義します。\n\n`$cfg['HideStructureActions']`[¶](#cfg_HideStructureActions)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nテーブル構造の各操作を「その他 」ドロップダウンの中に隠すかどうかを定義します。\n\n`$cfg['ShowColumnComments']`[¶](#cfg_ShowColumnComments)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nテーブル構造ビューのカラムとして、カラムのコメントを表示するかどうかを定義します。\n\n### 表示モード[¶](#browse-mode)\n\n`$cfg['TableNavigationLinksMode']`[¶](#cfg_TableNavigationLinksMode)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'icons'` |\n\nテーブルのナビゲーションリンクにアイコン (`'icons'`)、テキスト (`'text'`)、または両方 (`'both'`) のどれを表示するかを定義します。\n\n`$cfg['ActionLinksMode']`[¶](#cfg_ActionLinksMode)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'both'` |\n\n`icons` に設定すると、データベースおよびテーブルプロパティのリンクテキスト (表示、 検索、 挿入、など) の代わりにアイコンを表示します。アイコンとテキストの両方を表示したい場合は `'both'` に設定することができます。 `text` に設定すると、テキストのみを表示します。\n\n`$cfg['RowActionType']`[¶](#cfg_RowActionType)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'both'` |\n\nテーブルの行の操作の部分を、アイコン、テキスト、またはアイコンとテキストの両方のどれで表示するかです。値は `'icons'` (アイコン)、 `'text'` (テキスト)、 `'both'` (両方) のいずれかです。\n\n`$cfg['ShowAll']`[¶](#cfg_ShowAll)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nすべての場合において、表示モードでユーザに「すべて表示 」ボタンを表示するかどうかを定義します。デフォルトでは、取得する行数が多くなりすぎることによるパフォーマンスの問題を回避するため、小さなテーブル (500 行未満) のみに表示されます。\n\n`$cfg['MaxRows']`[¶](#cfg_MaxRows)\n\n| データ型: | 整数型 |\n| デフォルト値: | 25 |\n\nLIMIT 節を使用しなかった場合の結果セットの表示行数です。この場合において結果セットがこの行数を上回ったときは、「前へ 」および「次へ 」のリンクが表示されます。指定可能な値は、 25、50、100、250、500 です。\n\n`$cfg['Order']`[¶](#cfg_Order)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'SMART'` |\n\n昇順 (`ASC`)、降順 (`DESC`)、スマートな順番 (`SMART`) のいずれの方法でカラムを表示するかを定義します。スマートな順番とは、TIME、DATE、DATETIME、TIMESTAMP の場合は降順、それ以外の場合は昇順であり、これがデフォルトです。\n\nバージョン 3.4.0 で変更: phpMyAdmin 3.4.0 以降ではデフォルト値は `'SMART'` です。\n\n`$cfg['DisplayBinaryAsHex']`[¶](#cfg_DisplayBinaryAsHex)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n表示オプション「バイナリコンテンツを 16 進数で表示する」を既定でチェックするかどうかを定義します。\n\nバージョン 3.3.0 で追加.\n\nバージョン 4.3.0 で非推奨: この設定は削除されました。\n\n`$cfg['GridEditing']`[¶](#cfg_GridEditing)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'double-click'` |\n\nグリッド編集を起動するアクション (`double-click` または``click``) を定義します。 `disabled` の値で無効化することもできます。\n\n`$cfg['RelationalDisplay']`[¶](#cfg_RelationalDisplay)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'K'` |\n\nオプション > リレーションの初期動作を定義します。 `K` がデフォルトで、キーを表示するのに対し、 `D` はカラムを表示します。\n\n`$cfg['SaveCellsAtOnce']`[¶](#cfg_SaveCellsAtOnce)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nグリッド編集において、編集されたすべてのセルを一度に保存するかどうかを定義します。\n\n### 編集モード[¶](#editing-mode)\n\n`$cfg['ProtectBinary']`[¶](#cfg_ProtectBinary)\n\n| データ型: | 論理型または文字列型 |\n| デフォルト値: | `'blob'` |\n\nテーブルの内容を表示しているときに `BLOB` や `BINARY` カラムを保護して編集できないようにするかどうかを定義します。有効な値は次の通りです。\n\n* `false` はすべてのカラムの編集を許可します。\n* `'blob'` は `BLOBS` 以外のすべてのカラムの編集を許可します。\n* `'noblob'` は `BLOBS` 以外のすべてのカラムの編集を禁止します (`'blob'` の 逆)。\n* `'all'` ですべての `BINARY` カラムと `BLOB` カラムの編集を禁止します。\n\n`$cfg['ShowFunctionFields']`[¶](#cfg_ShowFunctionFields)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n挿入／編集モードで、MySQL 関数の項目が最初から表示されるかどうかを定義します。バージョン 2.10 以降、この設定はユーザインタフェースで切り替えることができます。\n\n`$cfg['ShowFieldTypesInDataEditView']`[¶](#cfg_ShowFieldTypesInDataEditView)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n編集／挿入モードで、データ型の項目が最初から表示されるかどうかを定義します。この設定はユーザインタフェースで切り替えることができます。\n\n`$cfg['InsertRows']`[¶](#cfg_InsertRows)\n\n| データ型: | 整数型 |\n| デフォルト値: | 2 |\n\n挿入ページから入力するデフォルトの行数を定義します。ユーザはページの下部から空行を追加または削除することで、手動でこれを変更することができます。\n\n`$cfg['ForeignKeyMaxLimit']`[¶](#cfg_ForeignKeyMaxLimit)\n\n| データ型: | 整数型 |\n| デフォルト値: | 100 |\n\n外部キーに指定された項目がこの値より少ない場合は、 [`$cfg['ForeignKeyDropdownOrder']`](#cfg_ForeignKeyDropdownOrder) の設定で記述したスタイルで外部キーのドロップダウンボックスが表示されます。\n\n`$cfg['ForeignKeyDropdownOrder']`[¶](#cfg_ForeignKeyDropdownOrder)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('content-id', 'id-content') |\n\n外部キーのドロップダウン項目には、いくつかの表示方法がありますが、キーと値データの両方が表示されます。この配列には、 `content-id` と `id-content` のいずれか、または両方が入ります。\n\n### エクスポートとインポートの設定[¶](#export-and-import-settings)\n\n`$cfg['ZipDump']`[¶](#cfg_ZipDump)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n`$cfg['GZipDump']`[¶](#cfg_GZipDump)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n`$cfg['BZipDump']`[¶](#cfg_BZipDump)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nダンプファイルを作成するときに zip/GZip/BZip2 圧縮を利用できるようにするかどうかを定義します\n\n`$cfg['CompressOnFly']`[¶](#cfg_CompressOnFly)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nGZip/BZip2 でエクスポートを圧縮する際、逐次圧縮を許可するかどうかを定義します。比較的小さなダンプの場合は関係ありませんが、許可すると、圧縮しない限り PHP のメモリ制限にひっかかるような大きなダンプも作成できるようになります。こうして生成したファイルは GZip/BZip2 ヘッダが多くなってしまいますが、まともなプログラムならどれでも正しく処理してくれます。\n\n`$cfg['Export']`[¶](#cfg_Export)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(...) |\n\nこの配列はエクスポートの際のデフォルトパラメータを定義します。項目名はエクスポートページに表示されるテキストとほとんど同じですので、意味は簡単にわかるでしょう。\n\n`$cfg['Export']['format']`[¶](#cfg_Export_format)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'sql'` |\n\nデフォルトのエクスポート形式。\n\n`$cfg['Export']['method']`[¶](#cfg_Export_method)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'quick'` |\n\nエクスポートページに表示される形式について定義します。有効な値は以下の通りです。\n\n* `quick` は、設定に必要な最小限のオプションを表示します\n* `custom` は、設定できるすべてのオプションを表示します\n* `custom-no-form` は `custom` と同じですが、 quick エクスポートのオプションは表示されません\n\n`$cfg['Export']['compression']`[¶](#cfg_Export_compression)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'none'` |\n\nデフォルトのエクスポート圧縮方式。指定できる値は、`'none'`、`'zip'`、[``](#system-message-1)'gzip'[``](#system-message-2)のいずれかです。\n\n`$cfg['Export']['charset']`[¶](#cfg_Export_charset)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n生成されるエクスポートの文字セットを定義します。デフォルトでは UTF-8 を想定して文字セット変換は行われません。\n\n`$cfg['Export']['file_template_table']`[¶](#cfg_Export_file_template_table)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@TABLE@'` |\n\nテーブルをエクスポートする際のデフォルトのファイル名のテンプレートです。\n\n参考\n\n[6.27 どのような書式の文字列が使えますか？](index.html#faq6-27)\n\n`$cfg['Export']['file_template_database']`[¶](#cfg_Export_file_template_database)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@DATABASE@'` |\n\nデータベースエクスポート用のデフォルトのファイル名テンプレートです。\n\n参考\n\n[6.27 どのような書式の文字列が使えますか？](index.html#faq6-27)\n\n`$cfg['Export']['file_template_server']`[¶](#cfg_Export_file_template_server)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@SERVER@'` |\n\nサーバをエクスポートする際のデフォルトのファイル名のテンプレートです。\n\n参考\n\n[6.27 どのような書式の文字列が使えますか？](index.html#faq6-27)\n\n`$cfg['Export']['remove_definer_from_definitions']`[¶](#cfg_Export_remove_definer_from_definitions)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nイベント、ビュー、ルーチン定義から DEFINER 句を削除します。\n\nバージョン 5.2.0 で追加.\n\n`$cfg['Import']`[¶](#cfg_Import)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(...) |\n\nこの配列はインポートの際のデフォルトパラメータを定義します。項目名はインポートページに表示されるテキストとほとんど同じですので、意味は簡単にわかるでしょう。\n\n`$cfg['Import']['charset']`[¶](#cfg_Import_charset)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nインポート用の文字セットを定義します。デフォルトでは UTF-8 を仮定し、文字セット変換は行われません。\n\n`$cfg['Schema']`[¶](#cfg_Schema)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(...) |\n\n`$cfg['Schema']['format']`[¶](#cfg_Schema_format)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'pdf'` |\n\nDefines the default format for schema export. Possible values are `'pdf'`, `'eps'`, `'dia'` or `'svg'`.\n\n### タブ表示設定[¶](#tabs-display-settings)\n\n`$cfg['TabsMode']`[¶](#cfg_TabsMode)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'both'` |\n\nメニュータブにアイコン (`'icons'`)、テキスト (`'text'`)、または両方 (`'both'`) のどれを表示するかを定義します。.\n\n`$cfg['PropertiesNumColumns']`[¶](#cfg_PropertiesNumColumns)\n\n| データ型: | 整数型 |\n| デフォルト値: | 1 |\n\nデータベースのプロパティを表示する際に何カラム分のテーブルを表示するか。 1 より大きい値に設定した場合、表示領域を広げるためデータベースのタイプは表示されなくなります。\n\n`$cfg['DefaultTabServer']`[¶](#cfg_DefaultTabServer)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'welcome'` |\n\nデフォルトでサーバビューに表示されるタブを定義します。指定可能な値はローカライズされた次のものと同等です。\n\n* `welcome` (複数ユーザのセットアップに推奨)\n* `databases`,\n* `status`\n* `variables`\n* `privileges`\n\n`$cfg['DefaultTabDatabase']`[¶](#cfg_DefaultTabDatabase)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'structure'` |\n\nデフォルトでデータベースビューに表示されるタブを定義します。指定可能な値はローカライズされた次のものと同等です。\n\n* `structure`\n* `sql`\n* `search`\n* `operations`\n\n`$cfg['DefaultTabTable']`[¶](#cfg_DefaultTabTable)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'browse'` |\n\nデフォルトでテーブルビューに表示されるタブを定義します。指定可能な値はローカライズされた次のものと同等です。\n\n* `structure`\n* `sql`\n* `search`\n* `insert`\n* `browse`\n\n### PDF オプション[¶](#pdf-options)\n\n`$cfg['PDFPageSizes']`[¶](#cfg_PDFPageSizes)\n\n| データ型: | 配列型 |\n| デフォルト値: | `array('A3', 'A4', 'A5', 'letter', 'legal')` |\n\nPDF ページを生成するのに利用できる紙の大きさの配列です。\n\nこれを変更する必要はありません。\n\n`$cfg['PDFDefaultPageSize']`[¶](#cfg_PDFDefaultPageSize)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'A4'` |\n\nPDF ページの生成時に使用するデフォルトのページの大きさです。有効な値は [`$cfg['PDFPageSizes']`](#cfg_PDFPageSizes) にあるいずれかです。\n\n### 言語[¶](#languages)\n\n`$cfg['DefaultLang']`[¶](#cfg_DefaultLang)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'en'` |\n\nブラウザーやユーザーが定義していない場合に使用するデフォルトの言語を定義します。対応する言語ファイルは、 locale/*code*/LC_MESSAGES/phpmyadmin.mo に存在しなければなりません。\n\n`$cfg['DefaultConnectionCollation']`[¶](#cfg_DefaultConnectionCollation)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'utf8mb4_general_ci'` |\n\nユーザが定義していない場合に使用するデフォルトの接続の照合順序を定義します。設定可能な値については [文字セットに関する MySQL のドキュメント](https://dev.mysql.com/doc/refman/5.7/ja/charset-charsets.html) を参照してください。\n\n`$cfg['Lang']`[¶](#cfg_Lang)\n\n| データ型: | 文字列型 |\n| デフォルト値: | 設定なし |\n\n強制的に使用する言語です。対応する言語ファイルは、 locale/*code*/LC_MESSAGES/phpmyadmin.mo に存在しなければなりません。\n\n`$cfg['FilterLanguages']`[¶](#cfg_FilterLanguages)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\n利用可能な言語の一覧を与えられた正規表現にマッチするものに限定します。例えば、チェコ語と英語のみに限定したければ、フィルタを `'^(cs|en)'` に設定します。\n\n`$cfg['RecodingEngine']`[¶](#cfg_RecodingEngine)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'auto'` |\n\n文字セットの変換にどの関数を利用するかを選択できます。可能な値は次の通りです。\n\n* `'auto'` - automatically use available one (first is tested iconv, then mbstring)\n* `'iconv'` - use iconv or libiconv functions\n* `'mb'` - use [mbstring](index.html#term-mbstring) extension\n* `'none'` - disable encoding conversion\n\n文字セットの変換が有効の場合、ファイルをエクスポートするときに文字セットを選択できるように、エクスポート／インポートページでプルダウンメニューが有効になります。このメニューのデフォルト値は [`$cfg['Export']['charset']`](#cfg_Export_charset) と [`$cfg['Import']['charset']`](#cfg_Import_charset) で設定されているものです。\n\nバージョン 6.0.0 で変更: Support for the Recode extension has been removed. The `'recode'` value is ignored and the default value (`'auto'`) is used instead.\n\n`$cfg['IconvExtraParams']`[¶](#cfg_IconvExtraParams)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'//TRANSLIT'` |\n\n文字セット変換で利用する iconv 向けのパラメータを指定します。詳しくは [iconv のドキュメント](https://www.gnu.org/savannah-checkouts/gnu/libiconv/documentation/libiconv-1.15/iconv_open.3.html) をご覧ください。デフォルトでは `//TRANSLIT` が使用されていて、無効な文字は書き直しが行われます。\n\n`$cfg['AvailableCharsets']`[¶](#cfg_AvailableCharsets)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(...) |\n\nAvailable character sets for MySQL conversion. You can add your own\n(any of supported by mbstring/iconv) or remove these which you don't use. Character sets will be shown in same order as here listed, so if you frequently use some of these move them to the top.\n\n### ウェブサーバ設定[¶](#web-server-settings)\n\n`$cfg['OBGzip']`[¶](#cfg_OBGzip)\n\n| データ型: | 文字列型/論理型 |\n| デフォルト値: | `'auto'` |\n\n[HTTP](index.html#term-http) 転送の速度を上げるために GZip 出力バッファリングを使用するかどうかを定義します。 true/false に設定すると有効/無効になります。 (文字列で) 'auto' にすると、phpMyAdmin は出力バッファリングを有効にしようとしますが、ブラウザの方で何かバッファリングに問題が発生した場合は自動的に無効にします。IE6 に特定のパッチをあてると、バッファリングを有効にしたときにデータが壊れる問題があることが分かっています。\n\n`$cfg['TrustedProxies']`[¶](#cfg_TrustedProxies)\n\n| データ型: | 配列型 |\n| デフォルト値: | array() |\n\n[`$cfg['Servers'][$i]['AllowDeny']['order']`](#cfg_Servers_AllowDeny_order) で信頼されているプロキシと信頼されているプロキシおよび HTTP ヘッダのリストです。このリストはデフォルトでは空です。プロキシ越しの IP アドレスの規則を使用したい場合には、信頼されたプロキシサーバで埋める必要があります。\n\n次の例では、 phpMyAdmin がプロキシ 1.2.3.4 からきた HTTP_X_FORWARDED_FOR (`X-Forwarded-For`) ヘッダを信頼するように指定しています。\n```\n$cfg['TrustedProxies'] = ['1.2.3.4' => 'HTTP_X_FORWARDED_FOR'];\n```\n[`$cfg['Servers'][$i]['AllowDeny']['rules']`](#cfg_Servers_AllowDeny_rules) の設定項目は、通常通りクライアントの IP アドレスを使用します。\n\n`$cfg['GD2Available']`[¶](#cfg_GD2Available)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'auto'` |\n\nGD ≧ 2 が利用できるかどうかを指定します。利用できる場合、MIME 変換の際に活用できます。使用可能な値は次の通りです。\n\n* auto - 自動検出\n* yes - GD 2 関数が利用できます\n* no - GD 2 関数は利用できません\n\n`$cfg['CheckConfigurationPermissions']`[¶](#cfg_CheckConfigurationPermissions)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n通常、設定ファイルのアクセス許可をチェックして、誰でも書き込み可能でないことを確認します。しかしながら、Windows 以外のサーバ上でマウントされた NTFS ファイルシステムに phpMyAdmin がインストールされている場合は、パーミッションが間違っているようなときでも、実際には検出することができません。この場合、システム管理者はこのパラメータを `false` に設定します。\n\n`$cfg['LinkLengthLimit']`[¶](#cfg_LinkLengthLimit)\n\n| データ型: | 整数型 |\n| デフォルト値: | 1000 |\n\nリンクの [URL](index.html#term-url) の長さを制限します。長さがこの制限を超えた場合、ボタンつきのフォームに置き換えられます。一部のウェブサーバ ([IIS](index.html#term-iis)) は長い [URL](index.html#term-url) に問題があるため、この設定が必要となります。\n\n`$cfg['CSPAllow']`[¶](#cfg_CSPAllow)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nContent Security Policy ヘッダで許可されているスクリプトや画像の source に含める追加の文字列です。\n\nこれは、外部の JavaScript ファイルを `config.footer.inc.php` または `config.header.inc.php` に含める場合に役立ちます。これは通常、 [Content Security Policy](index.html#term-content-security-policy) では許可されていません。\n\n一部のサイトを許可するには、文字列の中に列挙するだけです。\n```\n$cfg['CSPAllow'] = 'example.com example.net';\n```\nバージョン 4.0.4 で追加.\n\n`$cfg['DisableMultiTableMaintenance']`[¶](#cfg_DisableMultiTableMaintenance)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nデータベースの構造ページにおいて、複数のテーブルをマークして多くのテーブルを最適化するような操作を選択することができます。この操作はサーバの動作を遅くする可能性があるので、これを `true` に設定することで、この種の複数のメンテナンス操作ができなくします。\n\n### テーマ設定[¶](#theme-settings)\n\n> `themes/themename/scss/_variables.scss` を直接変更してください。ただし、変更は次の更新で上書きされます。\n\n### デザインのカスタマイズ[¶](#design-customization)\n\n`$cfg['NavigationTreePointerEnable']`[¶](#cfg_NavigationTreePointerEnable)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\ntrue に設定すると、ナビゲーションパネルの項目にマウスポインタを合わせると、その項目がマークされます (背景が強調表示されます)。\n\n`$cfg['BrowsePointerEnable']`[¶](#cfg_BrowsePointerEnable)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\ntrue に設定すると、参照ページの行にカーソルを合わせたときに、その行がマークされます (背景が強調表示されます)。\n\n`$cfg['BrowseMarkerEnable']`[¶](#cfg_BrowseMarkerEnable)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\ntrue に設定すると、チェックボックスを使用して行が選択されたとき、データ行がマークされます (背景が強調表示されます)。\n\n`$cfg['LimitChars']`[¶](#cfg_LimitChars)\n\n| データ型: | 整数型 |\n| デフォルト値: | 50 |\n\n表示ページで、数字以外のフィールドに表示する最大文字数です。表示ページ内のトグルボタンでオフにすることもできます。\n\n`$cfg['RowActionLinks']`[¶](#cfg_RowActionLinks)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'left'` |\n\nテーブルの内容を表示しているとき、行に関するリンク (編集、複製、削除) をどこに表示するかを定義します (左側 (left)、右側 (right)、左右両側 (both)、なし (nowhere) が設定できます)。\n\n`$cfg['RowActionLinksWithoutUnique']`[¶](#cfg_RowActionLinksWithoutUnique)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n選択範囲に [ユニークキー](index.html#term-unique-key) がない場合でも、複数の行操作を行うための各行のリンク (編集、コピー、削除) やチェックボックスを表示するかどうかを指定します。ユニークキーがない場合に行操作を使用すると、行を正確に選択する方法が保証されていないため、別な行やより多くの行が影響を受けることになる可能性があります。\n\n`$cfg['RememberSorting']`[¶](#cfg_RememberSorting)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n有効にすると、表示している各テーブルのソートが記憶されます。\n\n`$cfg['TablePrimaryKeyOrder']`[¶](#cfg_TablePrimaryKeyOrder)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'NONE'` |\n\nこれは [主キー](index.html#term-primary-key) を持つテーブルで、ソート順が外部的に定義されていない場合のデフォルトのソート順を定義します。指定可能な値は ['NONE', 'ASC', 'DESC'] のいずれかです。\n\n`$cfg['ShowBrowseComments']`[¶](#cfg_ShowBrowseComments)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n`$cfg['ShowPropertyComments']`[¶](#cfg_ShowPropertyComments)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n対応する変数を `true` に設定すると、表示またはプロパティでカラムのコメントが表示できるようになります。表示モードの場合、コメントはヘッダの中に表示されます。プロパティモードの場合、コメントはカラム名の下に CSS で整形された破線を使用して表示されます。コメントはカラムのツールチップとしても表示されます。\n\n`$cfg['FirstDayOfCalendar']`[¶](#cfg_FirstDayOfCalendar)\n\n| データ型: | 整数型 |\n| デフォルト値: | 0 |\n\nこれはカレンダーにおける週の最初の曜日を定義します。数値は 0 から 6 までを設定することができ、それぞれ７つの曜日、日曜日から土曜日までを表します。この値は:guilabel:サーバの設定 -> 機能 -> 一般 -> カレンダーの最初の曜日フィールド でユーザが設定することもできます。\n\n### テキスト入力項目[¶](#text-fields)\n\n`$cfg['CharEditing']`[¶](#cfg_CharEditing)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'input'` |\n\nCHAR カラムと VARCHAR カラムでどちらの編集用コントロールを利用するか定義します。データの編集と、構造の編集のデフォルト値にも適用されます。指定可能な値は次の通りです。\n\n* input - テキストのサイズを MySQL のカラムのサイズまでに制限できますが、カラムに改行があると問題になります\n* textarea - カラムに改行があっても問題ありませんが、長さの制限はできません\n\n`$cfg['MinSizeForInputField']`[¶](#cfg_MinSizeForInputField)\n\n| データ型: | 整数型 |\n| デフォルト値: | 4 |\n\nCHAR および VARCHAR カラムに対する入力項目の最小サイズを定義します。\n\n`$cfg['MaxSizeForInputField']`[¶](#cfg_MaxSizeForInputField)\n\n| データ型: | 整数型 |\n| デフォルト値: | 60 |\n\nCHAR および VARCHAR カラムに対する入力項目の最大サイズを定義します。\n\n`$cfg['TextareaCols']`[¶](#cfg_TextareaCols)\n\n| データ型: | 整数型 |\n| デフォルト値: | 40 |\n\n`$cfg['TextareaRows']`[¶](#cfg_TextareaRows)\n\n| データ型: | 整数型 |\n| デフォルト値: | 15 |\n\n`$cfg['CharTextareaCols']`[¶](#cfg_CharTextareaCols)\n\n| データ型: | 整数型 |\n| デフォルト値: | 40 |\n\n`$cfg['CharTextareaRows']`[¶](#cfg_CharTextareaRows)\n\n| データ型: | 整数型 |\n| デフォルト値: | 7 |\n\ntestarea の桁数と行数の数値です。この値は [SQL](index.html#term-sql) クエリの textarea の場合は 2 倍に、クエリウインドウ内の [SQL](index.html#term-sql) 用 textarea の場合は 1.25 倍になります。\n\nChar* の値は CHAR と VARCHAR を編集する際に使われます ([`$cfg['CharEditing']`](#cfg_CharEditing) でそのように設定されている場合)。\n\nバージョン 5.0.0 で変更: デフォルト値は 2 から 7 に変更されました。\n\n`$cfg['LongtextDoubleTextarea']`[¶](#cfg_LongtextDoubleTextarea)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nLONGTEXT カラムの textarea のサイズを倍にするかどうかを定義します。\n\n`$cfg['TextareaAutoSelect']`[¶](#cfg_TextareaAutoSelect)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nクリックしたときにクエリボックスの textarea 全体を選択するかどうかを定義します。\n\n`$cfg['EnableAutocompleteForTablesAndColumns']`[¶](#cfg_EnableAutocompleteForTablesAndColumns)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックス内でテーブル名やカラム名の自動補完を有効にするかどうかです。\n\n### SQL クエリボックス設定[¶](#sql-query-box-settings)\n\n`$cfg['SQLQuery']['Edit']`[¶](#cfg_SQLQuery_Edit)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックスにクエリを変更する編集リンクを表示するかどうか。\n\n`$cfg['SQLQuery']['Explain']`[¶](#cfg_SQLQuery_Explain)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックスに SELECT クエリを EXPLAIN するリンクを表示するかどうか。\n\n`$cfg['SQLQuery']['ShowAsPHP']`[¶](#cfg_SQLQuery_ShowAsPHP)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックスにクエリを PHP コードで形成するリンクを表示するかどうか。\n\n`$cfg['SQLQuery']['Refresh']`[¶](#cfg_SQLQuery_Refresh)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nSQL クエリボックスにクエリを再描画するリンクを表示するかどうか。\n\n### ウェブサーバのアップロード/保存/インポートディレクトリ[¶](#web-server-upload-save-import-directories)\n\nPHP がセーフモードになっている場合は、 phpMyAdmin スクリプトの所有者と同じユーザが所有者になっていなければなりません。\n\nphpMyAdmin がインストールされているディレクトリに `open_basedir` 制限が適用される場合は、 PHP インタプリタがアクセスできるディレクトリに一時ディレクトリを作成する必要があります。\n\nセキュリティ上の理由から、すべてのディレクトリをウェブサーバで公開されているツリーの外にしてください。このディレクトリがウェブサーバで公開されるのが避けられない場合は、ウェブサーバの設定 (例えば .htaccess ファイルまたは web.config ファイルを使用するなど) によってアクセスを制限するか、少なくとも空の `index.html` ファイルをそこに配置すれば、ディレクトリの一覧表示は不可能になります。ただし、ウェブサーバがディレクトリにアクセスできる限り、攻撃者はファイル名を推測してファイルをダウンロードすることができます。\n\n`$cfg['UploadDir']`[¶](#cfg_UploadDir)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nphpMyAdmin 以外の方法 (例えば FTP) でアップロードした [SQL](index.html#term-sql) ファイルのあるディレクトリ名。このディレクトリにあるファイルは、データベース名またはテーブル名をクリックしてから、インポートタブをクリックして表示されるドロップダウンボックスより利用できます。\n\nユーザごとにディレクトリを変えたい場合は、%u を使うとユーザ名に置換されます。\n\nなお、ファイル名の末尾は必ず \".sql\" (圧縮形式のサポートが有効になっている場合は \".sql.bz2\" や \".sql.gz\") でなければなりません。\n\nこの機能はファイルが大きすぎて [HTTP](index.html#term-http) でアップロードできないときや、PHP のファイルアップロード機能が無効になっている場合に有用です。\n\n警告\n\nこのディレクトリのセットアップ方法と使用を安全にする方法については、この節の冒頭 ([ウェブサーバのアップロード/保存/インポートディレクトリ](#web-dirs)) を参照してください。\n\n参考\n\n代替手法については [1.16 (メモリ、HTTP、タイムアウトのせいで) 大きなダンプファイルをアップロードできません。](index.html#faq1-16) を参照してください。\n\n`$cfg['SaveDir']`[¶](#cfg_SaveDir)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nエクスポートされたファイルを保存するウェブサーバのディレクトリ名です。\n\nユーザごとにディレクトリを指定したい場合は、 %u を使うとユーザ名に置換されます。\n\nこのディレクトリは存在しており、ウェブサーバの実行ユーザで書き込みできるようになっていなければなりません。\n\n警告\n\nこのディレクトリのセットアップ方法と使用を安全にする方法については、この節の冒頭 ([ウェブサーバのアップロード/保存/インポートディレクトリ](#web-dirs)) を参照してください。\n\n`$cfg['TempDir']`[¶](#cfg_TempDir)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'./tmp/'` |\n\n一時ファイルを保管可能なディレクトリの名前です。現在は以下のような様々な目的に使用されています。\n\n* ページの読み込みを高速化するテンプレートキャッシュ。\n* ESRI 図形ファイルのインポート、 [6.30 インポート: ESRI シェイプファイルはどうやってインポートできますか？](index.html#faq6-30) を参照。\n* アップロードされたファイルの `open_basedir` の制限の回避、 [1.11 インポートタブからファイルをアップロードすると 'open_basedir 制限' が出ます。](index.html#faq1-11) を参照してください。\n\nこのディレクトリは、実行されているウェブサーバにおいて必要なユーザのみアクセスできるよう、可能な限り厳格な権限を有している必要があります。root 権限を持っている場合は、このディレクトリの所有者としてウェブユーザを設定し、ウェブユーザだけでアクセスできるようにすればいいだけです。\n```\nchown www-data:www-data tmp chmod 700 tmp\n```\nディレクトリの所有者を変更できない場合は、 [ACL](index.html#term-acl) を使用して同様の設定を実現できます。\n```\nchmod 700 tmp setfacl -m \"g:www-data:rwx\" tmp setfacl -d -m \"g:www-data:rwx\" tmp\n```\n上記のどちらも動作しない場合、ディレクトリに対して **chmod 777** と設定することもできますが、そうするとシステム上のほかのユーザが、このディレクトリ内のデータの読み書きできるようになるリスクが生じる可能性があります。\n\n警告\n\nこのディレクトリのセットアップ方法と使用を安全にする方法については、この節の冒頭 ([ウェブサーバのアップロード/保存/インポートディレクトリ](#web-dirs)) を参照してください。\n\n### 様々な表示設定[¶](#various-display-setting)\n\n`$cfg['RepeatCells']`[¶](#cfg_RepeatCells)\n\n| データ型: | 整数型 |\n| デフォルト値: | 100 |\n\nX セルごとにヘッダを挿入します。0 の場合は繰り返しません。\n\n`$cfg['EditInWindow']`[¶](#cfg_EditInWindow)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n参考\n\n[Feature request to add a pop-up window back](https://github.com/phpmyadmin/phpmyadmin/issues/11983)\n\nバージョン 4.3.0 で非推奨: この設定は削除されました。\n\n`$cfg['QueryWindowWidth']`[¶](#cfg_QueryWindowWidth)\n\n| データ型: | 整数型 |\n| デフォルト値: | 550 |\n\nバージョン 4.3.0 で非推奨: この設定は削除されました。\n\n`$cfg['QueryWindowHeight']`[¶](#cfg_QueryWindowHeight)\n\n| データ型: | 整数型 |\n| デフォルト値: | 310 |\n\nバージョン 4.3.0 で非推奨: この設定は削除されました。\n\n`$cfg['QueryHistoryDB']`[¶](#cfg_QueryHistoryDB)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n`$cfg['QueryWindowDefTab']`[¶](#cfg_QueryWindowDefTab)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'sql'` |\n\nバージョン 4.3.0 で非推奨: この設定は削除されました。\n\n`$cfg['QueryHistoryMax']`[¶](#cfg_QueryHistoryMax)\n\n| データ型: | 整数型 |\n| デフォルト値: | 25 |\n\n[`$cfg['QueryHistoryDB']`](#cfg_QueryHistoryDB) を `true` に設定した場合、ユーザのクエリはすべてテーブルに記録されます。ただし、このテーブルはユーザが作成する必要があります ([`$cfg['Servers'][$i]['history']`](#cfg_Servers_history) を参照)。 false に設定した場合、フォームにはすべてのクエリが追加されますが、保存されるのはウインドウが開いている間のみです。\n\nJavaScript ベースのクエリウィンドウを使用している場合は、新しいテーブルやデータベースをクリックして閲覧するたびに更新され、クエリを使用した後に 編集 をクリックするとフォーカスされます。クエリのテキストエリアの下にある ウィンドウ外からこのクエリを上書きしない にチェックを入れることで、クエリウィンドウの更新を抑制することができます。そうすれば、テキストエリアの内容を失うことなくバックグラウンドでテーブル/データベースを閲覧できるので、最初に参照したテーブルを含むクエリを作成す る際には特に便利です。テキストエリアの内容を変更すると、チェックボックスは自動的にチェックされます。変更したにもかかわらず、どうしてもクエリウィンドウを更新したい場合はチェックを外してください。\n\n[`$cfg['QueryHistoryDB']`](#cfg_QueryHistoryDB) が `true` に設定されている場合、保存する履歴項目の数は [`$cfg['QueryHistoryMax']`](#cfg_QueryHistoryMax) で指定できます。\n\n`$cfg['AllowSharedBookmarks']`[¶](#cfg_AllowSharedBookmarks)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nバージョン 6.0.0 で追加.\n\nAllow users to create bookmarks that are available for all other users\n\n`$cfg['BrowseMIME']`[¶](#cfg_BrowseMIME)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n[変換機能](index.html#transformations) を有効にします。\n\n`$cfg['MaxExactCount']`[¶](#cfg_MaxExactCount)\n\n| データ型: | 整数型 |\n| デフォルト値: | 50000 |\n\nInnoDB テーブルにおいて、どの程度の大きさのテーブルまで `SELECT COUNT` で正確な行数を取得するかを指定します。`SHOW TABLE STATUS` によって返される概算の行数が設定した値より小さい場合は `SELECT COUNT` が使われますが、そうでない場合はこの概算数が使われます。\n\nバージョン 4.8.0 で変更: パフォーマンスの理由から、デフォルト値は 50000 に下げられました。\n\nバージョン 4.2.6 で変更: デフォルト値は 500000 に変更されました。\n\n参考\n\n[3.11 InnoDB のテーブルの行数が正しくありません。](index.html#faq3-11)\n\n`$cfg['MaxExactCountViews']`[¶](#cfg_MaxExactCountViews)\n\n| データ型: | 整数型 |\n| デフォルト値: | 0 |\n\nビューの場合は、正確な行数を取得するとパフォーマンスに影響を与える可能性があるので、この値は `SELECT COUNT ... LIMIT` を使用して表示される最大値です。 0 を設定した場合は、行カウントを省略します。\n\n`$cfg['NaturalOrder']`[¶](#cfg_NaturalOrder)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nデータベースやテーブルの名前を自然な順番でソートします (t1、t2、t10、のように)。いまのところナビゲーションパネルとデータベースビューのテーブル一覧に実装されています。\n\n`$cfg['InitialSlidersState']`[¶](#cfg_InitialSlidersState)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'closed'` |\n\n`'closed'` に設定した場合、ビジュアルスライダーは最初は閉じた状態になります。 `'open'` はその逆です。すべてのビジュアルスライダーを無効にするには、 `'disabled'` を使用してください。\n\n`$cfg['UserprefsDisallow']`[¶](#cfg_UserprefsDisallow)\n\n| データ型: | 配列型 |\n| デフォルト値: | array() |\n\nContains names of configuration options (keys in `$cfg` array) that users can't set through user preferences. For possible values, refer to classes under `src/Config/Forms/User/`.\n\n`$cfg['UserprefsDeveloperTab']`[¶](#cfg_UserprefsDeveloperTab)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nバージョン 3.4.0 で追加.\n\nユーザ設定環境に phpMyAdmin 開発者向け用のオプションタブを表示させます。\n\n### ページタイトル[¶](#page-titles)\n\nThe page title displayed by your browser's window or tab title bar can be customized. You can use [6.27 どのような書式の文字列が使えますか？](index.html#faq6-27).\nThe following four options allow customizing various parts of the phpMyAdmin interface. Note that the login page title cannot be changed.\n\n`$cfg['TitleTable']`[¶](#cfg_TitleTable)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@HTTP_HOST@ / @VSERVER@ / @DATABASE@ / @TABLE@ | @PHPMYADMIN@'` |\n\n`$cfg['TitleDatabase']`[¶](#cfg_TitleDatabase)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@HTTP_HOST@ / @VSERVER@ / @DATABASE@ | @PHPMYADMIN@'` |\n\n`$cfg['TitleServer']`[¶](#cfg_TitleServer)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@HTTP_HOST@ / @VSERVER@ | @PHPMYADMIN@'` |\n\n`$cfg['TitleDefault']`[¶](#cfg_TitleDefault)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'@HTTP_HOST@ | @PHPMYADMIN@'` |\n\n### テーマ管理設定[¶](#theme-manager-settings)\n\n`$cfg['ThemeManager']`[¶](#cfg_ThemeManager)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\nユーザが選択可能なテーマを有効にします。 [2.7 テーマの使い方と作り方](index.html#faqthemes) を参照してください。\n\n`$cfg['ThemeDefault']`[¶](#cfg_ThemeDefault)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'pmahomme'` |\n\nThe default theme (a subdirectory under `./public/themes/`).\n\n`$cfg['ThemePerServer']`[¶](#cfg_ThemePerServer)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nサーバごとに別々のテーマを許可するかどうか。\n\n`$cfg['FontSize']`[¶](#cfg_FontSize)\n\n| データ型: | 文字列型 |\n| デフォルト値: | '82%' |\n\nバージョン 5.0.0 で非推奨: ブラウザがより効率的になったため、この設定は削除されました。したがって、このオプションは必要ありません。\n\n使用するフォントの大きさです。 CSS に適用されます。\n\n### デフォルトクエリ[¶](#default-queries)\n\n`$cfg['DefaultQueryTable']`[¶](#cfg_DefaultQueryTable)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'SELECT * FROM @TABLE@ WHERE 1'` |\n\n`$cfg['DefaultQueryDatabase']`[¶](#cfg_DefaultQueryDatabase)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `''` |\n\nユーザが指定しなかった時に、クエリボックスに表示されるデフォルトのクエリです。標準の [6.27 どのような書式の文字列が使えますか？](index.html#faq6-27) を使用することができます。\n\n### MySQL 設定[¶](#mysql-settings)\n\n`$cfg['DefaultFunctions']`[¶](#cfg_DefaultFunctions)\n\n| データ型: | 配列型 |\n| デフォルト値: | `array('FUNC_CHAR' => '', 'FUNC_DATE' => '', 'FUNC_NUMBER' => '', 'FUNC_SPATIAL' => 'GeomFromText', 'FUNC_UUID' => 'UUID', 'first_timestamp' => 'NOW')` |\n\n行の挿入・変更時にデフォルトで選択されている関数で、メタタイプ (`FUNC_NUMBER`, `FUNC_DATE`, `FUNC_CHAR`, `FUNC_SPATIAL`, `FUNC_UUID`) と、テーブルの最初のタイムスタンプのカラムに使用される `first_timestamp` のための関数が定義されています。\n\n設定例\n```\n$cfg['DefaultFunctions'] = [\n 'FUNC_CHAR' => '',\n 'FUNC_DATE' => '',\n 'FUNC_NUMBER' => '',\n 'FUNC_SPATIAL' => 'ST_GeomFromText',\n 'FUNC_UUID' => 'UUID',\n 'first_timestamp' => 'UTC_TIMESTAMP',\n];\n```\n### デフォルトの変換オプション[¶](#default-options-for-transformations)\n\n`$cfg['DefaultTransformations']`[¶](#cfg_DefaultTransformations)\n\n| データ型: | 配列型 |\n| デフォルト値: | 以下に示すキーと値の配列 |\n\n`$cfg['DefaultTransformations']['Substring']`[¶](#cfg_DefaultTransformations_Substring)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(0, 'all', '…') |\n\n`$cfg['DefaultTransformations']['Bool2Text']`[¶](#cfg_DefaultTransformations_Bool2Text)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('T', 'F') |\n\n`$cfg['DefaultTransformations']['External']`[¶](#cfg_DefaultTransformations_External)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(0, '-f /dev/null -i -wrap -q', 1, 1) |\n\n`$cfg['DefaultTransformations']['PreApPend']`[¶](#cfg_DefaultTransformations_PreApPend)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('', '') |\n\n`$cfg['DefaultTransformations']['Hex']`[¶](#cfg_DefaultTransformations_Hex)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('2') |\n\n`$cfg['DefaultTransformations']['DateFormat']`[¶](#cfg_DefaultTransformations_DateFormat)\n\n| データ型: | 配列型 |\n| デフォルト値: | array(0, '', 'local') |\n\n`$cfg['DefaultTransformations']['Inline']`[¶](#cfg_DefaultTransformations_Inline)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('100', 100) |\n\n`$cfg['DefaultTransformations']['TextImageLink']`[¶](#cfg_DefaultTransformations_TextImageLink)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('', 100, 50) |\n\n`$cfg['DefaultTransformations']['TextLink']`[¶](#cfg_DefaultTransformations_TextLink)\n\n| データ型: | 配列型 |\n| デフォルト値: | array('', '', '') |\n\n### コンソール設定[¶](#console-settings)\n\n注釈\n\n以下の設定は主にユーザが変更するためのものです。\n\n`$cfg['Console']['StartHistory']`[¶](#cfg_Console_StartHistory)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n開始時にクエリ履歴を表示\n\n`$cfg['Console']['AlwaysExpand']`[¶](#cfg_Console_AlwaysExpand)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nクエリメッセージを常に展開する\n\n`$cfg['Console']['CurrentQuery']`[¶](#cfg_Console_CurrentQuery)\n\n| データ型: | 論理型 |\n| デフォルト値: | true |\n\n現在のクエリを表示\n\n`$cfg['Console']['EnterExecutes']`[¶](#cfg_Console_EnterExecutes)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nEnterでクエリを実行し、Shift + Enterで新しい行を挿入します\n\n`$cfg['Console']['DarkTheme']`[¶](#cfg_Console_DarkTheme)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n暗いテーマに切り替える\n\n`$cfg['Console']['Mode']`[¶](#cfg_Console_Mode)\n\n| データ型: | 文字列型 |\n| デフォルト値: | 'info' |\n\nコンソールモード\n\n`$cfg['Console']['Height']`[¶](#cfg_Console_Height)\n\n| データ型: | 整数型 |\n| デフォルト値: | 92 |\n\nコンソールの高さ\n\n### 開発者向け[¶](#developer)\n\n警告\n\nこの設定はパフォーマンスやセキュリティに重大な影響を与える可能性があります。\n\n`$cfg['environment']`[¶](#cfg_environment)\n\n| データ型: | 文字列型 |\n| デフォルト値: | `'production'` |\n\n動作環境を設定します。\n\nこれを変更する必要があるのは、 phpMyAdmin 自体を開発しているときのみです。`development` モードはいくつかの場所でデバッグ情報を表示する可能性があります。\n\n指定可能な値は `'production'` または `'development'` です。\n\n`$cfg['DBG']`[¶](#cfg_DBG)\n\n| データ型: | 配列型 |\n| デフォルト値: | [] |\n\n`$cfg['DBG']['sql']`[¶](#cfg_DBG_sql)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nコンソールの「SQL のデバッグ」タブで、クエリと実行時間の表示を有効にします。\n\n`$cfg['DBG']['sqllog']`[¶](#cfg_DBG_sqllog)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nsyslog へのクエリと実行時間のログ記録を有効にします。有効にするには、 [`$cfg['DBG']['sql']`](#cfg_DBG_sql) を有効にする必要があります。\n\n`$cfg['DBG']['demo']`[¶](#cfg_DBG_demo)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\nサーバが自分自身をデモサーバとして表示できるようにします。これは、 [phpMyAdmin デモサーバ](https://www.phpmyadmin.net/try/) に使用されます。\n\n現在のところ、以下の動作を変更します。\n\n* メインページに歓迎メッセージを表示します。\n* デモサーバにと使用している Git のリビジョンについての情報をフッタに表示します。\n* 設定が存在していても、セットアップスクリプトが有効になります。\n* セットアップで MySQL サーバへの接続を試みません。\n\n`$cfg['DBG']['simple2fa']`[¶](#cfg_DBG_simple2fa)\n\n| データ型: | 論理型 |\n| デフォルト値: | false |\n\n[単純な二要素認証](index.html#simple2fa) を使用して二要素認証をテストする際に使用されることがあります。\n\n### 設定例[¶](#examples)\n\nphpMyAdmin の一般的な設定については、以下の設定スニペットを参照してください。\n\n#### 基本的な例[¶](#basic-example)\n\n設定ファイルの例で、`config.inc.php` にコピーするといくつかの主要な設定レイアウトを得ることができます。このファイルは phpMyAdmin でと一緒に `config.sample.inc.php` として配布されています。なお、ここにはすべての設定オプションが含まれているわけではなく、よく使用されるものだけが含まれていることに注意してください。\n```\n<?php\n/**\n * phpMyAdmin sample configuration, you can use it as base for\n * manual configuration. For easier setup you can use setup/\n *\n * All directives are explained in documentation in the doc/ folder\n * or at <https://docs.phpmyadmin.net/>.\n */\n\ndeclare(strict_types=1);\n\n/**\n * This is needed for cookie based authentication to encrypt the cookie.\n * Needs to be a 32-bytes long string of random bytes. See FAQ 2.10.\n */\n$cfg['blowfish_secret'] = ''; /* YOU MUST FILL IN THIS FOR COOKIE AUTH! */\n\n/**\n * Servers configuration\n */\n$i = 0;\n\n/**\n * First server\n */\n$i++;\n/* Authentication type */\n$cfg['Servers'][$i]['auth_type'] = 'cookie';\n/* Server parameters */\n$cfg['Servers'][$i]['host'] = 'localhost';\n$cfg['Servers'][$i]['compress'] = false;\n$cfg['Servers'][$i]['AllowNoPassword'] = false;\n\n/**\n * phpMyAdmin configuration storage settings.\n */\n\n/* User used to manipulate with storage */\n// $cfg['Servers'][$i]['controlhost'] = '';\n// $cfg['Servers'][$i]['controlport'] = '';\n// $cfg['Servers'][$i]['controluser'] = 'pma';\n// $cfg['Servers'][$i]['controlpass'] = 'pmapass';\n\n/* Storage database and tables */\n// $cfg['Servers'][$i]['pmadb'] = 'phpmyadmin';\n// $cfg['Servers'][$i]['bookmarktable'] = 'pma__bookmark';\n// $cfg['Servers'][$i]['relation'] = 'pma__relation';\n// $cfg['Servers'][$i]['table_info'] = 'pma__table_info';\n// $cfg['Servers'][$i]['table_coords'] = 'pma__table_coords';\n// $cfg['Servers'][$i]['pdf_pages'] = 'pma__pdf_pages';\n// $cfg['Servers'][$i]['column_info'] = 'pma__column_info';\n// $cfg['Servers'][$i]['history'] = 'pma__history';\n// $cfg['Servers'][$i]['table_uiprefs'] = 'pma__table_uiprefs';\n// $cfg['Servers'][$i]['tracking'] = 'pma__tracking';\n// $cfg['Servers'][$i]['userconfig'] = 'pma__userconfig';\n// $cfg['Servers'][$i]['recent'] = 'pma__recent';\n// $cfg['Servers'][$i]['favorite'] = 'pma__favorite';\n// $cfg['Servers'][$i]['users'] = 'pma__users';\n// $cfg['Servers'][$i]['usergroups'] = 'pma__usergroups';\n// $cfg['Servers'][$i]['navigationhiding'] = 'pma__navigationhiding';\n// $cfg['Servers'][$i]['savedsearches'] = 'pma__savedsearches';\n// $cfg['Servers'][$i]['central_columns'] = 'pma__central_columns';\n// $cfg['Servers'][$i]['designer_settings'] = 'pma__designer_settings';\n// $cfg['Servers'][$i]['export_templates'] = 'pma__export_templates';\n\n/**\n * End of servers configuration\n */\n\n/**\n * Directories for saving/loading files from server\n */\n$cfg['UploadDir'] = '';\n$cfg['SaveDir'] = '';\n\n/**\n * Whether to display icons or text or both icons and text in table row\n * action segment. Value can be either of 'icons', 'text' or 'both'.\n * default = 'both'\n */\n//$cfg['RowActionType'] = 'icons';\n\n/**\n * Defines whether a user should be displayed a \"show all (records)\"\n * button in browse mode or not.\n * default = false\n */\n//$cfg['ShowAll'] = true;\n\n/**\n * Number of rows displayed when browsing a result set. If the result\n * set contains more rows, \"Previous\" and \"Next\".\n * Possible values: 25, 50, 100, 250, 500\n * default = 25\n */\n//$cfg['MaxRows'] = 50;\n\n/**\n * Disallow editing of binary fields\n * valid values are:\n * false allow editing\n * 'blob' allow editing except for BLOB fields\n * 'noblob' disallow editing except for BLOB fields\n * 'all' disallow editing\n * default = 'blob'\n */\n//$cfg['ProtectBinary'] = false;\n\n/**\n * Default language to use, if not browser-defined or user-defined\n * (you find all languages in the locale folder)\n * uncomment the desired line:\n * default = 'en'\n */\n//$cfg['DefaultLang'] = 'en';\n//$cfg['DefaultLang'] = 'de';\n\n/**\n * How many columns should be used for table display of a database?\n * (a value larger than 1 results in some information being hidden)\n * default = 1\n */\n//$cfg['PropertiesNumColumns'] = 2;\n\n/**\n * Set to true if you want DB-based query history.If false, this utilizes\n * JS-routines to display query history (lost by window close)\n *\n * This requires configuration storage enabled, see above.\n * default = false\n */\n//$cfg['QueryHistoryDB'] = true;\n\n/**\n * When using DB-based query history, how many entries should be kept?\n * default = 25\n */\n//$cfg['QueryHistoryMax'] = 100;\n\n/**\n * Whether or not to query the user before sending the error report to\n * the phpMyAdmin team when a JavaScript error occurs\n *\n * Available options\n * ('ask' | 'always' | 'never')\n * default = 'ask'\n */\n//$cfg['SendErrorReports'] = 'always';\n\n/**\n * 'URLQueryEncryption' defines whether phpMyAdmin will encrypt sensitive data from the URL query string.\n * 'URLQueryEncryptionSecretKey' is a 32 bytes long secret key used to encrypt/decrypt the URL query string.\n */\n//$cfg['URLQueryEncryption'] = true;\n//$cfg['URLQueryEncryptionSecretKey'] = '';\n\n/**\n * You can find more configuration options in the documentation\n * in the doc/ folder or at <https://docs.phpmyadmin.net/>.\n */\n```\n警告\n\nコントロールユーザー 'pma' がまだ存在しない場合は使用しないでください。また、パスワードとして 'pmapass' を使用しないでください。\n\n#### サインオン認証モードの例[¶](#example-for-signon-authentication)\n\nこの例は `examples/signon.php` を使用して [サインオン認証モード](index.html#auth-signon) の使い方のデモをします。\n```\n<?php\n$i = 0;\n$i++;\n$cfg['Servers'][$i]['auth_type'] = 'signon';\n$cfg['Servers'][$i]['SignonSession'] = 'SignonSession';\n$cfg['Servers'][$i]['SignonURL'] = 'examples/signon.php';\n```\n#### IP アドレスを限定した自動ログインの例[¶](#example-for-ip-address-limited-autologin)\n\nphpMyAdmin にローカルでアクセスするときには自動的にログインし、リモートアクセスする際にはパスワードを要求するようにしたいのであれば、次のスニペットで実現することができます。\n```\nif ($_SERVER['REMOTE_ADDR'] === '127.0.0.1') {\n $cfg['Servers'][$i]['auth_type'] = 'config';\n $cfg['Servers'][$i]['user'] = 'root';\n $cfg['Servers'][$i]['password'] = 'yourpassword';\n} else {\n $cfg['Servers'][$i]['auth_type'] = 'cookie';\n}\n```\n注釈\n\nIP アドレスに基づくフィルタリングは、インターネット上で信頼できないので、ローカル アドレスでのみ使用してください。\n\n#### 複数の MySQL サーバを使用した例[¶](#example-for-using-multiple-mysql-servers)\n\n[`$cfg['Servers']`](#cfg_Servers) を使用して任意の数のサーバを設定することができます。この例ではそのうち 2 つを設定しています。\n```\n<?php\n// The string is a hexadecimal representation of a 32-bytes long string of random bytes.\n$cfg['blowfish_secret'] = sodium_hex2bin('f16ce59f45714194371b48fe362072dc3b019da7861558cd4ad29e4d6fb13851');\n$i = 0;\n\n$i++; // server 1 :\n$cfg['Servers'][$i]['auth_type'] = 'cookie';\n$cfg['Servers'][$i]['verbose'] = 'no1';\n$cfg['Servers'][$i]['host'] = 'localhost';\n// more options for #1 ...\n\n$i++; // server 2 :\n$cfg['Servers'][$i]['auth_type'] = 'cookie';\n$cfg['Servers'][$i]['verbose'] = 'no2';\n$cfg['Servers'][$i]['host'] = 'remote.host.addr';//or ip:'10.9.8.1'\n// this server must allow remote clients, e.g., host 10.9.8.%\n// not only in mysql.host but also in the startup configuration\n// more options for #2 ...\n\n// end of server sections\n$cfg['ServerDefault'] = 0; // to choose the server on startup\n\n// further general options ...\n```\n#### SSL 経由で Google Cloud SQL を使用[¶](#google-cloud-sql-with-ssl)\n\nGoogle Cloud SQL に接続するには、現在のところ証明書の検証を無効にする必要があります。これは、証明書が発行された CN がインスタンス名と一致しているにもかかわらず、 IP アドレスに接続し、 PHP がこれらの2つを比較しようとすることが原因です。証明書の検証では、次のようなエラーメッセージが表示されます。\n```\nPeer certificate CN=`api-project-851612429544:pmatest' did not match expected CN=`8.8.8.8'\n```\n警告\n\n検証を無効にすると、トラフィックは暗号化されますが、中間者攻撃にさらされる可能性があります。\n\nSSL を使用して phpMyAdmin を Google Cloud SQL に接続するには、クライアントとサーバの証明書をダウンロードし、 phpMyAdmin にそれらを使用するように指示してください。\n```\n// IP address of your instance\n$cfg['Servers'][$i]['host'] = '8.8.8.8';\n// Use SSL for connection\n$cfg['Servers'][$i]['ssl'] = true;\n// Client secret key\n$cfg['Servers'][$i]['ssl_key'] = '../client-key.pem';\n// Client certificate\n$cfg['Servers'][$i]['ssl_cert'] = '../client-cert.pem';\n// Server certification authority\n$cfg['Servers'][$i]['ssl_ca'] = '../server-ca.pem';\n// Disable SSL verification (see above note)\n$cfg['Servers'][$i]['ssl_verify'] = false;\n```\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_key']`](#cfg_Servers_ssl_key)、 [`$cfg['Servers'][$i]['ssl_cert']`](#cfg_Servers_ssl_cert)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)、 <<https://bugs.php.net/bug.php?id=72048>#### Amazon RDS Aurora with SSL[¶](#amazon-rds-aurora-with-ssl)\n\nSSL を使用して phpMyAdmin を Amazon RDS Aurora の MySQL データベースインスタンスに接続するには、 CA サーバの証明書をダウンロードし、 phpMyAdmin にそれらを使用するように指示してください。\n```\n// Address of your instance\n$cfg['Servers'][$i]['host'] = 'replace-me-cluster-name.cluster-replace-me-id.replace-me-region.rds.amazonaws.com';\n// Use SSL for connection\n$cfg['Servers'][$i]['ssl'] = true;\n// You need to have the region CA file and the authority CA file (2019 edition CA for example) in the PEM bundle for it to work\n$cfg['Servers'][$i]['ssl_ca'] = '../rds-combined-ca-bundle.pem';\n// Enable SSL verification\n$cfg['Servers'][$i]['ssl_verify'] = true;\n```\n参考\n\n[データベースサーバへの接続で SSL を使用する](index.html#ssl)、 [`$cfg['Servers'][$i]['ssl']`](#cfg_Servers_ssl)、 [`$cfg['Servers'][$i]['ssl_ca']`](#cfg_Servers_ssl_ca)、 [`$cfg['Servers'][$i]['ssl_verify']`](#cfg_Servers_ssl_verify)\n\n参考\n\n* 現在のすべてのリージョンの RDS CA バンドル <https://s3.amazonaws.com/rds-downloads/rds-combined-ca-bundle.pem>\n* リージョン eu-west-3 のための親 CA のない RDS CA (2019 edition) <https://s3.amazonaws.com/rds-downloads/rds-ca-2019-eu-west-3.pem>\n* [利用可能な Amazon RDS CA ファイルの一覧](https://s3.amazonaws.com/rds-downloads/)\n* [Amazon MySQL Aurora セキュリティガイド](https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/AuroraMySQL.Security.html)\n* [リージョンごとにバンドルする Amazon 資格情報](https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/UsingWithRDS.SSL.html)\n\n#### hCaptcha を使用した reCaptcha[¶](#recaptcha-using-hcaptcha)\n```\n$cfg['CaptchaApi'] = 'https://www.hcaptcha.com/1/api.js';\n$cfg['CaptchaCsp'] = 'https://hcaptcha.com https://*.hcaptcha.com';\n$cfg['CaptchaRequestParam'] = 'h-captcha';\n$cfg['CaptchaResponseParam'] = 'h-captcha-response';\n$cfg['CaptchaSiteVerifyURL'] = 'https://hcaptcha.com/siteverify';\n// This is the secret key from hCaptcha dashboard\n$cfg['CaptchaLoginPrivateKey'] = '<KEY>';\n// This is the site key from hCaptcha dashboard\n$cfg['CaptchaLoginPublicKey'] = '<KEY>';\n```\n参考\n\n[hCaptcha ウェブサイト](https://www.hcaptcha.com/)\n\n参考\n\n[hCaptcha 開発者ガイド](https://docs.hcaptcha.com/)\n\n#### reCaptcha using Turnstile[¶](#recaptcha-using-turnstile)\n```\n$cfg['CaptchaMethod'] = 'checkbox';\n$cfg['CaptchaApi'] = 'https://challenges.cloudflare.com/turnstile/v0/api.js';\n$cfg['CaptchaCsp'] = 'https://challenges.cloudflare.com https://static.cloudflareinsights.com';\n$cfg['CaptchaRequestParam'] = 'cf-turnstile';\n$cfg['CaptchaResponseParam'] = 'cf-turnstile-response';\n$cfg['CaptchaLoginPublicKey'] = '<KEY>';\n$cfg['CaptchaLoginPrivateKey'] = '<KEY>';\n$cfg['CaptchaSiteVerifyURL'] = 'https://challenges.cloudflare.com/turnstile/v0/siteverify';\n```\n参考\n\n[Cloudflare Dashboard](https://dash.cloudflare.com/)\n\n参考\n\n[Turnstile Developer Guide](https://developers.cloudflare.com/turnstile/get-started/)\n\n#### reCaptcha using Google reCaptcha v2/v3[¶](#recaptcha-using-google-recaptcha-v2-v3)\n```\n$cfg['CaptchaLoginPublicKey'] = '<KEY>';\n$cfg['CaptchaLoginPrivateKey'] = '<KEY>';\n// Remove it if you dot not want the checkbox mode\n$cfg['CaptchaMethod'] = 'checkbox';\n```\n参考\n\n[Google reCaptcha Developer's Guide](https://developers.google.com/recaptcha/intro)\n\n参考\n\n[Google reCaptcha types](https://developers.google.com/recaptcha/docs/versions)\n\nユーザーガイド[¶](#user-guide)\n---\n\n### phpMyAdmin の設定[¶](#configuring-phpmyadmin)\n\nインタフェースのカスタマイズに使用できる設定がたくさんあります。これらの設定は [設定](index.html#config) に書かれています。設定にはいくつかの階層があります。\n\nグローバル設定は [設定](index.html#config) にあるように `config.inc.php` で設定します。これはデータベースへの接続やその他のシステム全体の設定を行うための唯一の方法です。\n\nこれに加えて、ユーザ毎の設定があり、それを [phpMyAdmin 環境保管領域](index.html#linked-tables) に永続的に保存され、 [ゼロ設定](index.html#zeroconf) で自動的に構成されます。 [phpMyAdmin 環境保管領域](index.html#linked-tables) が設定されていない場合、設定は一時的にセッションデータに保存されます。\n\nまた、ユーザ設定をファイルとしてダウンロードしたり、ブラウザのローカルストレージに保存しておいたりすることもできます。これらのオプションは 設定 タブにあります。ブラウザのローカルストレージに保存された設定は、 phpMyAdmin へのログイン時に自動的に読み取られます。\n\n### 二要素認証[¶](#two-factor-authentication)\n\nバージョン 4.8.0 で追加.\n\nphpMyAdmin 4.8.0 以降では、ログイン時に二要素認証を使用するよう設定することができます。使用するには、まず [phpMyAdmin 環境保管領域](index.html#linked-tables) を設定する必要があります。そうすると、すべてのユーザーが 設定 で 2 番目の認証要素を使用するよう選択することができるようになります。\n\nGit のソースリポジトリから phpMyAdmin を実行している場合は、依存関係を手動でインストールする必要があります。通常は次のようなコマンドで行います。\n```\ncomposer require pragmarx/google2fa-qrcode bacon/bacon-qr-code\n```\nまたは、 FIDO U2F でハードウェアのセキュリティキーを使用する場合は次のようになります。\n```\ncomposer require code-lts/u2f-php-server\n```\n#### 認証アプリ (2FA)[¶](#authentication-application-2fa)\n\n認証のためにアプリケーションを使用するのは、 HOTP と [TOTP](https://en.wikipedia.org/wiki/Time-based_One-time_Password_Algorithm) に基づいた非常に一般的なアプローチです。これは、 phpMyAdmin から認証アプリケーションに秘密鍵を送信することに基づいており、アプリケーションは、その後、このキーに基づいてワンタイムコードを生成することができます。 phpMyAdmin からアプリケーションにキーを入力する最も簡単な方法は、 QR コードをスキャンすることです。\n\nこれらの標準を実装するために携帯電話で利用できるアプリケーションは多数ありますが、最も広く利用されているのは以下のようなものです。\n\n* [FreeOTP (iOS, Android, Pebble)](https://freeotp.github.io/)\n* [Authy (iOS, Android, Chrome, OS X)](https://authy.com/)\n* [Google Authenticator (iOS)](https://apps.apple.com/us/app/google-authenticator/id388497605)\n* [Google Authenticator (Android)](https://play.google.com/store/apps/details?id=com.google.android.apps.authenticator2)\n* [LastPass Authenticator (iOS, Android, OS X, Windows)](https://lastpass.com/auth/)\n\n#### ハードウェアセキュリティキー (FIDO U2F)[¶](#hardware-security-key-fido-u2f)\n\nハードウェアトークンを使用することは、ソフトウェアベースの方法よりも安全と考えられています。 phpMyAdmin は [FIDO U2F](https://en.wikipedia.org/wiki/Universal_2nd_Factor) トークンに対応しています。\n\nこのトークンには様々な製造元があります。例を示します。\n\n* [youbico FIDO U2F セキュリティキー](https://www.yubico.com/fido-u2f/)\n* [HyperFIDO](https://www.hypersecu.com/hyperfido)\n* [Trezor Hardware Wallet](https://trezor.io/?offer_id=12&aff_id=1592&source=phpmyadmin) can act as an [U2F token](https://trezor.io/learn/a/what-is-u2f)\n* [List of Two Factor Auth (2FA) Dongles](https://www.dongleauth.com/dongles/)\n\n#### 単純な二要素認証[¶](#simple-two-factor-authentication)\n\nこの認証は、テストとデモンストレーションだけのために提供しているものであり、実際には二要素認証を提供せず、ボタンをクリックしてログインの確認をユーザに求めるだけです。\n\n本番では使用するべきではなく、 [`$cfg['DBG']['simple2fa']`](index.html#cfg_DBG_simple2fa) を設定しない限り無効にしてください。\n\n### 変換機能[¶](#transformations-1)\n\n注釈\n\n変換機能を使用するには、 [phpMyAdmin 環境保管領域](index.html#linked-tables) を設定する必要があります。\n\n#### はじめに[¶](#introduction)\n\n変換機能を有効にするには、 `column_info` テーブルと、適切な設定項目を設定する必要があります。手順については [設定](index.html#config) をご覧ください。\n\nphpMyAdmin には2種類の変換があります。ブラウザ表示変換は、 phpMyAdmin で閲覧した際にデータがどのように表示されるかにのみ影響を与えるもので、入力変換は phpMyAdmin で挿入される前の値に影響を与えるものです。各カラムの内容には異なる変換を適用することができます。それぞれの変換には、保存されたデータにどのように影響を与えるかを定義するオプションがあります。\n\n例えば、ファイル名を入れる `filename` というカラムがあるとします。ふつう phpMyAdmin ではファイル名しか表示されませんが、表示変換機能を使うと、このファイル名を HTML リンクに変換できます。 phpMyAdmin の構造の中でそのカラムのリンクをクリックすると、新しいブラウザウインドウにそのファイルが表示されます。変換オプションを使えば、その文字列の前後に付け加える文字列や、出力を保存する形式も指定できます。\n\n利用可能なすべての変換とそのオプションの一般的な概要については、既存のカラムの `変更` リンクをクリックするか、新しいカラムを作成するためのダイアログを開いてください。どちらの場合もカラム構造のページには「ブラウザ表示変換」と「入力変換」のリンクがあり、お使いのシステムで利用可能な各変換についての詳細な情報が表示されます。\n\n変換機能の効果的な使い方のチュートリアルについては、phpMyAdmin の公式ホームページの [Link の節](https://www.phpmyadmin.net/docs/) をご覧ください。\n\n#### 使い方[¶](#usage)\n\nテーブルの構造ページに移動してください (テーブルの [構造] リンクをクリックするとたどり着きます)。 [変更] (または変更アイコン) をクリックすると、項目の最後の方に変換に関する新しいフィールドが5つ表示されます。それぞれ「 [メディア型](index.html#term-media-type) 」、「ブラウザ表示変換」、「変換オプション」と呼ばれています。\n\n* 「 [メディア型](index.html#term-media-type) 」の項目はドロップダウンになっています。カラムの内容に対応した [メディア型](index.html#term-media-type) を選択してください。なお、多くの変換機能は [メディア型](index.html#term-media-type) を選択しないと有効にならないので注意してください。\n* [ブラウザ表示変換] はドロップダウンフィールドです。定義済みの変換を、数が増えていることを期待しつつ選択することができます。独自の変換を作成する方法については、以下を参照してください。変換機能にはグローバルなものと、 MIME タイプに結びつけられたものとがあります。グローバルな変換機能はどの MIME タイプでも利用できます。必要に応じて、 MIME タイプが考慮されます。 MIME タイプに結びつけられた変換機能は、ふつう特定の MIME タイプのみ ('image' など) を操作します。 MIME の主タイプを操作するものはたいていサブタイプを考慮に入れますが、特定のサブタイプ ('image/jpeg' など) のみを操作するものもあります。関数が定義されていない MIME タイプでも変換を使用することができます。正しい変換を選択したかどうかのセキュリティチェックはありませんので、出力がどのようになるかは注意してください。\n* [ブラウザ表示変換オプション] フィールドは、自由入力のテキストフィールドです。ここには変換機能固有のオプションを入力する必要があります。通常、変換はデフォルトのオプションで動作しますが、一般的には概要を見てどのオプションが必要なのかを確認すると良いでしょう。 ENUM/SET フィールドと同様に、複数のオプションは 'a','b','c',... (空白がないことに注意) という形式で分割しなければなりません。これは、内部的にはオプションが配列として解析され、最初の値が配列の最初の要素になるためです。 MIME の文字セットを指定したい場合は、 transformation_options で定義することができます。これは、特定の MIME 変換の事前に定義されたオプションの外側に、セットの最後の値として置かなければなりません。 \"'; charset=XXX'\" という形式を使用してください。2つのオプションを指定できる変換を使用していて、文字セットを追加したい場合は、 \"'最初のパラメータ','次のパラメータ','charset=us-ascii'\" のように入力してください。ただし、 \"'','','charset =us-ascii'\" のようにパラメータはデフォルトのままでも構いません。デフォルトのオプションは [`$cfg['DefaultTransformations']`](index.html#cfg_DefaultTransformations) で設定できます。\n* 「入力変換」は、上記の「ブラウザ表示変換」の操作に厳密に対応する別のドロップダウンメニューですが、データベースに挿入する前のデータに影響を与えます。これらは、特殊なエディタ (例えば、 phpMyAdmin SQL エディタインターフェイスの使用) やセレクタ (画像をアップロードするためなど) を提供するために最も一般的に使用されます。 IPv4 アドレスをバイナリに変換したり、正規表現を使ってデータを解析するなどの操作も可能です。\n* 最後に、「入力変換オプション」は、上記の「ブラウザ表示変換オプション」のセクションに相当し、オプションと必須のパラメータを入力する場所です。\n\n#### ファイル構造[¶](#file-structure)\n\nAll specific transformations for mimetypes are defined through class files in the directory `src/Plugins/Transformations/`. Each of them extends a certain transformation abstract class declared in\n`src/Plugins/Transformations/Abs`.\n\nこれらはカスタマイズを容易にし、新規または独自の変換を簡単に追加できるようにするために、ファイルに保存します。\n\nユーザが独自の MIME タイプを入力することはできませんが、そのために変換機能はいつでも確実に動作することができます。ある変換機能に未知の MIME タイプを適用しようとしても、変換関数は処理の方法を知らないので意味がありません。\n\nThere is a file called `src/Plugins/Transformations.php` that provides some basic functions which can be included by any other transform function.\n\nファイル名の規則は `[Mimetype]_[Subtype]_[Transformation Name].php` ですが、それが拡張する抽象クラスの名前は `[Transformation Name]TransformationsPlugin` です。変換プラグインで実装する必要のあるすべてのメソッドは次のとおりです。\n\n1. メインクラスの getMIMEType() および getMIMESubtype();\n2. 継承した抽象クラスの getName(), getInfo(), applyTransformation()。\n\ngetMIMEType(), getMIMESubtype(), getName() の各メソッドはそれぞれ MIME タイプ、 MIME サブタイプ、変換の名前を返します。 getInfo() は変換の説明と受け取る可能性があるオプションを返し、 applyTransformation() は変換プラグインの実際の作業を行うメソッドです。\n\nPlease see the `src/Plugins/Transformations/TEMPLATE` and\n`src/Plugins/Transformations/TEMPLATE_ABSTRACT` files for adding your own transformation plug-in. You can also generate a new transformation plug-in (with or without the abstract transformation class), by using\n`scripts/transformations_generator_plugin.sh` or\n`scripts/transformations_generator_main_class.sh`.\n\napplyTransformation() メソッドには常に 3 つの変数が渡されます。\n\n1. **$buffer** - カラム内のテキストが入ります。これが変換するテキストになります。\n2. **$options** - ユーザから変換関数に渡されたオプションが配列として入ります。\n3. **$meta** - カラムについての情報を持つオブジェクトが入ります。データは [mysql_fetch_field()](https://www.php.net/mysql_fetch_field) 関数の出力から抽出されます。そのため、この関数の [マニュアルページ](https://www.php.net/mysql_fetch_field) で説明されているオブジェクトのプロパティすべてが利用できますし、 unsigned/zerofill/not_null/... といったプロパティによってカラムを変換することもできます。変数 $meta->mimetype には、カラムの元の [メディア型](index.html#term-media-type) が入ります。 (すなわち 'text/plain', 'image/jpeg' など)\n\n### ブックマーク[¶](#bookmarks-1)\n\n注釈\n\nブックマーク機能を使用するには、 [phpMyAdmin 環境保管領域](index.html#linked-tables) を設定する必要があります。\n\n#### ブックマークの保存[¶](#storing-bookmarks)\n\n実行されたクエリはすべて、結果が表示されるページでブックマークすることができます。ページの最後に、 この SQL をブックマーク というラベルの付いたボタンがあります。ブックマークを保存するとすぐに、そのクエリはデータベースにリンクされます。これで、そのデータベースのクエリボックスが表示される各ページのブックマークドロップダウンが利用できるようになります。\n\n#### ブックマーク内の変数[¶](#variables-inside-bookmarks)\n\nクエリ内で、変数のプレースホルダを追加することもできます。これは、クエリの中に `/*` と `*/` で挟んだ SQL コメントを挿入することで行います。コメント内では、 `[VARIABLE{変数番号}]` の形の特別な文字列を使用します。 SQL コメントを除いたクエリ全体がそれ自体で有効でなければならないことに注意してください。そうでないと、ブックマークとして保存できません。また、 'VARIABLE' のテキストは、大文字と小文字が区別されることに注意してください。\n\nブックマークを実行するとき、クエリ ボックスページの *変数* 入力ボックスに入力されたすべてが、格納されているクエリの文字列 `/*[VARIABLE{変数番号}]/` に置き換えられます。\n\nまた、 `/*[VARIABLE{variable-number}]*/` 以外の文字列はすべてそのままクエリに残ることを忘れないようにしてください。ただし、 `/**/` は削除されます。ですから、次のような使い方もできます。\n```\n/*, [VARIABLE1] AS myname */\n```\nこれは、次のように展開されます。\n```\n, VARIABLE1 as myname\n```\nクエリ内で、 VARIABLE1 は入力ボックス「変数 1」に入力した文字列になります。\n\nもっと複雑な例です。例えば次のようなクエリを保存したとします。\n```\nSELECT Name, Address FROM addresses WHERE 1 /* AND Name LIKE '%[VARIABLE1]%' */\n```\nここで、例えば保存されたクエリ用の変数として \"phpMyAdmin\" と入力すると、最終的なクエリは次のようになります。\n```\nSELECT Name, Address FROM addresses WHERE 1 AND Name LIKE '%phpMyAdmin%'\n```\n`/**/` の構文の中に **空白が含まれていないことにご注意ください** 。ここに挿入された空白は、クエリの中でも後から空白として挿入されますので、予期せぬ結果を生むことがあります。特に \"LIKE ''\" 式で変数展開する場合はそうです。\n\n#### ブックマークを使用したテーブルの表示[¶](#browsing-a-table-using-a-bookmark)\n\nブックマークの名前がテーブルと同じである場合、そのテーブルを表示するときにクエリとして使用されます。\n\n参考\n\n[6.18 ブックマーク: ブックマークはどこで保管できますか？どうしてクエリボックスの下にブックマークがないのでしょうか？この変数は何でしょうか？](index.html#faqbookmark),\n[6.22 ブックマーク: テーブルの表示モードに入ったときに、自動的にデフォルトのブックマークを実行できますか？](index.html#faq6-22)\n\n### ユーザ管理[¶](#user-management)\n\nユーザ管理は、どのユーザが MySQL サーバへの接続を許可されているか、各データベースにどのような権限を持っているかを制御する手続きです。 phpMyAdmin は、ユーザ管理を処理するのではなく、ユーザ名とパスワードを MySQL に渡し、そのユーザが特定のアクションを実行することを許可されているかどうかを判断します。 phpMyAdmin 内では、管理者はユーザの作成、既存ユーザの権限の表示と編集、ユーザの削除を完全に制御することができます。\n\nphpMyAdmin 内では、ユーザ管理はメインページの ユーザアカウント タブから制御することができます。ユーザを作成、編集、削除することができます。\n\n#### 新しいユーザの作成[¶](#creating-a-new-user)\n\n新しいユーザを作成するには、 ユーザアカウント ページの下部にある ユーザアカウントを追加する リンクをクリックします (\"root \" ユーザなどの 「スーパーユーザ」である必要があります)。テキストボックスとドロップダウンを使用して、特定のニーズに合わせてユーザを設定します。次に、そのユーザのためにデータベースを作成し、特定のグローバル権限を付与するかどうかを選択できます。 ([実行] をクリックして) ユーザを作成したら、特定のデータベースに対するそのユーザの権限を定義することができます (この場合、グローバル権限は付与しないでください)。一般的に、ユーザに必要なのはグローバル権限 (USAGE 以外) ではなく、特定のデータベースに対する権限のみです。\n\n#### 既存のユーザの編集[¶](#editing-an-existing-user)\n\n既存のユーザを編集するには、 ユーザアカウント ページでそのユーザの右側にある鉛筆アイコンをクリックしてください。その後、グローバルおよびデータベース固有の権限を編集したり、パスワードを変更したり、それらの権限を新しいユーザにコピーしたりすることもできます。\n\n#### ユーザの削除[¶](#deleting-a-user)\n\nユーザアカウント ページで、削除するユーザーのチェックボックスをオンにし、 (存在する場合は) 同名のデータベースを削除するかどうかを選択し、 [実行] をクリックしてください。\n\n#### 特定のデータベースでユーザに権限を割り当てる[¶](#assigning-privileges-to-user-for-a-specific-database)\n\nユーザは、 (ホームページの ユーザアカウント リンクから) ユーザレコードを編集することでデータベースに割り当てられます。特定のテーブルに固有のユーザを作成する場合は、最初にそのユーザを (グローバル権限なしで) 作成した後で、戻ってそのユーザを編集してテーブルと個々のテーブルの権限を追加する必要があります。\n\n#### 設定可能なメニューとユーザグループ[¶](#configurable-menus-and-user-groups)\n\n[`$cfg['Servers'][$i]['users']`](index.html#cfg_Servers_users) と [`$cfg['Servers'][$i]['usergroups']`](index.html#cfg_Servers_usergroups) を有効にすることで、ユーザが phpMyAdmin ナビゲーションで何を見ることができるかをカスタマイズすることができます。\n\n警告\n\nこの機能は、ユーザから見えるものを制限するだけであり、すべての機能を使用することができます。そのため、これはセキュリティ上の制限とは考えてはいけません。ユーザができることを制限したい場合は、 MySQL の権限を設定してください。\n\nこの機能を有効にすると、 ユーザアカウント 管理インタフェースには、ユーザグループを管理するための2つ目のタブが追加され、各グループが表示することができるものを定義することができ (下の画像を参照)、それぞれのユーザをこれらのグループのうちの一つに割り当てることができます。ユーザには簡略化されたユーザインタフェースが表示されるので、 phpMyAdmin が提供するすべての機能に圧倒されてしまうかもしれない経験の浅いユーザにとっては有用かもしれません。\n\n### リレーション[¶](#relations-1)\n\nphpMyAdmin では、MySQL ネイティブ (InnoDB) のメソッドを使用してリレーションシップ (外部キーのようなもの) を作成することができ、必要に応じて phpMyAdmin 専用の機能を使用することができます。リレーションシップを編集するには、 *リレーションビュー* とドラッグ＆ドロップを行う *デザイナー* の2つの方法があります。\n\n注釈\n\nphpMyAdmin のリレーションのみを使用するには、 [phpMyAdmin 環境保管領域](index.html#linked-tables) を設定しておく必要があります。\n\n#### 技術情報[¶](#technical-info)\n\n今のところ、ネイティブでリレーションシップに対応している MySQL テーブル種別は InnoDB だけです。 InnoDB テーブルを使用する場合、 phpMyAdmin は実際の InnoDB リレーションを作成し、どのアプリケーションがデータベースにアクセスしても MySQL による強制が働きます。他のテーブル種別の場合、 phpMyAdmin は内部的にリレーションを強制しますが、他のアプリケーションには適用されません。\n\n#### リレーションビュー[¶](#relation-view)\n\n動作させるためには、まず [[pmadb|pmadb]] を適切に作成する必要があります。それが設定できたら、テーブルの [構造] ページを選択します。テーブルの定義の下には、 [リレーションビュー ] というリンクが表示されています。そのリンクをクリックすると、任意の (ほとんどの) フィールドに対して別のテーブルへのリンクを作成するためのページが表示されます。そこには主キーのみが表示されますので、参照しているフィールドが表示されていない場合は、おそらく何かうまくいっていません。下部のドロップダウンはレコードの名前として使用されるフィールドです。\n\n##### リレーションビューの例[¶](#relation-view-example)\n\n例えば、カテゴリとリンクがあり、1つのカテゴリに複数のリンクが含まれているとします。テーブル構造は次のようになります。\n\n* category.category_id (ユニークである必要がある)\n* category.name\n* link.link_id\n* link.category_id\n* link.uri.\n\nlink テーブルのリレーションビュー (テーブル構造の下) ページを開き、 category_id フィールドには、マスタレコードとして category.category_id を選択します。\n\n今、リンクテーブルを参照すると、 category_id フィールドは、適切なカテゴリレコードへのクリック可能なハイパーリンクになります。しかし、表示されるのはカテゴリの名前ではなく、 category_id だけです。\n\nこれを修正するには、 category テーブルのリレーションビューを開き、下部のドロップダウンで「名前」を選択します。今、再びリンクテーブルを参照して、 category_id のハイパーリンクにマウスを合わせると、関連するカテゴリの値がツールチップとして表示されます。\n\n#### デザイナ[¶](#designer)\n\nデザイナ機能は、 phpMyAdmin のリレーションをグラフィカルに作成、編集、表示する方法です。これらのリレーションは、 phpMyAdmin のリレーションビューで作成されたものと互換性があります。\n\nこの機能を使用するには、 [phpMyAdmin 環境保管領域](index.html#linked-tables) を適切に設定し、 [`$cfg['Servers'][$i]['table_coords']`](index.html#cfg_Servers_table_coords) を設定する必要があります。\n\nデザイナを使用するには、データベースの構造ページを選択し、 デザイナ タブを探してください。\n\nビューを PDF にエクスポートするには、最初に PDF ページを作成する必要があります。デザイナは、テーブルがどのように表示されるか、レイアウトを作成します。最終的にビューをエクスポートするには、 PDF ページでこれを作成し、デザイナで作成したレイアウトを選択する必要があります。\n\n参考\n\n[6.8 データベースの PDF スキーマを作るにはどうするのですか？](index.html#faqpdf)\n\n### グラフ機能[¶](#charts-1)\n\nバージョン 3.4.0 で追加.\n\nphpMyAdmin のバージョン 3.4.0 から、 [クエリ結果操作] エリアの [グラフで表示する] リンクをクリックすることで、 SQL クエリから簡単にグラフを生成することができます。\n\nウィンドウレイヤー [グラフで表示する] が表示され、以下のオプションでグラフをカスタマイズすることができます。\n\n* グラフの種類: グラフの種類を選択できます。対応している種類は、横棒グラフ、縦棒グラフ、折れ線グラフ、曲線グラフ、面グラフ、円グラフ、タイムラインです (現在選択されている系列に適用可能なグラフの種類のみが提供されます)。\n* X 軸: 主軸のフィールドを選択することができます。\n* 系列: グラフ化する系列を選択することができます。複数の系列を選択することができます。\n* タイトル: グラフの上に表示されるグラフのタイトルを指定することができます。\n* X 軸と Y 軸のラベル: 軸のラベルを指定することができます。\n* 開始行および行数: 結果セット内の指定した行数のみのグラフを生成することができます。\n\n#### グラフの実装[¶](#chart-implementation)\n\nphpMyAdmin のグラフは jQuery の [jqPlot](http://www.jqplot.com/) ライブラリを使用して描画しています。\n\n#### 設定例[¶](#examples)\n\n##### 円グラフ[¶](#pie-chart)\n\n円グラフのための単純な結果を生成できるクエリです。\n```\nSELECT 'Food' AS 'expense',\n 1250 AS 'amount' UNION SELECT 'Accommodation', 500 UNION SELECT 'Travel', 720 UNION SELECT 'Misc', 220\n```\nまた、このクエリの結果は次の通りです。\n\n| expense | amount |\n| --- | --- |\n| Food | 1250 |\n| Accommodation | 500 |\n| Travel | 720 |\n| Misc | 220 |\n\nexpense を X 軸および系列の値として選択します。\n\n##### 横棒グラフと縦棒グラフ[¶](#bar-and-column-chart)\n\n横棒グラフと縦棒グラフはどちらも積み上げに対応しています。どちらかの種類を選択すると、積み上げ形式を選択するチェックボックスが表示されます。\n\n横棒グラフや縦棒グラフのための単純な結果を生成できるクエリです。\n```\nSELECT\n 'ACADEMY DINOSAUR' AS 'title',\n 0.99 AS 'rental_rate',\n 20.99 AS 'replacement_cost' UNION SELECT 'ACE GOLDFINGER', 4.99, 12.99 UNION SELECT 'ADAPTATION HOLES', 2.99, 18.99 UNION SELECT 'AFFAIR PREJUDICE', 2.99, 26.99 UNION SELECT 'AFRICAN EGG', 2.99, 22.99\n```\nまた、このクエリの結果は次の通りです。\n\n| title | rental_rate | replacement_cost |\n| --- | --- | --- |\n| ACADEMY DINOSAUR | 0.99 | 20.99 |\n| ACE GOLDFINGER | 4.99 | 12.99 |\n| ADAPTATION HOLES | 2.99 | 18.99 |\n| AFFAIR PREJUDICE | 2.99 | 26.99 |\n| AFRICAN EGG | 2.99 | 22.99 |\n\nX 軸として title を、系列として rental_rate と replacement_cost を選択すると次のようになります。\n\n##### 散布図[¶](#scatter-chart)\n\n散布図は、1つまたは複数の変数の動きを別な変数と比較して識別するのに便利です。\n\n縦棒グラフと横棒グラフの節と同じデータセットを使用して、 X 軸として replacement_cost を、系列として rent_rate を選択します。\n\n##### 折れ線、曲線、タイムライングラフ[¶](#line-spline-and-timeline-charts)\n\nこれらのグラフは、基礎となるデータのトレンドを表すために使用することができます。曲線グラフは滑らかな線を描き、タイムライングラフは日付と時間の間の距離を考慮して X 軸を描きます。\n\n単純な線、曲線、タイムライングラフを生成できるクエリです。\n```\nSELECT\n DATE('2006-01-08') AS 'date',\n 2056 AS 'revenue',\n 1378 AS 'cost' UNION SELECT DATE('2006-01-09'), 1898, 2301 UNION SELECT DATE('2006-01-15'), 1560, 600 UNION SELECT DATE('2006-01-17'), 3457, 1565\n```\nまた、このクエリの結果は次の通りです。\n\n| date | revenue | cost |\n| --- | --- | --- |\n| 2016-01-08 | 2056 | 1378 |\n| 2006-01-09 | 1898 | 2301 |\n| 2006-01-15 | 1560 | 600 |\n| 2006-01-17 | 3457 | 1565 |\n\n### インポートとエクスポート[¶](#import-and-export)\n\n#### インポート[¶](#import)\n\nデータをインポートするには、 phpMyAdmin の [インポート] タブを開いてください。特定のデータベースやテーブルにデータをインポートするには、データベースまたはテーブルを開いてから [インポート] タブを開いてください。\n\n標準の [インポート] および [エクスポート] タブのほかに、ブラウザの phpMyAdmin インタフェースにファイルマネージャから SQL ファイルを直接ドラッグ＆ドロップすることもできます。\n\n大きなファイルのインポートで問題が発生した場合は、「 [1.16 (メモリ、HTTP、タイムアウトのせいで) 大きなダンプファイルをアップロードできません。](index.html#faq1-16)」を参照してください。\n\n以下の方法でインポートを行うことができます。\n\nフォームベースのアップロード\n\n> 対応している任意のファイル形式を、 (b|g)zip ファイル (例えば mydump.sql.gz) を含め使用することができます。\n\nフォームベースの SQL クエリ\n\n> 有効な SQL ダンプが利用できます。\n\nアップロードディレクトリの使用\n\n> phpMyAdmin がインストールされているウェブサーバ上のアップロードディレクトリを指定することができます。このディレクトリにファイルをアップロードした後、 phpMyAdmin のインポートダイアログでこのファイルを選択することができます、 [`$cfg['UploadDir']`](index.html#cfg_UploadDir) を参照してください。\n\nphpMyAdmin はよく使われる様々なファイル形式からインポートすることができます。\n\n##### CSV[¶](#csv)\n\nカンマ区切りファイル形式は、スプレッドシートやその他の様々なプログラムで、エクスポートやインポートによく使用されます。\n\n注釈\n\nCSV ファイルから 'auto_increment' フィールドを持つテーブルにデータをインポートするとき、CSV フィールド内のそれぞれのレコードで 'auto_increment' 値を '0' (ゼロ) に設定してください。これによって 'auto_increment' フィールドが正しく生成されるようになります。\n\nサーバやデータベースレベルで CSV ファイルをインポートできるようになりました。 CSV ファイルをインポートするためのテーブルを作成しなくても、最適な構造が決定され、データがインポートされます。その他の機能、要件、制限事項は従来通りです。\n\n##### LOAD DATA 文を使用した CSV の読み込み[¶](#csv-using-load-data)\n\nCSV と同様、内蔵の MySQL パーサのみを使用し、 phpMyAdmin のものは使用しません。\n\n##### ESRI シェープファイル[¶](#esri-shape-file)\n\nESRI シェイプファイルまたは単にシェイプファイルは、地理情報システム (GIS) ソフトウェアのための一般的な地理空間ベクトルデータフォーマットです。 Esri と他のソフトウェア製品間のデータ相互運用のための (ほぼ) オープンな仕様として、 Esri が開発・規定しています。\n\n##### MediaWiki[¶](#mediawiki)\n\nphpMyAdmin (バージョン 4.0 以降) でエクスポートできる MediaWiki ファイルもインポートできるようになりました。これは Wikipedia が表を表示するために使用しているファイル形式です。\n\n##### Open Document スプレッドシート (ODS)[¶](#open-document-spreadsheet-ods)\n\n1 つ以上のスプレッドシートを含む OpenDocument ワークブックが直接インポートできるようになりました。\n\nODS スプレッドシートをインポートするときは、インポートをできるだけ簡単にするために、スプレッドシートに特定の名前を付ける必要があります。\n\n###### テーブル名[¶](#table-name)\n\nインポート中、 phpMyAdmin はシート名をテーブル名として使用します。スプレッドシートプログラムでシート名を既存のテーブル名 (または作成したいテーブル名) と一致するように、変更する必要があります (ただし、操作タブから新しいテーブル名をすぐに変更できるので、これはあまり気にしなくてもよいでしょう)。\n\n###### カラム名[¶](#column-names)\n\nまた、スプレッドシートの最初の行には、列の名前が記載されたヘッダーを作成する必要があります (これは、スプレッドシートの最上部に新しい行を挿入することで実現できます)。インポート画面で、「ファイルの最初の行にテーブルのカラム名が含まれている」のチェックボックスを選択してください。\n\n注釈\n\n数式や計算は評価されず、直近で保存された値が読み込まれます。インポートする前にスプレッドシートのすべての値があることを確認してください。\n\n##### SQL[¶](#sql)\n\nSQL を使用してデータに対して任意の操作を行うことができ、またバックアップしたデータを復元する場合にも役立ちます。\n\n##### XML[¶](#xml)\n\nphpMyAdmin (バージョ ン3.3.0 以降)によってエクスポートされた XML ファイルがインポートできるようになりました。構造 (データベース、テーブル、ビュー、トリガーなど) やデータは、ファイルの内容に応じて作成されます。\n\n対応している XML スキーマはこの Wiki では文書化されていません。\n\n#### エクスポート[¶](#export)\n\nphpMyAdminは、ローカルディスク (またはウェブサーバの特別な [`$cfg['SaveDir']`](index.html#cfg_SaveDir) フォルダ) 上のテキストファイル (圧縮されている場合でも) に、一般的に使用されるさまざまな形式でエクスポートできます。\n\n##### CodeGen[¶](#codegen)\n\n[NHibernate](https://en.wikipedia.org/wiki/NHibernate) ファイル形式です。計画されているバージョンは Java、Hibernate、 PHP PDO、 JSON などです。したがって、仮の名前は codegen です。\n\n##### CSV[¶](#csv-1)\n\nカンマ区切りファイル形式は、スプレッドシートやその他の様々なプログラムで、エクスポートやインポートによく使用されます。\n\n##### MS Excel 用 CSV[¶](#csv-for-microsoft-excel)\n\nこれは多くの Microsoft Excel の英語版のほとんどにインポートできる CSV エクスポートが事前構成されただけのものです。一部のローカライズ版 (デンマーク語など) はフィールド区切りに \",\" ではなく \";\" が必要です。\n\n##### Microsoft Word 2000[¶](#microsoft-word-2000)\n\nMicrosoft Word 2000 以降 (または OpenOffice.org などの互換製品) を使用している場合は、このエクスポートが利用できます。\n\n##### JSON[¶](#json)\n\nJSON (JavaScript Object Notation) は、軽量のデータ交換形式です。人間にとって読み書きしやすく、機械にとって解釈や生成がしやすいものです。\n\nバージョン 4.7.0 で変更: 生成される JSON の構造は、 phpMyAdmin 4.7.0 で妥当な JSON データを出力するために変更されました。\n\n生成される JSON は、以下の属性を持ったオブジェクトのリストです。\n\n`type`[¶](#type)\nこのオブジェクトの型で、次のうちのいずれか１つです。\n\n`header`\nコメントと phpMyAdmin のバージョンを含むエクスポートヘッダです。\n`database`\nデータベースマーカの開始で、データベースの名前を含みます。\n`table`\nエクスポートするテーブルのデータです。\n\n`version`[¶](#version)\n`header` [`type`](#type) で使用され、 phpMyAdmin のバージョンを示します。\n\n`comment`[¶](#comment)\nオプションのテキストによるコメントです。\n\n`name`[¶](#name)\nオブジェクト名です。 [`type`](#type) によってテーブル名またはデータベース名になります。\n\n`database`[¶](#database)\n`table` [`type`](#type) の場合のデータベース名です。\n\n`data`[¶](#data)\n`table` [`type`](#type) の場合のテーブルの内容です。\n\n出力例:\n```\n[\n {\n \"comment\": \"Export to JSON plugin for PHPMyAdmin\",\n \"type\": \"header\",\n \"version\": \"4.7.0-dev\"\n },\n {\n \"name\": \"cars\",\n \"type\": \"database\"\n },\n {\n \"data\": [\n {\n \"car_id\": \"1\",\n \"description\": \"Green Chrysler 300\",\n \"make_id\": \"5\",\n \"mileage\": \"113688\",\n \"price\": \"13545.00\",\n \"transmission\": \"automatic\",\n \"yearmade\": \"2007\"\n }\n ],\n \"database\": \"cars\",\n \"name\": \"cars\",\n \"type\": \"table\"\n },\n {\n \"data\": [\n {\n \"make\": \"Chrysler\",\n \"make_id\": \"5\"\n }\n ],\n \"database\": \"cars\",\n \"name\": \"makes\",\n \"type\": \"table\"\n }\n]\n```\n##### LaTeX[¶](#latex)\n\nテーブルのデータや構造を LaTeX に埋め込みたいのであれば、これが正しい選択です。\n\nLaTeX は高品質の科学および数学の文書を生成するのに最適な組版システムです。これは単一の文字から完全な本まで、他の種類の文書を生成するのにも適しています。 LaTeX は整形エンジンに TeX を使用しています。 TeX および LaTeX についての詳細は [the Comprehensive TeX Archive Network](https://www.ctan.org/) および [short description od TeX](https://www.ctan.org/tex/) を参照してください。\n\n出力をレンダリングする前に、出力を LaTeX ドキュメントに埋め込む必要があります。以下にドキュメントの例を挙げます。\n```\n\\documentclass{article}\n\\title{phpMyAdmin SQL output}\n\\author{}\n\\usepackage{longtable,lscape}\n\\date{}\n\\setlength{\\parindent}{0pt}\n\\usepackage[left=2cm,top=2cm,right=2cm,nohead,nofoot]{geometry}\n\\pdfpagewidth 210mm\n\\pdfpageheight 297mm\n\\begin{document}\n\\maketitle\n\n% insert phpMyAdmin LaTeX Dump here\n\n\\end{document}\n```\n##### MediaWiki[¶](#mediawiki-1)\n\nテーブルとデータベースの両方を、ウィキペディアが表を表示するために使用する MediaWiki 形式でエクスポートすることができます。エクスポートできるものは構造、データ、テーブル名、ヘッダなどです。\n\n##### OpenDocument スプレッドシート[¶](#opendocument-spreadsheet)\n\n広く採用されているスプレッドシートデータのオープン標準です。 LibreOffice、 OpenOffice、 Microsoft Office、 Google Docs などの最近の多くのスプレッドシートプログラムは、この形式を処理することができます。\n\n##### OpenDocument テキスト[¶](#opendocument-text)\n\n広く採用されているテキストデータの新しい標準です。最新のワードプロセッサ (LibreOffice、 OpenOffice、 Microsoft Word、 AbiWord、 KWordなど) でこれを処理することができます。\n\n##### PDF[¶](#pdf)\n\nプレゼンテーション目的の場合、編集できない PDF は最適かもしれません。\n\n##### PHP array[¶](#php-array)\n\n選択されたテーブルやデータベースの内容を持った多次元配列を宣言する PHP ファイルを生成することができます。\n\n##### SQL[¶](#sql-1)\n\nSQL でエクスポートすると、データベースの復元に使用できるため、バックアップに有用です。\n\n「作成されたクエリの最大長」オプションは文書化されていないようです。しかし、実験では、大きく広がった INSERT を分割するため、それぞれが指定されたバイト数 (または文字数？) より大きくならないことが分かっています。したがって、ファイルをインポートするときに、大きなテーブルで \"Got a packet bigger than 'max_allowed_packet' bytes\" というエラーを回避することができます。\n\n参考\n\n<https://dev.mysql.com/doc/refman/5.7/ja/packet-too-large.html###### データオプション[¶](#data-options)\n\n**完全挿入** は、 SQL ダンプにカラム名を追加します。このパラメータにより、ダンプの可読性と信頼性が高まります。カラム名を追加すると、ダンプの大きさが増加しますが、拡張挿入と組み合わせると無視できる程度です。\n\n**拡張挿入** は、複数のデータ行を１つの INSERT クエリに結合します。これにより、大きな SQL ダンプではファイルの大きさを大幅に縮小でき、インポート時の INSERT の速度を上げることができるので、通常は推奨されます。\n\n##### Texy\n\n[Texy!](https://texy.info/) マークアップ形式です。例を [Texy! のデモ](https://texy.info/en/try/4q5we) で参照することができます。\n\n##### XML[¶](#xml-1)\n\nカスタムスクリプトで使用するために解析しやすいエクスポートです。\n\nバージョン 3.3.0 で変更: 使用する XML スキーマがバージョン 3.3.0 で変更されました\n\n##### YAML[¶](#yaml)\n\nYAML は、人間が読める形式であり、計算能力も高いデータシリアル化形式です (<<https://yaml.org>>)。\n\n### カスタムテーマ[¶](#custom-themes)\n\nphpMyAdmin には、サードパーティのテーマに対応しています。追加のテーマは、私たちのウェブサイト <<https://www.phpmyadmin.net/themes/>> からダウンロードできます。\n\n#### 設定[¶](#configuration)\n\nThemes are configured with [`$cfg['ThemeManager']`](index.html#cfg_ThemeManager) and\n[`$cfg['ThemeDefault']`](index.html#cfg_ThemeDefault). Under `./public/themes/`, you should not delete the directory `pmahomme` or its underlying structure, because this is the system theme used by phpMyAdmin. `pmahomme` contains all images and styles, for backwards compatibility and for all themes that would not include images or css-files. If [`$cfg['ThemeManager']`](index.html#cfg_ThemeManager) is enabled, you can select your favorite theme on the main page. Your selected theme will be stored in a cookie.\n\n#### カスタムテーマの作成[¶](#creating-custom-theme)\n\nテーマを作成するには、以下のようにします。\n\n* make a new subdirectory (for example \"your_theme_name\") under `./public/themes/`.\n* `pmahomme` から \"your_theme_name\" にファイルやディレクトリをコピーします\n* \"your_theme_name/css\" の CSS ファイルを編集します\n* \"your_theme_name/img\" に新しい画像を入れます\n* \"your_theme_name/scss\" の `_variables.scss` を編集します\n* \"your_theme_name\" の `theme.json` を編集してテーマのメタデータを設定します (下記参照)\n* テーマの新しいスクリーンショットを作成して、 \"your_theme_name/screen.png\" に保存します\n\n##### テーマのメタデータ[¶](#theme-metadata)\n\nバージョン 4.8.0 で変更: 4.8.0 以前は、テーマのメタデータは `info.inc.php` ファイルで渡されていました。これをは `theme.json` に置き換えられ、より簡単に解析ができるようになり (PHP コードを扱う必要がなくなり)、追加機能に対応するようになりました。\n\nテーマディレクトリには、テーマのメタデータを含むファイル `theme.json` があります。現在のところ、以下の要素があります。\n\n`name`\nテーマの表示名です。\n\n**このフィールドは必須です。**\n\n`version`\nテーマのバージョンです。自由に設定することができ、 phpMyAdmin のバージョンと一致させる必要はありません。\n\n**このフィールドは必須です。**\n\n`description`\nテーマの説明です。これはウェブサイトに表示されます。\n\n**このフィールドは必須です。**\n\n`author`\nテーマの作者の名前です。\n\n**このフィールドは必須です。**\n\n`url`\n作者のウェブサイトへのリンクです。そこでサポートを受けられるようにするといいでしょう。\n\n`supports`\n対応している phpMyAdmin のメジャーバージョンの配列です。\n\n**このフィールドは必須です。**\n\nたとえば、phpMyAdmin 4.8 に付属しているオリジナルテーマの定義は次の通りです。\n```\n{\n \"name\": \"Original\",\n \"version\": \"4.8\",\n \"description\": \"Original phpMyAdmin theme\",\n \"author\": \"phpMyAdmin developers\",\n \"url\": \"https://www.phpmyadmin.net/\",\n \"supports\": [\"4.8\"]\n}\n```\n##### 画像の共有[¶](#sharing-images)\n\n独自の記号やボタンを使用しない場合は、 \"your_theme_name\" から \"img\" ディレクトリを削除してください。デフォルトの (システムテーマである `pmahomme` の) アイコンやボタンが使われます。\n\n### その他の情報源[¶](#other-sources-of-information)\n\n#### 出版本[¶](#printed-book)\n\nphpMyAdmin を使用するための決定的なガイドは、 <NAME>le 著『Mastering phpMyAdmin for Effective MySQL Management』です。この本やその他の公式参考書についての情報は「[books at the phpMyAdmin site](https://www.phpmyadmin.net/docs/)」で見ることができます。\n\n#### チュートリアル[¶](#tutorials)\n\n興味を持つかもしれない外部のチュートリアルや記事です。\n\n##### チェコ語[¶](#cesky-czech)\n\n* [Seriál o phpMyAdminovi](https://cihar.com/publications/linuxsoft/)\n\n##### 英語[¶](#english)\n\n* [Having fun with phpMyAdmin's MIME-transformations & PDF-features](https://garv.in/tops/texte/mimetutorial)\n* [Learning SQL Using phpMyAdmin (古いチュートリアル)](http://www.php-editors.com/articles/sql_phpmyadmin.php)\n\n##### ロシア語[¶](#russian)\n\n* [phpMyAdmin に関するロシア語のサーバ](https://php-myadmin.ru/)\n\nFAQ - よくある質問[¶](#faq-frequently-asked-questions)\n---\n\nphpMyAdmin の機能やインタフェースの詳細については phpMyAdmin の公式ページにある [Link セクション](https://www.phpmyadmin.net/docs/) をご覧ください。\n\n### サーバ[¶](#server)\n\n#### 1.1 サーバが度々クラッシュします。その度に、特定のアクションを要求されたり、ブラウザに空白のページや暗号のような文字だらけのページが表示されます。どうしたらよいのでしょうか？[¶](#my-server-is-crashing-each-time-a-specific-action-is-required-or-phpmyadmin-sends-a-blank-page-or-a-page-full-of-cryptic-characters-to-my-browser-what-can-i-do)\n\n`config.inc.php` ファイルの [`$cfg['OBGzip']`](index.html#cfg_OBGzip) ディレクティブを `false` に、PHP の設定ファイルの `zlib.output_compression` 設定を `Off` にしてみてください。\n\n#### 1.2 phpMyAdmin を使うと Apache サーバがクラッシュします。[¶](#my-apache-server-crashes-when-using-phpmyadmin)\n\nまず、 Apache (および MySQL) の最新のバージョンを使用してみてください。それでもサーバがクラッシュするようなら、Apache の各種サポートグループに助けを求めてください。\n\n参考\n\n[1.1 サーバが度々クラッシュします。その度に、特定のアクションを要求されたり、ブラウザに空白のページや暗号のような文字だらけのページが表示されます。どうしたらよいのでしょうか？](#faq1-1)\n\n#### 1.3 (取り下げ)。[¶](#withdrawn)\n\n#### 1.4 phpMyAdmin を IIS 上で使うと、 \"The specified CGI application misbehaved by not returning a complete set of HTTP headers ...\" というエラーメッセージが表示されます。[¶](#using-phpmyadmin-on-iis-i-m-displayed-the-error-message-the-specified-cgi-application-misbehaved-by-not-returning-a-complete-set-of-http-headers)\n\nPHP の配布ファイルに入っている *install.txt* を読み忘れたのでしょう。 PHP の公式バグデータベースから [PHP バグレポート #12061](https://bugs.php.net/bug.php?id=12061) を見てみてください。\n\n#### 1.5 phpMyAdmin を IIS 上で使うと、 HTTP においてクラッシュしたり、エラーメッセージがたくさん表示されます。[¶](#using-phpmyadmin-on-iis-i-m-facing-crashes-and-or-many-error-messages-with-the-http)\n\nこれは PHP の [ISAPI](index.html#term-isapi) フィルタの既知の問題です。あまり安定していません。代わりにクッキー認証モードをお使いください。\n\n#### 1.6 PWS 上で phpMyAdmin が使えません。何も表示されません！[¶](#i-can-t-use-phpmyadmin-on-pws-nothing-is-displayed)\n\nThis seems to be a PWS bug. <NAME> found a workaround (at this time there is no better fix): remove or comment the `DOCTYPE`\ndeclarations (2 lines) from the scripts `src/Header.php`\nand `index.php`.\n\n#### 1.7 どうすればダンプや CSV エクスポートを gzip 圧縮できるのでしょうか？ 動いていないようですが。[¶](#how-can-i-gzip-a-dump-or-a-csv-export-it-does-not-seem-to-work)\n\nこれらの機能はプラットフォーム (Unix か Windows か、セーフモードかどうか、など) からの独立性を高めるために PHP の `gzencode()` 関数に基づいています。そのため、Zlib サポート (`--with-zlib`) が必要です。\n\n#### 1.8 テーブルにテキストファイルが挿入できません。セーフモードになっているというエラーが出ます。[¶](#i-cannot-insert-a-text-file-in-a-table-and-i-get-an-error-about-safe-mode-being-in-effect)\n\nアップロードされたファイルは PHP によって、 `php.ini` の変数 `upload_tmp_dir` で定義された \"upload dir\" の中に保存されます (ふつうシステムのデフォルトは */tmp* です)。セーフモードで動作している Apache サーバには、以下のセットアップを行い合理的に安全であるファイルのアップロードを有効化することをお勧めします。\n\n* **mkdir /tmp/php** でアップロード用の別なディレクトリを作ります\n* **chown apache.apache /tmp/php** で所有者を Apache サーバのユーザ／グループにします\n* **chmod 600 /tmp/php** で適切なパーミッションを設定します\n* `php.ini` に `upload_tmp_dir = /tmp/php` を追加します\n* Apache を再起動します\n\n#### 1.9 (取り下げ)。[¶](#withdrawn-1)\n\n#### 1.10 セキュアサーバ上で稼動させている phpMyAdmin のファイルアップロードで困っています。ブラウザは Internet Explorer で、 Apache サーバを使っています。[¶](#i-m-having-troubles-when-uploading-files-with-phpmyadmin-running-on-a-secure-server-my-browser-is-internet-explorer-and-i-m-using-the-apache-server)\n\nphpWizard フォーラムで \"<NAME>\" が勧めていたように、*httpd.conf* に以下の行を追加してください。\n```\nSetEnvIf User-Agent \".*MSIE.*\" nokeepalive ssl-unclean-shutdown\n```\nこうすると、Internet Explorer と SSL にまつわる多くの問題が解決されるようです。\n\n#### 1.11 インポートタブからファイルをアップロードすると 'open_basedir 制限' が出ます。[¶](#i-get-an-open-basedir-restriction-while-uploading-a-file-from-the-import-tab)\n\nバージョン 2.2.4 以降、phpMyAdmin はサーバの open_basedir 制限をサポートしています。しかしながら、一時ディレクトリを作成して、 [`$cfg['TempDir']`](index.html#cfg_TempDir) にそのディレクトリを設定する必要があります。アップロードしたファイルはそこに移され、 [SQL](index.html#term-sql) コマンドの実行が終わったら削除されます。\n\n#### 1.12 MySQL の root のパスワードをなくしてしまいました。どうしたらよいのでしょうか？[¶](#i-have-lost-my-mysql-root-password-what-can-i-do)\n\nphpMyAdmin は使用している MySQL サーバに対して認証を行いますので、 phpMyAdmin のパスワードを紛失した場合は、 MySQL レベルで復旧する必要があります。\n\nMySQL のマニュアルに [パーミッションをリセットする](https://dev.mysql.com/doc/refman/5.7/ja/resetting-permissions.html) 方法の説明があります。\n\nホスティングプロバイダによってインストールされた MySQL サーバを使用している場合は、そのサポートに連絡してパスワードを回復してください。\n\n#### 1.13 (取り下げ)。[¶](#withdrawn-2)\n\n#### 1.14 (取り下げ)。[¶](#withdrawn-3)\n\n#### 1.15 *mysql.user* のカラム名で問題が発生しました。[¶](#i-have-problems-with-mysql-user-column-names)\n\nMySQL の古いバージョンでは `User` と `Password` のカラムが `user` と `password` という名前でした。カラム名を現在の標準にあわせて修正してください。\n\n#### 1.16 (メモリ、HTTP、タイムアウトのせいで) 大きなダンプファイルをアップロードできません。[¶](#i-cannot-upload-big-dump-files-memory-http-or-timeout-problems)\n\nバージョン 2.7.0 以降はインポートエンジンが書き直されたため、この問題は起こらないはずです。可能であればお使いの phpMyAdmin を最新のバージョンにアップグレードして新しいインポート機能をご利用ください。\n\nまずは `php.ini` 設定ファイルの `max_execution_time`, `upload_max_filesize`, `memory_limit`, `post_max_size` の値を確認してください (あるいはプロバイダに確認してもらってください)。この 3 つの設定はいずれも PHP 経由で送信／取り扱いできるデータサイズの上限を決めるものです。また、 `post_max_size` は `upload_max_filesize` より大きくなければなりません。アップロードが大きすぎたり、ホスティングプロバイダが設定を変更したくない場合は、いくつかの回避策があります。\n\n* [`$cfg['UploadDir']`](index.html#cfg_UploadDir) 機能をご覧ください。この機能を使うと、SCP や FTP といったお好みの転送法でファイルをサーバにアップロードできるようになります。ファイルをアップロードしたら、phpMyAdmin はその一時ディレクトリからファイルをインポートできるようになります。詳しくはこのドキュメントの [設定](index.html#config) をご覧ください。\n* ([BigDump](https://www.ozerov.de/bigdump/) のような) ユーティリティを利用してアップロードの前にファイルを分割する方法もあります。このユーティリティはもとより、サードパーティ製のアプリケーションは一切サポートできませんが、そういったものを利用して成功したユーザがいることは承知しています。\n* シェル (コマンドライン) にアクセスできるのであれば、MySQL を利用して直接ファイルをインポートする方法もあります。その場合は MySQL の中で \"source\" コマンドを使ってください。\n```\nsource filename.sql;\n```\n#### 1.17 phpMyAdmin が対応しているデータベースのバージョンは？[¶](#which-database-versions-does-phpmyadmin-support)\n\n[MySQL](https://www.mysql.com/) では、バージョン 5.5 以降に対応しています。古い MySQL のバージョンに対しては、 [Downloads](https://www.phpmyadmin.net/downloads/) ページで古いバージョンの phpMyAdmin を提供しています (サポートが切れているかもしれません)。\n\n[MariaDB](https://mariadb.org/) はバージョン 5.5 以降に対応しています。\n\n#### 1.17a MySQL サーバに接続できません。かならず \"Client does not support authentication protocol requested by server; consider upgrading MySQL client\" というエラーメッセージが返ってきます[¶](#a-i-cannot-connect-to-the-mysql-server-it-always-returns-the-error-message-client-does-not-support-authentication-protocol-requested-by-server-consider-upgrading-mysql-client)\n\n古い MySQL クライアントライブラリで MySQL にアクセスしようとしています。 MySQL クライアントライブラリのバージョンは phpinfo() の出力でチェックできます。一般に、 [1.17 phpMyAdmin が対応しているデータベースのバージョンは？](#faq1-17) で示したマイナーバージョン以上のサーバを使用してください。この問題は一般的に 4.1 以上のバージョンの MySQL で起こります。MySQL の認証ハッシュが変わったのに、お使いの PHP が古い方法を試そうとするためです。この問題を適切に解決するには、お使いの MySQL のバージョンに合わせた適切なクライアントライブラリの [mysqli 拡張モジュール](https://www.php.net/mysqli) を使用するようにしてください。詳細 (とその対策) については [MySQL のドキュメント](https://dev.mysql.com/doc/refman/5.7/ja/common-errors.html) をご覧ください。\n\n#### 1.18 (取り下げ)。[¶](#withdrawn-4)\n\n#### 1.19 「リレーション表示」機能を実行できません。使っているフォントを認識してくれないようです。[¶](#i-can-t-run-the-display-relations-feature-because-the-script-seems-not-to-know-the-font-face-i-m-using)\n\nこの機能を実現するのに利用している [TCPDF](index.html#term-tcpdf) ライブラリは、いくつかの特別なファイルがないとフォントを利用できません。 [TCPDF マニュアル](https://tcpdf.org/) を参照してこれらのファイルを構築してください。\n\n#### 1.20 mysqli や mysql 拡張モジュールがないというエラーが出ます。[¶](#i-receive-an-error-about-missing-mysqli-and-mysql-extensions)\n\nPHP が MySQL サーバに接続する際には「MySQL 拡張モジュール」という MySQL の関数セットを必要とします。この拡張は PHP の配布ファイルに含まれている (コンパイルで組み込まれている) こともありますが、そうでない場合、動的に読み込む必要があります。拡張名はおそらく *mysqli.so* か *php_mysqli.dll* ですが、phpMyAdmin はこの拡張モジュールを読み込もうとして失敗しています。通常、この問題は \"PHP-MySQL\" または同様の名前のソフトウェアパッケージをインストールすることで解決できます。\n\nPHP が MySQL 拡張モジュールとして提供しているインタフェースは、 `mysql` と `mysqli` の 2 つがありました。 `mysql` インタフェースは PHP 7.0 で削除されました。\n\nこの問題は `php.ini` に間違ったパスが指定されていたり、間違った `php.ini` を使用していたりすると発生することもあります。\n\n拡張機能のファイルが `extension_dir` が指すフォルダに存在し、 `php.ini` の対応する行がコメントアウトされていないことを確認してください (現在の設定を確認するには `phpinfo()` が利用できます)。\n```\n[PHP]\n\n; Directory in which the loadable extensions (modules) reside.\nextension_dir = \"C:/Apache2/modules/php/ext\"\n```\n`php.ini` は (特に Windows では) 複数の場所から読み込まれる可能性がありますので、正しいものを更新していることを確認してください。 Apache を使用している場合、 `PHPIniDir` ディレクティブを使用してこのファイルに特定のパスを使用するように指示できます。\n```\nLoadModule php7_module \"C:/php7/php7apache2_4.dll\"\n<IfModule php7_module>\n PHPIniDir \"C:/php7\"\n <Location>\n AddType text/html .php\n AddHandler application/x-httpd-php .php\n </Location>\n</IfModule>\n```\nまれにこの問題は、 PHP に読み込まれている他の拡張モジュールが MySQL 拡張モジュールの読み込みを妨げていることで発生することもあります。まだ失敗する場合は、 `php.ini` から他のデータベースの拡張モジュールをコメントアウトしてみてください。\n\n#### 1.21 CGI 版の PHP を Unix で稼動させているのですが、クッキー認証を使ったログインができません。[¶](#i-am-running-the-cgi-version-of-php-under-unix-and-i-cannot-log-in-using-cookie-auth)\n\n`php.ini` の `mysql.max_links` を 1 より大きな値にしてください。\n\n#### 1.22 「テキストファイルの場所」フィールドが見つからないのでアップロードできません。[¶](#i-don-t-see-the-location-of-text-file-field-so-i-cannot-upload)\n\nいちばんありがちな理由は、 `php.ini` の `file_uploads` パラメータが \"on\" になっていないことです。\n\n#### 1.23 MySQL を Win32 マシンで稼動させているのですが、新規テーブルを作成するたびにテーブル名とカラム名が小文字に変わってしまいます！[¶](#i-m-running-mysql-on-a-win32-machine-each-time-i-create-a-new-table-the-table-and-column-names-are-changed-to-lowercase)\n\nこれは MySQL の設定項目の `lower_case_table_names` が Win32 版のデフォルトでは 1 (`ON`) になっているためです。この動作はこの設定を 0 (`OFF`) に変更するだけで変えられます。おそらく Windows ディレクトリにある `my.ini` ファイルを編集し、 [mysqld] グループに次の行を追加するだけです。\n```\nset-variable = lower_case_table_names=0\n```\n注釈\n\n大文字と小文字の区別のないファイルシステムで --lower-case-table-names=0 を用いてこの変数を 0 に強制的に設定し、 MyISAM にアクセスして大文字と小文字が異なるテーブル名を使用すると、インデックスが競合する可能性があります。\n\n次に、そのファイルを保存して MySQL サービスを再起動します。このディレクティブの値は次のクエリでいつでもチェックできます。\n```\nSHOW VARIABLES LIKE 'lower_case_table_names';\n```\n参考\n\n[MySQL リファレンスマニュアルの「識別子の大文字と小文字の区別」](https://dev.mysql.com/doc/refman/5.7/ja/identifier-case-sensitivity.html)\n\n#### 1.24 (取り下げ)。[¶](#withdrawn-5)\n\n#### 1.25 Windows XP で Apache に mod_gzip-1.3.26.1a を組み込んで稼動させているのですが、 SQL クエリを実行したときに変数が定義されていないといった問題が出ます。[¶](#i-am-running-apache-with-mod-gzip-1-3-26-1a-on-windows-xp-and-i-get-problems-such-as-undefined-variables-when-i-run-a-sql-query)\n\n<NAME> からのヒントとして、 httpd.conf に下記の 2 行があったら、以下のようにコメントにしてください。\n```\n# mod_gzip_item_include file \\.php$\n# mod_gzip_item_include mime \"application/x-httpd-php.*\"\n```\nこのバージョンの Apache (Windows) の mod_gzip には、PHP スクリプトの扱いに問題があるからです。もちろん、上記の変更を行ったら Apache を再起動する必要があります。\n\n#### 1.26 phpMyAdmin を IIS のドキュメントルートにインストールしたところなのですが、phpMyAdmin を実行しようとすると「No input file specified（入力ファイルが指定されていません）」というエラーが出ます。[¶](#i-just-installed-phpmyadmin-in-my-document-root-of-iis-but-i-get-the-error-no-input-file-specified-when-trying-to-run-phpmyadmin)\n\nこれはパーミッションの問題です。phpmyadmin フォルダを右クリックして、プロパティを選んでください。セキュリティタブを開き、 \"追加 (Add)\"をクリックして、一覧から \"IUSR_machine” を選択します。このユーザにパーミッションを設定すれば動くはずです。\n\n#### 1.27 巨大なページ (例えば、多くのテーブルある db_structure.php) を表示しようとすると空白ページが表示されます。[¶](#i-get-empty-page-when-i-want-to-view-huge-page-eg-db-structure-php-with-plenty-of-tables)\n\nこれは [PHP のバグ](https://bugs.php.net/bug.php?id=21079) で、GZIP 出力バッファリングが有効になっていると発生します。これ (`config.inc.php` の中の [`$cfg['OBGzip']`](index.html#cfg_OBGzip)) をオフにすれば動作するはずです。このバグは PHP 5.0.0 で修正されました。\n\n#### 1.28 MySQL サーバがときどきクエリを拒否して「Errorcode: 13」というメッセージを返してきます。どういうことでしょうか？[¶](#my-mysql-server-sometimes-refuses-queries-and-returns-the-message-errorcode-13-what-does-this-mean)\n\nこれは MySQL のバグです。 `lower_case_table_names` が 1 になっているのにデータベース／テーブル名に大文字が含まれていると起こることがあります。修正するには、この設定をオフにして、すべてのデータベース／テーブル名を小文字に変換してから、再度オンにしてください。また、MySQL 3.23.56 / 4.0.11-gamma からはバグフィックスも用意されています。\n\n#### 1.29 テーブルを作成したりカラムを編集したりすると、エラーが出てカラムが複製されてしまいます。[¶](#when-i-create-a-table-or-modify-a-column-i-get-an-error-and-the-columns-are-duplicated)\n\nApache の設定によっては PHP が .php ファイルの解釈を間違ってしまうことがあります。\n\nこの問題が起こるのは、下記のように 2 組の異なった (矛盾をきたす) 設定項目を使用しているためです。\n```\nSetOutputFilter PHP SetInputFilter PHP\n```\nおよび\n```\nAddType application/x-httpd-php .php\n```\n私たちが見たある例では、一方の設定が `/etc/httpd/conf/httpd.conf` に、もう一方の設定が `/etc/httpd/conf/addon-modules/php.conf` に入っていました。推奨される方法は `AddType` なので、前者の両方の行をコメントアウトして Apache を再起動します。\n```\n#SetOutputFilter PHP\n#SetInputFilter PHP\n```\n#### 1.30 \"navigation.php: Missing hash\" というエラーが出ます。[¶](#i-get-the-error-navigation-php-missing-hash)\n\nこの問題はサーバが Turck MMCache を稼動させていると起こることがわかっていますが、MMCache をバージョン 2.3.21 にアップグレードすれば解決します。\n\n#### 1.17 phpMyAdmin が対応している MySQL のバージョンは？[¶](#which-php-versions-does-phpmyadmin-support)\n\nリリース 4.5 以降は、 phpMyAdmin は PHP 5.5 以降のみに対応しています。リリース 4.1 の phpMyAdmin は PHP 5.3 以降のみに対応しています。 PHP 5.2 は、リリース 4.0.x を使用することができます。\n\nphpMyAdmin 4.6 以降は PHP 7 に対応しています。 PHP 7.1 は 4.6.5 以降で対応しており、 PHP 7.2 は 4.7.4 以降で対応しています。\n\nHHVM は phpMyAdmin 4.8 まで対応しています。\n\nSince release 5.0, phpMyAdmin supports only PHP 7.1 and newer.\nSince release 5.2, phpMyAdmin supports only PHP 7.2 and newer.\nSince release 6.0, phpMyAdmin supports only PHP 8.1 and newer.\n\n#### 1.32 IIS で HTTP 認証を利用できますか？[¶](#can-i-use-http-authentication-with-iis)\n\nはい。以下の手順は phpMyAdmin 2.6.1 を [IIS](index.html#term-iis) 5.1 の [ISAPI](index.html#term-isapi) モードで動かした PHP 4.3.9 で確認しました。\n\n1. `php.ini` ファイルに `cgi.rfc2616_headers = 0` を設定します 2. `ウェブサイトのプロパティ -> ディレクトリセキュリティ -> 匿名アクセス` ダイアログボックスで、`匿名アクセス` チェックボックスをチェックし、それ以外のチェックボックスのチェックを外します (つまり、有効になっている場合は `基本認証`、 `統合 Windows 認証`、 `ダイジェスト認証` のチェックを外します)。 `OK` をクリックします。\n3. `カスタムエラー` で、 `401;1` から `401;5` までを選択し、 `既定値に設定` ボタンをクリックします。\n\n参考\n\n[**RFC 2616**](https://tools.ietf.org/html/rfc2616.html)\n\n#### 1.33 (取り下げ)。[¶](#withdrawn-6)\n\n#### 1.34 データベースやテーブルのページに直接アクセスできますか？[¶](#can-i-directly-access-a-database-or-table-pages)\n\nはい。そのままでも `http://server/phpMyAdmin/index.php?server=X&db=database&table=table&target=script` のような [URL](index.html#term-url) を利用することができます。 `server` 引数には、 `config.inc.php` で参照した数値のホスト番号 (`$i` より) を使用することができます。 table と script の部分はオプションです。\n\n`http://server/phpMyAdmin/database[/table][/script]` のような URL を使いたい場合は、さらにいくつかの設定をする必要があります。以下の例は [Apache](https://httpd.apache.org) ウェブサーバにしか適用できません。まずはグローバル設定でいくつかの機能を有効にしてあることを確認してください。 phpMyAdmin をインストールしたディレクトリについては `Options SymLinksIfOwnerMatch` と `AllowOverride FileInfo` を有効にする必要がありますし、mod_rewrite を有効にしておく必要もあります。あとは、以下のような [.htaccess](index.html#term-htaccess) ファイルを phpMyAdmin をインストールした場所のルートフォルダに作成する必要があります (忘れずにディレクトリ名を修正してください)。\n```\nRewriteEngine On RewriteBase /path_to_phpMyAdmin RewriteRule ^([a-zA-Z0-9_]+)/([a-zA-Z0-9_]+)/([a-z_]+\\.php)$ index.php?db=$1&table=$2&target=$3 [R]\nRewriteRule ^([a-zA-Z0-9_]+)/([a-z_]+\\.php)$ index.php?db=$1&target=$2 [R]\nRewriteRule ^([a-zA-Z0-9_]+)/([a-zA-Z0-9_]+)$ index.php?db=$1&table=$2 [R]\nRewriteRule ^([a-zA-Z0-9_]+)$ index.php?db=$1 [R]\n```\n参考\n\n[4.8 phpMyAdmin を起動する URL 使うことができるパラメータはどれですか？](#faq4-8)\n\nバージョン 5.1.0 で変更: `target` 引数を使用した対応は phpMyAdmin 5.1.0 で削除されました。代わりに `route` 引数を使用してください。\n\n#### 1.35 Apache の CGI で HTTP 認証が使用できますか？[¶](#can-i-use-http-authentication-with-apache-cgi)\n\nはい。ただし、以下のリライト規則を使用して、 [CGI](index.html#term-cgi) へ認証用変数を渡す必要があります。\n```\nRewriteEngine On RewriteRule .* - [E=REMOTE_USER:%{HTTP:Authorization},L]\n```\n#### 1.36 \"500 Internal Server Error\" というエラーが出ます。[¶](#i-get-an-error-500-internal-server-error)\n\nこれには多くの要因があり、サーバのエラーログファイルを見れば手がかりが得られる場合があります。\n\n#### 1.37 異なるマシンのクラスタ上で phpMyAdmin を稼動させていますが、クッキー認証でのパスワード暗号化が機能しません。[¶](#i-run-phpmyadmin-on-cluster-of-different-machines-and-password-encryption-in-cookie-auth-doesn-t-work)\n\nクラスタが異なるアーキテクチャで構成されている場合、暗号化／復号の PHP コードが正しく動作しません。これは、コード内で pack/unpack 関数を使用していることが原因で発生します。唯一の解決策は、この状況でも正常に動作している openssl 拡張を使用することです。\n\n#### 1.38 Suhosin が有効になっているサーバ上で phpMyAdmin を使うことはできますか？[¶](#can-i-use-phpmyadmin-on-a-server-on-which-suhosin-is-enabled)\n\nはい。ただし、Suhosin のデフォルトの設定値は、一部の操作で問題があることが知られています。例えば、多くのカラムを持っていて [主キー](index.html#term-primary-key) がないテーブルや、文字列の [主キー](index.html#term-primary-key) を持っているテーブルの編集などです。\n\nSuhosin の設定はいくつかのケースでは誤動作につながる可能性があります。phpMyAdmin は 1 回の HTTP リクエスト内で多量のカラムの転送を必要とするアプリケーションであり、Suhosin は HTTP リクエストに対して何らかの防止を行おうとするものであるため、この問題を完全に回避することはできません。一般的に、すべての `suhosin.request.*`、 `suhosin.post.*`、 `suhosin.get.*` の設定項目は、phpMyAdmin の使用に対して悪影響を与えます。Suhosin によって削られた変数が発生したかをエラーログで確認できるので、この問題を診断して設定がうまく合うように調整することができます。\n\nSuhosin の設定オプションのほとんどは、デフォルト値で大抵の状況において動作するでしょう。ただし、少なくとも以下のパラメータは調整することをお勧めします。\n\n* [suhosin.request.max_vars](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-request-max-vars) should be increased (eg. 2048)\n* [suhosin.post.max_vars](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-post-max-vars) should be increased (eg. 2048)\n* [suhosin.request.max_array_index_length](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-request-max-array-index-length)\nshould be increased (eg. 256)\n* [suhosin.post.max_array_index_length](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-post-max-array-index-length)\nshould be increased (eg. 256)\n* [suhosin.request.max_totalname_length](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-request-max-totalname-length)\nshould be increased (eg. 8192)\n* [suhosin.post.max_totalname_length](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-post-max-totalname-length) should be increased (eg. 8192)\n* [suhosin.get.max_value_length](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-get-max-value-length)\nshould be increased (eg. 1024)\n* [suhosin.sql.bailout_on_error](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-sql-bailout-on-error)\nneeds to be disabled (the default)\n* [suhosin.log.*](https://suhosin5.suhosin.org/stories/configuration.html#logging-configuration) should not include [SQL](index.html#term-sql), otherwise you get big slowdown\n* [suhosin.sql.union](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-sql-union) must be disabled (which is the default).\n* [suhosin.sql.multiselect](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-sql-multiselect) must be disabled (which is the default).\n* [suhosin.sql.comment](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-sql-comment) must be disabled (which is the default).\n\nさらにセキュリティを高めるため、以下のとおり変更することをお勧めします。\n\n* [suhosin.executor.include.max_traversal](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-executor-include-max-traversal) should be enabled as a mitigation against local file inclusion attacks. We suggest setting this to 2 as `../` is used with the ReCaptcha library.\n* [suhosin.cookie.encrypt](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-cookie-encrypt) should be enabled.\n* [suhosin.executor.disable_emodifier](https://suhosin5.suhosin.org/stories/configuration.html#suhosin-executor-disable-emodifier) should be enabled.\n\n[`$cfg['SuhosinDisableWarning']`](index.html#cfg_SuhosinDisableWarning) 設定を使用して警告を無効にすることもできます。\n\n#### 1.39 https を経由して接続すると、ログインすることはできますが、接続が http にリダイレクトされてしまいます。この挙動の原因は何ですか？[¶](#when-i-try-to-connect-via-https-i-can-log-in-but-then-my-connection-is-redirected-back-to-http-what-can-cause-this-behavior)\n\nこれは、サイトが https を使用していることを PHP スクリプトが認識していないことが原因です。使用するウェブサーバに応じて、アクセスに使用する URL とスキームについて PHP に通知するように構成する必要があります。\n\nたとえば Apacheでは、設定で `SSLOptions` と `StdEnvVars` が有効になっていることを確認してください。\n\n参考\n\n<<https://httpd.apache.org/docs/2.4/mod/mod_ssl.html>#### 1.40 Apache のリバースプロキシを介して phpMyAdmin にアクセスすると、クッキーログインが機能しません。[¶](#when-accessing-phpmyadmin-via-an-apache-reverse-proxy-cookie-login-does-not-work)\n\nクッキー認証を使用している場合、 set-cookie ヘッダを書き換える必要があることを Apache が 認識する必要があります。 Apache 2.2 ドキュメントからの例です。\n```\nProxyPass /mirror/foo/ http://backend.example.com/\nProxyPassReverse /mirror/foo/ http://backend.example.com/\nProxyPassReverseCookieDomain backend.example.com public.example.com ProxyPassReverseCookiePath / /mirror/foo/\n```\n注: バックエンド URL が `http://host/~user/phpmyadmin` のようになる場合、 ProxyPassReverse* の行においてチルダ (~) は %7E のように URL エンコードする必要があります。これは phpMyAdmin に限ったものではなく、 Apache の動作です。\n```\nProxyPass /mirror/foo/ http://backend.example.com/~user/phpmyadmin ProxyPassReverse /mirror/foo/ http://backend.example.com/%7Euser/phpmyadmin ProxyPassReverseCookiePath /%7Euser/phpmyadmin /mirror/foo\n```\n参考\n\n<<https://httpd.apache.org/docs/2.2/mod/mod_proxy.html>>、 [`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri)\n\n#### 1.41 データベースを表示してその権限を参照しようとすると、未知のカラムに関するエラーが表示されます。[¶](#when-i-view-a-database-and-ask-to-see-its-privileges-i-get-an-error-about-an-unknown-column)\n\nMySQL サーバの権限テーブルが最新の状態ではありません。サーバ上で **mysql_upgrade** コマンドを実行する必要があります。\n\n#### 1.42 ロボットから phpMyAdmin へのアクセスを防ぐにはどうすればいいのでしょうか？[¶](#how-can-i-prevent-robots-from-accessing-phpmyadmin)\n\n[.htaccess](index.html#term-htaccess) に、ユーザエージェントフィールドに基づいてアクセスをフィルタリングするルールを追加することができます。防ぐ手立てとしてはきわめて簡単な方法ですが、少なくともいくつかの検索ロボットからは防ぐことが可能です。\n```\nRewriteEngine on\n\n# Allow only GET and POST verbs RewriteCond %{REQUEST_METHOD} !^(GET|POST)$ [NC,OR]\n\n# Ban Typical Vulnerability Scanners and others\n# Kick out Script Kiddies RewriteCond %{HTTP_USER_AGENT} ^(java|curl|wget).* [NC,OR]\nRewriteCond %{HTTP_USER_AGENT} ^.*(libwww-perl|curl|wget|python|nikto|wkito|pikto|scan|acunetix).* [NC,OR]\nRewriteCond %{HTTP_USER_AGENT} ^.*(winhttp|HTTrack|clshttp|archiver|loader|email|harvest|extract|grab|miner).* [NC,OR]\n\n# Ban Search Engines, Crawlers to your administrative panel\n# No reasons to access from bots\n# Ultimately Better than the useless robots.txt\n# Did google respect robots.txt?\n# Try google: intitle:phpMyAdmin intext:\"Welcome to phpMyAdmin *.*.*\" intext:\"Log in\" -wiki -forum -forums -questions intext:\"Cookies must be enabled\"\nRewriteCond %{HTTP_USER_AGENT} ^.*(AdsBot-Google|ia_archiver|Scooter|Ask.Jeeves|Baiduspider|Exabot|FAST.Enterprise.Crawler|FAST-WebCrawler|www\\.neomo\\.de|Gigabot|Mediapartners-Google|Google.Desktop|Feedfetcher-Google|Googlebot|heise-IT-Markt-Crawler|heritrix|ibm.com\\cs/crawler|ICCrawler|ichiro|MJ12bot|MetagerBot|msnbot-NewsBlogs|msnbot|msnbot-media|NG-Search|lucene.apache.org|NutchCVS|OmniExplorer_Bot|online.link.validator|psbot0|Seekbot|Sensis.Web.Crawler|SEO.search.Crawler|Seoma.\\[SEO.Crawler\\]|SEOsearch|Snappy|www.urltrends.com|www.tkl.iis.u-tokyo.ac.jp/~crawler|SynooBot|<EMAIL>|TurnitinBot|voyager|W3.SiteSearch.Crawler|W3C-checklink|W3C_Validator|www.WISEnutbot.com|yacybot|Yahoo-MMCrawler|Yahoo\\!.DE.Slurp|Yahoo\\!.Slurp|YahooSeeker).* [NC]\nRewriteRule .* - [F]\n```\n#### 1.43 数百のカラムがあるテーブルの構造を表示できないのはなぜですか？[¶](#why-can-t-i-display-the-structure-of-my-table-containing-hundreds-of-columns)\n\nPHP の `memory_limit` が小さすぎるからです。 `php.ini` で調整してください。\n\n#### 1.44 phpMyAdmin のディスク上のインストールサイズを減らすにはどうすればいいですか？[¶](#how-can-i-reduce-the-installed-size-of-phpmyadmin-on-disk)\n\n一部のユーザから、 phpMyAdmin のインストールサイズを縮小する要求があります。これは推奨できず、不足している機能について混乱を招く可能性がありますが、実行することはできます。削除すると安全に機能を削減できるファイルと対応する機能の一覧は次の通りです。\n\n* `./locale/` フォルダ、または、使用されていないサブフォルダ (インタフェースの翻訳)\n* Any unused themes in `./public/themes/` except the default theme pmahomme.\n* `./libraries/language_stats.inc.php` (翻訳統計)\n* `./doc/` (ドキュメント)\n* `./setup/` (セットアップスクリプト)\n* `./examples/` (構成例)\n* `./sql/` (拡張機能を設定するための SQL スクリプト)\n* `./js/src/` (./js/dist/ を再ビルドするためのソースファイル)\n* ‐`./js/global.d.ts` JS 型宣言ファイル\n* rm -rv vendor/tecnickcom/tcpdf && composer dump-autoload --no-interaction --optimize --dev を実行してください (PDF へのエクスポート)\n* rm -rv vendor/williamdes/mariadb-mysql-kbs && composer dump-autoload --no-interaction --optimize --dev を実行してください。 (MariaDB および MySQL のドキュメントへの外部リンク)\n* rm -rv vendor/code-lts/u2f-php-server && composer dump-autoload --no-interaction --optimize --dev を実行してください。 (U2F 二要素認証)\n* rm -rv vendor/pragmarx/* && composer dump-autoload --no-interaction --optimize --dev を実行してください (2FA 二要素認証)\n* rm -rv vendor/bacon/bacon-qr-code && composer dump-autoload --no-interaction --optimize --dev を実行してください (QR コード生成による 2FA 二要素認証)\n\n#### 1.45 ログインしようとすると、 caching_sha2_password が不明な認証方法であることに関するエラーメッセージが表示されます[¶](#i-get-an-error-message-about-unknown-authentication-method-caching-sha2-password-when-trying-to-log-in)\n\nMySQL バージョン 8 以降を使用してログインすると、次のようなエラーメッセージが表示される場合があります。\n\n> mysqli_real_connect(): The server requested authentication method unknown to the client [caching_sha2_password]\n> mysqli_real_connect(): (HY000/2054): The server requested authentication method unknown to the client\nこのエラーは、 PHP と MySQL 間のバージョン互換性の問題が原因です。 MySQL プロジェクトは新しい認証方法を導入しました (私たちのテストによれば、バージョン 8.0.11 から始まりました) が、 PHP にはその認証方法を使用する機能が含まれていませんでした。 PHPは、これが PHP バージョン 7.4 で修正されたことを報告しています。\n\nこれに遭遇したユーザは、 PHP インストールをアップグレードすることをお勧めしますが、回避策があります。次のようなコマンドで、 MySQL ユーザアカウントが古い認証を使用するように設定することができます。\n```\nALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'PASSWORD';\n```\n参考\n\n<<https://github.com/phpmyadmin/phpmyadmin/issues/14220>>、 <<https://stackoverflow.com/questions/49948350/phpmyadmin-on-mysql-8-0>>、 <<https://bugs.php.net/bug.php?id=76243>### 設定[¶](#configuration)\n\n#### 2.1 \"Warning: Cannot add header information - headers already sent by ...\" というエラーメッセージが表示されます。何が問題なのですか？[¶](#the-error-message-warning-cannot-add-header-information-headers-already-sent-by-is-displayed-what-s-the-problem)\n\n`config.inc.php` ファイルを修正して、先頭の `<?php` タグの前にも末尾の `?>` タグの後にも何もない (すなわち、改行、スペース、文字などがない) ようにしてください。\n\n#### 2.2 phpMyAdmin が MySQL に接続できません。何が悪いのでしょうか？[¶](#phpmyadmin-can-t-connect-to-mysql-what-s-wrong)\n\nPHP のセットアップに問題があるか、ユーザ名／パスワードが間違っているかのどちらかです。 mysql_connect を使う小さなスクリプトを書いて、動くかどうか確かめてみてください。動かないようなら、PHP をコンパイルするときに MySQL の対応を組み込んでいなかったのかもしれません。\n\n#### 2.3 \"Warning: MySQL Connection Failed: Can't connect to local MySQL server through socket '/tmp/mysql.sock' (111) ...\" というエラーメッセージが表示されます。どうすればよいのでしょうか？[¶](#the-error-message-warning-mysql-connection-failed-can-t-connect-to-local-mysql-server-through-socket-tmp-mysql-sock-111-is-displayed-what-can-i-do)\n\nエラーメッセージは Error #2002 - The server is not responding (or the local MySQL server's socket is not correctly configured) となることもあります。\n\nまず、 MySQL で使用されているソケットを特定する必要があります。これを行うには、サーバに接続し、 MySQL の bin ディレクトリに移動します。このディレクトリには、 *mysqladmin* という名前のファイルがあります。 `./mysqladmin variables` と入力すると、 MySQL サーバに関する一連の情報が得られ、その中にソケット (例えば */tmp/mysql.sock*) が含まれています。 ISP に接続情報を要求することもできます。自分自身でホスティングしている場合は、コマンドラインクライアント 'mysql' から接続し、 'status' と入力すると、接続タイプとソケットまたはポート番号が取得できます。\n\n次に、このソケットを使用するように PHP に指示する必要があります。これを `php.ini` 内で行うとすべての PHP が対象となり、 `config.inc.php` 内で行うと phpMyAdmin に対してのみ実行できます。例えば、 [`$cfg['Servers'][$i]['socket']`](index.html#cfg_Servers_socket) です。また、このファイルのパーミッションがウェブサーバで読み取り可能であることを確認してください。\n\n私の RedHat-Box では、MySQL のソケットは */var/lib/mysql/mysql.sock* です。 `php.ini` に次のような行がありますから\n```\nmysql.default_socket = /tmp/mysql.sock\n```\nこれを次のように変更してください\n```\nmysql.default_socket = /var/lib/mysql/mysql.sock\n```\nそれから apache を再起動すれば動くはずです。\n\n[MySQL ドキュメントの対応する部分](https://dev.mysql.com/doc/refman/5.7/ja/can-not-connect-to-server.html) も読んでください。\n\n#### 2.4 phpMyAdmin を実行しようとしているのですが、ブラウザに何も表示されません。どうすればよいのでしょうか？[¶](#nothing-is-displayed-by-my-browser-when-i-try-to-run-phpmyadmin-what-can-i-do)\n\nphpMyAdmin の設定ファイルで [`$cfg['OBGzip']`](index.html#cfg_OBGzip) の設定項目を `false` に設定してみてください。これが役立つかもしれません。また、PHP のバージョン番号を確かめてください。 \"b\" または \"alpha\" という文字が含まれている場合はテスト版の PHP が稼動しているということです。これはあまりよいことではありませんので、テスト版でないものにアップグレードしてください。\n\n#### 2.5 行を挿入や削除をしようとしたり、データベースやテーブルを削除したりしようとするたびに 404 (ページが見つかりません) エラーが表示されます。また、 HTTP またはクッキー認証をしているときはログインし直すように求められます。何が悪いのでしょうか？[¶](#each-time-i-want-to-insert-or-change-a-row-or-drop-a-database-or-a-table-an-error-404-page-not-found-is-displayed-or-with-http-or-cookie-authentication-i-m-asked-to-log-in-again-what-s-wrong)\n\nウェブサーバの設定から、 PHP_SELF または REQUEST_URI 変数が正しく設定されているか確認してみてください。\n\nphpMyAdmin をリバースプロキシ越しに実行している場合は、設定に合うように phpMyAdmin 設定ファイルの [`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri) 設定項目を設定してください。\n\n#### 2.6 localhost にポート転送しているホストの MySQL サーバにアクセスしようとすると、 \"Access denied for user: ['root@localhost](mailto:'root%40localhost)' (Using password: YES)\" というエラーが出ます。[¶](#i-get-an-access-denied-for-user-root-localhost-using-password-yes-error-when-trying-to-access-a-mysql-server-on-a-host-which-is-port-forwarded-for-my-localhost)\n\nポート転送を介して別のホストにリダイレクトするローカルホスト上のポートを使用している場合、 MySQL は期待どおりにローカルホストを解決できません。 <NAME> は「解決策は次のとおりです。ホストが \"localhost\" の場合 MySQLは (コマンドラインツール **mysql** も) 常にソケット接続を使用して処理を高速化しようとします。そして、それはポート転送を備えたこの構成では機能しません。ホスト名として \"127.0.0.1\" を入力すると、すべてが正しくなり、 MySQL はその [TCP](index.html#term-tcp) 接続を使用します。」と説明しています。\n\n#### 2.7 テーマの使い方と作り方[¶](#using-and-creating-themes)\n\n[カスタムテーマ](index.html#themes) を参照してください。\n\n#### 2.8 \"Missing parameters\" というエラーが出ます。どうしたらよいのでしょうか？[¶](#i-get-missing-parameters-errors-what-can-i-do)\n\n確認すべき点がいくつかあります。\n\n* `config.inc.php` の中で、 [`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri) の設定項目を空欄にしてみてください。 [4.7 認証ウインドウが複数回表示されます。なぜでしょうか？](#faq4-7) も参照してください。\n* インストールされている PHP が壊れているか、Zend Optimizer を更新する必要があるかもしれません。<<https://bugs.php.net/bug.php?id=31134>> を参照してください。\n* Hardened PHP を使っていて、ini の設定項目 `varfilter.max_request_variables` がデフォルト値 (200) などの低い値になっている場合、テーブルのカラム数が多いとこのエラーが出ることがあります。適切な値に調整してください (ヒントをくれた Klaus Dorninger に感謝)。\n* `php.ini` の設定項目 `arg_separator.input` の値が \";\" であった場合はこのエラーになります。 \"&;\" に置き換えてください。\n* If you are using [Suhosin](https://suhosin5.suhosin.org/stories/index.html), you might want to increase [request limits](https://suhosin5.suhosin.org/stories/faq.html).\n* `php.ini` の設定項目 `session.save_path` で指定したディレクトリが、存在しないか読み取り専用になっている (これは [PHP インストーラのバグ](https://bugs.php.net/bug.php?id=39842) によって起こります)。\n\n#### 2.9 アップロード進行状況バーが見えるようにする[¶](#seeing-an-upload-progress-bar)\n\nアップロード中に進行状況バーを表示できるようにするには、サーバが [uploadprogress](https://pecl.php.net/package/uploadprogress) 拡張に対応している、もしくは PHP 5.4.0 以降である必要があります。それに加えて、PHP において JSON 拡張モジュールが有効になっていなければなりません。\n\nPHP 5.4.0以降を使用している場合は、 `php.ini` で `session.upload_progress.enabled` を `1` に設定する必要があります。ただし、 phpMyAdmin バージョン 4.0.4 以降、問題のある動作のため、セッションベースのアップロードの進捗状況は一時的に非アクティブ化されています。\n\n#### 2.10 ランダムなバイト列を生成するには[¶](#how-to-generate-a-string-of-random-bytes)\n\n暗号に適したランダムなバイト列を生成する方法の1つに、 [PHP](index.html#term-php) の random_bytes<https://www.php.net/random_bytes> 関数を使用する方法があります。この関数はバイナリ文字列を返すので、返す値をコピーできるようにする前に印刷可能な形式に変換しておく必要があります。\n\n例えば、 [`$cfg['blowfish_secret']`](index.html#cfg_blowfish_secret) 設定ディレクティブでは、32バイト長の文字列を要求します。次のコマンドを使用すると、この文字列の16進数表現を生成することができます。\n```\nphp -r 'echo bin2hex(random_bytes(32)) . PHP_EOL;'\n```\n上記の例では、次のようなものが出力されます。\n```\nf16ce59f45714194371b48fe362072dc3b019da7861558cd4ad29e4d6fb13851\n```\nそして、この16進数の値を設定ファイルで使用することができます。\n```\n$cfg['blowfish_secret'] = sodium_hex2bin('f16ce59f45714194371b48fe362072dc3b019da7861558cd4ad29e4d6fb13851');\n```\nここでは、[`sodium_hex2bin<https://www.php.net/sodium_hex2bin>`_](#system-message-1) 関数を使用して、16進数の値をバイナリ形式へ戻しています。\n\n### 既知の制限[¶](#known-limitations)\n\n#### 3.1 HTTP 認証を使っているときにログアウトすると、同じユーザ名では再ログインできません。[¶](#when-using-http-authentication-a-user-who-logged-out-can-not-log-in-again-in-with-the-same-nick)\n\nこれは phpMyAdmin が利用している認証のメカニズム (プロトコル) による制限です。この問題を回避するには、開いているブラウザのウィンドウを一度すべて閉じてから、phpMyAdmin に戻ってください。再ログインできるようになっているはずです。\n\n#### 3.2 大きなテーブルを圧縮モードでダンプするとメモリ制限のエラーや時間制限のエラーが出ます。[¶](#when-dumping-a-large-table-in-compressed-mode-i-get-a-memory-limit-error-or-a-time-limit-error)\n\n圧縮されたダンプがメモリ上に生成されるために、PHP のメモリ制限にひっかかるのが原因です。 gzip/bzip2 エクスポートについてはバージョン 2.5.4 以降での [`$cfg['CompressOnFly']`](index.html#cfg_CompressOnFly) (逐次圧縮) を使うとこの問題を克服できます (デフォルトで有効)。 zip エクスポートではこの方法が行えませんので、大きめのダンプの zip ファイルが必要な場合、別の方法をとる必要があります。\n\n#### 3.3 InnoDB テーブルでテーブルやカラムの名称を変更すると外部キーのリレーションが切れます。[¶](#with-innodb-tables-i-lose-foreign-key-relationships-when-i-rename-a-table-or-a-column)\n\nこれは InnoDB のバグです。 <<http://bugs.mysql.com/bug.php?id=21704>> を参照してください。\n\n#### 3.4 MySQL サーバの配布ファイルにバンドルされてきた mysqldump ツールで作成したダンプをインポートできません。[¶](#i-am-unable-to-import-dumps-i-created-with-the-mysqldump-tool-bundled-with-the-mysql-server-distribution)\n\nこの問題は、古いバージョンの `mysqldump` が次のような無効なコメントを作成するためです。\n```\n-- MySQL dump 8.22\n--\n-- Host: localhost Database: database\n---\n-- Server version 3.23.54\n```\nこのコードで無効なのはハイフン - を並べた区切り線の部分です。この区切り線は、mysqldump で作成したダンプにはかならず一度登場します。このダンプを利用するには、ダンプを修正して MySQL で有効な形にする必要があります。つまり、 `-- ---` のように先頭 2 つのハイフンのあとに空白を入れるか、 `#---` のように行の先頭に # を付け加える必要があるということです。\n\n#### 3.5 入れ子になったフォルダを使用すると、複数の階層が間違った方法で表示されます。[¶](#when-using-nested-folders-multiple-hierarchies-are-displayed-in-a-wrong-manner)\n\n区切り文字列を文字なしで複数回使用したり、テーブル名の最初や最後に使用したりしないでください。必要な場合は、別の TableSeparator を使用するか、その機能を無効にすることを検討してください。\n\n参考\n\n[`$cfg['NavigationTreeTableSeparator']`](index.html#cfg_NavigationTreeTableSeparator)\n\n#### 3.6 (取り下げ)。[¶](#withdrawn-7)\n\n#### 3.7 カラム数の多い（100 以上）テーブルがあるのですが、このテーブルを表示しようとすると \"Warning: unable to parse url\" というエラーがたくさん出ます。どうすれば直るのでしょうか？[¶](#i-have-table-with-many-100-columns-and-when-i-try-to-browse-table-i-get-series-of-errors-like-warning-unable-to-parse-url-how-can-this-be-fixed)\n\nテーブルに [主キー](index.html#term-primary-key) も [ユニークキー](index.html#term-unique-key) もない場合は、行を特定するために長い式を使う必要があります。これが parse_url 関数で問題を起こしています。解決策は、 [主キー](index.html#term-primary-key) や [ユニークキー](index.html#term-unique-key) を作成することです。\n\n#### 3.8 カラムに MIME 変換を適用したら、 (クリック可能な) HTML フォームが使えません！[¶](#i-cannot-use-clickable-html-forms-in-columns-where-i-put-a-mime-transformation-onto)\n\nphpMyAdmin が結果を表示するテーブルは (複数行削除チェックボックス用の) フォームコンテナに囲まれているため、その中に入れ子にするフォームを置くことはできません。ただし、 tbl_row_delete.php を対象とした親フォームのコンテナはそのまま残して、その中に独自の入力要素のみ加えるようにすれば、どんなフォームでもテーブルの中に入れることができます。送信用の input フィールドをカスタマイズすると、フォームのデータは表示しているページに再送されますので、変換機能のなかで $HTTP_POST_VARS を有効にしてください。 変換機能の効果的な使い方のチュートリアルについては、 phpMyAdmin の公式ホームページの [Link の部分](https://www.phpmyadmin.net/docs/) をご覧ください。\n\n#### 3.9 MySQL サーバに \"--sql_mode=ANSI\" を適用するとエラーメッセージが出ます。[¶](#i-get-error-messages-when-using-sql-mode-ansi-for-the-mysql-server)\n\nMySQL が ANSI 互換モードで実行されているときは、 [SQL](index.html#term-sql) の組み立て方に大きく変わる部分があります (<<https://dev.mysql.com/doc/refman/5.7/ja/sql-mode.html>> を参照)。とりわけ重要なのが、引用符 (\") が識別子を囲む文字として解釈され、文字列を囲む文字とはみなされなくなることです。そのため、 phpMyAdmin 内部の多くの操作が無効な [SQL](index.html#term-sql) 文になるのです。この動作には回避策がありません。この問題についての最新情報は [issue #7383](https://github.com/phpmyadmin/phpmyadmin/issues/7383) に投稿されます。\n\n#### 3.10 主キーがなく、同じ表記がある場合。 SELECT の結果、同じ値を持つカラムが複数表示された場合 (例えば `SELECT lastname from employees where firstname like 'A%'` を実行して \"Smith\" という値が 2 つ表示された場合)、編集をクリックしても意図した通りの行を編集しているのか分かりません。[¶](#homonyms-and-no-primary-key-when-the-results-of-a-select-display-more-that-one-column-with-the-same-value-for-example-select-lastname-from-employees-where-firstname-like-a-and-two-smith-values-are-displayed-if-i-click-edit-i-cannot-be-sure-that-i-am-editing-the-intended-row)\n\nテーブルに [主キー](index.html#term-primary-key) を設定するようにしてください。そうすると phpMyAdmin は編集や削除のリンクに主キーを使用するようになります。\n\n#### 3.11 InnoDB のテーブルの行数が正しくありません。[¶](#the-number-of-rows-for-innodb-tables-is-not-correct)\n\nphpMyAdmin は簡潔な方法で行数を取得していますが、この方法では InnoDB テーブルの場合に概数しか返ってきません。この結果を修正する方法は [`$cfg['MaxExactCount']`](index.html#cfg_MaxExactCount) を参照してください。ただし、これは性能に深刻な影響を与える可能性があります。もっとも、概算の行数をクリックすると、正確な行数に簡単に置き換えることができます。これは、最下部に表示されている行数の合計値をクリックすれば、すべてのテーブルを一度に更新できます。\n\n参考\n\n[`$cfg['MaxExactCount']`](index.html#cfg_MaxExactCount)\n\n#### 3.12 (取り下げ)。[¶](#withdrawn-8)\n\n#### 3.13 `USE` の後にハイフンを含むデータベース名を入力するとエラーが出ます。[¶](#i-get-an-error-when-entering-use-followed-by-a-db-name-containing-an-hyphen)\n\n我々が MySQL 5.1.49 で行ったテストでは、API がそのような構文の USE コマンドを認めていないことを確認しています。\n\n#### 3.14 SELECT 権限を持っていないカラムが 1 つでもあると、テーブルを参照することができません。[¶](#i-am-not-able-to-browse-a-table-when-i-don-t-have-the-right-to-select-one-of-the-columns)\n\nこれは初期の頃から phpMyAdmin の制限として知られており、将来的に解決される見込みはありません。\n\n#### 3.15 (取り下げ)。[¶](#withdrawn-9)\n\n#### 3.16 (取り下げ)。[¶](#withdrawn-10)\n\n#### 3.17 (取り下げ)。[¶](#withdrawn-11)\n\n#### 3.18 複数のテーブルを含む CSV ファイルをインポートすると、単一のテーブルにまとめられてしまいます。[¶](#when-i-import-a-csv-file-that-contains-multiple-tables-they-are-lumped-together-into-a-single-table)\n\n[CSV](index.html#term-csv) 形式の中で複数のテーブルを区分する確実な方法はありません。当分の間は、複数のテーブルを含む [CSV](index.html#term-csv) ファイルを分割する必要があります。\n\n#### 3.19 ファイルをインポートすると、 phpMyAdmin は int、 decimal、 varchar 型のみを使用してデータ構造を定めてしまいました。[¶](#when-i-import-a-file-and-have-phpmyadmin-determine-the-appropriate-data-structure-it-only-uses-int-decimal-and-varchar-types)\n\n現在、インポート時の型の検出システムは、これらの MySQL 型しかカラムに割り当てません。将来的にはさらに追加される可能性がありますが、当面はインポート後に必要に応じて構造を編集する必要があります。また、 phpMyAdmin は、特定のカラムにある最大のサイズの要素を、適切な型のカラムサイズとして使用することに注意してください。その列に大きな要素を追加することがわかっている場合は、それに応じてカラムのサイズを手動で調整する必要があります。これは効率のために行われます。\n\n#### 3.20 アップグレード後、一部のブックマークがなくなったり、内容が表示されなかったりします。[¶](#after-upgrading-some-bookmarks-are-gone-or-their-content-cannot-be-shown)\n\nある時点で、ブックマークの内容の保存に使用される文字セットが変更されました。新しい phpMyAdmin のバージョンでブックマークを再作成することをお勧めします。\n\n#### 3.21 á などの Unicode 文字を含むユーザ名でログインすることができません。[¶](#i-am-unable-to-log-in-with-a-username-containing-unicode-characters-such-as-a)\n\nこれは、 MySQL サーバがデフォルトの文字セットとして UTF-8 を使用するように設定されていない場合に発生する可能性があります。これは、 PHP と MySQL サーバの相互作用の制限です。 PHP が認証前に文字セットを設定する方法はありません。\n\n参考\n\n[phpMyAdmin issue 12232](https://github.com/phpmyadmin/phpmyadmin/issues/12232), [MySQL ドキュメントのノート](https://www.php.net/manual/ja/mysqli.real-connect.php#refsect1-mysqli.real-connect-notes)\n\n### ISP やマルチユーザのインストール[¶](#isps-multi-user-installations)\n\n#### 4.1 当方は ISP です。 phpMyAdmin のセントラルコピーを一つだけセットアップするようにできますか？それとも顧客ごとにインストールする必要がありますか？[¶](#i-m-an-isp-can-i-setup-one-central-copy-of-phpmyadmin-or-do-i-need-to-install-it-for-each-customer)\n\nバージョン 2.0.3 以降、phpMyAdmin はユーザ全員が使えるセントラルコピーをセットアップできるようになりました。この機能の開発は、 NetCologne GmbH 社がスポンサーになってくださいました。このためには MySQL のユーザ管理、および phpMyAdmin の [HTTP](index.html#term-http) またはクッキー認証を正しくセットアップする必要があります。\n\n参考\n\n[認証モードの使い方](index.html#authentication-modes)\n\n#### 4.2 phpMyAdmin を悪意のあるアクセスから守るようにするお勧めの方法はありますか？[¶](#what-s-the-preferred-way-of-making-phpmyadmin-secure-against-evil-access)\n\nこれはシステムによりますが、外部の人からアクセスできないサーバで実行している場合は、ウェブサーバ にバンドルされているディレクトリ保護機能を使えば十分です (例えば、Apache なら [.htaccess](index.html#term-htaccess) ファイルを利用できます)。外部の人がサーバに telnet でアクセスできる場合は、 phpMyAdmin の [HTTP](index.html#term-http) またはクッキー認証機能を使用してください。\n\nお勧めの方法:\n\n* `config.inc.php` ファイルは `chmod 660` にしておいてください。\n* phpMyAdmin ファイルはすべて chown -R phpmy.apache を実行しておいてください。ここで phpmy にはあなただけがパスワードを知っているユーザ、 apache には Apache を実行しているグループ名が入ります。\n* PHP およびウェブブラウザのセキュリティ推奨事項に従ってください。\n\n#### 4.3 */lang* や */libraries* の中のファイルをインクルードできないというエラーが出ます。[¶](#i-get-errors-about-not-being-able-to-include-a-file-in-lang-or-in-libraries)\n\n`php.ini` を確認するか、システム管理者に確認を依頼するかしてください。 `include_path` には \".\" を含める必要があり、 `open_basedir` を使用する場合は、 phpMyAdmin の通常の操作を許可するためには \".\" および \"./lang\" を含める必要があります。\n\n#### 4.4 HTTP 認証を使用すると必ず「Access denied (アクセスは拒否されました)」になります。[¶](#phpmyadmin-always-gives-access-denied-when-using-http-authentication)\n\nいくつかの理由が考えられます。\n\n* [`$cfg['Servers'][$i]['controluser']`](index.html#cfg_Servers_controluser) や [`$cfg['Servers'][$i]['controlpass']`](index.html#cfg_Servers_controlpass) が間違っている。\n* ログインダイアログで指定したユーザ名／パスワードが無効である。\n* phpMyAdmin ディレクトリに別のセキュリティ機構がセットアップされている (例えば [.htaccess](index.html#term-htaccess) ファイル)。これは phpMyAdmin の認証の邪魔になりますので除去してください。\n\n#### 4.5 ユーザに独自のデータベースの作成を許可することはできますか？[¶](#is-it-possible-to-let-users-create-their-own-databases)\n\nバージョン 2.2.5 以降、ユーザ管理ページでユーザのデータベース名にワイルドカードを入れたり (例えば「joe%」)、権限を与えることができるようになりました。例えば、 `SELECT、INSERT、UPDATE、DELETE、CREATE、DROP、INDEX、ALTER` 権限を与えれば、ユーザが自分のデータベースを作成／管理できるようになります。\n\n#### 4.6 どうすればホストベースの認証の追加指定を利用できますか？[¶](#how-can-i-use-the-host-based-authentication-additions)\n\n古い [.htaccess](index.html#term-htaccess) ファイルに既存のルールがある場合は、それを持ってきて `'deny'`/`'allow'` と `'from'` の文字列の間にユーザ名を加えてください。ユーザ名にワイルドカード `'%'` が使えるようになっている場合はとても便利です。それが済んだら、あとは更新した行を [`$cfg['Servers'][$i]['AllowDeny']['rules']`](index.html#cfg_Servers_AllowDeny_rules) 配列に加えるだけです。\n\nできあいのサンプルが欲しい場合は、下記をお試しください。これは ’root' ユーザがプライベートネットワークの [IP](index.html#term-ip) ブロックに含まれないネットワークからログインするのを防ぐものです。\n```\n//block root from logging in except from the private networks\n$cfg['Servers'][$i]['AllowDeny']['order'] = 'deny,allow';\n$cfg['Servers'][$i]['AllowDeny']['rules'] = [\n 'deny root from all',\n 'allow root from localhost',\n 'allow root from 10.0.0.0/8',\n 'allow root from 192.168.0.0/16',\n 'allow root from 172.16.0.0/12',\n];\n```\n#### 4.7 認証ウインドウが複数回表示されます。なぜでしょうか？[¶](#authentication-window-is-displayed-more-than-once-why)\n\nこれは phpMyAdmin を起動するために使用した [URL](index.html#term-url) が、 [`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri) に設定されている URL と異なるためです。例えば、 \"www\" が抜けていたり、設定ファイルではドメイン名で登録してあるのに [IP](index.html#term-ip) アドレスで入力した場合などです。\n\n#### 4.8 phpMyAdmin を起動する URL 使うことができるパラメータはどれですか？[¶](#which-parameters-can-i-use-in-the-url-that-starts-phpmyadmin)\n\nphpMyAdmin の起動時には、 `db` と `server` の引数を使用することができます。最後のものにはホストのインデックス番号 (設定ファイルの `$i`) または設定ファイル内にあるホスト名のどちらかを指定することができます。\n\n例えば、特定のデータベースに直接ジャンプするには、 URL を `https://example.com/phpmyadmin/?db=sakila` のように構築することができます。\n\n参考\n\n[1.34 データベースやテーブルのページに直接アクセスできますか？](#faq1-34)\n\nバージョン 4.9.0 で変更: `pma_username` と `pma_password` 引数を使用した対応は phpMyAdmin 4.9.0 で削除されました ([PMASA-2019-4](https://www.phpmyadmin.net/security/PMASA-2019-4/) を参照)。\n\n### ブラウザまたはクライアント OS[¶](#browsers-or-client-os)\n\n#### 5.1 カラム数が 14 を超えるテーブルを作ろうとすると、メモリ不足のエラーが出てコントロールが動作しなくなります。[¶](#i-get-an-out-of-memory-error-and-my-controls-are-non-functional-when-trying-to-create-a-table-with-more-than-14-columns)\n\nこの問題は Win98/98SE 環境下でしか再現できませんでした。 WinNT4 や Win2K 環境下でテストすると 60 を超えるカラムでも簡単に作成できました。回避策はカラム数を減らして作成し、それからテーブルのプロパティに戻って、残りのカラムを追加することです。\n\n#### 5.2 Xitami 2.5b4 を使うと phpMyAdmin がフォームのフィールドを処理しなくなります。[¶](#with-xitami-2-5b4-phpmyadmin-won-t-process-form-fields)\n\nこれは phpMyAdmin の問題ではなく、Xitami の既知のバグです。フォームを使うスクリプトやウェブサイトすべてで起こる問題です。 Xitami サーバをアップグレードまたはダウングレードしてください。\n\n#### 5.3 Konqueror でうまくテーブルをダンプできません (phpMyAdmin 2.2.2)。[¶](#i-have-problems-dumping-tables-with-konqueror-phpmyadmin-2-2-2)\n\nKonqueror 2.1.1 の場合、無圧縮、 zip、 gzip のダンプは動作します。ただし、ダンプで提案されるファイル名は常に、 'tbl_dump.php' となります。 bzip2 のダンプは動作しないようです。 Konqueror 2.2.1 の場合、無圧縮のダンプは動作します。 zip ダンプはユーザの一時ディレクトリに置かれますので、 Konqueror を閉じる前に移動しないと消滅します。 gzip ダンプはエラーメッセージが出ます。 Konqueror 2.2.2 ではテストが必要です。\n\n#### 5.4 Internet Explorer がクッキーを保存しないため、クッキー認証モードが利用できません。[¶](#i-can-t-use-the-cookie-authentication-mode-because-internet-explorer-never-stores-the-cookies)\n\nマイクロソフトの Internet Explorer は、クッキーに関しては本当にバグが多いようです。少なくともバージョン 6 まではそうです。\n\n#### 5.5 (取り下げ)。[¶](#withdrawn-12)\n\n#### 5.6 (取り下げ)。[¶](#withdrawn-13)\n\n#### 5.7 ブラウザで再読み込み (リロード) すると、ようこそページに戻ってしまいます。[¶](#i-refresh-reload-my-browser-and-come-back-to-the-welcome-page)\n\nブラウザによっては再読み込みしたいフレームのなかで右クリックできますので、右フレームのなかで右クリックして再読み込みしてください。\n\n#### 5.8 Mozilla 0.9.7 では、クエリボックスで修正したクエリをうまく送信できません。[¶](#with-mozilla-0-9-7-i-have-problems-sending-a-query-modified-in-the-query-box)\n\nMozilla のバグのようです。0.9.6 では OK でした。Mozilla の将来のバージョンでも注意していきます。\n\n#### 5.9 Mozilla の 0.9.? 〜 1.0 と Netscape 7.0-PR1 では SQL クエリの編集領域で空白を入力できません。ページがスクロールダウンしてしまいます。[¶](#with-mozilla-0-9-to-1-0-and-netscape-7-0-pr1-i-can-t-type-a-whitespace-in-the-sql-query-edit-area-the-page-scrolls-down)\n\nこれは Mozilla のバグです (<a href=\"<http://bugzilla.mozilla.org/>\">BugZilla</a> のバグ #26882 を参照)。\n\n#### 5.10 (取り下げ)。[¶](#withdrawn-14)\n\n#### 5.11 ドイツ語のウムラウトなどの拡張 ASCII 文字が正しく表示されません。[¶](#extended-ascii-characters-like-german-umlauts-are-displayed-wrong)\n\nブラウザの文字セットが phpMyAdmin のスタートページで選択した言語ファイルの文字セットと合っているか確認してください。また、最近のブラウザならたいてい対応している自動検出モードを試してみる手もあります。\n\n#### 5.12 Mac OS X：Safari ブラウザでは特殊文字が「?」になってしまいます。[¶](#mac-os-x-safari-browser-changes-special-characters-to)\n\nこの問題を報告してくれた [macOS](index.html#term-macos) ユーザによると、Chimera、Netscape、Mozilla ではこの問題は起こらないそうです。\n\n#### 5.13 (取り下げ)[¶](#withdrawn-15)\n\n#### 5.14 (取り下げ)[¶](#withdrawn-16)\n\n#### 5.15 (取り下げ)[¶](#withdrawn-17)\n\n#### 5.16 Internet Explorer で「アクセスが拒否されました（Access is denied）」という JavaScript のエラーが出ます。あるいは、 Windows で phpMyAdmin を実行できません。[¶](#with-internet-explorer-i-get-access-is-denied-javascript-errors-or-i-cannot-make-phpmyadmin-work-under-windows)\n\n以下の点を確認してください。\n\n* `config.inc.php` の [`$cfg['PmaAbsoluteUri']`](index.html#cfg_PmaAbsoluteUri) の設定を [IP](index.html#term-ip) アドレスに設定して、ドメイン名を含む [URL](index.html#term-url) で phpMyAdmin を起動しているか、またはその逆の状況になっているかもしれません。\n* IE や Microsoft Security Center のセキュリティ設定が高すぎるためにスクリプトの実行をブロックされている。\n* Windows Firewall が Apache と MySQL をブロックしていること。 \"in\" と \"out\" の両方で [HTTP](index.html#term-http) のポート (80 または 443) と MySQL のポート (通常は 3306) が開いている必要があります。\n\n#### 5.17 Firefox でデータ行を削除したりデータベースを削除したりできません。[¶](#with-firefox-i-cannot-delete-rows-of-data-or-drop-a-database)\n\n多くのユーザが、Firefox にインストールしたタブブラウザ拡張が問題を起こしていることを確認しています。\n\n#### 5.18 (取り下げ)[¶](#withdrawn-18)\n\n#### 5.19 ブラウザで JavaScript エラーが発生します。[¶](#i-get-javascript-errors-in-my-browser)\n\nブラウザの拡張機能をいくつか組み合わせた場合の問題だと報告されています。トラブルを解決するには、すべての拡張機能を無効にしてブラウザのキャッシュをクリアし、問題が発生しなくなるかを確認してください。\n\n#### 5.20 Content Security Policy 違反のエラーが出ます。[¶](#i-get-errors-about-violating-content-security-policy)\n\n次のようなエラーが発生した場合です。\n```\nRefused to apply inline style because it violates the following Content Security Policy directive\n```\nこれは通常、 *Content Security Policy* ヘッダを不正に書き換えるソフトウェアが原因で発生します。通常、これはそのようなエラーを引き起こしているアンチウイルスプロキシまたはブラウザアドオンによって引き起こされます。\n\nこれらのエラーが表示された場合は、ウイルス対策ソフトの HTTP プロキシを無効にするか、 *Content Security Policy* の書き換えを無効にしてみてください。それでも問題が解決しない場合は、ブラウザ拡張機能を無効にしてみてください。\n\nまたは、サーバの構成の問題である可能性もあります (ウェブサーバが *Content Security Policy* ヘッダを発行するように構成されている場合、 phpMyAdmin のヘッダをオーバーライドする可能性があります)。\n\n次のプログラムがこの種のエラーを引き起こすことが知られています。\n\n* カスペルスキーインターネットセキュリティ\n\n#### 5.21 テーブルを参照したり、 SQL クエリを実行したりすると、安全でない可能性のある操作に関するエラーが発生します。[¶](#i-get-errors-about-potentially-unsafe-operation-when-browsing-table-or-executing-sql-query)\n\n次のようなエラーが発生した場合です。\n```\nA potentially unsafe operation has been detected in your request to this site.\n```\nこれは通常、リクエストフィルタリングを行うウェブアプリケーションファイアウォールが原因で発生します。 SQL インジェクションを防止するためのものですが、 phpMyAdmin は SQL クエリを実行するように設計されたツールであるため、使用できなくなるものです。\n\nウェブアプリケーションファイアウォールの設定で phpMyAdmin のスクリプトを許可するか、 phpMyAdmin のパスに対して完全に無効にするかしてください。\n\n次のプログラムがこの種のエラーを引き起こすことが知られています。\n\n* Wordfence Web Application Firewall\n\n### phpMyAdmin の使用[¶](#using-phpmyadmin)\n\n#### 6.1 テーブルに新しい行が挿入できません。または、テーブルが作成できません。MySQL が SQL エラーを返します。[¶](#i-can-t-insert-new-rows-into-a-table-i-can-t-create-a-table-mysql-brings-up-a-sql-error)\n\n[SQL](index.html#term-sql) のエラーを注意深く調べてみてください。よく問題になるのが、カラムのデータ型の指定を間違ていることです。よくある間違いには次のようなものがあります。\n\n* `VARCHAR` を size 引数なしで使用している\n* `TEXT` または `BLOB` に size 引数をつけて使用している\n\nまた、MySQL マニュアルの文法の章を見て、文法が正しいか確認してください。\n\n#### 6.2 テーブルを作るときに２つのカラムにインデックスを設定したのですが、phpMyAdmin がその２つのカラムに１つしかインデックスを生成しません。[¶](#when-i-create-a-table-i-set-an-index-for-two-columns-and-phpmyadmin-generates-only-one-index-with-those-two-columns)\n\nこれは、複数カラムのインデックスの作り方です。インデックスを２つ作りたいときは、テーブルを作成するときに最初のインデックスを作り、保存してから、テーブルのプロパティを表示し、インデックスのリンクをクリックして次のインデックスを作るようにしてください。\n\n#### 6.3 テーブルに NULL 値を挿入するにはどうするのですか？[¶](#how-can-i-insert-a-null-value-into-my-table)\n\nバージョン 2.2.3 以降、 null にできるカラムにはそれぞれチェックボックスが用意されています。 2.2.3 より前は、カラムの値として引用符なしで \"null\" と入力する必要がありました。バージョン 2.5.5 以降では、本当の NULL 値を得るにはチェックボックスを使う必要があります。 \"NULL\" 入力すると、そのカラムには NULL 値ではなく、文字で NULL が入ります（これは PHP4 の動作です)。\n\n#### 6.4 データベースやテーブルのバックアップはどうするのですか？[¶](#how-can-i-backup-my-database-or-table)\n\nナビゲーションパネルでデータベース名またはテーブル名をクリックすると、プロパティが表示されます。次に、メニューの [エクスポート] をクリックすると、構造、データ、またはその両方をダンプすることができます。これにより、データベース/テーブルの再作成に使用できる標準の [SQL](index.html#term-sql) ステートメントが生成されます。 phpMyAdmin が結果のダンプを端末に送信できるように、 [ファイルとして保存] を選択する必要があります。 PHP の構成に応じて、ダンプを圧縮するオプションが表示されます。 [`$cfg['ExecTimeLimit']`](index.html#cfg_ExecTimeLimit) 構成変数も参照してください。このテーマに関する追加のヘルプについては、このドキュメントで「ダンプ」という単語を探してください。\n\n#### 6.5 どうすればダンプからデータベースやテーブルを復元 (アップロード) できますか？どうすれば \".sql\" ファイルを実行できますか？[¶](#how-can-i-restore-upload-my-database-or-table-using-a-dump-how-can-i-run-a-sql-file)\n\nナビゲーションパネルでデータベース名をクリックすると、プロパティが表示されます。右側のフレームのタブのリストから [インポート] を選択します (または、 phpMyAdmin のバージョンが 2.7.0 より前の場合は [[SQL](index.html#term-sql)])。 [テキストファイルの場所] の節で、ダンプファイル名へのパスを入力するか、 [参照] ボタンを使用します。次に、 [実行] をクリックします。バージョン 2.7.0 では、インポートエンジンが書き直されています。可能であれば、新しい機能を利用するためにアップグレードすることをお勧めします。このテーマに関する追加のヘルプについては、このドキュメントで「アップロード」という単語を探してください。\n\n注: 古いバージョンの MySQL からエクスポートされたダンプを新しいバージョンの MySQL にインポートする際にエラーが発生した場合は、 [6.41 古いバージョンの MySQL (5.7.6より前) からエクスポートされたダンプを新しいバージョンの MySQL (5.7.7 以降) にインポートしているときにインポートエラーが発生します。同じ古いバージョンにインポートすると正常に動作するのに？](#faq6-41) を確認してください。\n\n#### 6.6 どうすれば定型問い合わせの際にリレーションテーブルを使えるのでしょうか？[¶](#how-can-i-use-the-relation-table-in-query-by-example)\n\nこれは、 \"mydb\" データベースにあるテーブル persons, towns, countries の例です。 `pma__relation` テーブルがない場合は、構成の節の説明に従って作成してください。次に、サンプルテーブルを作成します。\n```\nCREATE TABLE REL_countries (\ncountry_code char(1) NOT NULL default '',\ndescription varchar(10) NOT NULL default '',\nPRIMARY KEY (country_code)\n) ENGINE=MyISAM;\n\nINSERT INTO REL_countries VALUES ('C', 'Canada');\n\nCREATE TABLE REL_persons (\nid tinyint(4) NOT NULL auto_increment,\nperson_name varchar(32) NOT NULL default '',\ntown_code varchar(5) default '0',\ncountry_code char(1) NOT NULL default '',\nPRIMARY KEY (id)\n) ENGINE=MyISAM;\n\nINSERT INTO REL_persons VALUES (11, 'Marc', 'S', 'C');\nINSERT INTO REL_persons VALUES (15, 'Paul', 'S', 'C');\n\nCREATE TABLE REL_towns (\ntown_code varchar(5) NOT NULL default '0',\ndescription varchar(30) NOT NULL default '',\nPRIMARY KEY (town_code)\n) ENGINE=MyISAM;\n\nINSERT INTO REL_towns VALUES ('S', 'Sherbrooke');\nINSERT INTO REL_towns VALUES ('M', 'Montréal');\n```\n適切なリンクと表示情報をセットアップするには、以下のようにします。\n\n* \"REL_persons\" テーブルの [構造] をクリックし、次に [リレーションビュー] をクリックする\n* \"town_code\" については、データベース、テーブル、カラムの各ドロップダウンでそれぞれ \"mydb\", \"REL_towns\", \"town_code\" を選択する\n* \"country_code\" については、データベース、テーブル、カラムの各ドロップダウンでそれぞれ \"mydb\", \"REL_countries\", \"country_code\" を選択する\n* \"REL_towns\" テーブルの [構造]、次に [リレーションビュー] をクリックする\n* [表示するカラムを選択 ] 欄で \"description\" を選択する\n* \"REL_countries\" テーブルについて直前の2つの手順を繰り返す\n\nそれから、以下のようにテストをします。\n\n* ナビゲーションパネルでデータベース名をクリックする\n* [クエリ] を選択する\n* persons, towns, countries の各テーブルを使用する\n* [クエリを更新する] をクリックする\n* カラムの行で persons.person_name を選択し、 [表示] チェックボックスをクリックする\n* 残り 2 つのカラムの towns.description と countries.descriptions についても同様にする\n* [クエリを更新する] をクリックすると、クエリボックスに正しく結合が生成されたことが分かる\n* [クエリを実行する] をクリックする\n\n#### 6.7 どうすれば [表示するカラム] 機能が利用できますか？[¶](#how-can-i-use-the-display-column-feature)\n\n前の例に引き続き、「構成」の章で説明されているように `pma__table_info` を作成した後、 persons テーブルを表示して、 town code または country code の上にマウスを移動します。 「列の表示」がドロップダウンの利用な可能な値を有効にするための追加機能については、 [6.21 編集／挿入モードで、外部のテーブルに基づいた利用可能なカラムの値の一覧を見るにはどうすればよいでしょうか？](#faq6-21) も参照してください。\n\n#### 6.8 データベースの PDF スキーマを作るにはどうするのですか？[¶](#how-can-i-produce-a-pdf-schema-of-my-database)\n\nまず、 \"relation\"、 \"table_coords\"、 \"pdf_pages\" という設定変数に値を入れる必要があります。\n\n* ナビゲーションパネルでデータベースを選択する。\n* 上部のナビゲーションバーで [デザイナ] を選択する。\n* 好きなようにテーブルを動かします。\n* 左のメニューから [スキーマのエクスポート] を選択してください。\n* エクスポートのモーダルが開きます。\n* エクスポートの種類を [PDF](index.html#term-pdf) に選択し、その他の設定を調整することができます。\n* フォームを送信すると、ファイルのダウンロードが始まります。\n\n参考\n\n[リレーション](index.html#relations)\n\n#### 6.9 phpMyAdmin がカラムのデータ型を変えてしまいます！[¶](#phpmyadmin-is-changing-the-type-of-one-of-my-columns)\n\nこれは MySQL が [暗黙のカラム指定の変更](https://dev.mysql.com/doc/refman/5.7/ja/silent-column-changes.html) を行うためです。\n\n#### 6.10 権限を作成するとき、データベース名にアンダースコアを入れるとどうなりますか？[¶](#when-creating-a-privilege-what-happens-with-underscores-in-the-database-name)\n\nアンダースコアの前に をつけないと、ワイルドカードの扱いとなり、アンダースコアは「任意の 1 文字」を表します。従って、データベース名が \"john_db\" の場合、そのユーザは john1db、john2db … への権限を得ることになります。アンダースコアの前に を付けた場合は、データベース名に実際のアンダースコアがあることを意味します。\n\n#### 6.11 統計ページにある ø という変わった記号は何ですか？[¶](#what-is-the-curious-symbol-o-in-the-statistics-pages)\n\n「平均」の意味です。\n\n#### 6.12 エクスポートのオプションについて教えてください。[¶](#i-want-to-understand-some-export-options)\n\n**構造:**\n\n* 「DROP TABLE を追加する」は、インポート中に既存のテーブルが存在していたら [そのテーブルを削除する](https://dev.mysql.com/doc/refman/5.6/ja/drop-table.html) よう MySQL に指示する行を追加します。エクスポート後にテーブルを削除するわけではなく、インポートファイルにのみ影響します。\n* \"IF NOT EXISTS” は、テーブルが存在しないときのみ作成します。設定されていない場合、既に存在するテーブル名で異なる構造を指定した場合にエラーになることがあります。\n* 「AUTO_INCREMENT 値を追加する」は、 (あれば) AUTO_INCREMENT 値もバックアップに含めるようにします。\n* 「テーブルやカラムの名前を逆クォートで囲む」は、特殊文字を含むカラム名やテーブル名を保護します。\n* 「コメントの追加」は、 pmadb に設定されているカラムのコメント、リレーション、メディア型を [SQL](index.html#term-sql) のコメント文の形 (*/* xxx */*) でダンプに含めます。\n\n**データ:**\n\n* 「完全な INSERT 文を作成する」は、すべての INSERT コマンドにカラム名を付与して、より詳しく記述します (ただし、結果のファイルは大きくなります)。\n* 「長い INSERT 文を作成する」は、ダンプファイルを短くするために INSERT の述語とテーブル名を一度しか使わないようにします。\n* 「遅延インサートを使用する」については、 [MySQL マニュアル - INSERT DELAYED 構文](https://dev.mysql.com/doc/refman/5.7/ja/insert-delayed.html) の説明をご覧ください。\n* 「INSERT IGNORE を使用する」は、エラーを警告として扱います。こちらも、詳しくは [MySQL マニュアル - INSERT 構文](https://dev.mysql.com/doc/refman/5.7/ja/insert.html) にありますが、これを選択すると、基本的に無効な値があった場合に文全体を失敗とするのではなく、値を調整して挿入が行われます。\n\n#### 6.13 名前にピリオドを含むデータベースを作りたいのですが。[¶](#i-would-like-to-create-a-database-with-a-dot-in-its-name)\n\nこれは良くないことです。 MySQL の構文では通例データベースとテーブルの名前を参照するのに \"database.table\" と書きますし、さらに悪いことに、 MySQL ではピリオドがついたデータベースを作成することはできるものの、使用したり削除したりすることができません。\n\n#### 6.14 (取り下げ)。[¶](#withdrawn-19)\n\n#### 6.15 BLOB のカラム追加して、それにインデックスをつけたいのですが、 MySQL が \"BLOB column '...' used in key specification without a key length\" と報告します。[¶](#i-want-to-add-a-blob-column-and-put-an-index-on-it-but-mysql-says-blob-column-used-in-key-specification-without-a-key-length)\n\nこれを行う正しい方法は、インデックスなしでカラムを作成し、テーブル構造を表示して「インデックスを作成」ダイアログを使用することです。このページ上で BLOB カラムを選択し、インデックスにサイズを指定できます。これは、BLOBカラムにインデックスを作成するための条件です。\n\n#### 6.16 どうしたら多くの編集項目があるページ内で簡単に移動できますか？[¶](#how-can-i-simply-move-in-page-with-plenty-editing-fields)\n\n多くのページでは `Ctrl+矢印` (Safari では `Option+矢印`) を使用することで、たくさんの編集フィールド (テーブルの構造の変更、行の編集など) を移動することができます。\n\n#### 6.17 変換機能: 独自の MIME タイプを入力できません！本当にこの機能は役に立つんですか？[¶](#transformations-i-can-t-enter-my-own-mimetype-what-is-this-feature-then-useful-for)\n\nメディア型に変換を加えることができない場合、メディア型を定義しても意味がありません。カラムにコメントを付けることができるだけです。独自のメディア型を入力すると、深刻な構文チェックの問題と検証が発生するため、これにより、リスクの高い誤ったユーザ入力状況が発生します。代わりに、関数または空のメディア型定義を使用してメディア型を初期化する必要があります。\n\n加えて、利用できるメディア型の一覧もあります。誰もこれらのメディア型を覚えて、入力できるわけではありませんよね？\n\n#### 6.18 ブックマーク: ブックマークはどこで保管できますか？どうしてクエリボックスの下にブックマークがないのでしょうか？この変数は何でしょうか？[¶](#bookmarks-where-can-i-store-bookmarks-why-can-t-i-see-any-bookmarks-below-the-query-box-what-are-these-variables-for)\n\nブックマーク機能を使用するには、 [phpMyAdmin 環境保管領域](index.html#linked-tables) を構成しておく必要があります。それが済んだら、 SQL タブでブックマークを使用できます。\n\n参考\n\n[ブックマーク](index.html#bookmarks)\n\n#### 6.19 エクスポートされたテーブルを含めるための簡単な LATEX ドキュメントを作成するにはどうすればよいですか？[¶](#how-can-i-create-simple-latex-document-to-include-exported-table)\n\nLATEX ドキュメントにテーブルをインクルードすれば簡単にできます。最小限のサンプルドキュメントは次のようになります (エクスポートしたテーブルが `table.tex` というファイルに入っているとします)。\n```\n\\documentclass{article} % or any class you want\n\\usepackage{longtable} % for displaying table\n\\begin{document} % start of document\n\\include{table} % including exported table\n\\end{document} % end of document\n```\n#### 6.20 自分のものではないデータベースがたくさん見えます。また、そういったデータベースにアクセスできません。[¶](#i-see-a-lot-of-databases-which-are-not-mine-and-cannot-access-them)\n\nあなたはグローバル権限のうち CREATE TEMPORARY TABLES, SHOW DATABASES, LOCK TABLES のうちいずれか１つを持っています。これらの権限があるとすべてのデータベース名が見えてしまいます。ユーザにこれらの権限が必要ない場合は、削除すればデータベース一覧が短くなります。\n\n参考\n\n<<https://bugs.mysql.com/bug.php?id=179>#### 6.21 編集／挿入モードで、外部のテーブルに基づいた利用可能なカラムの値の一覧を見るにはどうすればよいでしょうか？[¶](#in-edit-insert-mode-how-can-i-see-a-list-of-possible-values-for-a-column-based-on-some-foreign-table)\n\nテーブル間に適切なリンクを設定し、外部のテーブルに「表示カラム」を設定する必要があります。例については、 [6.6 どうすれば定型問い合わせの際にリレーションテーブルを使えるのでしょうか？](#faq6-6) を参照してください。次に、外部テーブルの値が100以下である場合は、値のドロップダウンリストが表示されます。 2 つの値のリストが表示されます。最初のリストにはキーと表示カラムが含まれ、2番目のリストには表示列とキーが含まれます。これは、キーまたは表示列の最初の文字を入力できるようにするためです。 100 以上の値の場合、外部キー値を参照して1つを選択するための個別のウィンドウが表示されます。デフォルトの制限である 100 を変更するには、 [`$cfg['ForeignKeyMaxLimit']`](index.html#cfg_ForeignKeyMaxLimit) を参照してください。\n\n#### 6.22 ブックマーク: テーブルの表示モードに入ったときに、自動的にデフォルトのブックマークを実行できますか？[¶](#bookmarks-can-i-execute-a-default-bookmark-automatically-when-entering-browse-mode-for-a-table)\n\nできます。ブックマークのラベルをテーブル名と同じにして、ブックマークを公開しないでおけば、実行されます。\n\n参考\n\n[ブックマーク](index.html#bookmarks)\n\n#### 6.23 エクスポート: phpMyAdmin が Microsoft Excel ファイルをエクスポートできると聞いたのですが？[¶](#export-i-heard-phpmyadmin-can-export-microsoft-excel-files)\n\nMicrosoft Excel では [CSV](index.html#term-csv) が簡単に利用できます。\n\nバージョン 3.4.5 で変更: phpMyAdmin 3.4.5 以降、Microsoft Excel 97 以降の形式での直接エクスポートには対応しなくなりました。\n\n#### 6.24 phpMyAdmin が MySQL 4.1.x ネイティブのカラムコメントに対応するようになりましたが、pmadb に保存されているカラムコメントはどうなるのでしょうか？[¶](#now-that-phpmyadmin-supports-native-mysql-4-1-x-column-comments-what-happens-to-my-column-comments-stored-in-pmadb)\n\nテーブルの「構造」ページに入ったときに、自動的にそのテーブルの pmadb スタイルのカラムコメントがネイティブのカラムコメントに移行されます。\n\n#### 6.25 (取り下げ)。[¶](#withdrawn-20)\n\n#### 6.26 行の範囲選択はどうやるのですか？[¶](#how-can-i-select-a-range-of-rows)\n\n範囲の最初の行をクリックして、シフトキーを押しながら範囲の最後の行をクリックします。これは、表示モードまたは構造ページのように、行を閲覧していればいつでも動作します。\n\n#### 6.27 どのような書式の文字列が使えますか？[¶](#what-format-strings-can-i-use)\n\nphpMyAdmin は書式を受け入れるすべての場所において、 `@VARIABLE@` 記法および`strftime <<https://www.php.net/strftime>>`_ 書式文字列が利用できます。変数の展開は文脈に依存しますが (テーブルを選択していないとテーブル名を得られないなど)、以下の変数を使用することができます。\n\n`@HTTP_HOST@`\nphpMyAdmin を稼動させている HTTP ホスト\n`@SERVER@`\nMySQL サーバ名\n`@VERBOSE@`\n[`$cfg['Servers'][$i]['verbose']`](index.html#cfg_Servers_verbose) で定義された詳細な MySQL サーバ名\n`@VSERVER@`\n設定されていれば詳細な MySQL サーバの名前、そうでなければ通常の名前\n`@DATABASE@`\n現在開いているデータベース\n`@TABLE@`\n現在開いているテーブル\n`@COLUMNS@`\n現在開いているテーブルのカラム\n`@PHPMYADMIN@`\nphpMyAdmin とバージョン番号\n\n#### 6.28 (取り下げ)。[¶](#withdrawn-21)\n\n#### 6.29 なぜクエリの結果のテーブルからグラフが作れないのですか？[¶](#why-can-t-i-get-a-chart-from-my-query-result-table)\n\nすべてのテーブルをグラフにできるわけではありません。グラフとして視覚化できるのは、1列、2列、3列のテーブルのみです。さらに、グラフのスクリプトがテーブルを理解するためには、テーブルが特定の形式である必要があります。現在対応している形式は [グラフ機能](index.html#charts) にあります。\n\n#### 6.30 インポート: ESRI シェイプファイルはどうやってインポートできますか？[¶](#import-how-can-i-import-esri-shapefiles)\n\nESRI シェイプファイルは、実際には単独ファイルではなく複数のファイルの集合で、空間データが含まれている .shp ファイルと、その空間データに関連するデータが含まれている .dbf ファイルから構成されています。.dbf ファイルから関連するデータを読み込むには、PHP に dBase 拡張 (--enable-dbase) が必要になります。そうでない場合は、空間データのみがインポートされます。\n\nこれらのファイルの集合のアップロードは、以下のいずれかの方法を使用することができます。\n\n[`$cfg['UploadDir']`](index.html#cfg_UploadDir) を使用してアップロードディレクトリを構成し、同じファイル名で .shp ファイルと .dbf ファイルの両方をアップロードし、インポートページから .shp ファイルを選択します。\n\n.shp ファイルと .dbf ファイルを使用して zip アーカイブを作成し、インポートします。これを機能させるには、 [`$cfg['TempDir']`](index.html#cfg_TempDir) をウェブサーバのユーザが書き込むことができる場所 (例えば `'./tmp'`) に設定する必要があります。\n\nUNIX ベースのシステムで一時ディレクトリを作成するには、以下のようにします。\n```\ncd phpMyAdmin mkdir tmp chmod o+rwx tmp\n```\n#### 6.31 どうやってデザイナでリレーションを作成できますか？[¶](#how-do-i-create-a-relation-in-designer)\n\nリレーションを選択するには、クリックします。表示されるカラムはピンク色で表示されます。カラムを表示カラムとして設定/解除するには、 [表示するカラムの選択] アイコンをクリックしてから、適切なカラム名をクリックしてください。\n\n#### 6.32 ズーム検索機能はどのように使うことができますか？[¶](#how-can-i-use-the-zoom-search-feature)\n\n検索プロット機能は、テーブル検索とは異なった機能です。データを散布図に描くことにより、テーブルデータを調査するものです。この機能は、テーブルを選択して 検索 タブをクリックしたところから使用できます。 テーブル検索`ページ内のタブに、 :guilabel:`検索プロット の項目があります。\n\n例として [6.6 どうすれば定型問い合わせの際にリレーションテーブルを使えるのでしょうか？](#faq6-6) の REL_persons テーブルを考えてみてください。検索プロットを使用するには、id と town_code というように、2 つのカラムを選択する必要があります。id の値が一方の軸に置かれた場合、town_code はもう一方の軸に置かれます。それぞれの行は、id と town_code を基に点として散布図内に配置されます。表示されている入力項目より、追加の絞り込み条件を 2 つまで含めることができます。\n\n各点のラベルとして表示される項目を選択することができます。テーブルに表示するカラム ([6.7 どうすれば [表示するカラム] 機能が利用できますか？](#faqdisplay) を参照) が設定されている場合は、特に指定しない限りそれがラベルとして扱われます。また、プロットする結果の最大数で、散布図内に表示させたいプロットの最大数が指定できます。描画の指定がよければ、 [実行] をクリックすると散布図が表示されます。\n\n作成された散布図は、マウスホイールでズームの調整が行えます。また、散布図を通じて各点の評価が行えます。細部が判別できる程度まで拡大して、配置されている点の中から評価したいものを探します。点をクリックするとダイアログが開き、描画されている点に対応する行のデータ値が表示されます。必要であればこれらのデータ値は編集することが可能で、 [実行] をクリックすると UPDATE クエリによって内容が変更されます。簡単な使用方法が、散布図の上にある「使い方」リンクをクリックすることにより表示されます。\n\n#### 6.33 テーブル閲覧時に、どうすればカラム名をコピーできますか？[¶](#when-browsing-a-table-how-can-i-copy-a-column-name)\n\nコピーするためにブラウズテーブルのヘッダセル内のカラム名を選択するのは難しいです。カラムはリンク先の列名をクリックしてソートするだけでなく、ヘッダセルをドラッグして並べ替えることもできるからです。カラム名をコピーするには、ツールチップの指示に従って、カラム名の横にある空の領域をダブルクリックしてください。そうすると、カラム名の入力ボックスが表示されます。この入力ボックス内のカラム名を右クリックしてクリップボードにコピーすることができます。\n\n#### 6.34 お気に入りテーブル機能を使用するにはどうすればよいですか？[¶](#how-can-i-use-the-favorite-tables-feature)\n\nお気に入りテーブル機能は、最近使用したテーブル機能と非常によく似ています。これは、データベースで頻繁に使用されるテーブルのショートカットをナビゲーションパネルに追加することができます。リストからそれを選択するだけで、リスト内の任意のテーブルに移動することができます。 phpMyAdmin 環境保管領域 を設定していない場合、これらのテーブルはブラウザのローカルストレージに保存されます。そうでない場合は、これらの項目は phpMyAdmin 環境保管領域 に保存されます。\n\n重要: phpMyAdmin 環境保管領域 がない場合、お気に入りのテーブルはブラウザごとに選択したものに基づくため、異なるものになる可能性があります。\n\nお気に入りリストにテーブルを追加するには、データベースのテーブルリストのテーブル名の前にある 灰色 の星をクリックし、黄色になるまで待ってください。リストからテーブルを削除するには、黄色の星をクリックし、再び灰色になるまで待ってください。\n\n`config.inc.php` ファイルの [`$cfg['NumFavoriteTables']`](index.html#cfg_NumFavoriteTables) を使用すると、ナビゲーションパネルに表示されるお気に入りテーブルの最大数を定義することができます。既定値は 10 です。\n\n#### 6.35 範囲検索機能はどのようにして使うのですか？[¶](#how-can-i-use-the-range-search-feature)\n\n範囲検索機能を利用すると、 [検索] タブから表の検索操作を実行している間に、特定のカラムの値の範囲を指定することができます。\n\nこの機能を使用するには、カラム名の前にある演算子選択リストから BETWEEN 演算子または NOT BETWEEN 演算子をクリックするだけです。上記のオプションのいずれかを選択すると、そのカラムの 最小値 と 最大値 を尋ねるダイアログボックスが表示されます。 BETWEEN の場合は指定された値の範囲のみが含まれ、 NOT BETWEEN の場合には最終結果から除外されます。\n\n注: 範囲検索機能は Numeric および Date データ型のカラムでのみ機能します。\n\n#### 6.36 主要カラム機能とは何ですか？この機能はどのように使うのですか？[¶](#what-is-central-columns-and-how-can-i-use-this-feature)\n\nその名前が示すように、主要カラム機能はデータベースごとに主要なカラムのリストを管理することで、同じデータ要素の類似した名前を避け、同じデータ要素のデータ型の一貫性をもたらします。主要リストを使用すると、データベース内の任意のテーブル構造に要素を追加することができるので、似たようなカラム名やカラム定義を記述する手間が省けます。\n\n主要カラムのリストに追加するには、テーブル構造のページに移動し、追加したいカラムをチェックして、 [主要カラムに追加] をクリックしてください。データベースの複数のテーブルから一意のカラムをすべて追加する場合は、データベース構造ページに移動し、対象としたいテーブルを確認してから「主要カラムリストへ追加」を選択してください。\n\n主要カラムリストからカラムを削除する場合は、テーブル構造ページに移動し、削除したいカラムを確認してから、「主要カラムリストから削除」をクリックするだけです。データベースから複数のテーブルからすべてのカラムを削除したい場合は、データベース構造ページに移動し、対象とするテーブルを確認してから「主要カラムリストから削除」を選択してください。\n\n主要カラムリストを表示したり管理したりするには、主要カラムを管理したいデータベースを選択し、トップメニューから「主要カラム」をクリックします。主要カラムリストの編集、削除、新しいカラムの追加ができるページが表示されます。\n\n#### 6.37 テーブル構造の改善機能はどのように使うのですか？[¶](#how-can-i-use-improve-table-structure-feature)\n\nテーブル構造の改善機能は、テーブルの構造を第三正規形にするのに役立ちます。ユーザにウィザードが表示され、正規化のための様々なステップの間に要素について質問を行い、それに応じて新しい構造を提案し、テーブルを第一/第ニ/第三正規形に持ち込むことができます。ウィザードの起動時に、ユーザはテーブル構造をどの正規形まで正規化したいかを選択することができます。\n\nここでは、第一、第二、第三の3種類の正規形をすべてテストすることができるテーブルの例です。\n```\nCREATE TABLE `VetOffice` (\n `petName` varchar(64) NOT NULL,\n `petBreed` varchar(64) NOT NULL,\n `petType` varchar(64) NOT NULL,\n `petDOB` date NOT NULL,\n `ownerLastName` varchar(64) NOT NULL,\n `ownerFirstName` varchar(64) NOT NULL,\n `ownerPhone1` int(12) NOT NULL,\n `ownerPhone2` int(12) NOT NULL,\n `ownerEmail` varchar(64) NOT NULL,\n);\n```\n上記のテーブルは [主キー](index.html#term-primary-key) がないので第一正規形ではありません。主キーは (petName, ownerLastName, ownerFirstName) になると考えられます。 [主キー](index.html#term-primary-key) が提案された通りに選択された場合でも、結果のテーブルには下記の依存関係があるため、第二正規形にも第三正規形にもなりません。\n```\n(OwnerLastName, OwnerFirstName) -> OwnerEmail\n(OwnerLastName, OwnerFirstName) -> OwnerPhone PetBreed -> PetType\n```\nすなわち、 OwnerEmail は OwnerLastName と OwnerFirstName に依存しています。 OwnerPhone は OwnerLastName と OwnerFirstName に依存しています。 PetType は PetBreed に依存しています。\n\n#### 6.38 どうすればオートインクリメント値を再設定できますか？[¶](#how-can-i-reassign-auto-incremented-values)\n\nAUTO_INCREMENT の値が連続していることを好むユーザもいますが、行を削除した後はそうなるとは限りません。\n\nこれを実現するための手順を以下に示します。これらの手順は、ある時点で手動で検証を行う必要があるため、手動で行います。\n\n* テーブルへの排他的なアクセス権を持っていることを確認する\n* [主キー](index.html#term-primary-key) の列 (すなわち id) の AUTO_INCREMENT 設定を削除する\n* [構造] > [インデックス] で主キーを削除する\n* 新しいカラム future_id を主キー、 AUTO_INCREMENT として作成する\n* テーブルを参照して、新しいインクリメント値が期待通りであることを確認する\n* 古い ID カラムを削除する\n* future_id カラムの名前を id に変更する\n* [構造] > [カラムの移動] で新しい id カラムを移動する\n\n#### 6.39 データベース、テーブル、カラム、プロシージャの名前を変更、コピー、移動時に表示される [権限を調整]とは何ですか？[¶](#what-is-the-adjust-privileges-option-when-renaming-copying-or-moving-a-database-table-column-or-procedure)\n\nデータベース/テーブル/カラム/プロシージャの名前の変更/コピー/移動時に、 MySQL は自分自身ではこれらのオブジェクトに対する元の権限を変更しません。このオプションを選択することで、 phpMyAdmin がテーブルの権限を調整するので、ユーザは新しいアイテムで同じ権限を持つことができます。\n\n例えば、 ['bob'@'localhost](mailto:'bob'%40'localhost)' が 'id' という名前のカラムに 'SELECT' 権限を持っていたとします。ここで、このカラムの名前が 'id_new' と変更されると、 MySQL 自身はカラムの権限を新しいカラム名に調整**しません**。 phpMyAdmin はこの調整を自動的に行うことができます。\n\n注:\n\n* データベースの権限を調整すると、すべてのデータベースに関する要素 (テーブル、カラム、プロシージャ) の権限もデータベースの新しい名前に調整されます。\n* 同様に、テーブルの権限を調整すると、新しいテーブル内の全カラムの権限も調整されます。\n* 権限を調整する際、その操作を行うユーザは以下の権限を持っている**必要があります**。\n\t+ mysql.`db`, mysql.`columns_priv`, mysql.`tables_priv`, mysql.`procs_priv` に対する SELECT, INSERT, UPDATE, DELETE 権限\n\t+ 権限の FLUSH (グローバル)\n\nしたがって、これらのオブジェクトの名前変更/コピー/移動中にデータベース/テーブル/カラム/プロシージャをそのまま複製する場合は、このオプションがオンになっていることを確認してください。\n\n#### 6.40 [SQL] ページに「パラメータのバインド」チェックボックスが表示されます。どうやってパラメータのついた SQL クエリを作成するのですか？[¶](#i-see-bind-parameters-checkbox-in-the-sql-page-how-do-i-write-parameterized-sql-queries)\n\nバージョン 4.5 から、 phpMyAdmin では [SQL] ページでパラメータを指定したクエリを実行できるようになりました。パラメータの前にはコロン (:) を付け、「パラメータのバインド」チェックボックスをチェックすると、これらのパラメータが識別され、パラメータの入力フィールドが表示されます。フィールドに入力された値は、実行される前にクエリ内で置換されます。\n\n#### 6.41 古いバージョンの MySQL (5.7.6より前) からエクスポートされたダンプを新しいバージョンの MySQL (5.7.7 以降) にインポートしているときにインポートエラーが発生します。同じ古いバージョンにインポートすると正常に動作するのに？[¶](#i-get-import-errors-while-importing-the-dumps-exported-from-older-mysql-versions-pre-5-7-6-into-newer-mysql-versions-5-7-7-but-they-work-fine-when-imported-back-on-same-older-versions)\n\n5.7.7 以前の MySQL サーバからエクスポートしたダンプをバージョン 5.7.7 以降の新しい MySQL サーバにインポートしているときに *#1031 - Table storage engine for 'table_name' doesn't have this option* のようなエラーが発生した場合は、 InnoDB テーブルが ROW_FORMAT=FIXED に対応していないからかもしれません。さらに、 [innodb_strict_mode](https://dev.mysql.com/doc/refman/5.7/ja/innodb-parameters.html#sysvar_innodb_strict_mode) の値によって、これが警告として報告されるか、エラーとして報告されるかが定義されます。\n\nMySQL バージョン 5.7.9 以降では、 innodb_strict_mode のデフォルト値が ON であるため、このような CREATE TABLE または ALTER TABLE 文が検出されるとエラーが生成されます。\n\nインポート中にこのようなエラーを防ぐには、次の2つの方法があります。\n\n* インポートを開始する前に innodb_strict_mode の値を OFF に変更し、インポートが正常に完了した後に ON にする。\n* これは、次の 2 つの方法で実現できます。\n\t+ [変数] ページへ移動し、 innodb_strict_mode の値を編集する\n\t+ SET GLOBAL `innodb_strict_mode = '[value]'` というクエリを実行する\n\nインポートが完了したら、 innodb_strict_mode の値を元の値にリセットすることが推奨されています。\n\n### phpMyAdmin プロジェクト[¶](#phpmyadmin-project)\n\n#### 7.1 バグを見つけました。開発者に知らせるにはどうすればよいですか？[¶](#i-have-found-a-bug-how-do-i-inform-developers)\n\n課題追跡システムが <<https://github.com/phpmyadmin/phpmyadmin/issues>> にあります。セキュリティ上の問題については <<https://www.phpmyadmin.net/security>> の説明を参照し、開発者に直接メールを送ってください。\n\n#### 7.2 メッセージを新しい言語に翻訳したり、既存の言語を更新したりしたいのですが、どこから始めるのですか？[¶](#i-want-to-translate-the-messages-to-a-new-language-or-upgrade-an-existing-language-where-do-i-start)\n\n翻訳はとても歓迎しますし、必要なものは言語スキルだけです。もっとも簡単な方法は [オンライン翻訳サービス](https://hosted.weblate.org/projects/phpmyadmin/) を使用する方法です。 [私たちのウェブサイトの翻訳の節](https://www.phpmyadmin.net/translate/) に翻訳でできることのすべてを見ることができます。\n\n#### 7.3 phpMyAdmin の開発に協力したいのですが、どのように進めればよいでしょうか？[¶](#i-would-like-to-help-out-with-the-development-of-phpmyadmin-how-should-i-proceed)\n\n私たちは phpMyAdmin の開発に対するすべての協力を歓迎します。協力できるすべてのことが [私たちのウェブサイトの貢献の節](https://www.phpmyadmin.net/contribute/) にあります。\n\n参考\n\n[開発者向け情報](index.html#developers)\n\n### セキュリティ[¶](#security)\n\n#### 8.1 phpMyAdmin に対して発行されたセキュリティアラートについての情報はどこで入手できますか？[¶](#where-can-i-get-information-about-the-security-alerts-issued-for-phpmyadmin)\n\n<<https://www.phpmyadmin.net/security/>> を参照してください。\n\n#### 8.2 phpMyAdmin を総当たり攻撃から守るにはどうすれば良いですか？[¶](#how-can-i-protect-phpmyadmin-against-brute-force-attacks)\n\nApache ウェブサーバを使用する場合、 phpMyAdmin は Apache の環境に認証情報をエクスポートして、 Apache のログに記録することができます。現在、２つの変数を利用することができます。\n\n`userID`\n現在アクティブなユーザのユーザ名（ログインする必要はありません）。\n`userStatus`\n現在アクティブなユーザのステータスで、 `ok` (ユーザがログインした), `mysql-denied` (MySQL がユーザのログインを拒否した), `allow-denied` (allow/deny ルールで拒否されたユーザ), `root-denied` (設定で root が拒否された), `empty-denied` (空のパスワードが拒否された) のうちの一つです。\n\nApache の LogFormat 設定は、次のようなものです。\n```\nLogFormat \"%h %l %u %t \\\"%r\\\" %>s %b \\\"%{Referer}i\\\" \\\"%{User-Agent}i\\\" %{userID}n %{userStatus}n\" pma_combined\n```\nあとで、ログ解析ツールを使用して、侵入を試みている可能性のあるものを検出することができます。\n\n#### 8.3 あるファイルを直接読み込むとき、なぜパスが公開されてしまうのですか？[¶](#why-are-there-path-disclosures-when-directly-loading-certain-files)\n\nこれはサーバ設定の問題です。本番サイトでは `display_errors` を有効にしないでください。\n\n#### 8.4 phpMyAdmin からエクスポートした CSV ファイルで式インジェクション攻撃ができてしまいます。[¶](#csv-files-exported-from-phpmyadmin-could-allow-a-formula-injection-attack)\n\nMicrosoft Excel などの表計算プログラムにインポートすると、任意のコマンドを実行できる可能性のある [CSV](index.html#term-csv) ファイルを生成することが可能です。\n\nphpMyAdmin によって生成された CSV ファイルには、表計算プログラムが数式として解釈するテキストが含まれている可能性がありますが、これらのフィールドをエスケープすることが適切な動作であるとは考えていません。エスケープしたいテキスト出力とエスケープすべき数式を適切に区別してエスケープする方法はありません。私たちはこれについて長々と議論してきましたが、代わりに入力上のそのようなデータを適切に解析してサニタイズするのは、表計算プログラムの責任であると感じています。\n\nGoogle も [同様の見解](https://sites.google.com/site/bughunteruniversity/nonvuln/csv-excel-formula-injection) を持っています。\n\n### 同期[¶](#synchronization)\n\n#### 9.1 (取り下げ).[¶](#withdrawn-22)\n\n#### 9.2 (取り下げ).[¶](#withdrawn-23)\n\n開発者向け情報[¶](#developers-information)\n---\n\nphpMyAdmin はオープンソースですから、協力してくださる方は歓迎します。これまでにもほかの方々が多くのすばらしい機能を書いてくださいました。みなさんにもできることはあります。phpMyAdmin を便利なツールにしていきましょう。\n\n協力することができるすべての項目は、 [私たちのウェブサイトの contribute の節](https://www.phpmyadmin.net/contribute/) で確認することができます。\n\nセキュリティポリシー[¶](#security-policy)\n---\n\nphpMyAdmin 開発チームは、 phpMyAdmin を可能な限り安全にするために多くの努力をしています。しかし、 phpMyAdmin のようなウェブアプリケーションは、多くの攻撃に対して脆弱である可能性があり、それを悪用する新しい方法がまだ模索されています。\n\n報告されたすべての脆弱性に対して、私たちは phpMyAdmin セキュリティアナウンス (PMASA) を発行し、それには CVE ID も割り当てられます。類似する脆弱性を一つの PMASA にグループ化することもあります (例えば、複数の XSS 脆弱性を一つの PMASA の下で発表することがあります)。\n\n脆弱性を発見したと思われる場合は、 [セキュリティ問題の報告](#reporting-security) を参照してください。\n\n### よくある脆弱性[¶](#typical-vulnerabilities)\n\nこの節では、私たちのコードベースに現れる可能性のある典型的な脆弱性について説明します。このリストは決して完全なものではなく、典型的な攻撃の一面を示すためのものです。\n\n#### クロスサイトスクリプティング (XSS)[¶](#cross-site-scripting-xss)\n\nphpMyAdmin がユーザデータの一部、例えばユーザのデータベース内の何かを表示するとき、 HTML の特殊文字をすべてエスケープしなければなりません。このエスケープが行われていない場所があった場合、悪意のあるユーザーがデータベースに特別に作られたコンテンツを流し込み、そのデータベースの他のユーザを騙して何かを実行させてしまう可能性があります。これは、例えば、いくつもの厄介なことをする JavaScript のコードの一部である可能性があります。\n\nphpMyAdmin は、ブラウザ向けの HTML にレンダリングされる前に、すべてのユーザデータをエスケープするようにしています。\n\n参考\n\n[ウィキペディアの「クロスサイトスクリプティング」](https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%AD%E3%82%B9%E3%82%B5%E3%82%A4%E3%83%88%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%97%E3%83%86%E3%82%A3%E3%83%B3%E3%82%B0)\n\n#### クロスサイトリクエストフォージェリ (CSRF)[¶](#cross-site-request-forgery-csrf)\n\n攻撃者が phpMyAdmin のユーザを騙して、 phpMyAdmin のアクションを誘発するリンクをクリックさせます。このリンクは、電子メールで送信されるか、どこかのウェブサイトから送信されるかのいずれかです。これが成功した場合、攻撃者がユーザの権限を使って何らかのアクションを実行できるようになります。\n\nこれを緩和するために、 phpMyAdmin はセンシティブなリクエストにトークンを送信する必要があります。これは、攻撃者が現在有効なトークンを提示せず、提示されたリンクに含めるというものです。\n\nトークンはログインするたびに再生成されるので、一般的には限られた期間しか有効ではなく、攻撃者が有効なものを入手するのが難しくなります。\n\n参考\n\n[ウィキペディアの「クロスサイトリクエストフォージェリ」](https://en.wikipedia.org/wiki/Cross-site_request_forgery)\n\n#### SQL インジェクション[¶](#sql-injection)\n\nphpMyAdmin の全体的な目的は SQL クエリを実行することであるため、これは第一の懸念事項ではありません。 mysql の制御接続に関係する場合には SQL インジェクションに気を付けなければなりません。この制御接続は、ログイン中のユーザが持っていない権限を持っていることがあるからです。例えば [phpMyAdmin 環境保管領域](index.html#linked-tables) へのアクセスです。\n\n(管理用) クエリに含まれるユーザデータは、常に DatabaseInterface::quoteString() を通して実行する必要があります。\n\n参考\n\n[Wikipedia での SQL インジェクションの記事](https://ja.wikipedia.org/wiki/SQL%E3%82%A4%E3%83%B3%E3%82%B8%E3%82%A7%E3%82%AF%E3%82%B7%E3%83%A7%E3%83%B3)\n\n#### 総当たり攻撃[¶](#brute-force-attack)\n\nphpMyAdmin 自体は、認証の試行回数を制限することはありません。これは、このようなことから保護する方法がないステートレス環境で動作する必要があるためです。\n\nこれを軽減するには、 Captcha を使用したり、 fail2ban などの外部ツールを利用したりすることができます。これは [phpMyAdmin のインストールを安全にする](index.html#securing) でより詳しく説明しています。\n\n参考\n\n[ウィキペディアの「総当たり攻撃」](https://ja.wikipedia.org/wiki/%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E6%94%BB%E6%92%83)\n\n### セキュリティ問題の報告[¶](#reporting-security-issues)\n\nphpMyAdmin のプログラムコードにセキュリティ上の問題を発見した場合は、それを公開する前に事前に [phpMyAdmin セキュリティチーム](mailto:security%40phpmyadmin.net) に連絡してください。このようにすれば私たちが修正を準備し、あなたの発表と同時に修正版をリリースすることができます。また、私たちのセキュリティアナウンスの中で、あなたにクレジットが与えられることになります。オプションで、レポートは以下のフィンガープリントで PGP キー ID `DA68AB39218AB947` で暗号化することができます。\n```\npub 4096R/DA68AB39218AB947 2016-08-02\n Key fingerprint = <KEY> uid phpMyAdmin Security Team <<EMAIL>>\nsub 4096R/5E4176FB497A31F7 2016-08-02\n```\n鍵は鍵サーバから取得するか、ダウンロードサーバにある [phpMyAdmin キーリング](https://files.phpmyadmin.net/phpmyadmin.keyring) や [Keybase](https://keybase.io/phpmyadmin_sec) を使用して入手することができます。\n\nphpMyAdmin をより安全にするための改善提案があるのであれば、私たちの [問題追跡システム](https://github.com/phpmyadmin/phpmyadmin/issues) に報告してください。既存の改善提案は、 [hardening label](https://github.com/phpmyadmin/phpmyadmin/labels/hardening) で見ることができます。\n\nphpMyAdmin の配布とパッケージ化[¶](#distributing-and-packaging-phpmyadmin)\n---\n\nこのドキュメントは、 Linux ディストリビューションなどの他のソフトウェアパッケージ内で、またはウェブサーバと MySQL サーバを含むすべてを1つのパッケージにまとめて phpMyAdmin を再配布したい人に助言することを目的としています。\n\n一般に、いくつかの基本的な側面 (いくつかのファイルへのパスと動作) は `libraries/vendor_config.php` でカスタマイズできます。\n\nたとえば、セットアップスクリプトで var に設定ファイルを生成するようにする場合は、 `SETUP_CONFIG_FILE` を `/var/lib/phpmyadmin/config.inc.php` に変更してください。また、おそらくディレクトリが書き込み可能であるかのチェックもスキップしたいでしょうから、 `SETUP_DIR_WRITABLE` を false に設定してください。\n\n### 外部ライブラリ[¶](#external-libraries)\n\nphpMyAdminにはいくつかの外部ライブラリが含まれており、利用可能な場合はシステムライブラリに置き換たほうがよい場合もありますが、新しいバージョンが同梱したバージョンと互換性があるかどうかをテストする必要があることに注意してください。\n\n現在知られている外部ライブラリのリストは以下の通りです。\n\njs/vendor js の jQuery フレームワークライブラリと様々な js のライブラリです。\nvendor/\nダウンロードキットには、依存関係としてさまざまな Composer パッケージが含まれています。\n\n### 特定のファイルのライセンス[¶](#specific-files-licenses)\n\nphpMyAdmin 配布テーマには、ライセンス下にあるコンテンツが含まれています。\n\n* The icons of the Original and pmahomme themes are from the [Silk Icons](https://web.archive.org/web/20221201060206/http://www.famfamfam.com/lab/icons/silk/).\n* Some icons of the Metro theme are from the [Silk Icons](https://web.archive.org/web/20221201060206/http://www.famfamfam.com/lab/icons/silk/).\n* themes/*/img/b_rename.svg は [Icons8](https://thenounproject.com/Icons8/) の一つで、 [Android L Icon Pack Collection](https://thenounproject.com/Icons8/collection/android-l-icon-pack/) によるアイコン [rename](https://thenounproject.com/term/rename/61456/) です。\n* themes/metro/img/user.svg は IcoMoon のうちの一つ、 [user](https://github.com/Keyamoon/IcoMoon-Free/blob/master/SVG/114-user.svg) です\n\nCC BY 4.0 または GPL\n\n### ベンダー向けのライセンス情報[¶](#licenses-for-vendors)\n\n* Silk Icons are under the [CC BY 2.5 or CC BY 3.0](https://web.archive.org/web/20221201060206/http://www.famfamfam.com/lab/icons/silk/) licenses.\n* Icons8 の rename は [\"パブリックドメイン\"](https://creativecommons.org/publicdomain/zero/1.0/) (CC0 1.0) ライセンスです。\n* IcoMoon Free は [\"CC BY 4.0 または GPL\"](https://github.com/Keyamoon/IcoMoon-Free/blob/master/License.txt) です。\n\n著作権[¶](#copyright-1)\n---\n```\nCopyright (C) 1998-2000 <NAME> <tobias_at_ratschiller.com>\nCopyright (C) 2001-2018 <NAME> <marc_at_infomarc.info>\n <NAME> <om_at_omnis.ch>\n <NAME> <robbat2_at_users.sourceforge.net>\n <NAME> <me_at_derrabus.de>\n <NAME> <michal_at_cihar.com>\n <NAME> <me_at_supergarv.de>\n <NAME> <mkkeck_at_users.sourceforge.net>\n <NAME> <cybot_tm_at_users.sourceforge.net>\n [check credits for more details]\n```\nこのプログラムはフリーソフトウェアです。Free Software Foundation よって公表された GNU General Public License バージョン 2 (GPLv2) の条件の下において、再配布や変更を行うことができます。\n\nこのプログラムは、役に立つことを期待して配布されていますが、いかなる保証もありません。特定の目的に対する商業上または適合上の暗黙的な保証もありません。詳細については GNU General Public License (GPL) を参照してください。\n\nこのプログラムと共に GNU General Public License (GPL) のコピーを受け取っているはずです。もし、ない場合は <<https://www.gnu.org/licenses/>> を参照してください。\n\n### サードパーティのライセンス[¶](#third-party-licenses)\n\nphpMyAdmin には、いくつかのサードパーティ製ライブラリが、それぞれのライセンスの下で含まれています。\n\njs/vendor/jquery/ 以下のファイルを入手した jQuery のライセンスは (MIT|GPL) で、それぞれのライセンスのコピーがこのリポジトリにあります (GPL は LICENSE、 MIT は js/vendor/jquery/MIT-LICENSE.txt)。\n\nダウンロードキットには、いくつかのコンポーザーライブラリが追加で含まれています。ベンダー/ディレクトリのライセンス情報を参照してください。\n\n貢献者一覧[¶](#credits-1)\n---\n\n### 貢献者一覧（年代順）[¶](#credits-in-chronological-order)\n\n* <NAME> <tobias_at_ratschiller.com>\n\t+ phpMyAdmin プロジェクトの創始者\n\t+ 1998 年から 2000 年夏までの管理者\n* <NAME> <marc_at_infomarc.info>\n\t+ 多言語版 (1998 年 12 月)\n\t+ 様々な修正と改善\n\t+ [SQL](index.html#term-sql) アナライザの最初のバージョン (の大半)\n\t+ 2001 年から 2015 年までの管理者\n* <NAME> <om_at_omnis.ch>\n\t+ 2001 年 3 月に SourceForge phpMyAdmin プロジェクトを立ち上げ\n\t+ 既存のさまざまな CVS ツリーの同期をとり、新機能、バグフィックスを反映\n\t+ 多言語対応の改善。動的言語選択\n\t+ たくさんのバグ修正と改善\n* <NAME> <lolo_at_phpheaven.net>\n\t+ JavaScript、DHTML、DOM の書き直し、最適化\n\t+ スクリプトを書き直して [PEAR](index.html#term-pear) のコーディング基準にあわせ、XHTML1.0 と CSS2 準拠のコードを生成するようにした\n\t+ 言語検知システムの改善\n\t+ たくさんのバグ修正と改善\n* <NAME> <robbat2_at_users.sourceforge.net>\n\t+ データベースのメンテナンスコントロール\n\t+ テーブル種別コード\n\t+ ホスト認証 [IP](index.html#term-ip) アドレスによる許可/拒否\n\t+ データベースを使用した設定 (未完)\n\t+ [SQL](index.html#term-sql) パーサと書式整備機能\n\t+ [SQL](index.html#term-sql) バリデータ\n\t+ たくさんのバグ修正と改善\n* <NAME> <armel.fauveau_at_globalis-ms.com>\n\t+ ブックマーク機能\n\t+ 複数ダンプ機能\n\t+ gzip ダンプ機能\n\t+ zip ダンプ機能\n* <NAME> <glund_at_silversoft.dk>\n\t+ 修正多数\n\t+ phpwizard.net の旧 phpMyAdmin ユーザフォーラムのモデレータ\n* <NAME> <korakot_at_iname.com>\n\t+ 「新しい行として挿入する」機能\n* <NAME> <webmaster_at_trafficg.com>\n\t+ ダンプコードの書き直しと修正\n\t+ バグフィックス\n* <NAME> <alberty_at_neptunlabs.de>\n\t+ PHP4 向けにダンプコードを書き直し\n\t+ mySQL テーブル統計機能\n\t+ バグフィックス\n* <NAME> <gandon_at_isia.cma.fr>\n\t+ バージョン 2.1.0.1 の主著者\n\t+ バグフィックス\n* <NAME> <me_at_derrabus.de>\n\t+ MySQL 4.0 / 4.1 / 5.0 との互換性\n\t+ MySQLi サポートによる抽象データベースインタフェース (PMA_DBI)\n\t+ 権限の管理\n\t+ [XML](index.html#term-xml) エクスポート\n\t+ 様々な機能や修正\n\t+ ドイツ語ファイルの更新\n* <NAME> <mike.beck_at_web.de>\n\t+ 定型問い合わせにおける自動結合処理\n\t+ 印刷用表示（printview）における links カラム\n\t+ リレーションビュー\n* <NAME> <michal_at_cihar.com>\n\t+ インデックス作成／表示機能の強化\n\t+ MySQL とは異なる HTML 文字セットを利用する機能\n\t+ エクスポート機能の改善\n\t+ 様々な機能や修正\n\t+ チェコ語ファイルの更新\n\t+ phpMyAdminの現在のウェブサイト\n* \"MySQL Form Generator for PHPMyAdmin\" の <NAME> (<https://sourceforge.net/projects/phpmysqlformgen/>)\n\t+ 複数テーブルを印刷用表示するためのパッチを提案\n* <NAME> <me_at_supergarv.de>\n\t+ テーブルの行を縦に表示するパッチの作成\n\t+ Javascript ベースのクエリウィンドウ + [SQL](index.html#term-sql) 履歴の作成\n\t+ カラム／データベースコメントの改善\n\t+ (MIME) - カラムの変換\n\t+ 左フレームのデータベースに独自の別名を利用\n\t+ テーブルの階層／入れ子表示\n\t+ [PDF](index.html#term-pdf) リレーションを WYSIWYG 配布するための [PDF](index.html#term-pdf) スクラッチボード\n\t+ 新しいアイコンセット\n\t+ カラムプロパティページの縦表示\n\t+ バグフィックス、追加機能、サポート、ドイツ語の追加を少々\n* <NAME> <kawada_at_den.fujifilm.co.jp>\n\t+ 日本語漢字エンコード変換機能\n* <NAME> <d3xter_at_users.sourceforge.net> および <NAME>\n\t+ クッキー認証モード\n* <NAME> <n8falke_at_users.sourceforge.net>\n\t+ テーブルリレーションリンク機能\n* <NAME> <delorme.maxime_at_free.fr>\n\t+ [PDF](index.html#term-pdf) スキーマ出力。 \"FPDF\" ライブラリ (<<http://www.fpdf.org/>> を参照) の <NAME>、 \"UFPDF\" ライブラリの Steven Wittens、 \"TCPDF\" ライブラリ (<<https://tcpdf.org/>> を参照) の Nicola Asuni にも感謝。\n* <NAME> <olof.edlund_at_upright.se>\n\t+ [SQL](index.html#term-sql) バリデータサーバ\n* <NAME> <ivanlanin_at_users.sourceforge.net>\n\t+ phpMyAdmin ロゴ（2004 年 6 月まで）\n* <NAME> <mike_at_graftonhall.co.nz>\n\t+ Horde プロジェクトより、blowfish ライブラリ (リリース 4.0 で終了)\n* <NAME> <ne0x_at_users.sourceforge.net>\n\t+ mysqli サポート\n\t+ たくさんのバグ修正と改善\n* Nicola Asuni (Tecnick.com)\n\t+ TCPDF ライブラリ (<<https://tcpdf.org>>)\n* <NAME> <mkkeck_at_users.sourceforge.net>\n\t+ 2.6.0 向けの再デザイン\n\t+ phpMyAdmin の帆船ロゴ（2004 年 6 月）\n* <NAME>\n\t+ カンファレンスでの発表\n* <NAME> <cybot_tm_at_users.sourceforge.net>\n\t+ インタフェースの改善\n\t+ バグフィックス多数\n* <NAME>\n\t+ 新しいレプリケーションデザイナ\n* <NAME> (Google Summer of Code 2008)\n\t+ BLOB ストリームをサポート (バージョン 4.0 からは非サポート)\n* <NAME> (Google Summer of Code 2008, 2010 and 2011)\n\t+ セットアップスクリプトの改良\n\t+ ユーザ設定機能\n\t+ Drizzle のサポート\n* <NAME> (Google Summer of Code 2009)\n\t+ インポートシステムの改良\n* <NAME> (Google Summer of Code 2009)\n\t+ コマンド追跡機能\n* <NAME> (Google Summer of Code 2009)\n\t+ 同期機能 (リリース 4.0 で削除)\n* <NAME> (Google Summer of Code 2009)\n\t+ レプリケーションサポート\n* <NAME> (Google Summer of Code 2010)\n\t+ 複数のフォーマットへのリレーションスキーマのエクスポート\n* <NAME> (Google Summer of Code 2010)\n\t+ ユーザインタフェースの改善\n\t+ ENUM/SET エディタ\n\t+ エクスポート／インポートの簡易インタフェース\n* <NAME> (Google Summer of Code 2010)\n\t+ Ajax 化したインタフェース\n* <NAME> (Google Summer of Code 2010)\n\t+ グラフ機能\n* <NAME>\n\t+ PBMS PHP 拡張による BLOB ストリームのサポート (バージョン 4.0 からは非サポート)\n* <NAME> (Google Summer of Code 2010)\n\t+ グラフィカルなクエリデザイナ\n* <NAME> (Google Summer of Code 2011)\n\t+ OpenGIS サポート\n* <NAME> (Google Summer of Code 2011)\n\t+ 検索プロット\n* <NAME> (Google Summer of Code 2011)\n\t+ ブラウザモードの改良\n* <NAME> (Google Summer of Code 2011)\n\t+ AJAX 化\n* <NAME> (Google Summer of Code 2011)\n\t+ ステータスページのクエリ集計とグラフ\n* <NAME> (Google Summer of Code 2011)\n\t+ 自動化されたテスト\n* <NAME> (Google Summer of Code 2011 および 2012)\n\t+ ストアドルーチン、トリガ、イベントのサポートの改善\n\t+ イタリア語の翻訳更新\n\t+ フレームの削除、新しいナビゲーション\n* <NAME>\n\t+ バグフィックス多数\n\t+ オランダ語の翻訳更新\n* <NAME> (Google Summer of Code 2012)\n\t+ 新しいプラグインとプロパティのシステム\n* <NAME> (Google Summer of Code 2012)\n\t+ 構造改善\n* <NAME> (Google Summer of Code 2012)\n\t+ 構造改善\n* <NAME> (Google Summer of Code 2012)\n\t+ 構造改善\n* <NAME> (Google Summer of Code 2012)\n\t+ 自動化されたテスト\n* <NAME>ginton (phpseclib.sourceforge.net)\n\t+ phpseclib\n* <NAME> (Google Summer of Code 2013)\n\t+ 構造改善\n* <NAME> (Google Summer of Code 2013)\n\t+ 構造改善\n* <NAME> (Google Summer of Code 2013)\n\t+ AJAX のエラー報告\n* <NAME> (Google Summer of Code 2013)\n\t+ 自動化されたテスト\n* <NAME> (Google Summer of Code 2013)\n\t+ 自動化されたテスト\n* <NAME> (Google Summer of Code 2013)\n\t+ インタフェースの改善\n* <NAME>\n\t+ 例によるクエリの読み込み/保存 (データベース検索ブックマーク)\n* <NAME> (Google Summer of Code 2014)\n\t+ 主要カラムリスト\n\t+ テーブル構造の改善 (正規化)\n* <NAME> (Google Summer of Code 2014)\n\t+ インタフェースの改善\n* <NAME> (Google Summer of Code 2014)\n\t+ PHP エラーレポート\n* <NAME> (Google Summer of Code 2014)\n\t+ SQL クエリコンソール\n* <NAME> (Google Summer of Code 2014)\n\t+ 構造改善: デザイナーとスキーマの統合\n* <NAME> (Google Summer of Code 2014)\n\t+ カスタムフィールドハンドラ (MIME 変換に基づく入力)\n\t+ テーブル/カラムの名前を変更してエクスポート\n* <NAME> (Google Summer of Code 2015)\n\t+ 新しいパーサとアナライザ\n* <NAME> (Google Summer of Code 2015)\n\t+ ページ関連の設定\n\t+ SQL デバッグのコンソールへの統合\n\t+ その他のユーザインタフェースの改善\n* <NAME> (Google Summer of Code 2015)\n\t+ CSS を使用した印刷ビュー\n\t+ その他のユーザインタフェースの改善と新機能\n* <NAME> (Google Summer of Code 2017)\n\t+ エラー報告サーバの改良\n\t+ Selenium テストの改良\n* <NAME> (Google Summer of Code 2017)\n\t+ モバイルユーザインタフェース\n\t+ インライン JavaScript コードの除去\n\t+ その他のユーザインタフェースの改善\n* <NAME> (Google Summer of Code 2017)\n\t+ 複数テーブルのクエリインタフェース\n\t+ デザイナーでほかのデータベースのテーブルで作業できるようにした\n\t+ その他のユーザインタフェースの改善\n* <NAME>\n\t+ 主要な改良と JavaScript コアへのアップグレード\n\t+ JavaScript ライブラリ機能の近代化\n\t+ テンプレートの最新化と Twig の導入\n* <NAME>\n\t+ PHPStan に基づくコーディングスタイルの改善\n\t+ 外部の MySQL および MariaDB のドキュメントへのリンクの改善\n\t+ その他の多数のバグ修正\n* <NAME>\n\t+ 総合的なセキュリティ評価と提案\n* <NAME> (Google Summer of Code 2018)\n\t+ 次のような様々な改善点があります。\n\t\t- ユーザ設定のローカルストレージへの統合\n\t\t- セッションの期限切れ後のモーダルログインの使用\n\t\t- CHECK CONSTRAINTS の対応の追加\n\t\t- その他\n* <NAME> (Google Summer of Code 2018)\n\t+ テーマ自動生成ツール\n* <NAME> (Google Summer of Code 2018)\n\t+ Twig テンプレートの構造改善およびその他の内部コードの改善\n* Piyush Vijay (Google Summer of Code 2018)\n\t+ Webpack、Babel、Yarn、eslint、Jsdoc の導入を含む JavaScript コードの最新化\n\nその他、バージョン 2.1.0 以降、細々とした修正、強化、バグフィックス、新規言語サポート等をしてくださった方々。\n\n<NAME>, Ricardo ?, <NAME>, <NAME>,\n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>,\n<NAME>, <NAME>, <NAME>, <NAME>,\n<NAME>, <NAME>, <NAME>, \"Sakamoto\", <NAME>, www.securereality.com.au, <NAME>, <NAME>, <NAME>,\n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>.,\n<NAME>, <NAME>, <NAME>, Vinay,\n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>, \"Manuzhai\".\n\n### 翻訳者[¶](#translators)\n\n以下の方々が phpMyAdmin の翻訳に貢献しました。\n\n* アルバニア語\n\n> \t+ <NAME> <acokaj_at_shkoder.net>\n>\n* アラビア語\n\n> \t+ <NAME> <a.saleh.ismael_at_gmail.com>\n> \t+ <NAME> <egbrave_at_hotmail.com>\n> \t+ <NAME> <persiste1_at_gmail.com>\n>\n* アルメニア語\n\n> \t+ <NAME> <aaleksanyants_at_yahoo.com>\n>\n* アゼルバイジャン語\n\n> \t+ Mircəlal <01youknowme_at_gmail.com>\n> \t+ Huseyn <huseyn_esgerov_at_mail.ru>\n> \t+ <NAME> <sevdimaliisayev_at_mail.ru>\n> \t+ Jafar <sharifov_at_programmer.net>\n>\n* ベラルーシ語\n\n> \t+ <NAME> <vipals_at_gmail.com>\n>\n* ブルガリア語\n\n> \t+ <NAME> <bkehayov_at_gmail.com>\n> \t+ <NAME> <blagynchy_at_gmail.com>\n> \t+ <NAME> <hudsonvsm_at_gmail.com>\n> \t+ P <plamen_mbx_at_yahoo.com>\n> \t+ krasimir <vip_at_krasio-valia.com>\n>\n* カタルーニャ語\n\n> \t+ j<NAME> <jconstanti_at_yahoo.es>\n> \t+ <NAME> <xvnavarro_at_gmail.com>\n>\n* 中国語 (中国)\n\n> \t+ <NAME> <3092849_at_qq.com>\n> \t+ <NAME> <clanboy_at_163.com>\n> \t+ disorderman <disorderman_at_qq.com>\n> \t+ <NAME> <duguying2008_at_gmail.com>\n> \t+ <fundawang_at_gmail.com>\n> \t+ popcorner <memoword_at_163.com>\n> \t+ <NAME> <qyz.yswy_at_hotmail.com>\n> \t+ zz <tczzjin_at_gmail.com>\n> \t+ <NAME> <wengshiyu_at_gmail.com>\n> \t+ whh <whhlcj_at_126.com>\n>\n* 中国語 (台湾)\n\n> \t+ <NAME> <albb0920_at_gmail.com>\n> \t+ <NAME> <cwlin0416_at_gmail.com>\n> \t+ <NAME> <xs910203_at_gmail.com>\n>\n* ケルン語\n\n> \t+ Purodha <publi_at_web.de>\n>\n* チェコ語\n\n> \t+ <NAME> <ales_at_hakl.net>\n> \t+ <NAME> <dalibor.straka3_at_gmail.com>\n> \t+ <NAME> <martin_at_vidner.net>\n> \t+ <NAME> <ondrasek.simecek_at_gmail.com>\n> \t+ <NAME> <palider_at_seznam.cz>\n> \t+ <NAME> <petr.katerinak_at_gmail.com>\n>\n* デンマーク語\n\n> \t+ Aputsiaĸ <NAME> <aj_at_isit.gl>\n> \t+ <NAME> <dennis.jakobsen_at_gmail.com>\n> \t+ Jonas <jonas.den.smarte_at_gmail.com>\n> \t+ <NAME> <just.my.smtp.server_at_gmail.com>\n>\n* オランダ語\n\n> \t+ 1. Voogt <a.voogt_at_hccnet.nl>\n> \t+ dingo thirteen <dingo13_at_gmail.com>\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n> \t+ <NAME> <ruleant_at_users.sourceforge.net>\n> \t+ <NAME> <strijbol.niko_at_gmail.com>\n>\n* 英語 (イギリス)\n\n> \t+ <NAME> <dries.verschuere_at_outlook.com>\n> \t+ <NAME> <j.francisco.o.rocha_at_zoho.com>\n> \t+ <NAME> <marc_at_infomarc.info>\n> \t+ <NAME> <tomastik.m_at_gmail.com>\n>\n* エスペラント語\n\n> \t+ Eliovir <eliovir_at_gmail.com>\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n>\n* エストニア語\n\n> \t+ <NAME> <kristjanrats_at_gmail.com>\n>\n* フィンランド語\n\n> \t+ <NAME> <jremes_at_outlook.com>\n> \t+ <NAME> <lari_at_oesch.me>\n>\n* フランス語\n\n> \t+ <NAME> <marc_at_infomarc.info>\n>\n* フリジア語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n>\n* ガリシア語\n\n> \t+ <NAME> <xosecalvo_at_gmail.com>\n>\n* ドイツ語\n\n> \t+ <NAME> <github.com-t3if_at_ladisch.de>\n> \t+ <NAME> <jan.zassenhaus_at_jgerman.de>\n> \t+ <NAME> <lasse_at_mydom.de>\n> \t+ <NAME> <matthias_at_bluthardt.org>\n> \t+ <NAME> <michael.koch_at_enough.de>\n> \t+ Ann + J.M. <phpMyAdmin_at_ZweiSteinSoft.de>\n> \t+ <pma_at_sebastianmendel.de>\n> \t+ <NAME> <rohmberger_at_hotmail.de>\n> \t+ <NAME> <sqrt_at_entless.org>\n>\n* ギリシア語\n\n> \t+ Παναγιώτης Παπάζογλου <papaz_p_at_yahoo.com>\n>\n* ヘブライ語\n\n> \t+ <NAME> <mmh15_at_windowslive.com>\n> \t+ <NAME> <sh.yaron_at_gmail.com>\n> \t+ <NAME> <visokereyal_at_gmail.com>\n>\n* ヒンズー語\n\n> \t+ <NAME> <atulpratapsingh05_at_gmail.com>\n> \t+ Yogeshwar <charanyogeshwar_at_gmail.com>\n> \t+ <NAME> <devenbansod.bits_at_gmail.com>\n> \t+ <NAME> <kushagra4296_at_gmail.com>\n> \t+ <NAME> <nisargjhaveri_at_gmail.com>\n> \t+ <NAME> <roohan_cena_at_yahoo.co.in>\n> \t+ <NAME> <yug.scorpio_at_gmail.com>\n>\n* ハンガリー語\n\n> \t+ <NAME> <erosakos02_at_gmail.com>\n> \t+ <NAME> <leedermeister_at_gmail.com>\n> \t+ <NAME> <undernetangel_at_gmail.com>\n> \t+ <NAME> <urbalazs_at_gmail.com>\n>\n* インドネシア語\n\n> \t+ <NAME> <Deky40_at_gmail.com>\n> \t+ <NAME> <andika_at_gmail.com>\n> \t+ <NAME> <da2n_s_at_yahoo.co.id>\n> \t+ <NAME> <dadan.setia_at_gmail.com>\n> \t+ <NAME> <edwin_at_yohanesedwin.com>\n> \t+ <NAME> <fadhiilrachman_at_gmail.com>\n> \t+ Benny <tarzq28_at_gmail.com>\n> \t+ <NAME> <tommy_at_surbakti.net>\n> \t+ <NAME> <zufar.bogor_at_gmail.com>\n>\n* インターリングア\n\n> \t+ <NAME> <g.sora_at_tiscali.it>\n>\n* イタリア語\n\n> \t+ <NAME> <francesco.giacobazzi_at_ferrania.it>\n> \t+ <NAME> <ironpotts_at_gmail.com>\n> \t+ <NAME> <stefano.ste.martinelli_at_gmail.com>\n>\n* 日本語\n\n> \t+ k725 <alexalex.kobayashi_at_gmail.com>\n> \t+ <NAME> <hiroshi.chiyokawa_at_gmail.com>\n> \t+ <NAME> <orzkun_at_ageage.jp>\n> \t+ worldwideskier <worldwideskier_at_yahoo.co.jp>\n>\n* カンナダ語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n> \t+ <NAME> <shameem.sam_at_gmail.com>\n>\n* 韓国語\n\n> \t+ <NAME> <bskim45_at_gmail.com>\n> \t+ <NAME> <cdac1234_at_gmail.com>\n> \t+ <NAME> <dckyoung_at_gmail.com>\n> \t+ <NAME> <greatymh_at_gmail.com>\n> \t+ JongDeok <human.zion_at_gmail.com>\n> \t+ <NAME> <kim_at_nhn.com>\n> \t+ 이경준 <kyungjun2_at_gmail.com>\n> \t+ <NAME> <skshin_at_gmail.com>\n> \t+ <NAME> <virusyoon_at_gmail.com>\n> \t+ <NAME> <youngminz.kr_at_gmail.com>\n>\n* 中央クルド語\n\n> \t+ <NAME> <alan.hilal94_at_gmail.com>\n> \t+ <NAME> <aso.naderi_at_gmail.com>\n> \t+ muhammad <esy_vb_at_yahoo.com>\n> \t+ <NAME> <zhyarabdulla94_at_gmail.com>\n>\n* ラトビア語\n\n> \t+ Latvian TV <dnighttv_at_gmail.com>\n> \t+ <NAME> <edgarsneims5092_at_inbox.lv>\n> \t+ Ukko <perkontevs_at_gmail.com>\n>\n* リンブルフ語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n>\n* リトアニア語\n\n> \t+ <NAME> <v.motuzas_at_gmail.com>\n>\n* マレー語\n\n> \t+ <NAME> <amir.overlord666_at_gmail.com>\n> \t+ diprofinfiniti <anonynuine-999_at_yahoo.com>\n>\n* ネパール語\n\n> \t+ <NAME> <nnabinn_at_hotmail.com>\n>\n* ノルウェー語ブークモール\n\n> \t+ <NAME> <borge947_at_gmail.com>\n> \t+ <NAME> <danorse_at_gmail.com>\n> \t+ <NAME> <efroys_at_gmail.com>\n> \t+ <NAME> <kurt_at_kheds.com>\n> \t+ <NAME> <ph3n1x.nobody_at_gmail.com>\n> \t+ Sebastian <sebastian_at_sgundersen.com>\n> \t+ Tomas <tomas_at_tomasruud.com>\n>\n* ペルシア語\n\n> \t+ ashkan shirian <ashkan.shirian_at_gmail.com>\n> \t+ HM <goodlinuxuser_at_chmail.ir>\n>\n* ポーランド語\n\n> \t+ Andrzej <andrzej_at_kynu.pl>\n> \t+ Przemo <info_at_opsbielany.waw.pl>\n> \t+ <NAME> <krystian4842_at_gmail.com>\n> \t+ <NAME> <maciejka45_at_gmail.com>\n> \t+ <NAME> <vonflynee_at_gmail.com>\n>\n* ポルトガル語\n\n> \t+ <NAME> <alexandre.badalo_at_sapo.pt>\n> \t+ <NAME> <geral_at_jonilive.com>\n> \t+ <NAME> <p.m42.ribeiro_at_gmail.com>\n> \t+ <NAME> <sandro123iv_at_gmail.com>\n>\n* ポルトガル語 (ブラジル)\n\n> \t+ <NAME> <alexrohleder96_at_outlook.com>\n> \t+ <NAME> <brunomendax_at_gmail.com>\n> \t+ <NAME> <danilo.eng_at_globomail.com>\n> \t+ <NAME> <douglas.kollar_at_pg.df.gov.br>\n> \t+ <NAME> <douglaseccker_at_hotmail.com>\n> \t+ <NAME> <edjacobjunior_at_gmail.com>\n> \t+ <NAME> <g.szsilva_at_gmail.com>\n> \t+ <NAME> <gui_at_webseibt.net>\n> \t+ <NAME> <helder.bs.santana_at_gmail.com>\n> \t+ <NAME> <jrzancan_at_hotmail.com>\n> \t+ Luis <luis.eduardo.braschi_at_outlook.com>\n> \t+ <NAME> <malgeri_at_gmail.com>\n> \t+ <NAME> <marc_at_infomarc.info>\n> \t+ <NAME> <renatomdd_at_yahoo.com.br>\n> \t+ <NAME> <thiago.casotti_at_uol.com.br>\n> \t+ <NAME> <victor.laureano_at_gmail.com>\n> \t+ <NAME> <vinipitta_at_gmail.com>\n> \t+ <NAME> <washingtonbruno_at_msn.com>\n> \t+ <NAME> <yansilvagabriel_at_gmail.com>\n>\n* パンジャブ語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n>\n* ルーマニア語\n\n> \t+ Alex <amihaita_at_yahoo.com>\n> \t+ <NAME> <costa1988sv_at_gmail.com>\n> \t+ <NAME> <john_at_panevo.ro>\n> \t+ <NAME> <molnar.raul_at_wservices.eu>\n> \t+ Deleted User <noreply_at_weblate.org>\n> \t+ <NAME> <stefan.murariu_at_yahoo.com>\n>\n* ロシア語\n\n> \t+ <NAME> <aaleksanyants_at_yahoo.com>\n> \t+ <ddrmoscow_at_gmail.com>\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n> \t+ <NAME> <khomutov.ivan_at_mail.ru>\n> \t+ <NAME> <orion1979_at_yandex.ru>\n> \t+ <NAME> <salvadoporjc_at_gmail.com>\n> \t+ <NAME> <unlucky_at_inbox.ru>\n>\n* セルビア語\n\n> \t+ Smart Kid <kidsmart33_at_gmail.com>\n>\n* シンハラ語\n\n> \t+ <NAME> <madhura.cj_at_gmail.com>\n>\n* スロバキア語\n\n> \t+ <NAME> <martin_at_whistler.sk>\n> \t+ <NAME> <parkourpotex_at_gmail.com>\n> \t+ <NAME> <pistej2_at_gmail.com>\n>\n* スロベニア語\n\n> \t+ Domen <mitenem_at_outlook.com>\n>\n* スペイン語\n\n> \t+ <NAME>, MD <phpmyadmin_at_cerebroperiferico.com>\n> \t+ <NAME> <floss.dev_at_gmail.com>\n> \t+ Franco <fulanodetal.github1_at_openaliasbox.org>\n> \t+ <NAME> <luisan00_at_hotmail.com>\n> \t+ Macofe <macofe.languagetool_at_gmail.com>\n> \t+ <NAME> <matiasbellone+weblate_at_gmail.com>\n> \t+ <NAME>. <ra4_at_openmailbox.org>\n> \t+ FAMMA TV NOTICIAS MEDIOS DE CO <revistafammatvmusic.oficial_at_gmail.com>\n> \t+ <NAME> <ronniesimonf_at_gmail.com>\n>\n* スウェーデン語\n\n> \t+ <NAME> <anders.jonsson_at_norsjovallen.se>\n>\n* タミル語\n\n> \t+ கணேஷ் குமார் <GANESHTHEONE_at_gmail.com>\n> \t+ <NAME> <achch1990_at_gmail.com>\n> \t+ <NAME> <rifthy456_at_gmail.com>\n>\n* タイ語\n\n> \t+ <nontawat39_at_gmail.com>\n> \t+ <NAME>. <somthanat_at_gmail.com>\n>\n* トルコ語\n\n> \t+ <NAME> <hitowerdigit_at_hotmail.com>\n>\n* ウクライナ語\n\n> \t+ <NAME> <nitrotoll_at_gmail.com>\n> \t+ Igor <vmta_at_yahoo.com>\n> \t+ <NAME> <vperekupka_at_gmail.com>\n>\n* ベトナム語\n\n> \t+ <NAME> <baophan94_at_icloud.com>\n> \t+ <NAME> <mr.hungdx_at_gmail.com>\n> \t+ <NAME> <trinhminhbao_at_gmail.com>\n>\n* 西フラマン語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n### ドキュメントの翻訳者[¶](#documentation-translators)\n\n以下の方々が phpMyAdmin のドキュメントの翻訳に貢献してくださいました。\n\n* アルバニア語\n\n> \t+ <NAME> <acokaj_at_shkoder.net>\n>\n* アラビア語\n\n> \t+ <NAME> <ahmedtek1993_at_gmail.com>\n> \t+ <NAME> <omar_2412_at_live.com>\n>\n* アルメニア語\n\n> \t+ <NAME> <aaleksanyants_at_yahoo.com>\n>\n* アゼルバイジャン語\n\n> \t+ Mircəlal <01youknowme_at_gmail.com>\n> \t+ <NAME> <sevdimaliisayev_at_mail.ru>\n>\n* カタルーニャ語\n\n> \t+ j<NAME> <jconstanti_at_yahoo.es>\n> \t+ <NAME> <joan_at_montane.cat>\n> \t+ <NAME> <xvnavarro_at_gmail.com>\n>\n* 中国語 (中国)\n\n> \t+ <NAME> <3092849_at_qq.com>\n> \t+ 罗攀登 <6375lpd_at_gmail.com>\n> \t+ disorderman <disorderman_at_qq.com>\n> \t+ ITXiaoPang <djh1017555_at_126.com>\n> \t+ tunnel213 <tunnel213_at_aliyun.com>\n> \t+ <NAME> <wengshiyu_at_gmail.com>\n> \t+ whh <whhlcj_at_126.com>\n>\n* 中国語 (台湾)\n\n> \t+ <NAME> <cwlin0416_at_gmail.com>\n> \t+ <NAME> <xs910203_at_gmail.com>\n>\n* チェコ語\n\n> \t+ <NAME> <ales_at_hakl.net>\n> \t+ <NAME> <michal_at_cihar.com>\n> \t+ <NAME> <palider_at_seznam.cz>\n> \t+ <NAME> <petr.katerinak_at_gmail.com>\n>\n* デンマーク語\n\n> \t+ Aputsiaĸ <NAME> <aj_at_isit.gl>\n> \t+ <NAME> <just.my.smtp.server_at_gmail.com>\n>\n* オランダ語\n\n> \t+ 1. Voogt <a.voogt_at_hccnet.nl>\n> \t+ dingo thirteen <dingo13_at_gmail.com>\n> \t+ <NAME> <dries.verschuere_at_outlook.com>\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n> \t+ <NAME> <nast3zz_at_gmail.com>\n> \t+ <NAME> <ray_at_datahuis.net>\n> \t+ <NAME> <ruleant_at_users.sourceforge.net>\n> \t+ <NAME> <tom.hofman_at_gmail.com>\n>\n* エストニア語\n\n> \t+ <NAME> <kristjanrats_at_gmail.com>\n>\n* フィンランド語\n\n> \t+ Juha <jremes_at_outlook.com>\n>\n* フランス語\n\n> \t+ <NAME> <cedric.corazza_at_wanadoo.fr>\n> \t+ <NAME> <etienne.gilli_at_gmail.com>\n> \t+ <NAME> <marc_at_infomarc.info>\n> \t+ Donavan_Martin <mart.donavan_at_hotmail.com>\n>\n* フリジア語\n\n> \t+ <NAME> <info_at_robinvandervliet.nl>\n>\n* ガリシア語\n\n> \t+ <NAME> <xosecalvo_at_gmail.com>\n>\n* ドイツ語\n\n> \t+ Daniel <d.gnauk89_at_googlemail.com>\n> \t+ <NAME> <janhenrikm_at_yahoo.de>\n> \t+ <NAME> <lasse_at_mydom.de>\n> \t+ <NAME> <michael.koch_at_enough.de>\n> \t+ Ann + J.M. <phpMyAdmin_at_ZweiSteinSoft.de>\n> \t+ <NAME> <predatorix_at_web.de>\n> \t+ <NAME> <rohmberger_at_hotmail.de>\n> \t+ <NAME> <sqrt_at_entless.org>\n>\n* ギリシア語\n\n> \t+ Παναγιώτης Παπάζογλου <papaz_p_at_yahoo.com>\n>\n* ハンガリー語\n\n> \t+ <NAME> <urbalazs_at_gmail.com>\n>\n* イタリア語\n\n> \t+ <NAME> <francesco.giacobazzi_at_ferrania.it>\n> \t+ <NAME> <ironpotts_at_gmail.com>\n> \t+ <NAME> <stefano.ste.martinelli_at_gmail.com>\n> \t+ TWS <tablettws_at_gmail.com>\n>\n* 日本語\n\n> \t+ <NAME> <ek_at_luna.miko.im>\n> \t+ <NAME> <hiroshi.chiyokawa_at_gmail.com>\n>\n* リトアニア語\n\n> \t+ <NAME> <atvejis_at_gmail.com>\n> \t+ Dovydas <dovy.buz_at_gmail.com>\n>\n* ノルウェー語ブークモール\n\n> \t+ <NAME> <danorse_at_gmail.com>\n> \t+ <NAME> <kurt_at_kheds.com>\n>\n* ポルトガル語 (ブラジル)\n\n> \t+ <NAME> <alemoretti2010_at_hotmail.com>\n> \t+ <NAME> <douglas.kollar_at_pg.df.gov.br>\n> \t+ <NAME> <gui_at_webseibt.net>\n> \t+ <NAME> <helder.bs.santana_at_gmail.com>\n> \t+ <NAME> <michal_at_cihar.com>\n> \t+ <NAME> <michel.ekio_at_gmail.com>\n> \t+ <NAME> <mrdaniloazevedo_at_gmail.com>\n> \t+ <NAME> <thiago.casotti_at_uol.com.br>\n> \t+ <NAME> <vinipitta_at_gmail.com>\n> \t+ <NAME> <yansilvagabriel_at_gmail.com>\n>\n* スロバキア語\n\n> \t+ <NAME> <martin_at_whistler.sk>\n> \t+ <NAME> <michal_at_cihar.com>\n> \t+ <NAME> <pistej2_at_gmail.com>\n>\n* スロベニア語\n\n> \t+ Domen <mitenem_at_outlook.com>\n>\n* スペイン語\n\n> \t+ <NAME> <floss.dev_at_gmail.com>\n> \t+ Franco <fulanodetal.github1_at_openaliasbox.org>\n> \t+ <NAME> <matiasbellone+weblate_at_gmail.com>\n> \t+ <NAME> <ronniesimonf_at_gmail.com>\n>\n* トルコ語\n\n> \t+ <NAME> <hitowerdigit_at_hotmail.com>\n### バージョン 2.1.0 当時の貢献者一覧[¶](#original-credits-of-version-2-1-0)\n\nこのソフトのベースとなったのは <NAME> の MySQL-Webadmin です。PHP3 を使ってウェブベースの MySQL インタフェースを作るというのは元々彼のアイデアだったのです。私も、彼のソースコードはいっさい利用していませんが、いくつかのコンセプトはお借りしました。phpMyAdmin を作ったのは、彼がもうその（偉大な）ツールの開発を続けるつもりがないと言ったからです。\n\n以下の方々に感謝します。\n\n* <NAME> <ak-lsml_at_living-source.com> はテーブルやデータベースを削除するときのチェックコードを提供してくださいました。また、tbl_create.php3 に主キーを指定できるようにしたらどうかと薦めてくださったのも彼です。バージョン 1.1.1 にはバグレポートだけでなくldi_*.php3-set（テキストファイルのインポート）も提供してくださいました。小さな改善も多数いただいています。\n* <NAME> <jan_at_nrw.net> は、バージョン 1.3.0 で導入された変更点の大部分を作ってくださいました (特に重要なものとしては認証があります)。バージョン 1.4.1 ではテーブルダンプ機能を増強してくださいました。バグフィックスや援助も多数いただいています。\n* <NAME> <DelislMa_at_CollegeSherbrooke.qc.ca> は、文字列を別ファイルにアウトソースすることで phpMyAdmin を言語に依存しないものにしました。フランス語への翻訳にも貢献しました。\n* <NAME> <abravo_at_hq.admiral.ru> は、tbl_select.php3 を提供してくださいました。これはテーブルのいくつかのフィールドのみを表示する機能です。\n* <NAME> <chrisj_at_ctel.net>。tbl_change.php3 に MySQL 関数のサポートを追加してくださいました。2.0 では「定型問い合わせ」機能も追加してくださっています。\n* <NAME> <walton_at_nordicdms.com>。複数のサーバのサポートを追加してくださいました。バグフィックスをくださる常連でもあります。\n* <NAME> <ga244_at_is8.nyu.edu>。バージョン 2.0.6 のランダムアクセス機能を提供してくださいました。\n\n細々とした修正、強化、バグフィックス、新規言語サポート等をしてくださった方々。\n\n<NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>,\n<NAME>, <NAME>.\n\nまた、提案、バグレポート、単なる感想など、私にメールをくださったすべての方々に感謝します。\n\n用語集[¶](#glossary-1)\n---\n\nフリー百科事典 Wikipedia より\n\n.htaccess Apache のディレクトリ単位での設定ファイルのデフォルト名。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/.htaccess>ACL Access Control List (アクセス制御リスト)\nBlowfish\n[<NAME>](https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%AB%E3%83%BC%E3%82%B9%E3%83%BB%E3%82%B7%E3%83%A5%E3%83%8A%E3%82%A4%E3%82%A2%E3%83%BC) が1993年に開発したキーを持つ対称ブロック暗号。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Blowfish>ブラウザ World Wide Web 上のウェブサイトでウェブページに一般的に置かれているテキスト、画像、その他の情報をユーザに対して表示や双方向通信することができるアプリケーション。\n\n参考\n\n<<http://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A7%E3%83%96%E3%83%96%E3%83%A9%E3%82%A6%E3%82%B6>bzip2 <NAME> 氏により開発されたフリーソフトウェアでオープンソースのデータ圧縮アルゴリズムおよびプログラム。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Bzip2>CGI CGI (コモン・ゲートウェイ・インタフェース) は、クライアントのウェブブラウザが、ウェブサーバ上で実行されるプログラムからのデータを要求することができる重要な World Wide Web 技術です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Common_Gateway_Interface>変更履歴 プロジェクトに対して行われた変更のログまたは記録。\n\n参考\n\n<<https://en.wikipedia.org/wiki/Changelog>クライアント ネットワークなどを介して他のコンピュータ上の (リモート) サービスにアクセスするコンピュータシステムのこと。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%A9%E3%82%A4%E3%82%A2%E3%83%B3%E3%83%88_(%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF)>カラム 特定の単一の型のデータ値の集まり。テーブルの各行に対しての一要素でもある。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E5%B1%9E%E6%80%A7_(%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9)>クッキー サーバにアクセスするたびにサーバから送信され World Wide Web ブラウザから送り返される情報のひとかたまり。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/HTTP_cookie>CSV カンマ区切りの値\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Comma-Separated_Values>DB\n[データベース](#term-database) を参照 データベース\n組織化されたデータの集まり。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9>エンジン\n[ストレージエンジン](#term-storage-engines) を参照 PHP 拡張モジュール PHP を追加機能で拡張する PHP モジュール。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%A9%E3%82%B0%E3%82%A4%E3%83%B3>FAQ Frequently Asked Questions は、よく尋ねられる質問とその答えの一覧です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/FAQ>フィールド 分割されたデータの一部分、またはカラム。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A3%E3%83%BC%E3%83%AB%E3%83%89_(%E8%A8%88%E7%AE%97%E6%A9%9F%E7%A7%91%E5%AD%A6)>外部キー データベースの行のカラムまたはカラムの集合の１つ。これらは、(通常は異なる) テーブル内における別のデータベースの行のキーを形成しているカラムキーまたはカラム集合キーを指している。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E5%A4%96%E9%83%A8%E3%82%AD%E3%83%BC>GD <NAME>ell 氏他によって開発された動的に画像を操作するためのグラフィックライブラリ。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/GD_Graphics_Library>GD2\n[GD](#term-gd) を参照 GZip\nGZip はGNU zip の略称で、GNU フリーソフトウェアファイル圧縮プログラムのことです。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Gzip>ホスト コンピュータネットワークに接続された任意のマシンのこと。ホスト名を持っているノード。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%9B%E3%82%B9%E3%83%88_(%E3%83%8D%E3%83%83%E3%83%88%E3%83%AF%E3%83%BC%E3%82%AF)>ホスト名 ネットワーク接続された端末のネットワーク上における一意の名前。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%9B%E3%82%B9%E3%83%88%E5%90%8D>HTTP HTTP (ハイパーテキスト転送プロトコル) は、 World Wide Web 上で情報を転送したり伝えたりするために使用される主な方法です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Hypertext_Transfer_Protocol>HTTPS セキュリティ対策を付加した [HTTP](#term-http) 接続。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/HTTPS>IEC 国際電気標準会議\nIIS IIS (Internet Information Services) は Microsoft Windows を使用しているサーバ用のインターネット基礎サービスのセットです。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Internet_Information_Services>インデックス テーブル内の行に素早くアクセスできるようにするための機能。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E7%B4%A2%E5%BC%95_(%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9)>IP インターネット・プロトコル (Internet Protocol) は、パケット交換ネットワーク間でデータを通信するための、送信元と宛先のホストで使用されるデータ指向のプロトコルです。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Internet_Protocol>IP アドレス インターネット・プロトコル標準で使用される、ネットワーク上で相互に識別し通信する端末に使用される一意の番号。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/IP%E3%82%A2%E3%83%89%E3%83%AC%E3%82%B9>IPv6 IPv6 (Internet Protocol version 6) は Internet Protocol ([IP](#term-ip)) の最新版であり、その前身の IPv4 がアドレスを使い果たしたことの長年の問題に対処するように設計されています。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/IPv6>ISAPI Internet Server Application Programming Interface は Internet Information Services (IIS) の API です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/ISAPI>ISP ISP (インターネット・サービス・プロバイダ) は、インターネット関連サービスへのユーザアクセスを提供している企業や組織です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%82%A4%E3%83%B3%E3%82%BF%E3%83%BC%E3%83%8D%E3%83%83%E3%83%88%E3%82%B5%E3%83%BC%E3%83%93%E3%82%B9%E3%83%97%E3%83%AD%E3%83%90%E3%82%A4%E3%83%80>ISO 国際標準化機構\n\n参考\n\n[ISO 組織ウェブサイト](https://www.iso.org/about-us.html)\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E5%9B%BD%E9%9A%9B%E6%A8%99%E6%BA%96%E5%8C%96%E6%A9%9F%E6%A7%8B>JPEG 写真画像の非可逆圧縮に使われる最も一般的で標準的な方法。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/JPEG>JPG\n[JPEG](#term-jpeg) を参照 キー\n[インデックス](#term-index) を参照 LaTeX\nTeX 組版プログラムのための文書準備システム。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/LaTeX>Mac Apple Macintosh は、 Apple Inc. が設計、開発、製造、販売しているパソコンの製品群です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Macintosh>macOS 一般消費者およびプロの市場向けに現在出荷されている全ての Apple Macintosh コンピュータに含まれているオペレーティングシステム。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/MacOS>mbstring PHP mbstring 機能は、マルチバイト文字セット、特に UTF-8 で表された言語の対応を提供します。\n\nこの拡張モジュールのインストールで問題が発生したときは、 [1.20 mysqli や mysql 拡張モジュールがないというエラーが出ます。](index.html#faqmysql) に良いヒントが書かれているので参照してください。\n\n参考\n\n<<https://www.php.net/manual/ja/book.mbstring.php>メディア型 メディア型 (以前は MIME タイプと呼ばれていた) は 2 つの部分からなる識別子で、インターネットで転送されるファイル形式とファイルの内容を識別します。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%A1%E3%83%87%E3%82%A3%E3%82%A2%E3%82%BF%E3%82%A4%E3%83%97>MIME 多目的インターネットメール拡張は、電子メール書式におけるインターネット標準です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Multipurpose_Internet_Mail_Extensions>モジュール Apache HTTP サーバ httpd の拡張機能。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Apache_HTTP_Server>mod_proxy_fcgi Fast CGI インタフェースを実装するための Apache モジュールです。 PHP は CGI モジュール、 FastCGI、または直接の Apache モジュールとして実行することができます。\n\n参考\n\n<<https://en.wikipedia.org/wiki/Mod_proxy>MySQL マルチスレッド、マルチユーザの SQL (Structured Query Language) によるデータベース管理システム (DBMS)。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/MySQL>MySQLi 改良された MySQL クライアントの PHP 拡張モジュール。\n\n参考\n\n[PHP マニュアルの MySQL 改良版拡張モジュール](https://www.php.net/manual/ja/book.mysqli.php)\n\n参考\n\n<<https://en.wikipedia.org/wiki/MySQLi>mysql MySQL クライアントの PHP 拡張。\n\n参考\n\n<<https://www.php.net/manual/ja/book.mysql.php>OpenDocument オフィス文書のオープン標準の一つ。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/OpenDocument>OS X\n[macOS](#term-macos) を参照。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/MacOS>PDF PDF (ポータブル・ドキュメント・フォーマット) は、 Adobe Systems よって開発された装置や解像度に依存しない形式で二次元ドキュメントを表現するためのファイル形式。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Portable_Document_Format>PEAR PHP 拡張モジュールとアプリケーションのリポジトリ。\n\n参考\n\n[PEAR ウェブサイト](https://pear.php.net/)\n\n参考\n\n[Wikipedia の PEAR ページ](https://ja.wikipedia.org/wiki/PEAR)\n\nPCRE PCRE (Perl Compatible Regular Expressions) は Perl 互換の PHP 正規表現関数群です\n\n参考\n\n<<https://www.php.net/pcre>参考\n\n[PHP マニュアルの 正規表現 (Perl 互換)](https://www.php.net/pcre)\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Perl_Compatible_Regular_Expressions>PHP\n「PHP: Hypertext Preprocessor」の略称。オープンソース。主にサーバ側のアプリケーション開発と動的なウェブコンテンツのために使用されるリフレクションプログラミング言語。最近では、ソフトウェアアプリケーションの広い範囲で使われている。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/PHP_(%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0%E8%A8%80%E8%AA%9E)>ポート データが送受信される接続。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%9D%E3%83%BC%E3%83%88_(%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF%E3%83%8D%E3%83%83%E3%83%88%E3%83%AF%E3%83%BC%E3%82%AF)>主キー 主キーは、テーブル内の1つ以上のフィールドに対するインデックスで、テーブル内のそれぞれの行で一意の値を持ちます。テーブル内のデータをにアクセスしたり識別したりしやすいように、すべてのテーブルに主キーを設定すべきです。テーブルに主キーを設定できるのは一つだけで、常に **主キー** と呼ばれます。実際、主キーは **主キー** という名前の [ユニークキー](#term-unique-key) にすぎません。主キーが定義されていない場合、存在すれば最初の *ユニークキー* を主キーとして使用します。\n\n主キーはテーブルを作成する際に作成することができます (phpMyAdmin では、主キーの一部にしたい各フィールドの主キーチェックボックスをチェックするだけです)。\n\n既存のテーブルには、 ALTER TABLE または CREATE INDEX で主キーを追加することができます (phpMyAdmin では、テーブルの構造ページのフィールド一覧の下にある「インデックスの追加」をクリックするだけです)。\n\nRFC RFC (Request for Comments) は、インターネット技術に適用される新しい研究、技術革新、方法論を書き連ねた文書です。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Request_for_Comments>RFC 1952 GZIP ファイル形式仕様書 4.3 版\n\n参考\n\n[**RFC 1952**](https://tools.ietf.org/html/rfc1952.html)\n\n行 (レコード、組)\nテーブル内において単一の、暗黙的に構造化されたデータ項目を表します。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E7%B5%84_(%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9)>サーバ ネットワークを介して他のコンピュータシステムにサービスを提供するコンピュータシステムのこと。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%82%B5%E3%83%BC%E3%83%90>Sodium Sodium の PHP 拡張。\n\n参考\n\n[PHP マニュアルの Sodium 拡張モジュール](https://www.php.net/manual/ja/book.sodium.php)\n\nストレージエンジン MySQL は、ディスク上のデータを保存するためにいくつかの異なる形式を使用することができますが、これらはストレージエンジンやテーブル種別と呼ばれています。 phpMyAdmin では、操作タブからユーザーが特定のテーブルのストレージエンジンを変更することができます。\n\n一般的なテーブル種別は InnoDB と MyISAM ですが、その他にも多くのテーブル種別が存在しており、状況によってはそれが望ましい場合もあります。\n\n参考\n\n[MySQL ドキュメントの Alternative Storage Engines についての章](https://dev.mysql.com/doc/refman/8.0/ja/storage-engines.html)\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9%E3%82%A8%E3%83%B3%E3%82%B8%E3%83%B3>ソケット プロセス間通信の一形式。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/UNIX%E3%83%89%E3%83%A1%E3%82%A4%E3%83%B3%E3%82%BD%E3%82%B1%E3%83%83%E3%83%88>SSL SSL (TLS に置き換えられました) は、インターネット上の安全な通信を提供する暗号プロトコルです。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Transport_Layer_Security>ストアドプロシージャ リレーショナルデータベースシステムにアクセスするアプリケーションで使用可能なサブルーチン\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%82%B9%E3%83%88%E3%82%A2%E3%83%89%E3%83%97%E3%83%AD%E3%82%B7%E3%83%BC%E3%82%B8%E3%83%A3>SQL 構造化問い合わせ言語\n\n参考\n\n<<https://ja.wikipedia.org/wiki/SQL>テーブル テーブル (表) は、水平方向の行と垂直方向のカラム (列) で構成、定義、保存されているデータ要素 (セル) の組み合わせです。各項目は、ラベルかキーによって、もしくは他の項目との関係における位置によって、一意に識別することができます。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E8%A1%A8_(%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9)>tar アーカイブファイル形式の一種で Tape ARchive の略。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Tar>TCP TCP (Transmission Control Protocol) は、インターネット・プロトコル群の中核となるプロトコルの一つ。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%82%A4%E3%83%B3%E3%82%BF%E3%83%BC%E3%83%8D%E3%83%83%E3%83%88%E3%83%BB%E3%83%97%E3%83%AD%E3%83%88%E3%82%B3%E3%83%AB%E3%83%BB%E3%82%B9%E3%82%A4%E3%83%BC%E3%83%88>TCPDF PDF ファイルを生成するための PHP ライブラリ。\n\n参考\n\n<<https://tcpdf.org/>参考\n\n<<https://en.wikipedia.org/wiki/TCPDF>トリガ データベース内の特定のテーブルまたはビュー上の特定のイベントに応答して自動的に実行される手続き型のコード\n\n参考\n\n<<https://ja.wikipedia.org/wiki/%E3%83%87%E3%83%BC%E3%82%BF%E3%83%99%E3%83%BC%E3%82%B9%E3%83%88%E3%83%AA%E3%82%AC>ユニークキー ユニークキーとは、テーブル内の1つ以上のフィールドに対するインデックスで、各行に対して一意の値を持ちます。 最初のユニークキーは、*主キー* が定義されていない場合は [主キー](#term-primary-key) として扱われます。\nURL URL (Uniform Resource Locator) は文字の並びで、標準化された形式に準拠しており、インターネット上の文書や画像などを場所で参照するために使用されます。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Uniform_Resource_Locator>ウェブサーバ クライアントからの HTTP リクエストの受け入れおよびそれらに対するウェブページの提供を行うコンピュータ (プログラム)。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Web%E3%82%B5%E3%83%BC%E3%83%90>XML 個別の目的に応じたマークアップ言語作成のための、W3C 勧告の汎用マークアップ言語。多くの異なる種類のデータを記述することが可能。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Extensible_Markup_Language>ZIP 有名なデータ圧縮とアーカイブの形式。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/ZIP_(%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%83%95%E3%82%A9%E3%83%BC%E3%83%9E%E3%83%83%E3%83%88)>Zlib\n[Jean-loup Gailly](https://en.wikipedia.org/wiki/Jean-Loup_Gailly) と [Mark Adler](https://en.wikipedia.org/wiki/Mark_Adler) 両氏によるオープンソースでクロスプラットフォームのデータ圧縮ライブラリ。\n\n参考\n\n<<https://ja.wikipedia.org/wiki/Zlib>コンテンツセキュリティポリシー HTTP の Content-Security-Policy レスポンスヘッダにより、ウェブサイトの管理者が特定のページから読み込むことができるリソースを制御することができます。\n\n参考\n\n<<https://en.wikipedia.org/wiki/Content_Security_Policy>参考\n\n<<https://developer.mozilla.org/ja/docs/Web/HTTP/CSP>インデックスとテーブル[¶](#indices-and-tables)\n===\n\n* [索引](genindex.html)\n* [検索ページ](search.html)\n* [用語集](index.html#glossary)\n\n### [Table of Contents](index.html#document-index)\n\n* [はじめに](index.html#document-intro)\n\t+ [対応している機能](index.html#supported-features)\n\t+ [ショートカットキー](index.html#shortcut-keys)\n\t+ [ユーザについて一言](index.html#a-word-about-users)\n* [要件](index.html#document-require)\n\t+ [ウェブサーバ](index.html#web-server)\n\t+ [PHP](index.html#php)\n\t+ [データベース](index.html#database)\n\t+ [ウェブブラウザ](index.html#web-browser)\n* [インストール](index.html#document-setup)\n\t+ [Linux ディストリビューション](index.html#linux-distributions)\n\t+ [Windows へのインストール](index.html#installing-on-windows)\n\t+ [Git からのインストール](index.html#installing-from-git)\n\t+ [Composer を使用したインストール](index.html#installing-using-composer)\n\t+ [Docker を使用したインストール](index.html#installing-using-docker)\n\t+ [IBM クラウド](index.html#ibm-cloud)\n\t+ [クイックインストール](index.html#quick-install-1)\n\t+ [phpMyAdmin リリースの検証](index.html#verifying-phpmyadmin-releases)\n\t+ [phpMyAdmin 環境保管領域](index.html#phpmyadmin-configuration-storage)\n\t+ [旧版からのアップグレード](index.html#upgrading-from-an-older-version)\n\t+ [認証モードの使い方](index.html#using-authentication-modes)\n\t+ [phpMyAdmin のインストールを安全にする](index.html#securing-your-phpmyadmin-installation)\n\t+ [データベースサーバへの接続で SSL を使用する](index.html#using-ssl-for-connection-to-database-server)\n\t+ [既知の問題](index.html#known-issues)\n* [設定](index.html#document-config)\n\t+ [基本設定](index.html#basic-settings)\n\t+ [サーバ接続設定](index.html#server-connection-settings)\n\t+ [一般設定](index.html#generic-settings)\n\t+ [クッキー認証オプション](index.html#cookie-authentication-options)\n\t+ [ナビゲーションパネルの設定](index.html#navigation-panel-setup)\n\t+ [メインパネル](index.html#main-panel)\n\t+ [データベースの構造](index.html#database-structure)\n\t+ [表示モード](index.html#browse-mode)\n\t+ [編集モード](index.html#editing-mode)\n\t+ [エクスポートとインポートの設定](index.html#export-and-import-settings)\n\t+ [タブ表示設定](index.html#tabs-display-settings)\n\t+ [PDF オプション](index.html#pdf-options)\n\t+ [言語](index.html#languages)\n\t+ [ウェブサーバ設定](index.html#web-server-settings)\n\t+ [テーマ設定](index.html#theme-settings)\n\t+ [デザインのカスタマイズ](index.html#design-customization)\n\t+ [テキスト入力項目](index.html#text-fields)\n\t+ [SQL クエリボックス設定](index.html#sql-query-box-settings)\n\t+ [ウェブサーバのアップロード/保存/インポートディレクトリ](index.html#web-server-upload-save-import-directories)\n\t+ [様々な表示設定](index.html#various-display-setting)\n\t+ [ページタイトル](index.html#page-titles)\n\t+ [テーマ管理設定](index.html#theme-manager-settings)\n\t+ [デフォルトクエリ](index.html#default-queries)\n\t+ [MySQL 設定](index.html#mysql-settings)\n\t+ [デフォルトの変換オプション](index.html#default-options-for-transformations)\n\t+ [コンソール設定](index.html#console-settings)\n\t+ [開発者向け](index.html#developer)\n\t+ [設定例](index.html#examples)\n* [ユーザーガイド](index.html#document-user)\n\t+ [phpMyAdmin の設定](index.html#document-settings)\n\t+ [二要素認証](index.html#document-two_factor)\n\t+ [変換機能](index.html#document-transformations)\n\t+ [ブックマーク](index.html#document-bookmarks)\n\t+ [ユーザ管理](index.html#document-privileges)\n\t+ [リレーション](index.html#document-relations)\n\t+ [グラフ機能](index.html#document-charts)\n\t+ [インポートとエクスポート](index.html#document-import_export)\n\t+ [カスタムテーマ](index.html#document-themes)\n\t+ [その他の情報源](index.html#document-other)\n* [FAQ - よくある質問](index.html#document-faq)\n\t+ [サーバ](index.html#server)\n\t+ [設定](index.html#configuration)\n\t+ [既知の制限](index.html#known-limitations)\n\t+ [ISP やマルチユーザのインストール](index.html#isps-multi-user-installations)\n\t+ [ブラウザまたはクライアント OS](index.html#browsers-or-client-os)\n\t+ [phpMyAdmin の使用](index.html#using-phpmyadmin)\n\t+ [phpMyAdmin プロジェクト](index.html#phpmyadmin-project)\n\t+ [セキュリティ](index.html#security)\n\t+ [同期](index.html#synchronization)\n* [開発者向け情報](index.html#document-developers)\n* [セキュリティポリシー](index.html#document-security)\n\t+ [よくある脆弱性](index.html#typical-vulnerabilities)\n\t+ [セキュリティ問題の報告](index.html#reporting-security-issues)\n* [phpMyAdmin の配布とパッケージ化](index.html#document-vendors)\n\t+ [外部ライブラリ](index.html#external-libraries)\n\t+ [特定のファイルのライセンス](index.html#specific-files-licenses)\n\t+ [ベンダー向けのライセンス情報](index.html#licenses-for-vendors)\n* [著作権](index.html#document-copyright)\n\t+ [サードパーティのライセンス](index.html#third-party-licenses)\n* [貢献者一覧](index.html#document-credits)\n\t+ [貢献者一覧（年代順）](index.html#credits-in-chronological-order)\n\t+ [翻訳者](index.html#translators)\n\t+ [ドキュメントの翻訳者](index.html#documentation-translators)\n\t+ [バージョン 2.1.0 当時の貢献者一覧](index.html#original-credits-of-version-2-1-0)\n* [用語集](index.html#document-glossary)\n\n### クイック検索\n\n### ナビゲーション\n\n* [phpMyAdmin 6.0.0-dev ドキュメント](index.html#document-index) »"}}},{"rowIdx":59496,"cells":{"project":{"kind":"string","value":"shunter"},"source":{"kind":"string","value":"npm"},"language":{"kind":"string","value":"JavaScript"},"content":{"kind":"string","value":"Shunter is a [Node.js](https://nodejs.org/) application built to read JSON and translate it into HTML.\n\nIt helps you create a loosely-coupled front end which can serve traffic from one or more back end applications - great for use in multi-language, multi-disciplinary teams or just to make your project more flexible and future-proofed.\n\nShunter does not contain an API client, or any Controller logic (in the [MVC](https://en.wikipedia.org/wiki/Model%E2%80%93view%E2%80%93controller) sense). Instead, Shunter simply proxies requests to a back end server, then:\n\n1. If the back end wants Shunter to render the response, it returns the application state as JSON, served with a certain HTTP header. This initiates the templating process in Shunter.\n2. If the back end wishes to serve the response, it omits the header and Shunter proxies the request back to the client.\n\nKey Features\n---\n\n* Enforces decoupling of templates from underlying applications\n* Enables multiple applications to use the same unified front end\n* Makes full site redesigns or swapping out back end applications a doddle\n* Completely technology-agnostic; if your application outputs JSON, it can work with Shunter\n* Asset concatenation, minification, cache-busting, and other performance optimisations built-in\n* Outputs any type of content you like, e.g. HTML, RSS, RDF\n* Well-tested and supported, serving [Scientific American](http://www.scientificamerican.com) as well as [many](http://www.nature.com/npjscilearn/) [high-traffic](http://www.nature.com/srep) [sites](http://www.nature.com/search) across nature.com\n\nGetting Started\n---\n\nIf you're new to Shunter, we recommend reading the [Getting Started Guide](https://github.com/springernature/shunter/blob/HEAD/docs/getting-started.md). This will teach you the basics, and how to create your first Shunter-based application.\n\nOnce you're familiar with Shunter's basics you can refer to the [API Documentation](https://github.com/springernature/shunter/blob/HEAD/docs/usage/index.md) for a full breakdown about how to work with Shunter.\n\nRequirements\n---\n\nShunter requires [Node.js](https://nodejs.org/) 4.x–6.x. This should be easy to get running on Mac and Linux.\n\nOne of Shunter's dependencies is a native addon module so it requires a working C compiler. Windows doesn't come with one by default so you may find the following links helpful:\n\n* [node-gyp on Windows](https://github.com/nodejs/node-gyp#on-windows)\n* [node-gyp Visual Studio 2010 Setup](https://github.com/TooTallNate/node-gyp/wiki/Visual-Studio-2010-Setup)\n* [contextify – Specified platform toolset (v110) is not installed or invalid](http://zxtech.wordpress.com/2013/02/20/contextify-specified-platform-toolset-v110-is-not-installed-or-invalid/)\n\nSee the [Getting started documentation](https://github.com/springernature/shunter/blob/HEAD/docs/getting-started.md#prerequisites)\nfor more information on Shunter's requirements.\n\nSupport and Migration\n---\n\nThe last major version of Shunter is version 4. Old major versions are supported for 6 months after a new major version is released. This means that patch-level changes will be added and bugs will be fixed. We maintain a [support guide](https://github.com/springernature/shunter/blob/HEAD/docs/support.md) which documents the major versions and their support levels.\n\nIf you'd like to know more about how we support our open source projects, including the full release process, check out our [support practices document](https://github.com/springernature/frontend/blob/master/practices/open-source-support.md).\n\nIf you're migrating between major versions of Shunter, we maintain a [migration guide](https://github.com/springernature/shunter/blob/HEAD/docs/migration/index.md) to help you.\n\nContributing\n---\n\nWe'd love for you to contribute to Shunter. We maintain a [developer guide](https://github.com/springernature/shunter/blob/HEAD/docs/developer-guide.md) to help people get started with working on Shunter itself. It outlines the structure of the application and some of the development practices we uphold.\n\nWe also label [issues that might be a good starting-point](https://github.com/springernature/shunter/labels/good-starter-issue) for new developers to the project.\n\nLicense\n---\n\nShunter is licensed under the [Lesser General Public License (LGPL-3.0)](https://github.com/springernature/shunter/blob/HEAD/LICENSE). \n\nCopyright © 2015, <NAME>\nReadme\n---\n\n### Keywords\n\n* proxy\n* front-end\n* dust\n* templates\n* asset pipeline\n* renderer"}}},{"rowIdx":59497,"cells":{"project":{"kind":"string","value":"github.com/asciinema/asciinema-cli"},"source":{"kind":"string","value":"go"},"language":{"kind":"string","value":"Go"},"content":{"kind":"string","value":"README\n [¶](#section-readme)\n---\n\n### asciinema\n\n[](https://travis-ci.org/asciinema/asciinema)\n[](https://raw.githubusercontent.com/asciinema/asciinema/master/LICENSE)\n\nTerminal session recorder and the best companion of\n[asciinema.org](https://asciinema.org).\n\n[](https://asciinema.org/a/624fjx2rx7k3pctdozw7m8b24?autoplay=1)\n\n#### Installation\n\n##### Using package manager\n\nasciinema is available in repositories of most popular package managers on Mac OS X, Linux and FreeBSD. Look for package named `asciinema`. See the\n[list of available packages](https://asciinema.org/docs/installation).\n\n##### Building from source\n\nTo build asciinema from source you need to have\n[Go development toolchain](http://golang.org/doc/install) installed.\n\n###### With `go get`\n\nYou can use `go get` to fetch the source, build and install asciinema at\n`$GOPATH/bin/asciinema` in one go:\n```\ngo get github.com/asciinema/asciinema\n```\n###### With `make`\n\nDownload the source code into your `$GOPATH`:\n```\nmkdir -p $GOPATH/src/github.com/asciinema git clone https://github.com/asciinema/asciinema.git $GOPATH/src/github.com/asciinema/asciinema\n```\nBuild the binary:\n```\ncd $GOPATH/src/github.com/asciinema/asciinema make build\n```\nThis will produce asciinema binary at\n`$GOPATH/src/github.com/asciinema/asciinema/bin/asciinema`.\n\nTo install it system wide (to `/usr/local`):\n```\nsudo make install\n```\nIf you want to install it in other location:\n```\nPREFIX=/the/prefix make install\n```\n#### Usage\n\nasciinema is composed of multiple commands, similar to `git`, `apt-get` or\n`brew`.\n\nWhen you run `asciinema` with no arguments help message is displayed, listing all available commands with their options.\n\n##### `rec [filename]`\n\n**Record terminal session.**\n\nThis is the single most important command in asciinema, since it is how you utilize this tool's main job.\n\nBy running `asciinema rec [filename]` you start a new recording session. The command (process) that is recorded can be specified with `-c` option (see below), and defaults to `$SHELL` which is what you want in most cases.\n\nRecording finishes when you exit the shell (hit Ctrl+D or type\n`exit`). If the recorded process is not a shell then recording finishes when the process exits.\n\nIf the `filename` argument is given then the resulting recording (called\n[asciicast](https://github.com/asciinema/asciinema-cli/blob/v1.2.0/doc/asciicast-v1.md)) is saved to a local file. It can later be replayed with `asciinema play <filename>` and/or uploaded to asciinema.org with\n`asciinema upload <filename>`. If the `filename` argument is omitted then\n(after asking for confirmation) the resulting asciicast is uploaded to asciinema.org for further playback in a web browser.\n\n`ASCIINEMA_REC=1` is added to recorded process environment variables. This can be used by your shell's config file (`.bashrc`, `.zshrc`) to alter the prompt or play a sound when shell is being recorded.\n\nAvailable options:\n\n* `-c, --command=<command>` - Specify command to record, defaults to $SHELL\n* `-t, --title=<title>` - Specify the title of the asciicast\n* `-w, --max-wait=<sec>` - Reduce recorded terminal inactivity to max seconds\n* `-y, --yes` - Answer \"yes\" to all prompts (e.g. upload confirmation)\n* `-q, --quiet` - Be quiet, suppress all notices/warnings (implies -y)\n\n##### `play <filename>`\n\n**Replay recorded asciicast in a terminal.**\n\nThis command replays given asciicast (as recorded by `rec` command) directly in your terminal.\n\nPlaying from a local file:\n```\nasciinema play /path/to/asciicast.json\n```\nPlaying from HTTP(S) URL:\n```\nasciinema play https://asciinema.org/a/22124.json asciinema play http://example.com/demo.json\n```\nPlaying from asciicast page URL (requires `<link rel=\"alternate\" type=\"application/asciicast+json\" href=\"....json\">` in page's HTML):\n```\nasciinema play https://asciinema.org/a/22124 asciinema play http://example.com/blog/post.html\n```\nPlaying from stdin:\n```\ncat /path/to/asciicast.json | asciinema play -\nssh user@host cat asciicast.json | asciinema play -\n```\nPlaying from IPFS:\n```\nasciinema play ipfs:/ipfs/<KEY>V asciinema play fs:/ipfs/<KEY>\n```\nAvailable options:\n\n* `-w, --max-wait=<sec>` - Reduce replayed terminal inactivity to max seconds\n\nNOTE: it is recommended to run `asciinema play` in a terminal of dimensions not smaller than the one used for recording as there's no \"transcoding\" of control sequences for new terminal size.\n\n##### `upload <filename>`\n\n**Upload recorded asciicast to asciinema.org site.**\n\nThis command uploads given asciicast (as recorded by `rec` command) to asciinema.org for further playback in a web browser.\n\n`asciinema rec demo.json` + `asciinema play demo.json` + `asciinema upload demo.json` is a nice combo for when you want to review an asciicast before publishing it on asciinema.org.\n\n##### `auth`\n\n**Assign local API token to asciinema.org account.**\n\nOn every machine you install asciinema recorder, you get a new, unique API token. This command connects this local token with your asciinema.org account,\nand links all asciicasts recorded on this machine with the account.\n\nThis command displays the URL you should open in your web browser. If you never logged in to asciinema.org then your account will be created when opening the URL.\n\nNOTE: it is **necessary** to do this if you want to **edit or delete** your recordings on asciinema.org.\n\nYou can synchronize your config file (which keeps the API token) across the machines but that's not necessary. You can assign new tokens to your account from as many machines as you want.\n\n#### Configuration file\n\nasciinema uses a config file to keep API token and user settings. In most cases the location of this file is `$HOME/.config/asciinema/config`.\n\nWhen you first run `asciinema`, local API token is generated and saved in the file (unless the file already exists). It looks like this:\n```\n[api]\ntoken = d5a2dce4-173f-45b2-a405-ac33d7b70c5f\n```\nThere are several options you can set in this file. Here's a config with all available options set:\n```\n[api]\ntoken = d5a2dce4-173f-45b2-a405-ac33d7b70c5f url = https://asciinema.example.com\n\n[record]\ncommand = /bin/bash -l maxwait = 2 yes = true\n\n[play]\nmaxwait = 1\n```\nThe options in `[api]` section are related to API location and authentication.\nTo tell asciinema recorder to use your own asciinema site instance rather than the default one (asciinema.org), you can set `url` option. API URL can also be passed via `ASCIINEMA_API_URL` environment variable.\n\nThe options in `[record]` and `[play]` sections have the same meaning as the options you pass to `asciinema rec`/`asciinema play` command. If you happen to often use either `-c`, `-w` or `-y` with these commands then consider saving it as a default in the config file.\n\n##### Configuration file locations\n\nIn fact, the following locations are checked for the presence of the config file (in the given order):\n\n* `$ASCIINEMA_CONFIG_HOME/config` - if you have set `$ASCIINEMA_CONFIG_HOME`\n* `$XDG_CONFIG_HOME/asciinema/config` - on Linux, `$XDG_CONFIG_HOME` usually points to `$HOME/.config/`\n* `$HOME/.config/asciinema/config` - in most cases it's here\n* `$HOME/.asciinema/config` - created by asciinema versions prior to 1.1\n\nThe first one which is found is used.\n\n#### Contributing\n\nIf you want to contribute to this project check out\n[Contributing](https://asciinema.org/contributing) page.\n\n#### Authors\n\nDeveloped with passion by [<NAME>](http://ku1ik.com) and great open source [contributors](https://github.com/asciinema/asciinema/contributors)\n\n#### License\n\nCopyright © 2011-2016 <NAME>.\n\nAll code is licensed under the GPL, v3 or later. See LICENSE file for details.\n\nDocumentation\n [¶](#section-documentation)\n---\n\n\nThere is no documentation for this package."}}},{"rowIdx":59498,"cells":{"project":{"kind":"string","value":"ecan"},"source":{"kind":"string","value":"cran"},"language":{"kind":"string","value":"R"},"content":{"kind":"string","value":"Package ‘ecan’\n July 7, 2023\nTitle Ecological Analysis and Visualization\nVersion 0.2.1\nDescription Support ecological analyses such as ordination and clustering.\n Contains consistent and easy wrapper functions of 'stat', 'vegan', and\n 'labdsv' packages, and visualisation functions of ordination and clustering.\nLicense MIT + file LICENSE\nEncoding UTF-8\nRoxygenNote 7.2.3\nDepends R (>= 3.5.0)\nURL https://github.com/matutosi/ecan\n https://github.com/matutosi/ecan/tree/develop (devel)\nImports MASS, cluster, dendextend, dplyr, ggplot2, jsonlite, labdsv,\n magrittr, purrr, rlang, stringr, tibble, tidyr, vegan\nSuggests ggdendro, knitr, rmarkdown, testthat (>= 3.0.0),\nConfig/testthat/edition 3\nNeedsCompilation no\nAuthor <NAME> [aut, cre]\nMaintainer <NAME> <<EMAIL>>\nRepository CRAN\nDate/Publication 2023-07-07 12:20:06 UTC\nR topics documented:\ncluste... 2\n... 3\ndf2tabl... 4\ndraw_layer_constructio... 5\ngen_exampl... 6\nind_va... 7\nis_one2mult... 8\nordinatio... 9\npad2longes... 11\nread_bis... 11\nshd... 12\n cluster Helper function for clustering methods\nDescription\n Helper function for clustering methods\n Helper function for calculate distance\n Add group names to hclust labels.\n Add colors to dendrogram\nUsage\n cluster(x, c_method, d_method)\n distance(x, d_method)\n cls_add_group(cls, df, indiv, group, pad = TRUE)\n cls_color(cls, df, indiv, group)\nArguments\n x A community data matrix. rownames: stands. colnames: species.\n c_method A string of clustering method. \"ward.D\", \"ward.D2\", \"single\", \"complete\", \"av-\n erage\" (= UPGMA), \"mcquitty\" (= WPGMA), \"median\" (= WPGMC), \"cen-\n troid\" (= UPGMC), or \"diana\".\n d_method A string of distance method. \"correlation\", \"manhattan\", \"euclidean\", \"can-\n berra\", \"clark\", \"bray\", \"kulczynski\", \"jaccard\", \"gower\", \"altGower\", \"morisita\",\n \"horn\", \"mountford\", \"raup\", \"binomial\", \"chao\", \"cao\", \"mahalanobis\", \"chisq\",\n \"chord\", \"aitchison\", or \"robust.aitchison\".\n cls A result of cluster or dendrogram.\n df A data.frame to be added into ord scores\n indiv, group A string to specify individual and group name of column in df.\n pad A logical to specify padding strings.\nValue\n cluster() returns result of clustering. $clustering_method: c_method $distance_method: d_method\n distance() returns distance matrix.\n Inputing cls return a color vector,\n inputing dend return a dend with color.\nExamples\n library(dplyr)\n df <-\n tibble::tibble(\n stand = paste0(\"ST_\", c(\"A\", \"A\", \"A\", \"B\", \"B\", \"C\", \"C\", \"C\", \"C\")),\n species = paste0(\"sp_\", c(\"a\", \"e\", \"d\", \"e\", \"b\", \"e\", \"d\", \"b\", \"a\")),\n abundance = c(3, 3, 1, 9, 5, 4, 3, 3, 1))\n cls <-\n df2table(df) %>%\n cluster(c_method = \"average\", d_method = \"bray\")\n library(ggdendro)\n # show standard cluster\n ggdendro::ggdendrogram(cls)\n # show cluster with group\n data(dune, package = \"vegan\")\n data(dune.env, package = \"vegan\")\n cls <-\n cluster(dune, c_method = \"average\", d_method = \"bray\")\n df <- tibble::rownames_to_column(dune.env, \"stand\")\n cls <- cls_add_group(cls, df, indiv = \"stand\", group = \"Use\")\n ggdendro::ggdendrogram(cls)\n d Calculating diversity\nDescription\n Calculating diversity\nUsage\n d(x)\n h(x, base = exp(1))\nArguments\n x, base A numeric vector.\nValue\n A numeric vector.\n df2table Convert data.frame and table to each other.\nDescription\n Convert data.frame and table to each other.\nUsage\n df2table(df, st = \"stand\", sp = \"species\", ab = \"abundance\")\n table2df(tbl, st = \"stand\", sp = \"species\", ab = \"abundance\")\n dist2df(dist)\nArguments\n df A data.frame.\n st, sp, ab A string.\n tbl A table. community matrix. rownames: stands. colnames: species.\n dist A distance table.\nValue\n df2table() return table,\n table2df() return data.frame,\n dist2df() return data.frame.\nExamples\n tibble::tibble(\n st = paste0(\"st_\", rep(1:2, times = 2)),\n sp = paste0(\"sp_\", rep(1:2, each = 2)),\n ab = runif(4)) %>%\n dplyr::bind_rows(., .) %>%\n print() %>%\n df2table(\"st\", \"sp\", \"ab\")\n draw_layer_construction\n Draw layer construction plot\nDescription\n Draw layer construction plot\n Add mid point and bin width of layer heights.\n Compute mid point of layer heights.\n Compute bin width of layer heights.\nUsage\n draw_layer_construction(\n df,\n stand = \"stand\",\n height = \"height\",\n cover = \"cover\",\n group = \"\",\n ...\n )\n add_mid_p_bin_w(df, height = \"height\")\n mid_point(x)\n bin_width(x)\nArguments\n df A dataframe including columns: stand, layer height and cover. Optional column:\n stand group.\n stand, height, cover, group\n A string to specify stand, height, cover, group column.\n ... Extra arguments for geom_bar().\n x A numeric vector.\nValue\n draw_layer_construction() returns gg object, add_mid_p_bin_w() returns dataframe including mid_point\n and bin_width columns. mid_point() and bin_width() return a numeric vector.\nExamples\n library(dplyr)\n n <- 10\n height_max <- 20\n ly_list <- c(\"B\", \"S\", \"K\")\n st_list <- LETTERS[1]\n sp_list <- letters[1:9]\n st_group <- NULL\n sp_group <- rep(letters[24:26], 3)\n cover_list <- 2^(0:4)\n df <- gen_example(n = n, use_layer = TRUE,\n height_max = height_max, ly_list = ly_list,\n st_list = st_list, sp_list = sp_list,\n st_group = st_group, sp_group = sp_group,\n cover_list = cover_list)\n # select stand and summarise by sp_group\n df %>%\n dplyr::group_by(height, sp_group) %>%\n dplyr::summarise(cover = sum(cover), .groups = \"drop\") %>%\n draw_layer_construction(group = \"sp_group\", colour = \"white\")\n gen_example Generate vegetation example\nDescription\n Stand, species, and cover are basic. Layer, height, st_group, are sp_group optional.\nUsage\n gen_example(\n n = 300,\n use_layer = TRUE,\n height_max = 20,\n ly_list = \"\",\n st_list = LETTERS[1:9],\n sp_list = letters[1:9],\n st_group = NULL,\n sp_group = NULL,\n cover_list = 2^(0:6)\n )\nArguments\n n A numeric to generate no of occurrences.\n use_layer A logical. If FALSE, height_max and ly_list will be omitted.\n height_max A numeric. The highest layer of samples.\n ly_list, st_list, sp_list, st_group, sp_group\n A string vector. st_group and sp_group are optional (default is NULL). Length\n of st_list and sp_list should be the same as st_group and sp_group, respectively.\n cover_list A numeric vector.\nValue\n A dataframe with columns: stand, layer, species, cover, st_group and sp_group.\nExamples\n n <- 300\n height_max <- 20\n ly_list <- c(\"B1\", \"B2\", \"S1\", \"S2\", \"K\")\n st_list <- LETTERS[1:9]\n sp_list <- letters[1:9]\n st_group <- rep(LETTERS[24:26], 3)\n sp_group <- rep(letters[24:26], 3)\n cover_list <- 2^(0:6)\n gen_example(n = n, use_layer = TRUE,\n height_max = height_max, ly_list = ly_list,\n st_list = st_list, sp_list = sp_list,\n st_group = st_group, sp_group = sp_group,\n cover_list = cover_list)\n ind_val Helper function for Indicator Species Analysis\nDescription\n Calculating diversity indices such as species richness (s), Shannon’s H’ (h), Simpson’ D (d), Simp-\n son’s inverse D (i).\nUsage\n ind_val(\n df,\n stand = NULL,\n species = NULL,\n abundance = NULL,\n group = NULL,\n row_data = FALSE\n )\nArguments\n df A data.frame, which has three cols: stand, species, abundance. Community\n matrix should be converted using table2df().\n stand, species, abundance\n A text to specify each column. If NULL, 1st, 2nd, 3rd column will be used.\n group A text to specify group column.\n row_data A logical. TRUE: return row result data of labdsv::indval().\nValue\n A data.frame.\nExamples\n library(dplyr)\n library(tibble)\n data(dune, package = \"vegan\")\n data(dune.env, package = \"vegan\")\n df <-\n dune %>%\n table2df(st = \"stand\", sp = \"species\", ab = \"cover\") %>%\n dplyr::left_join(tibble::rownames_to_column(dune.env, \"stand\"))\n ind_val(df, abundance = \"cover\", group = \"Moisture\")\n is_one2multi Check cols one-to-one, or one-to-multi in data.frame\nDescription\n Check cols one-to-one, or one-to-multi in data.frame\nUsage\n is_one2multi(df, col_1, col_2)\n is_one2one(df, col_1, col_2)\n is_multi2multi(df, col_1, col_2)\n cols_one2multi(df, col, inculde_self = TRUE)\n select_one2multi(df, col, inculde_self = TRUE)\n unique_length(df, col_1, col_2)\nArguments\n df A data.frame\n col, col_1, col_2\n A string to specify a colname.\n inculde_self A logical. If TRUE, return value including input col.\nValue\n is_one2multi(), is_one2one(), is_multi2multi() return a logical. cols_one2multi() returns strings of\n colnames that has one2multi relation to input col. unique_length() returns a list.\nExamples\n df <- tibble::tibble(\n x = rep(letters[1:6], each = 1),\n x_grp = rep(letters[1:3], each = 2),\n y = rep(LETTERS[1:3], each = 2),\n y_grp = rep(LETTERS[1:3], each = 2),\n z = rep(LETTERS[1:3], each = 2),\n z_grp = rep(LETTERS[1:3], times = 2))\n unique_length(df, \"x\", \"x_grp\")\n is_one2one(df, \"x\", \"x_grp\")\n is_one2one(df, \"y\", \"y_grp\")\n is_one2one(df, \"z\", \"z_grp\")\n ordination Helper function for ordination methods\nDescription\n Helper function for ordination methods\nUsage\n ordination(tbl, o_method, d_method = NULL, ...)\n ord_plot(ord, score = \"st_scores\", x = 1, y = 2)\n ord_add_group(ord, score = \"st_scores\", df, indiv, group)\n ord_extract_score(ord, score = \"st_scores\", row_name = NULL)\nArguments\n tbl A community data matrix. rownames: stands. colnames: species.\n o_method A string of ordination method. \"pca\", \"ca\", \"dca\", \"pcoa\", or \"nmds\". \"fspa\" is\n removed, because package dave was archived.\n d_method A string of distance method. \"correlation\", \"manhattan\", \"euclidean\", \"can-\n berra\", \"clark\", \"bray\", \"kulczynski\", \"jaccard\", \"gower\", \"altGower\", \"morisita\",\n \"horn\", \"mountford\", \"raup\", \"binomial\", \"chao\", \"cao\", \"mahalanobis\", \"chisq\",\n \"chord\", \"aitchison\", or \"robust.aitchison\".\n ... Other parameters for PCA.\n ord A result of ordination().\n score A string to specify score for plot. \"st_scores\" means stands and \"sp_scores\"\n species.\n x, y A column number for x and y axis.\n df A data.frame to be added into ord scores\n indiv, group, row_name\n A string to specify indiv, group, row_name column in df.\nValue\n ordination() returns result of ordination. $st_scores: scores for stand. $sp_scores: scores for\n species. $eig_val: eigen value for stand. $results_raw: results of original ordination function.\n $ordination_method: o_method. $distance_method: d_method. ord_plot() returns ggplot2 object.\n ord_extract_score() extracts stand or species scores from ordination result. ord_add_group() adds\n group data.frame into ordination scores.\nExamples\n library(ggplot2)\n library(vegan)\n data(dune)\n data(dune.env)\n df <-\n table2df(dune) %>%\n dplyr::left_join(tibble::rownames_to_column(dune.env, \"stand\"))\n sp_dammy <-\n tibble::tibble(\"species\" = colnames(dune),\n \"dammy_1\" = stringr::str_sub(colnames(dune), 1, 1),\n \"dammy_6\" = stringr::str_sub(colnames(dune), 6, 6))\n df <- dplyr::left_join(df, sp_dammy)\n ord_dca <- ordination(dune, o_method = \"dca\")\n ord_pca <-\n df %>%\n df2table() %>%\n ordination(o_method = \"pca\")\n ord_dca_st <-\n ord_extract_score(ord_dca, score = \"st_scores\")\n ord_pca_sp <-\n ord_add_group(ord_pca,\n score = \"sp_scores\", df, indiv = \"species\", group = \"dammy_1\")\n pad2longest Pad a string to the longest width of the strings.\nDescription\n Pad a string to the longest width of the strings.\nUsage\n pad2longest(string, side = \"right\", pad = \" \")\nArguments\n string Strings.\n side Side on which padding character is added (left, right or both).\n pad Single padding character (default is spaces).\nValue\n Strings.\nExamples\n x <- c(\"a\", \"ab\", \"abc\")\n pad2longest(x, side = \"right\", pad = \" \")\n read_biss Read data from BiSS (Biodiversity Investigation Support System) to\n data frame.\nDescription\n BiSS data is formatted as JSON.\nUsage\n read_biss(txt, join = TRUE)\nArguments\n txt A JSON string, URL or file.\n join A logical. TRUE: join plot and occurrence, FALSE: do not join.\nValue\n A data frame.\nExamples\n library(dplyr)\n # path <- \"set file path\"\n path <- \"https://raw.githubusercontent.com/matutosi/biodiv/main/man/example.json\"\n read_biss(path)\n shdi Helper function for calculating diversity\nDescription\n Calculating diversity indices such as species richness (s), Shannon’s H’ (h), Simpson’ D (d), Simp-\n son’s inverse D (i).\nUsage\n shdi(df, stand = NULL, species = NULL, abundance = NULL)\nArguments\n df A data.frame, which has three cols: stand, species, abundance. Community\n matrix should be converted using table2df().\n stand, species, abundance\n A text to specify each column. If NULL, 1st, 2nd, 3rd column will be used.\nValue\n A data.frame. Including species richness (s), Shannon’s H’ (h), Simpson’ D (d), Simpson’s inverse\n D (i).\nExamples\n data(dune, package = \"vegan\")\n df <- table2df(dune)\n shdi(df)"}}},{"rowIdx":59499,"cells":{"project":{"kind":"string","value":"base64url"},"source":{"kind":"string","value":"rust"},"language":{"kind":"string","value":"Rust"},"content":{"kind":"string","value":"Crate base64url\n===\n\nImplementation of the encode and decode operations on base64url (as defined in IETF RFC 4648) String.\nThe encoded string restricted to containing the 2^6 UTF-8 code points without padding.\n\nIn general, we use `-` and `_` instead of `+` and `/`, without paddings.\n\nFunctions\n---\n\n* decodedecode takes in a string and tries to decode it into a Vector of bytes. It returns a base64::DecodeError if `string`\nis not valid Base64URL.\n* encodeencode takes in a slice of bytes and returns the bytes encoded as a base64url String.\n\nCrate base64url\n===\n\nImplementation of the encode and decode operations on base64url (as defined in IETF RFC 4648) String.\nThe encoded string restricted to containing the 2^6 UTF-8 code points without padding.\n\nIn general, we use `-` and `_` instead of `+` and `/`, without paddings.\n\nFunctions\n---\n\n* decodedecode takes in a string and tries to decode it into a Vector of bytes. It returns a base64::DecodeError if `string`\nis not valid Base64URL.\n* encodeencode takes in a slice of bytes and returns the bytes encoded as a base64url String.\n\nFunction base64url::decode\n===\n\n\n```\npub fn decode<T: ?Sized + AsRef<[u8]>>(\n base64_url: &T\n) -> Result<Vec<u8>, DecodeError>\n```\ndecode takes in a string and tries to decode it into a Vector of bytes. It returns a base64::DecodeError if `string`\nis not valid Base64URL.\n\nFunction base64url::encode\n===\n\n\n```\npub fn encode<T: AsRef<[u8]>>(bytes: T) -> String\n```\nencode takes in a slice of bytes and returns the bytes encoded as a base64url String."}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":594,"numItemsPerPage":100,"numTotalItems":59733,"offset":59400,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc3ODg3MDc3OCwic3ViIjoiL2RhdGFzZXRzL1NpdmlsVGFyYW0vc3RhcmNvZGVyMi1kb2N1bWVudGF0aW9uIiwiZXhwIjoxNzc4ODc0Mzc4LCJpc3MiOiJodHRwczovL2h1Z2dpbmdmYWNlLmNvIn0.AkLxcr9u0n-hea4_NFuPRB-EckP1bXj-04LzhfO_y7kSnjOsGum2REo6luE0janLiBpEyEmQkLzvG6LOQM6zDA","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"train","numRows":59733,"numBytesParquet":1850870873}]},"discussionsStats":{"closed":0,"open":2,"total":2},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[{"views":[{"key":"default/train","displayName":"train","viewName":"train"}],"sql":"-- The SQL console is powered by DuckDB WASM and runs entirely in the browser.\n-- Get started by typing a query or selecting a view from the options below.\nSELECT *\nFROM train\nWHERE source = 'free_programming_book'\n AND lower(content) LIKE '%python%'\n AND LOWER(content) LIKE '%algorithms%';","title":"Python Algorithms in Free Books","createdAt":"2025-04-03T17:17:56.697Z","slug":"RUf2lH9","private":false,"justification":"Retrieves entries related to both Python and algorithms from a specific source, providing a filtered dataset but lacking broader analytical depth.","viewNames":["train"]},{"views":[{"key":"default/train","displayName":"train","viewName":"train"}],"sql":"-- The SQL console is powered by DuckDB WASM and runs entirely in the browser.\n-- Get started by typing a query or selecting a view from the options below.\nSELECT *\nFROM train\nWHERE source = 'free_programming_book'\n AND language = 'Python'\nLIMIT 100;","title":"Python Code from Free Books","createdAt":"2025-04-03T11:27:46.424Z","slug":"WGn_NVw","private":false,"justification":"This query retrieves a limited number of records related to Python programming books, providing basic filtering but minimal analytical insight.","viewNames":["train"]}],"user":[]}}">
Search is not available for this dataset
project stringlengths 1 235 | source stringclasses 16
values | language stringclasses 48
values | content stringlengths 909 64.8M |
|---|---|---|---|
leptos_viz | rust | Rust | Crate leptos_viz
===
Provides functions to easily integrate Leptos with Viz.
For more details on how to use the integrations, see the
`examples`
directory in the Leptos repository.
Structs
---
* RequestPartsA struct to hold the parts of the incoming Request. Since `http::Request` isn’t cloneable, we’re forced to co... |
alexandria-scrna-data-library | readthedoc | YAML | Date:
Categories:
Tags:
A Single-Cell RNA-Seq and Analytics Platform for Global Health
This is the work-in-progress documentation for the Alexandria platform and all associated tool workflows and notebooks.
## Background¶
Alexandria is a single-cell portal and data resource for the global health community. Alexa... |
@carbon/charts-angular | npm | JavaScript | Carbon Charts - Angular
===
Carbon Charts Angular is a thin Angular wrapper around the vanilla JavaScript `@carbon/charts` component library. This release is aimed at Angular >= 6 and < 16.
If you need support for Angular 16 or higher, please try `@carbon/charts-angular@next`.
The required styles should be imported ... |
smallarea | cran | R | Package ‘smallarea’
October 14, 2022
Type Package
Title Fits a Fay Herriot Model
Version 0.1
Date 2015-10-03
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Description Inference techniques for Fay Herriot Model.
License GPL (>= 2)
Depends MASS
NeedsCompilation no
Repository CRAN
Da... |
github.com/aws/aws-sdk-go-v2/service/iotsecuretunneling | go | Go | None
Documentation
[¶](#section-documentation)
---
### Overview [¶](#pkg-overview)
Package iotsecuretunneling provides the API client, operations, and parameter types for AWS IoT Secure Tunneling.
IoT Secure Tunneling IoT Secure Tunneling creates remote connections to devices deployed in the field. For more info... |
interoptopus_reference_project | rust | Rust | Crate interoptopus\_reference\_project
===
A reference project for Interoptopus.
This project tries to use every Interoptopus feature at least once.
When submitting new features or making changes to existing ones the types and functions in here will ensure existing backends still work as expected.
Note, many items h... |
GITHUB_papers-we-love_papers-we-love.zip_unzipped_shazam-audio-search-algorithm.pdf | free_programming_book | Unknown | An Industrial-Strength Audio Search Algorithm <NAME> <EMAIL> Shazam Entertainment, Ltd.
USA:
2925 Ross Road Palo Alto, CA 94303 United Kingdom:
375 Kensington High Street 4th Floor Block F London W14 8Q We have developed and commercially deployed a flexible audio search engine. The algorithm is noise and distortion res... |
github.com/VirtusLab/render | go | Go | README
[¶](#section-readme)
---
### render
[](https://github.com/VirtusLab/render/releases/tag/v0.3.0)
[](https://travis-ci.org/VirtusLab/render)
[
Encoding UTF-8
RoxygenNote 7.2.3
Suggests testthat (>= 3.0.0), ggplot2, magrittr, palmerpenguins,
knitr, rmarkdown, spell... |
torchgeo | readthedoc | YAML | Spack 0.12.1 documentation
[Spack](index.html#document-index)
---
Spack[¶](#spack)
===
> These are docs for the Spack package manager. For sphere packing, see [pyspack](https://pyspack.readthedocs.io).
Spack is a package management tool designed to support multiple versions and configurations of software on a wide... |
template | ctan | TeX | **Wiener linguistische gazette**
Rezension
**Titel des besprochenen Werks**
_Besprochen von: <NAME>/<NAME>_
Sonderdruck aus: _Wiener Linguistische Gazette_ (WLG) 8o (2017): 1-4
**Eigentumer, Herausgeber und Verleger:**
Universitat Wien, Institut fur Sprachwissenschaft
Sensengasse 3a
1090 Wien
Osterreich
**Red... |
chanjo | readthedoc | Unknown | Chanjo Documentation
Release 3.2.0
<NAME>
December 22, 2015
Contents 2.1 Installatio... 3 2.2 Introduction & Dem... 4 2.3 Interface Walkthroug... 7 2.4 Public AP... 10 2.5 Developer’s Guid... 12 2.6 Release note... 14 2.7 FA... 16
... |
fairsubset | cran | R | Package ‘fairsubset’
October 13, 2022
Type Package
Title Choose Representative Subsets
Version 1.0
Date 2020-08-14
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Description Allows user to obtain subsets of columns of data or vectors within a list. These sub-
sets will match ... |
elsdoc | ctan | TeX |
* some easier ways for formatting list and theorem environments are provided while people can still use amsthm.sty package;
* natbib.sty is the main citation processing package which can comprehensively handle all kinds of citations and works perfectly with hyperref.sty in combination with hypernat.sty;
* long title p... |
@greguintow/apollo-server-plugin-operation-registry | npm | JavaScript | Operation Registry Plugin
===
The operation registry plugin is the interface into the Apollo Platform's **operation registry** and enables operation **safelisting**, which allows selective execution based on the operation. Safelisting eliminates the risk of unexpected operations that could cause downtime from being ru... |
model4you | cran | R | Package ‘model4you’
October 13, 2022
Title Stratified and Personalised Models Based on Model-Based Trees
and Forests
Date 2020-12-23
Version 0.9-7
Description Model-based trees for subgroup analyses in clinical trials and
model-based forests for the estimation and p... |
tornado | readthedoc | Unknown | Tornado Documentation
Release 6.3.3
The Tornado Authors
Aug 11, 2023
CONTENTS 6.1 User’s guid... 13 6.2 Web framewor... 40 6.3 HTTP servers and client... 83 6.4 Asynchronous networkin... 101 6.5 Coroutines and concurrenc... 120 6.6 Integration with other service... 135 6.7 Util... |
ollggamma | cran | R | Package ‘ollggamma’
October 14, 2022
Title Odd Log-Logistic Generalized Gamma Probability Distribution
Version 1.0.2
Description Density, distribution function, quantile function and random generation for the Odd Log-
Logistic Generalized Gamma pro-
posed in Pratav... |
hms | cran | R | Package ‘hms’
March 21, 2023
Title Pretty Time of Day
Date 2023-03-21
Version 1.1.3
Description Implements an S3 class for storing and formatting time-of-day
values, based on the 'difftime' class.
Imports lifecycle, methods, pkgconfig, rlang (>= 1.0.2), vctrs (>=
... |
ex_figures | hex | Erlang | ExFigures
===
Elixir wrapper for Appfigures [API](https://docs.appfigures.com)
based on [Tesla](https://github.com/teamon/tesla) library.
Appfigures provides a RESTful way to interact with reports and account data.
* [API Overview](https://docs.appfigures.com/) of what is can do
* [Getting started guide](https://doc... |
spack-tutorial | readthedoc | YAML | Spack Tutorial documentation
[Spack Tutorial](index.html#document-index)
---
Tutorial: Spack 101[¶](#tutorial-spack-101)
===
This is a full day introduction to Spack with lectures and live demos. It was presented as a tutorial at [Supercomputing 2017](http://sc17.supercomputing.org) on November 13, 2017.
You can u... |
SDMPlay | cran | R | Package ‘SDMPlay’
October 12, 2022
Type Package
Title Species Distribution Modelling Playground
Version 2.0
Date 2021-09-14
Maintainer <NAME> <<EMAIL>>
Description Species distribution modelling (SDM) has been developed for several years to ad-
dress conservation issues... |
atomic_fn | rust | Rust | Crate atomic_fn
===
A small, no_std crate that adds atomic function pointers.
See `AtomicFnPtr` for examples.
Structs
---
AtomicFnPtrA function pointer type which can be safely shared between threads.
Traits
---
FnPtr
Struct atomic_fn::AtomicFnPtr
===
```
#[repr(C, align(8))]pub struct AtomicFnPtr<T: FnPtr> { /... |
nintendo64-pac | rust | Rust | Crate nintendo64_pac
===
Nintendo 64 PAC
---
Provides access to low-level Nintendo 64 memory in a type- and memory-safe way.
Modules
---
* aiAudio Interface Wrapper
* dpcDP Command Wrapper
* dpsDP Span Wrapper
* mi
* pc
* pi
* rdram
* ri
* si
* sp
* vi
Structs
---
* HardwareContains references to each hardware pe... |
gold | hex | Erlang | gold v0.16.2
API Reference
===
Modules
---
[Gold](Gold.html)
Opinionated interface to Bitcoin core JSON-RPC API.
Currently in MVP mode: architecture is ready and stable, doesn’t fully implement all of the RPC commands yet
[Gold.Transaction](Gold.Transaction.html)
Struct which holds all transaction data
[PoisonedD... |
github.com/go-gem/gem | go | Go | README
[¶](#section-readme)
---
### Gem Web Framework
[](https://godoc.org/github.com/go-gem/gem)
[](https://travis-ci.org/go-gem/gem)
[
* [next](development/architecture.html) |
* [Adhocracy 2.0dev documentation](#) »
Welcome to Adhocracy’s documentation
===
Adhocracy is a web-based platform that ... |
advpistepper | readthedoc | Unknown | AdvPiStepper 0.9.0.alpha documentation
[AdvPiStepper](index.html#document-index)
---
Welcome to AdvPiStepper’s documentation
===
AdvPiStepper is a driver for all kinds of stepper motors, written in Python for the Raspberry Pi, using the pigpio library.
Features[¶](#fea... |
aprof | cran | R | Package ‘aprof’
October 12, 2022
Type Package
Title Amdahl's Profiler, Directed Optimization Made Easy
Version 0.4.1
Date 2018-05-17
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Description Assists the evaluation of whether and
where to focus code optimization, using Amdah... |
pypi_yutto.jsonl | personal_doc | Unknown | #
𝓫𝓲𝓵𝓲𝓵𝓲
🍻 bilibili video and danmaku downloader | B 站视频、弹幕下载器
可以开始了哟
多线程 + 分块下载，总之就是很快啦～
自动下载弹幕并可转换为 ass 弹幕～
即便一次没下完也可以接着下载～
## # 我所支持的 url
嘛～我也是比较挑剔的，目前我只支持以下几种视频 url
* 投稿视频主页：
```
https://www.bilibili.com/video/avxxxxxx
```
嘛，这种 av 号的我会支持 *
```
https://b23.tv/avxxxxxx
```
短链接也可以考虑 *
```
https... |
deno_webidl | rust | Rust | Struct deno_webidl::deno_webidl
===
```
pub struct deno_webidl {}
```
An extension for use with the Deno JS runtime.
To use it, provide it as an argument when instantiating your runtime:
```
use deno_core::{ JsRuntime, RuntimeOptions };
let mut extensions = vec![deno_webidl::init_ops_and_esm()];
let mut js_runtime ... |
gravity_mailbox | ruby | Ruby | [](https://badge.fury.io/rb/gravity_mailbox)
[](https://github.com/petalmd/gravity_mailbox/actions/workflows/main.yml)
 monorepo.
* [About](#about)
+ [Status](#status)
- [HIC SUNT DRACONES](#hic-sunt-dracones)
* [Installation](#installation)
* [Dependencies](#dependencies)
* [Usage examples](#usage-examples)
* [API](#api)
* [Authors](#authors)
* [Lic... |
spBayes | cran | R | Package ‘spBayes’
October 14, 2022
Version 0.4-6
Date 2022-05-12
Title Univariate and Multivariate Spatial-Temporal Modeling
Maintainer <NAME> <<EMAIL>>
Author <NAME> [aut, cre],
<NAME> [aut]
Depends R (>= 1.8.0)
Imports coda, sp, magic, Formula, Matrix
Suggests MBA
Des... |
rAmCharts4 | cran | R | Package ‘rAmCharts4’
October 14, 2022
Title Interface to the JavaScript Library 'amCharts 4'
Version 1.6.0
Maintainer <NAME> <<EMAIL>>
Description Creates JavaScript charts. The charts can be included in 'Shiny' apps and R mark-
down documents, or viewed from the R conso... |
github.com/grpc/grpc-go/examples | go | Go | README
[¶](#section-readme)
---
### gRPC in 3 minutes (Go)
#### BACKGROUND
For this sample, we've already generated the server and client stubs from [helloworld.proto](https://github.com/grpc/grpc-go/blob/v1.14.0/examples/helloworld/helloworld/helloworld.proto).
#### PREREQUISITES
* This requires Go 1.6 or later
... |
mxkssd | cran | R | Package ‘mxkssd’
October 13, 2022
Version 1.2
Date 2022-02-21
Title Efficient Mixed-Level k-Circulant Supersaturated Designs
Author <NAME> <<EMAIL>>
Maintainer <NAME> <<EMAIL>>
Depends R(>= 2.13.0)
Description Generates efficient balanced mixed-level k-circulant supersaturated d... |
viz-router | rust | Rust | Crate viz_router
===
Router for Viz Web Framework
Structs
---
* PathMatched route path infomation.
* PathTreeA path tree.
* ResourcesA resourceful route provides a mapping between HTTP verbs and URLs to handlers.
* RouteA collection of verb-handler pair.
* RouterA routes collection.
* TreeStore all final routes.
Fu... |
bonny | hex | Erlang |
README
===
[](https://hex.pm/packages/bonny)
[](https://coveralls.io/github/coryodaniel/bonny?branch=master)
[![Last Updated]... |
github.com/polycube-network/polycube | go | Go | README
[¶](#section-readme)
---
### Polycube
[](http://130.192.225.104:8080/job/polycube_netgroup/)
[
---
### Node feature discovery for [Kubernetes](https://kubernetes.io)
[](https://travis-ci.org/kubernetes-sigs/node-feature-discovery)
[ provides a wrapper for DaData API.
Example
---
Firs we need to define a configuration module.
```
defmodule MyApp.Dadata do
use ExDadata, otp_app: :my_app end
```
Then we can set our configuration in `config.exs` file:
```
config :my_app, MyApp.Dadata,
api_key: "<a... |
inforion | readthedoc | Unknown | InforION
Release 2.1
2021-05-03
Usage 2.1 Install from Package Manager... 5 2.2 Build from Sourc... 5 3.1 Python 3 Installer Downloa... 7 3.2 Run the Installe... 8 4.1 Installatio... 9 4.2 Upgrad... 9 4.3 Show Versio... 9 6.1 Descriptio... 15 6.2 Parameter... 15 6.3 Exampl... 15 7.1 creat... 17 7.2 delet... 18 8.... |
spc | cran | R | Package ‘spc’
October 24, 2022
Version 0.6.7
Date 2022-10-24
Title Statistical Process Control -- Calculation of ARL and Other
Control Chart Performance Measures
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Depends R (>= 1.8.0)
Description Evaluation of control charts by m... |
NPRED | cran | R | Package ‘NPRED’
June 21, 2023
Title Predictor Identifier: Nonparametric Prediction
Version 1.0.7
Author <NAME> [aut] (<https://orcid.org/0000-0002-6758-0519>),
<NAME> [aut],
<NAME> [aut],
<NAME> [aut],
<NAME> [aut, cre] (<https://orcid.org/0000-0002-... |
multiROC | cran | R | Package ‘multiROC’
October 13, 2022
Title Calculating and Visualizing ROC and PR Curves Across Multi-Class
Classifications
Version 1.1.1
Description
Tools to solve real-world problems with multiple classes classifications by computing the areas un-
der ROC a... |
github.com/monochromegane/the_platinum_searcher | go | Go | README
[¶](#section-readme)
---
### The Platinum Searcher [Build Status](https://travis-ci.org/monochromegane/the_platinum_searcher) [wercker status](https://app.wercker.com/project/bykey/59ef90ac217537abc0994546958037f3)
A code search tool similar to `ack` and `the_silver_searcher(ag)`. It supports multi platforms ... |
rusda | cran | R | Package ‘rusda’
October 14, 2022
Type Package
Title Interface to USDA Databases
Version 1.0.8
Date 2016-03-18
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Imports XML, httr (>= 0.6.1), plyr, foreach, stringr, testthat,
taxize, RCurl
Description An interface to the web ser... |
viralmodels | cran | R | Package ‘viralmodels’
September 29, 2023
Title Viral Load and CD4 Lymphocytes Regression Models
Version 1.1.0
Description
Provides a comprehensive framework for building, evaluating, and visualizing regression mod-
els for analyzing viral load and CD4 (Cluster of Di... |
lithos | readthedoc | YAML | Lithos 0.18.4 documentation
[Lithos](index.html#document-index)
---
Welcome to Lithos’s documentation
===
Contents:
Configuration Overview[¶](#configuration-overview)
---
Lithos has 4 configs:
1. `/etc/lithos/master.yaml` – global configuration for whole lithos daemon. Emp... |
egui_extras | rust | Rust | Crate egui_extras
===
This is a crate that adds some features on top top of `egui`.
This crate are for experimental features, and features that require big dependencies that does not belong in `egui`.
### Feature flags
* **`all_loaders`** — Shorthand for enabling the different types of image loaders (`file`, `http`... |
github.com/graphikDB/graphik | go | Go | README
[¶](#section-readme)
---
<https://graphikdb.github.io/graphik/[](https://godoc.org/github.com/graphikDB/graphik)
### Quick Start
Download sample .env & docke... |
nucleide | rust | Rust | Crate nucleide
===
Nucleide
---
A crate to manipulate custom sections of a WebAssembly module to view/edit application metadata.
Specification
---
Nucleide specifies WASM metadata that is read by the Nucleic Desktop Environment. It includes the WebAssembly 2.0 and the Daku 1.0.0-beta.0 specifications.
Daku program... |
nemo-arethusa-plugin | readthedoc | Unknown | nemo\_arethusa\_plugin documentation
[nemo\_arethusa\_plugin](index.html#document-index)
---
Arethusa for Nemo Plugin[¶](#arethusa-for-nemo-plugin)
===
Arethusa for CapiTainS Nemo[¶](#arethusa-for-capitains-nemo)
===
This repository contains a plugin for embedding Arethusa in [Flask Capitains Nemo](https://github.... |
simpleNeural | cran | R | Package ‘simpleNeural’
October 14, 2022
Version 0.1.3
Date 2020-02-18
Title An Easy to Use Multilayer Perceptron
Description Trains neural networks (multilayer perceptrons with one hidden layer) for bi- or multi-
class classification.
Depends R (>= 3.6)
Suggests verificat... |
fechner | cran | R | Package ‘fechner’
October 13, 2022
Version 1.0-3
Date 2016-06-05
Title Fechnerian Scaling of Discrete Object Sets
Description Functions and example datasets for Fechnerian scaling of discrete
object sets. User can compute Fechnerian distances among objects representing
... |
@aws-sdk/credential-provider-node | npm | JavaScript | [@aws-sdk/credential-provider-node](#aws-sdkcredential-provider-node)
===
[AWS Credential Provider for Node.JS](#aws-credential-provider-for-nodejs)
---
This module provides a factory function, `fromEnv`, that will attempt to source AWS credentials from a Node.JS environment. It will attempt to find credentials from ... |
bayesanova | cran | R | Package ‘bayesanova’
October 12, 2022
Type Package
Title Bayesian Inference in the Analysis of Variance via Markov Chain
Monte Carlo in Gaussian Mixture Models
Version 1.5
Date 2021-10-27
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Description Provides a Bayesian version of... |
GITHUB_raaminz_training.zip_unzipped_1_-_Introduction_to_Spring.pdf | free_programming_book | Unknown | Spring Introduction
Presented by <NAME> Twitter: @zare88r
Spring
JEE web standalone
( lightweight )
)(Spring Core
)Expert One-on-One: J2EE Design and Development by <NAME> (Wrox, 2002
.
5 July 2016
IOC
Inversion of Control
. container
Java Servlet
container
Servlet Container... |
TSLSTM | cran | R | Package ‘TSLSTM’
October 12, 2022
Type Package
Title Long Short Term Memory (LSTM) Model for Time Series Forecasting
Version 0.1.0
Author Dr. <NAME> [aut, cre],
Dr. <NAME> [aut]
Maintainer Dr. <NAME> <<EMAIL>>
Description The LSTM (Long Short-Term Memory) model is a Recur... |
numpy | devdocs | Haskell |
NumPy documentation
===================
**Version**: 1.23
**Download documentation**: [PDF Version](https://numpy.org/doc/stable/numpy-user.pdf) | [Historical versions of documentation](https://numpy.org/doc/)
**Useful links**: [Installation](https://numpy.org/install/) | [Source Repository](https://github.com/... |
roxyglobals | cran | R | Package ‘roxyglobals’
August 21, 2023
Title 'Roxygen2' Global Variable Declarations
Version 1.0.0
Description Generate utils::globalVariables() from 'roxygen2' @global and @autoglobal tags.
License MIT + file LICENSE
URL https://github.com/anthonynorth/roxyglobals
BugReports ht... |
SafeVote | cran | R | Package ‘SafeVote’
January 18, 2023
Type Package
Title Election Vote Counting with Safety Features
Version 1.0.0
Date 2023-01-18
Description Fork of 'vote_2.3-2', Raftery et al. (2021)
<DOI:10.32614/RJ-2021-086>, with additional support
for stochastic experimentat... |
github.com/ribice/glice | go | Go | README
[¶](#section-readme)
---
### glice
[](https://travis-ci.org/ribice/glice)
[](https://coveralls.io/github/ribice/glice?branch=master)
[![Go Report Card]... |
pypi_bcolz.jsonl | personal_doc | Dart | * Optimized Hyper-slicing in PyTables with Blosc2 NDim
* Dynamic plugins in C-Blosc2
* Bytedelta: Enhance Your Compression Toolset
* Introducing Blosc2 NDim
* 100 Trillion Rows Baby
* 20 years of PyTables
* Blosc2 Meets PyTables: Making HDF5 I/O Performance Awesome
* User Defined Pipeline for Python-Blosc2
* Ne... |
rkafkajars | cran | R | Package ‘rkafkajars’
October 14, 2022
Type Package
Title External Jars Required for Package 'rkafka'
Version 1.2
Date 2021-12-01
Author <NAME> [aut,cre], <NAME> and Yammer Inc.[ctb,cph],Sun Microsys-
tems Inc.[ctb,cph],<NAME>[ctb,cph],<NAME>[ctb],Junit[ctb,cph],The Apache ... |
rusoto_pinpoint_sms_voice | rust | Rust | Crate rusoto_pinpoint_sms_voice
===
Pinpoint SMS and Voice Messaging public facing APIs
If you’re using the service, you’re probably looking for PinpointSmsVoiceClient and PinpointSmsVoice.
Structs
---
CallInstructionsMessageTypeAn object that defines a message that contains text formatted using Amazon Pinpoint Voi... |
bisectr | cran | R | Package ‘bisectr’
October 12, 2022
Title Tools to find bad commits with git bisect
Version 0.1.0
Author <NAME> <<EMAIL>>
Maintainer <NAME> <<EMAIL>>
Description Tools to find bad commits with git bisect. See
https://github.com/wch/bisectr for examples and test script
... |
web-platform-compat | readthedoc | JSON | web-platform-compat 0.1.0 documentation
web-platform-compat[¶](#web-platform-compat)
===
The Web Platform Compatibility API will support compatibility data on the
[Mozilla Developer Network](https://developer.mozilla.org). This currently takes the form of browser compatibility tables, such as the one on the [CSS disp... |
github.com/docker/docker/pkg/chrootarchive | go | Go | None
Documentation
[¶](#section-documentation)
---
[Rendered for](https://go.dev/about#build-context)
linux/amd64 windows/amd64 darwin/amd64 js/wasm
### Index [¶](#pkg-index)
* [func ApplyLayer(dest string, layer io.Reader) (size int64, err error)](#ApplyLayer)
* [func ApplyUncompressedLayer(dest string, layer ... |
capnproto.org/go/capnp/v3 | go | Go | README
[¶](#section-readme)
---
### Cap'n Proto bindings for Go
[](https://goreportcard.com/report/capnproto.org/go/capnp/v3)
[
---
### Go Router
[](https://travis-ci.org/takama/router)
[](https://godoc.org/github.com/takama/router)
[ as a lightweig... |
daymetr | cran | R | Package ‘daymetr’
September 15, 2023
Title Interface to the 'Daymet' Web Services
Version 1.7.1
Description Programmatic interface to the 'Daymet' web services
(<http://daymet.ornl.gov>). Allows for easy downloads of
'Daymet' climate data directly to your R workspac... |
opencv | rust | Rust | Module opencv::alphamat
===
Alpha Matting
---
Alpha matting is used to extract a foreground object with soft boundaries from a background image.
This module is dedicated to computing alpha matte of objects in images from a given input image and a greyscale trimap image that contains information about the foreground,... |
@ckeditor/ckeditor5-build-multi-root | npm | JavaScript | [CKEditor 5 multi-root editor build](#ckeditor5-multi-root-editor-build)
===
The multi-root editor build for CKEditor 5. Read more about the [multi-root editor build](https://ckeditor.com/docs/ckeditor5/latest/installation/getting-started/predefined-builds.html#multi-root-editor) and see the [demo](https://ckeditor.co... |
@thi.ng/rdom-canvas | npm | JavaScript | This project is part of the
[@thi.ng/umbrella](https://github.com/thi-ng/umbrella/) monorepo and anti-framework.
* [About](#about)
+ [General usage](#general-usage)
+ [Control attributes](#control-attributes)
* [Status](#status)
* [Related packages](#related-packages)
* [Installation](#installation)
* [Dependencies]... |
GRMustache | cocoapods | Objective-C | grmustache.swift
===
Welcome to the documentation for the grmustache.swift framework! In this guide, we will explore the features, usage, and advantages of using grmustache.swift in your Swift projects.
What is grmustache.swift?
---
grmustache.swift is a powerful and lightweight implementation of the Mustache templa... |
atsame54_xpro | rust | Rust | Module atsame54_xpro::pins
===
SAM E54 XPlained Pro Pin Definitions
Structs
---
* PinsBSP replacement for the HAL
`Pins` type
Constants
---
* ADC0_ANALOG0_IDDynPinId
for the `Adc0Analog0` alias.
* ADC0_ANALOG0_MODEDynPinMode
for the `Adc0Analog0` alias.
* ADC0_ANALOG1_IDDynPinId
for the `Adc0Analog1` alias.
* A... |
novapo-medusa-payment-manual | npm | JavaScript | Manual Payment
===
A minimal payment provider that allows merchants to handle payments manually.
[Medusa Website](https://medusajs.com/) | [Medusa Repository](https://github.com/medusajs/medusa)
Features
---
* Provides a restriction-free payment provider that can be used during checkout and while processing orders.... |
FME | cran | R | Package ‘FME’
July 5, 2023
Version 1.3.6.3
Title A Flexible Modelling Environment for Inverse Modelling,
Sensitivity, Identifiability and Monte Carlo Analysis
Author <NAME> [aut, cre] (<https://orcid.org/0000-0003-4603-7100>),
<NAME> [aut] (<https://orcid.org/... |
CodableAlamofire | cocoapods | Objective-C | codablealamofire
===
**CodableAlamofire**
---
**CodableAlamofire** is a powerful and user-friendly library that integrates **Alamofire** with **Codable** to effortlessly parse JSON responses into Swift objects. This library makes working with web services and APIs seamless and efficient by handling all the data seria... |
mtsta | cran | R | Package ‘mtsta’
September 19, 2023
Title Accessing the Red List of Montane Tree Species of the Tropical
Andes
Version 0.0.0.1
Description Access the 'Red List of Montane Tree Species of the Tropical Andes' Tejedor Gar-
avito et al.(2014, ISBN:978-1-905164-60-8). This ... |
django-user-accounts | readthedoc | Python | django-user-accounts 2.0.3 documentation
[django-user-accounts](index.html#document-index)
---
django-user-accounts[¶](#django-user-accounts)
===
Provides user accounts to a Django project.
Development[¶](#development)
---
The source repository can be found at <https://github.com/pinax/django-user-accounts/### Co... |
CorrBin | cran | R | Package ‘CorrBin’
September 29, 2023
Title Nonparametrics with Clustered Binary and Multinomial Data
Version 1.6.1
Date 2023-09-28
Encoding UTF-8
Depends R(>= 2.6.0)
Imports boot, combinat, geepack, dirmult, mvtnorm
Suggests lattice
Description Implements non-parametric analyse... |
r2redux | cran | R | Package ‘r2redux’
September 19, 2023
Title R2 Statistic
Version 1.0.16
Description R2 statistic for significance test. Variance and covariance of R2 values used to as-
sess the 95% CI and p-value of the R2 difference.
License GPL (>= 3)
URL https://github.com/mommy003/r2re... |
flashClust | cran | R | Package ‘flashClust’
October 13, 2022
Version 1.01-2
Date 2012-08-21
Title Implementation of optimal hierarchical clustering
Author code by <NAME> and R development team, modifications and
packaging by <NAME>
Maintainer <NAME> <<EMAIL>>
Depends R (>= 2.3.0)
ZipData no
Lic... |
bartCause | cran | R | Package ‘bartCause’
January 23, 2023
Version 1.0-6
Date 2023-01-23
Title Causal Inference using Bayesian Additive Regression Trees
Depends R (>= 3.1-0)
Imports dbarts (>= 0.9-16), methods, stats, graphics, parallel, utils,
grDevices
Suggests testthat (>= 0.9-0), lme4, rp... |
velociraptr | cran | R | Package ‘velociraptr’
October 12, 2022
Type Package
Title Fossil Analysis
Version 1.1.0
Author <NAME>
Maintainer <NAME> <<EMAIL>>
Description Functions for downloading, reshaping, culling, cleaning, and analyzing fos-
sil data from the Paleobiology Database <https://pale... |
mcbette | cran | R | Package ‘mcbette’
September 27, 2023
Title Model Comparison Using 'babette'
Version 1.15.2
Maintainer <NAME> <<EMAIL>>
Description 'BEAST2' (<https://www.beast2.org>) is a widely used
Bayesian phylogenetic tool, that uses DNA/RNA/protein data
and many model priors to... |
asphalt-influxdb | readthedoc | Python | asphalt-influxdb 2.1.0.post3 documentation
[asphalt-influxdb](index.html#document-index)
---
This Asphalt framework component provides connectivity to [InfluxDB](https://www.influxdata.com/) database servers.
Table of contents[¶](#table-of-contents)
===
Configuration[¶](#configuration)
---
The typical InfluxDB co... |
phpmyadmin-japanese | readthedoc | PHP | phpMyAdmin 6.0.0-dev ドキュメント
### ナビゲーション
* [phpMyAdmin 6.0.0-dev ドキュメント](index.html#document-index) »
phpMyAdmin 日本語ドキュメント[¶](#welcome-to-phpmyadmin-s-documentation)
===
目次:
はじめに[¶](#introduction)
---
phpMyAdmin は、 MySQL または MariaDB データベースサーバの管理を扱うことを目的とした、 PHP で記述されたフリーソフトウェアのツールです。 phpMyAdmin を使用して、データベースの作成、クエリ... |
shunter | npm | JavaScript | Shunter is a [Node.js](https://nodejs.org/) application built to read JSON and translate it into HTML.
It helps you create a loosely-coupled front end which can serve traffic from one or more back end applications - great for use in multi-language, multi-disciplinary teams or just to make your project more flexible an... |
github.com/asciinema/asciinema-cli | go | Go | README
[¶](#section-readme)
---
### asciinema
[](https://travis-ci.org/asciinema/asciinema)
[](https://raw.githubusercontent.com/asciinema/asciinema/master/LICENSE)
Terminal sessio... |
ecan | cran | R | Package ‘ecan’
July 7, 2023
Title Ecological Analysis and Visualization
Version 0.2.1
Description Support ecological analyses such as ordination and clustering.
Contains consistent and easy wrapper functions of 'stat', 'vegan', and
'labdsv' packages, and visu... |
base64url | rust | Rust | Crate base64url
===
Implementation of the encode and decode operations on base64url (as defined in IETF RFC 4648) String.
The encoded string restricted to containing the 2^6 UTF-8 code points without padding.
In general, we use `-` and `_` instead of `+` and `/`, without paddings.
Functions
---
* decodedecode takes... |
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