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@@ -385,3 +385,6 @@ tuning-competition-baseline/.venv/lib/python3.11/site-packages/nvidia/cudnn/lib/
 .venv/lib/python3.11/site-packages/numpy/distutils/__pycache__/misc_util.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
 .venv/lib/python3.11/site-packages/numpy/distutils/__pycache__/ccompiler_opt.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
 .venv/lib/python3.11/site-packages/numpy/distutils/__pycache__/system_info.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
+.venv/lib/python3.11/site-packages/numpy/testing/_private/__pycache__/utils.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
+.venv/lib/python3.11/site-packages/numpy/ma/__pycache__/core.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
+.venv/lib/python3.11/site-packages/numpy/testing/tests/__pycache__/test_utils.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text

.venv/lib/python3.11/site-packages/numpy/lib/__init__.py

@@ -0,0 +1,92 @@
+"""
+**Note:** almost all functions in the ``numpy.lib`` namespace
+are also present in the main ``numpy`` namespace.  Please use the
+functions as ``np.<funcname>`` where possible.
+
+``numpy.lib`` is mostly a space for implementing functions that don't
+belong in core or in another NumPy submodule with a clear purpose
+(e.g. ``random``, ``fft``, ``linalg``, ``ma``).
+
+Most contains basic functions that are used by several submodules and are
+useful to have in the main name-space.
+
+"""
+
+# Public submodules
+# Note: recfunctions and (maybe) format are public too, but not imported
+from . import mixins
+from . import scimath as emath
+
+# Private submodules
+# load module names. See https://github.com/networkx/networkx/issues/5838
+from . import type_check
+from . import index_tricks
+from . import function_base
+from . import nanfunctions
+from . import shape_base
+from . import stride_tricks
+from . import twodim_base
+from . import ufunclike
+from . import histograms
+from . import polynomial
+from . import utils
+from . import arraysetops
+from . import npyio
+from . import arrayterator
+from . import arraypad
+from . import _version
+
+from .type_check import *
+from .index_tricks import *
+from .function_base import *
+from .nanfunctions import *
+from .shape_base import *
+from .stride_tricks import *
+from .twodim_base import *
+from .ufunclike import *
+from .histograms import *
+
+from .polynomial import *
+from .utils import *
+from .arraysetops import *
+from .npyio import *
+from .arrayterator import Arrayterator
+from .arraypad import *
+from ._version import *
+from numpy.core._multiarray_umath import tracemalloc_domain
+
+__all__ = ['emath', 'tracemalloc_domain', 'Arrayterator']
+__all__ += type_check.__all__
+__all__ += index_tricks.__all__
+__all__ += function_base.__all__
+__all__ += shape_base.__all__
+__all__ += stride_tricks.__all__
+__all__ += twodim_base.__all__
+__all__ += ufunclike.__all__
+__all__ += arraypad.__all__
+__all__ += polynomial.__all__
+__all__ += utils.__all__
+__all__ += arraysetops.__all__
+__all__ += npyio.__all__
+__all__ += nanfunctions.__all__
+__all__ += histograms.__all__
+
+from numpy._pytesttester import PytestTester
+test = PytestTester(__name__)
+del PytestTester
+
+def __getattr__(attr):
+    # Warn for reprecated attributes
+    import math
+    import warnings
+
+    if attr == 'math':
+        warnings.warn(
+            "`np.lib.math` is a deprecated alias for the standard library "
+            "`math` module (Deprecated Numpy 1.25). Replace usages of "
+            "`numpy.lib.math` with `math`", DeprecationWarning, stacklevel=2)
+        return math
+    else:
+        raise AttributeError("module {!r} has no attribute "
+                             "{!r}".format(__name__, attr))
+        

.venv/lib/python3.11/site-packages/numpy/lib/_version.py

@@ -0,0 +1,155 @@
+"""Utility to compare (NumPy) version strings.
+
+The NumpyVersion class allows properly comparing numpy version strings.
+The LooseVersion and StrictVersion classes that distutils provides don't
+work; they don't recognize anything like alpha/beta/rc/dev versions.
+
+"""
+import re
+
+
+__all__ = ['NumpyVersion']
+
+
+class NumpyVersion():
+    """Parse and compare numpy version strings.
+
+    NumPy has the following versioning scheme (numbers given are examples; they
+    can be > 9 in principle):
+
+    - Released version: '1.8.0', '1.8.1', etc.
+    - Alpha: '1.8.0a1', '1.8.0a2', etc.
+    - Beta: '1.8.0b1', '1.8.0b2', etc.
+    - Release candidates: '1.8.0rc1', '1.8.0rc2', etc.
+    - Development versions: '1.8.0.dev-f1234afa' (git commit hash appended)
+    - Development versions after a1: '1.8.0a1.dev-f1234afa',
+                                     '1.8.0b2.dev-f1234afa',
+                                     '1.8.1rc1.dev-f1234afa', etc.
+    - Development versions (no git hash available): '1.8.0.dev-Unknown'
+
+    Comparing needs to be done against a valid version string or other
+    `NumpyVersion` instance. Note that all development versions of the same
+    (pre-)release compare equal.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    vstring : str
+        NumPy version string (``np.__version__``).
+
+    Examples
+    --------
+    >>> from numpy.lib import NumpyVersion
+    >>> if NumpyVersion(np.__version__) < '1.7.0':
+    ...     print('skip')
+    >>> # skip
+
+    >>> NumpyVersion('1.7')  # raises ValueError, add ".0"
+    Traceback (most recent call last):
+        ...
+    ValueError: Not a valid numpy version string
+
+    """
+
+    def __init__(self, vstring):
+        self.vstring = vstring
+        ver_main = re.match(r'\d+\.\d+\.\d+', vstring)
+        if not ver_main:
+            raise ValueError("Not a valid numpy version string")
+
+        self.version = ver_main.group()
+        self.major, self.minor, self.bugfix = [int(x) for x in
+            self.version.split('.')]
+        if len(vstring) == ver_main.end():
+            self.pre_release = 'final'
+        else:
+            alpha = re.match(r'a\d', vstring[ver_main.end():])
+            beta = re.match(r'b\d', vstring[ver_main.end():])
+            rc = re.match(r'rc\d', vstring[ver_main.end():])
+            pre_rel = [m for m in [alpha, beta, rc] if m is not None]
+            if pre_rel:
+                self.pre_release = pre_rel[0].group()
+            else:
+                self.pre_release = ''
+
+        self.is_devversion = bool(re.search(r'.dev', vstring))
+
+    def _compare_version(self, other):
+        """Compare major.minor.bugfix"""
+        if self.major == other.major:
+            if self.minor == other.minor:
+                if self.bugfix == other.bugfix:
+                    vercmp = 0
+                elif self.bugfix > other.bugfix:
+                    vercmp = 1
+                else:
+                    vercmp = -1
+            elif self.minor > other.minor:
+                vercmp = 1
+            else:
+                vercmp = -1
+        elif self.major > other.major:
+            vercmp = 1
+        else:
+            vercmp = -1
+
+        return vercmp
+
+    def _compare_pre_release(self, other):
+        """Compare alpha/beta/rc/final."""
+        if self.pre_release == other.pre_release:
+            vercmp = 0
+        elif self.pre_release == 'final':
+            vercmp = 1
+        elif other.pre_release == 'final':
+            vercmp = -1
+        elif self.pre_release > other.pre_release:
+            vercmp = 1
+        else:
+            vercmp = -1
+
+        return vercmp
+
+    def _compare(self, other):
+        if not isinstance(other, (str, NumpyVersion)):
+            raise ValueError("Invalid object to compare with NumpyVersion.")
+
+        if isinstance(other, str):
+            other = NumpyVersion(other)
+
+        vercmp = self._compare_version(other)
+        if vercmp == 0:
+            # Same x.y.z version, check for alpha/beta/rc
+            vercmp = self._compare_pre_release(other)
+            if vercmp == 0:
+                # Same version and same pre-release, check if dev version
+                if self.is_devversion is other.is_devversion:
+                    vercmp = 0
+                elif self.is_devversion:
+                    vercmp = -1
+                else:
+                    vercmp = 1
+
+        return vercmp
+
+    def __lt__(self, other):
+        return self._compare(other) < 0
+
+    def __le__(self, other):
+        return self._compare(other) <= 0
+
+    def __eq__(self, other):
+        return self._compare(other) == 0
+
+    def __ne__(self, other):
+        return self._compare(other) != 0
+
+    def __gt__(self, other):
+        return self._compare(other) > 0
+
+    def __ge__(self, other):
+        return self._compare(other) >= 0
+
+    def __repr__(self):
+        return "NumpyVersion(%s)" % self.vstring

.venv/lib/python3.11/site-packages/numpy/lib/arraypad.py

@@ -0,0 +1,882 @@
+"""
+The arraypad module contains a group of functions to pad values onto the edges
+of an n-dimensional array.
+
+"""
+import numpy as np
+from numpy.core.overrides import array_function_dispatch
+from numpy.lib.index_tricks import ndindex
+
+
+__all__ = ['pad']
+
+
+###############################################################################
+# Private utility functions.
+
+
+def _round_if_needed(arr, dtype):
+    """
+    Rounds arr inplace if destination dtype is integer.
+
+    Parameters
+    ----------
+    arr : ndarray
+        Input array.
+    dtype : dtype
+        The dtype of the destination array.
+    """
+    if np.issubdtype(dtype, np.integer):
+        arr.round(out=arr)
+
+
+def _slice_at_axis(sl, axis):
+    """
+    Construct tuple of slices to slice an array in the given dimension.
+
+    Parameters
+    ----------
+    sl : slice
+        The slice for the given dimension.
+    axis : int
+        The axis to which `sl` is applied. All other dimensions are left
+        "unsliced".
+
+    Returns
+    -------
+    sl : tuple of slices
+        A tuple with slices matching `shape` in length.
+
+    Examples
+    --------
+    >>> _slice_at_axis(slice(None, 3, -1), 1)
+    (slice(None, None, None), slice(None, 3, -1), (...,))
+    """
+    return (slice(None),) * axis + (sl,) + (...,)
+
+
+def _view_roi(array, original_area_slice, axis):
+    """
+    Get a view of the current region of interest during iterative padding.
+
+    When padding multiple dimensions iteratively corner values are
+    unnecessarily overwritten multiple times. This function reduces the
+    working area for the first dimensions so that corners are excluded.
+
+    Parameters
+    ----------
+    array : ndarray
+        The array with the region of interest.
+    original_area_slice : tuple of slices
+        Denotes the area with original values of the unpadded array.
+    axis : int
+        The currently padded dimension assuming that `axis` is padded before
+        `axis` + 1.
+
+    Returns
+    -------
+    roi : ndarray
+        The region of interest of the original `array`.
+    """
+    axis += 1
+    sl = (slice(None),) * axis + original_area_slice[axis:]
+    return array[sl]
+
+
+def _pad_simple(array, pad_width, fill_value=None):
+    """
+    Pad array on all sides with either a single value or undefined values.
+
+    Parameters
+    ----------
+    array : ndarray
+        Array to grow.
+    pad_width : sequence of tuple[int, int]
+        Pad width on both sides for each dimension in `arr`.
+    fill_value : scalar, optional
+        If provided the padded area is filled with this value, otherwise
+        the pad area left undefined.
+
+    Returns
+    -------
+    padded : ndarray
+        The padded array with the same dtype as`array`. Its order will default
+        to C-style if `array` is not F-contiguous.
+    original_area_slice : tuple
+        A tuple of slices pointing to the area of the original array.
+    """
+    # Allocate grown array
+    new_shape = tuple(
+        left + size + right
+        for size, (left, right) in zip(array.shape, pad_width)
+    )
+    order = 'F' if array.flags.fnc else 'C'  # Fortran and not also C-order
+    padded = np.empty(new_shape, dtype=array.dtype, order=order)
+
+    if fill_value is not None:
+        padded.fill(fill_value)
+
+    # Copy old array into correct space
+    original_area_slice = tuple(
+        slice(left, left + size)
+        for size, (left, right) in zip(array.shape, pad_width)
+    )
+    padded[original_area_slice] = array
+
+    return padded, original_area_slice
+
+
+def _set_pad_area(padded, axis, width_pair, value_pair):
+    """
+    Set empty-padded area in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Array with the pad area which is modified inplace.
+    axis : int
+        Dimension with the pad area to set.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    value_pair : tuple of scalars or ndarrays
+        Values inserted into the pad area on each side. It must match or be
+        broadcastable to the shape of `arr`.
+    """
+    left_slice = _slice_at_axis(slice(None, width_pair[0]), axis)
+    padded[left_slice] = value_pair[0]
+
+    right_slice = _slice_at_axis(
+        slice(padded.shape[axis] - width_pair[1], None), axis)
+    padded[right_slice] = value_pair[1]
+
+
+def _get_edges(padded, axis, width_pair):
+    """
+    Retrieve edge values from empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the edges are considered.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+
+    Returns
+    -------
+    left_edge, right_edge : ndarray
+        Edge values of the valid area in `padded` in the given dimension. Its
+        shape will always match `padded` except for the dimension given by
+        `axis` which will have a length of 1.
+    """
+    left_index = width_pair[0]
+    left_slice = _slice_at_axis(slice(left_index, left_index + 1), axis)
+    left_edge = padded[left_slice]
+
+    right_index = padded.shape[axis] - width_pair[1]
+    right_slice = _slice_at_axis(slice(right_index - 1, right_index), axis)
+    right_edge = padded[right_slice]
+
+    return left_edge, right_edge
+
+
+def _get_linear_ramps(padded, axis, width_pair, end_value_pair):
+    """
+    Construct linear ramps for empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the ramps are constructed.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    end_value_pair : (scalar, scalar)
+        End values for the linear ramps which form the edge of the fully padded
+        array. These values are included in the linear ramps.
+
+    Returns
+    -------
+    left_ramp, right_ramp : ndarray
+        Linear ramps to set on both sides of `padded`.
+    """
+    edge_pair = _get_edges(padded, axis, width_pair)
+
+    left_ramp, right_ramp = (
+        np.linspace(
+            start=end_value,
+            stop=edge.squeeze(axis), # Dimension is replaced by linspace
+            num=width,
+            endpoint=False,
+            dtype=padded.dtype,
+            axis=axis
+        )
+        for end_value, edge, width in zip(
+            end_value_pair, edge_pair, width_pair
+        )
+    )
+        
+    # Reverse linear space in appropriate dimension
+    right_ramp = right_ramp[_slice_at_axis(slice(None, None, -1), axis)]
+
+    return left_ramp, right_ramp
+
+
+def _get_stats(padded, axis, width_pair, length_pair, stat_func):
+    """
+    Calculate statistic for the empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the statistic is calculated.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    length_pair : 2-element sequence of None or int
+        Gives the number of values in valid area from each side that is
+        taken into account when calculating the statistic. If None the entire
+        valid area in `padded` is considered.
+    stat_func : function
+        Function to compute statistic. The expected signature is
+        ``stat_func(x: ndarray, axis: int, keepdims: bool) -> ndarray``.
+
+    Returns
+    -------
+    left_stat, right_stat : ndarray
+        Calculated statistic for both sides of `padded`.
+    """
+    # Calculate indices of the edges of the area with original values
+    left_index = width_pair[0]
+    right_index = padded.shape[axis] - width_pair[1]
+    # as well as its length
+    max_length = right_index - left_index
+
+    # Limit stat_lengths to max_length
+    left_length, right_length = length_pair
+    if left_length is None or max_length < left_length:
+        left_length = max_length
+    if right_length is None or max_length < right_length:
+        right_length = max_length
+
+    if (left_length == 0 or right_length == 0) \
+            and stat_func in {np.amax, np.amin}:
+        # amax and amin can't operate on an empty array,
+        # raise a more descriptive warning here instead of the default one
+        raise ValueError("stat_length of 0 yields no value for padding")
+
+    # Calculate statistic for the left side
+    left_slice = _slice_at_axis(
+        slice(left_index, left_index + left_length), axis)
+    left_chunk = padded[left_slice]
+    left_stat = stat_func(left_chunk, axis=axis, keepdims=True)
+    _round_if_needed(left_stat, padded.dtype)
+
+    if left_length == right_length == max_length:
+        # return early as right_stat must be identical to left_stat
+        return left_stat, left_stat
+
+    # Calculate statistic for the right side
+    right_slice = _slice_at_axis(
+        slice(right_index - right_length, right_index), axis)
+    right_chunk = padded[right_slice]
+    right_stat = stat_func(right_chunk, axis=axis, keepdims=True)
+    _round_if_needed(right_stat, padded.dtype)
+
+    return left_stat, right_stat
+
+
+def _set_reflect_both(padded, axis, width_pair, method, include_edge=False):
+    """
+    Pad `axis` of `arr` with reflection.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Input array of arbitrary shape.
+    axis : int
+        Axis along which to pad `arr`.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    method : str
+        Controls method of reflection; options are 'even' or 'odd'.
+    include_edge : bool
+        If true, edge value is included in reflection, otherwise the edge
+        value forms the symmetric axis to the reflection.
+
+    Returns
+    -------
+    pad_amt : tuple of ints, length 2
+        New index positions of padding to do along the `axis`. If these are
+        both 0, padding is done in this dimension.
+    """
+    left_pad, right_pad = width_pair
+    old_length = padded.shape[axis] - right_pad - left_pad
+
+    if include_edge:
+        # Edge is included, we need to offset the pad amount by 1
+        edge_offset = 1
+    else:
+        edge_offset = 0  # Edge is not included, no need to offset pad amount
+        old_length -= 1  # but must be omitted from the chunk
+
+    if left_pad > 0:
+        # Pad with reflected values on left side:
+        # First limit chunk size which can't be larger than pad area
+        chunk_length = min(old_length, left_pad)
+        # Slice right to left, stop on or next to edge, start relative to stop
+        stop = left_pad - edge_offset
+        start = stop + chunk_length
+        left_slice = _slice_at_axis(slice(start, stop, -1), axis)
+        left_chunk = padded[left_slice]
+
+        if method == "odd":
+            # Negate chunk and align with edge
+            edge_slice = _slice_at_axis(slice(left_pad, left_pad + 1), axis)
+            left_chunk = 2 * padded[edge_slice] - left_chunk
+
+        # Insert chunk into padded area
+        start = left_pad - chunk_length
+        stop = left_pad
+        pad_area = _slice_at_axis(slice(start, stop), axis)
+        padded[pad_area] = left_chunk
+        # Adjust pointer to left edge for next iteration
+        left_pad -= chunk_length
+
+    if right_pad > 0:
+        # Pad with reflected values on right side:
+        # First limit chunk size which can't be larger than pad area
+        chunk_length = min(old_length, right_pad)
+        # Slice right to left, start on or next to edge, stop relative to start
+        start = -right_pad + edge_offset - 2
+        stop = start - chunk_length
+        right_slice = _slice_at_axis(slice(start, stop, -1), axis)
+        right_chunk = padded[right_slice]
+
+        if method == "odd":
+            # Negate chunk and align with edge
+            edge_slice = _slice_at_axis(
+                slice(-right_pad - 1, -right_pad), axis)
+            right_chunk = 2 * padded[edge_slice] - right_chunk
+
+        # Insert chunk into padded area
+        start = padded.shape[axis] - right_pad
+        stop = start + chunk_length
+        pad_area = _slice_at_axis(slice(start, stop), axis)
+        padded[pad_area] = right_chunk
+        # Adjust pointer to right edge for next iteration
+        right_pad -= chunk_length
+
+    return left_pad, right_pad
+
+
+def _set_wrap_both(padded, axis, width_pair, original_period):
+    """
+    Pad `axis` of `arr` with wrapped values.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Input array of arbitrary shape.
+    axis : int
+        Axis along which to pad `arr`.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    original_period : int
+        Original length of data on `axis` of `arr`.
+
+    Returns
+    -------
+    pad_amt : tuple of ints, length 2
+        New index positions of padding to do along the `axis`. If these are
+        both 0, padding is done in this dimension.
+    """
+    left_pad, right_pad = width_pair
+    period = padded.shape[axis] - right_pad - left_pad
+    # Avoid wrapping with only a subset of the original area by ensuring period
+    # can only be a multiple of the original area's length.
+    period = period // original_period * original_period
+
+    # If the current dimension of `arr` doesn't contain enough valid values
+    # (not part of the undefined pad area) we need to pad multiple times.
+    # Each time the pad area shrinks on both sides which is communicated with
+    # these variables.
+    new_left_pad = 0
+    new_right_pad = 0
+
+    if left_pad > 0:
+        # Pad with wrapped values on left side
+        # First slice chunk from left side of the non-pad area.
+        # Use min(period, left_pad) to ensure that chunk is not larger than
+        # pad area.
+        slice_end = left_pad + period
+        slice_start = slice_end - min(period, left_pad)
+        right_slice = _slice_at_axis(slice(slice_start, slice_end), axis)
+        right_chunk = padded[right_slice]
+
+        if left_pad > period:
+            # Chunk is smaller than pad area
+            pad_area = _slice_at_axis(slice(left_pad - period, left_pad), axis)
+            new_left_pad = left_pad - period
+        else:
+            # Chunk matches pad area
+            pad_area = _slice_at_axis(slice(None, left_pad), axis)
+        padded[pad_area] = right_chunk
+
+    if right_pad > 0:
+        # Pad with wrapped values on right side
+        # First slice chunk from right side of the non-pad area.
+        # Use min(period, right_pad) to ensure that chunk is not larger than
+        # pad area.
+        slice_start = -right_pad - period
+        slice_end = slice_start + min(period, right_pad)
+        left_slice = _slice_at_axis(slice(slice_start, slice_end), axis)
+        left_chunk = padded[left_slice]
+
+        if right_pad > period:
+            # Chunk is smaller than pad area
+            pad_area = _slice_at_axis(
+                slice(-right_pad, -right_pad + period), axis)
+            new_right_pad = right_pad - period
+        else:
+            # Chunk matches pad area
+            pad_area = _slice_at_axis(slice(-right_pad, None), axis)
+        padded[pad_area] = left_chunk
+
+    return new_left_pad, new_right_pad
+
+
+def _as_pairs(x, ndim, as_index=False):
+    """
+    Broadcast `x` to an array with the shape (`ndim`, 2).
+
+    A helper function for `pad` that prepares and validates arguments like
+    `pad_width` for iteration in pairs.
+
+    Parameters
+    ----------
+    x : {None, scalar, array-like}
+        The object to broadcast to the shape (`ndim`, 2).
+    ndim : int
+        Number of pairs the broadcasted `x` will have.
+    as_index : bool, optional
+        If `x` is not None, try to round each element of `x` to an integer
+        (dtype `np.intp`) and ensure every element is positive.
+
+    Returns
+    -------
+    pairs : nested iterables, shape (`ndim`, 2)
+        The broadcasted version of `x`.
+
+    Raises
+    ------
+    ValueError
+        If `as_index` is True and `x` contains negative elements.
+        Or if `x` is not broadcastable to the shape (`ndim`, 2).
+    """
+    if x is None:
+        # Pass through None as a special case, otherwise np.round(x) fails
+        # with an AttributeError
+        return ((None, None),) * ndim
+
+    x = np.array(x)
+    if as_index:
+        x = np.round(x).astype(np.intp, copy=False)
+
+    if x.ndim < 3:
+        # Optimization: Possibly use faster paths for cases where `x` has
+        # only 1 or 2 elements. `np.broadcast_to` could handle these as well
+        # but is currently slower
+
+        if x.size == 1:
+            # x was supplied as a single value
+            x = x.ravel()  # Ensure x[0] works for x.ndim == 0, 1, 2
+            if as_index and x < 0:
+                raise ValueError("index can't contain negative values")
+            return ((x[0], x[0]),) * ndim
+
+        if x.size == 2 and x.shape != (2, 1):
+            # x was supplied with a single value for each side
+            # but except case when each dimension has a single value
+            # which should be broadcasted to a pair,
+            # e.g. [[1], [2]] -> [[1, 1], [2, 2]] not [[1, 2], [1, 2]]
+            x = x.ravel()  # Ensure x[0], x[1] works
+            if as_index and (x[0] < 0 or x[1] < 0):
+                raise ValueError("index can't contain negative values")
+            return ((x[0], x[1]),) * ndim
+
+    if as_index and x.min() < 0:
+        raise ValueError("index can't contain negative values")
+
+    # Converting the array with `tolist` seems to improve performance
+    # when iterating and indexing the result (see usage in `pad`)
+    return np.broadcast_to(x, (ndim, 2)).tolist()
+
+
+def _pad_dispatcher(array, pad_width, mode=None, **kwargs):
+    return (array,)
+
+
+###############################################################################
+# Public functions
+
+
+@array_function_dispatch(_pad_dispatcher, module='numpy')
+def pad(array, pad_width, mode='constant', **kwargs):
+    """
+    Pad an array.
+
+    Parameters
+    ----------
+    array : array_like of rank N
+        The array to pad.
+    pad_width : {sequence, array_like, int}
+        Number of values padded to the edges of each axis.
+        ``((before_1, after_1), ... (before_N, after_N))`` unique pad widths
+        for each axis.
+        ``(before, after)`` or ``((before, after),)`` yields same before
+        and after pad for each axis.
+        ``(pad,)`` or ``int`` is a shortcut for before = after = pad width
+        for all axes.
+    mode : str or function, optional
+        One of the following string values or a user supplied function.
+
+        'constant' (default)
+            Pads with a constant value.
+        'edge'
+            Pads with the edge values of array.
+        'linear_ramp'
+            Pads with the linear ramp between end_value and the
+            array edge value.
+        'maximum'
+            Pads with the maximum value of all or part of the
+            vector along each axis.
+        'mean'
+            Pads with the mean value of all or part of the
+            vector along each axis.
+        'median'
+            Pads with the median value of all or part of the
+            vector along each axis.
+        'minimum'
+            Pads with the minimum value of all or part of the
+            vector along each axis.
+        'reflect'
+            Pads with the reflection of the vector mirrored on
+            the first and last values of the vector along each
+            axis.
+        'symmetric'
+            Pads with the reflection of the vector mirrored
+            along the edge of the array.
+        'wrap'
+            Pads with the wrap of the vector along the axis.
+            The first values are used to pad the end and the
+            end values are used to pad the beginning.
+        'empty'
+            Pads with undefined values.
+
+            .. versionadded:: 1.17
+
+        <function>
+            Padding function, see Notes.
+    stat_length : sequence or int, optional
+        Used in 'maximum', 'mean', 'median', and 'minimum'.  Number of
+        values at edge of each axis used to calculate the statistic value.
+
+        ``((before_1, after_1), ... (before_N, after_N))`` unique statistic
+        lengths for each axis.
+
+        ``(before, after)`` or ``((before, after),)`` yields same before
+        and after statistic lengths for each axis.
+
+        ``(stat_length,)`` or ``int`` is a shortcut for
+        ``before = after = statistic`` length for all axes.
+
+        Default is ``None``, to use the entire axis.
+    constant_values : sequence or scalar, optional
+        Used in 'constant'.  The values to set the padded values for each
+        axis.
+
+        ``((before_1, after_1), ... (before_N, after_N))`` unique pad constants
+        for each axis.
+
+        ``(before, after)`` or ``((before, after),)`` yields same before
+        and after constants for each axis.
+
+        ``(constant,)`` or ``constant`` is a shortcut for
+        ``before = after = constant`` for all axes.
+
+        Default is 0.
+    end_values : sequence or scalar, optional
+        Used in 'linear_ramp'.  The values used for the ending value of the
+        linear_ramp and that will form the edge of the padded array.
+
+        ``((before_1, after_1), ... (before_N, after_N))`` unique end values
+        for each axis.
+
+        ``(before, after)`` or ``((before, after),)`` yields same before
+        and after end values for each axis.
+
+        ``(constant,)`` or ``constant`` is a shortcut for
+        ``before = after = constant`` for all axes.
+
+        Default is 0.
+    reflect_type : {'even', 'odd'}, optional
+        Used in 'reflect', and 'symmetric'.  The 'even' style is the
+        default with an unaltered reflection around the edge value.  For
+        the 'odd' style, the extended part of the array is created by
+        subtracting the reflected values from two times the edge value.
+
+    Returns
+    -------
+    pad : ndarray
+        Padded array of rank equal to `array` with shape increased
+        according to `pad_width`.
+
+    Notes
+    -----
+    .. versionadded:: 1.7.0
+
+    For an array with rank greater than 1, some of the padding of later
+    axes is calculated from padding of previous axes.  This is easiest to
+    think about with a rank 2 array where the corners of the padded array
+    are calculated by using padded values from the first axis.
+
+    The padding function, if used, should modify a rank 1 array in-place. It
+    has the following signature::
+
+        padding_func(vector, iaxis_pad_width, iaxis, kwargs)
+
+    where
+
+        vector : ndarray
+            A rank 1 array already padded with zeros.  Padded values are
+            vector[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:].
+        iaxis_pad_width : tuple
+            A 2-tuple of ints, iaxis_pad_width[0] represents the number of
+            values padded at the beginning of vector where
+            iaxis_pad_width[1] represents the number of values padded at
+            the end of vector.
+        iaxis : int
+            The axis currently being calculated.
+        kwargs : dict
+            Any keyword arguments the function requires.
+
+    Examples
+    --------
+    >>> a = [1, 2, 3, 4, 5]
+    >>> np.pad(a, (2, 3), 'constant', constant_values=(4, 6))
+    array([4, 4, 1, ..., 6, 6, 6])
+
+    >>> np.pad(a, (2, 3), 'edge')
+    array([1, 1, 1, ..., 5, 5, 5])
+
+    >>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
+    array([ 5,  3,  1,  2,  3,  4,  5,  2, -1, -4])
+
+    >>> np.pad(a, (2,), 'maximum')
+    array([5, 5, 1, 2, 3, 4, 5, 5, 5])
+
+    >>> np.pad(a, (2,), 'mean')
+    array([3, 3, 1, 2, 3, 4, 5, 3, 3])
+
+    >>> np.pad(a, (2,), 'median')
+    array([3, 3, 1, 2, 3, 4, 5, 3, 3])
+
+    >>> a = [[1, 2], [3, 4]]
+    >>> np.pad(a, ((3, 2), (2, 3)), 'minimum')
+    array([[1, 1, 1, 2, 1, 1, 1],
+           [1, 1, 1, 2, 1, 1, 1],
+           [1, 1, 1, 2, 1, 1, 1],
+           [1, 1, 1, 2, 1, 1, 1],
+           [3, 3, 3, 4, 3, 3, 3],
+           [1, 1, 1, 2, 1, 1, 1],
+           [1, 1, 1, 2, 1, 1, 1]])
+
+    >>> a = [1, 2, 3, 4, 5]
+    >>> np.pad(a, (2, 3), 'reflect')
+    array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
+
+    >>> np.pad(a, (2, 3), 'reflect', reflect_type='odd')
+    array([-1,  0,  1,  2,  3,  4,  5,  6,  7,  8])
+
+    >>> np.pad(a, (2, 3), 'symmetric')
+    array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
+
+    >>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd')
+    array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])
+
+    >>> np.pad(a, (2, 3), 'wrap')
+    array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])
+
+    >>> def pad_with(vector, pad_width, iaxis, kwargs):
+    ...     pad_value = kwargs.get('padder', 10)
+    ...     vector[:pad_width[0]] = pad_value
+    ...     vector[-pad_width[1]:] = pad_value
+    >>> a = np.arange(6)
+    >>> a = a.reshape((2, 3))
+    >>> np.pad(a, 2, pad_with)
+    array([[10, 10, 10, 10, 10, 10, 10],
+           [10, 10, 10, 10, 10, 10, 10],
+           [10, 10,  0,  1,  2, 10, 10],
+           [10, 10,  3,  4,  5, 10, 10],
+           [10, 10, 10, 10, 10, 10, 10],
+           [10, 10, 10, 10, 10, 10, 10]])
+    >>> np.pad(a, 2, pad_with, padder=100)
+    array([[100, 100, 100, 100, 100, 100, 100],
+           [100, 100, 100, 100, 100, 100, 100],
+           [100, 100,   0,   1,   2, 100, 100],
+           [100, 100,   3,   4,   5, 100, 100],
+           [100, 100, 100, 100, 100, 100, 100],
+           [100, 100, 100, 100, 100, 100, 100]])
+    """
+    array = np.asarray(array)
+    pad_width = np.asarray(pad_width)
+
+    if not pad_width.dtype.kind == 'i':
+        raise TypeError('`pad_width` must be of integral type.')
+
+    # Broadcast to shape (array.ndim, 2)
+    pad_width = _as_pairs(pad_width, array.ndim, as_index=True)
+
+    if callable(mode):
+        # Old behavior: Use user-supplied function with np.apply_along_axis
+        function = mode
+        # Create a new zero padded array
+        padded, _ = _pad_simple(array, pad_width, fill_value=0)
+        # And apply along each axis
+
+        for axis in range(padded.ndim):
+            # Iterate using ndindex as in apply_along_axis, but assuming that
+            # function operates inplace on the padded array.
+
+            # view with the iteration axis at the end
+            view = np.moveaxis(padded, axis, -1)
+
+            # compute indices for the iteration axes, and append a trailing
+            # ellipsis to prevent 0d arrays decaying to scalars (gh-8642)
+            inds = ndindex(view.shape[:-1])
+            inds = (ind + (Ellipsis,) for ind in inds)
+            for ind in inds:
+                function(view[ind], pad_width[axis], axis, kwargs)
+
+        return padded
+
+    # Make sure that no unsupported keywords were passed for the current mode
+    allowed_kwargs = {
+        'empty': [], 'edge': [], 'wrap': [],
+        'constant': ['constant_values'],
+        'linear_ramp': ['end_values'],
+        'maximum': ['stat_length'],
+        'mean': ['stat_length'],
+        'median': ['stat_length'],
+        'minimum': ['stat_length'],
+        'reflect': ['reflect_type'],
+        'symmetric': ['reflect_type'],
+    }
+    try:
+        unsupported_kwargs = set(kwargs) - set(allowed_kwargs[mode])
+    except KeyError:
+        raise ValueError("mode '{}' is not supported".format(mode)) from None
+    if unsupported_kwargs:
+        raise ValueError("unsupported keyword arguments for mode '{}': {}"
+                         .format(mode, unsupported_kwargs))
+
+    stat_functions = {"maximum": np.amax, "minimum": np.amin,
+                      "mean": np.mean, "median": np.median}
+
+    # Create array with final shape and original values
+    # (padded area is undefined)
+    padded, original_area_slice = _pad_simple(array, pad_width)
+    # And prepare iteration over all dimensions
+    # (zipping may be more readable than using enumerate)
+    axes = range(padded.ndim)
+
+    if mode == "constant":
+        values = kwargs.get("constant_values", 0)
+        values = _as_pairs(values, padded.ndim)
+        for axis, width_pair, value_pair in zip(axes, pad_width, values):
+            roi = _view_roi(padded, original_area_slice, axis)
+            _set_pad_area(roi, axis, width_pair, value_pair)
+
+    elif mode == "empty":
+        pass  # Do nothing as _pad_simple already returned the correct result
+
+    elif array.size == 0:
+        # Only modes "constant" and "empty" can extend empty axes, all other
+        # modes depend on `array` not being empty
+        # -> ensure every empty axis is only "padded with 0"
+        for axis, width_pair in zip(axes, pad_width):
+            if array.shape[axis] == 0 and any(width_pair):
+                raise ValueError(
+                    "can't extend empty axis {} using modes other than "
+                    "'constant' or 'empty'".format(axis)
+                )
+        # passed, don't need to do anything more as _pad_simple already
+        # returned the correct result
+
+    elif mode == "edge":
+        for axis, width_pair in zip(axes, pad_width):
+            roi = _view_roi(padded, original_area_slice, axis)
+            edge_pair = _get_edges(roi, axis, width_pair)
+            _set_pad_area(roi, axis, width_pair, edge_pair)
+
+    elif mode == "linear_ramp":
+        end_values = kwargs.get("end_values", 0)
+        end_values = _as_pairs(end_values, padded.ndim)
+        for axis, width_pair, value_pair in zip(axes, pad_width, end_values):
+            roi = _view_roi(padded, original_area_slice, axis)
+            ramp_pair = _get_linear_ramps(roi, axis, width_pair, value_pair)
+            _set_pad_area(roi, axis, width_pair, ramp_pair)
+
+    elif mode in stat_functions:
+        func = stat_functions[mode]
+        length = kwargs.get("stat_length", None)
+        length = _as_pairs(length, padded.ndim, as_index=True)
+        for axis, width_pair, length_pair in zip(axes, pad_width, length):
+            roi = _view_roi(padded, original_area_slice, axis)
+            stat_pair = _get_stats(roi, axis, width_pair, length_pair, func)
+            _set_pad_area(roi, axis, width_pair, stat_pair)
+
+    elif mode in {"reflect", "symmetric"}:
+        method = kwargs.get("reflect_type", "even")
+        include_edge = True if mode == "symmetric" else False
+        for axis, (left_index, right_index) in zip(axes, pad_width):
+            if array.shape[axis] == 1 and (left_index > 0 or right_index > 0):
+                # Extending singleton dimension for 'reflect' is legacy
+                # behavior; it really should raise an error.
+                edge_pair = _get_edges(padded, axis, (left_index, right_index))
+                _set_pad_area(
+                    padded, axis, (left_index, right_index), edge_pair)
+                continue
+
+            roi = _view_roi(padded, original_area_slice, axis)
+            while left_index > 0 or right_index > 0:
+                # Iteratively pad until dimension is filled with reflected
+                # values. This is necessary if the pad area is larger than
+                # the length of the original values in the current dimension.
+                left_index, right_index = _set_reflect_both(
+                    roi, axis, (left_index, right_index),
+                    method, include_edge
+                )
+
+    elif mode == "wrap":
+        for axis, (left_index, right_index) in zip(axes, pad_width):
+            roi = _view_roi(padded, original_area_slice, axis)
+            original_period = padded.shape[axis] - right_index - left_index
+            while left_index > 0 or right_index > 0:
+                # Iteratively pad until dimension is filled with wrapped
+                # values. This is necessary if the pad area is larger than
+                # the length of the original values in the current dimension.
+                left_index, right_index = _set_wrap_both(
+                    roi, axis, (left_index, right_index), original_period)
+
+    return padded

.venv/lib/python3.11/site-packages/numpy/lib/arraysetops.pyi

@@ -0,0 +1,362 @@
+from typing import (
+    Literal as L,
+    Any,
+    TypeVar,
+    overload,
+    SupportsIndex,
+)
+
+from numpy import (
+    generic,
+    number,
+    bool_,
+    ushort,
+    ubyte,
+    uintc,
+    uint,
+    ulonglong,
+    short,
+    int8,
+    byte,
+    intc,
+    int_,
+    intp,
+    longlong,
+    half,
+    single,
+    double,
+    longdouble,
+    csingle,
+    cdouble,
+    clongdouble,
+    timedelta64,
+    datetime64,
+    object_,
+    str_,
+    bytes_,
+    void,
+)
+
+from numpy._typing import (
+    ArrayLike,
+    NDArray,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeDT64_co,
+    _ArrayLikeTD64_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeNumber_co,
+)
+
+_SCT = TypeVar("_SCT", bound=generic)
+_NumberType = TypeVar("_NumberType", bound=number[Any])
+
+# Explicitly set all allowed values to prevent accidental castings to
+# abstract dtypes (their common super-type).
+#
+# Only relevant if two or more arguments are parametrized, (e.g. `setdiff1d`)
+# which could result in, for example, `int64` and `float64`producing a
+# `number[_64Bit]` array
+_SCTNoCast = TypeVar(
+    "_SCTNoCast",
+    bool_,
+    ushort,
+    ubyte,
+    uintc,
+    uint,
+    ulonglong,
+    short,
+    byte,
+    intc,
+    int_,
+    longlong,
+    half,
+    single,
+    double,
+    longdouble,
+    csingle,
+    cdouble,
+    clongdouble,
+    timedelta64,
+    datetime64,
+    object_,
+    str_,
+    bytes_,
+    void,
+)
+
+__all__: list[str]
+
+@overload
+def ediff1d(
+    ary: _ArrayLikeBool_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[int8]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLike[_NumberType],
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[_NumberType]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeNumber_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[Any]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeDT64_co | _ArrayLikeTD64_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeObject_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> NDArray[Any]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp], NDArray[intp]]: ...
+
+@overload
+def intersect1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+    return_indices: L[False] = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def intersect1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    return_indices: L[False] = ...,
+) -> NDArray[Any]: ...
+@overload
+def intersect1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+    return_indices: L[True] = ...,
+) -> tuple[NDArray[_SCTNoCast], NDArray[intp], NDArray[intp]]: ...
+@overload
+def intersect1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    return_indices: L[True] = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+
+@overload
+def setxor1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def setxor1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+) -> NDArray[Any]: ...
+
+def in1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    invert: bool = ...,
+) -> NDArray[bool_]: ...
+
+def isin(
+    element: ArrayLike,
+    test_elements: ArrayLike,
+    assume_unique: bool = ...,
+    invert: bool = ...,
+    *,
+    kind: None | str = ...,
+) -> NDArray[bool_]: ...
+
+@overload
+def union1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def union1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+) -> NDArray[Any]: ...
+
+@overload
+def setdiff1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def setdiff1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+) -> NDArray[Any]: ...

.venv/lib/python3.11/site-packages/numpy/lib/nanfunctions.py

@@ -0,0 +1,1887 @@
+"""
+Functions that ignore NaN.
+
+Functions
+---------
+
+- `nanmin` -- minimum non-NaN value
+- `nanmax` -- maximum non-NaN value
+- `nanargmin` -- index of minimum non-NaN value
+- `nanargmax` -- index of maximum non-NaN value
+- `nansum` -- sum of non-NaN values
+- `nanprod` -- product of non-NaN values
+- `nancumsum` -- cumulative sum of non-NaN values
+- `nancumprod` -- cumulative product of non-NaN values
+- `nanmean` -- mean of non-NaN values
+- `nanvar` -- variance of non-NaN values
+- `nanstd` -- standard deviation of non-NaN values
+- `nanmedian` -- median of non-NaN values
+- `nanquantile` -- qth quantile of non-NaN values
+- `nanpercentile` -- qth percentile of non-NaN values
+
+"""
+import functools
+import warnings
+import numpy as np
+from numpy.lib import function_base
+from numpy.core import overrides
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+__all__ = [
+    'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
+    'nanmedian', 'nanpercentile', 'nanvar', 'nanstd', 'nanprod',
+    'nancumsum', 'nancumprod', 'nanquantile'
+    ]
+
+
+def _nan_mask(a, out=None):
+    """
+    Parameters
+    ----------
+    a : array-like
+        Input array with at least 1 dimension.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  The default
+        is ``None``; if provided, it must have the same shape as the
+        expected output and will prevent the allocation of a new array.
+
+    Returns
+    -------
+    y : bool ndarray or True
+        A bool array where ``np.nan`` positions are marked with ``False``
+        and other positions are marked with ``True``. If the type of ``a``
+        is such that it can't possibly contain ``np.nan``, returns ``True``.
+    """
+    # we assume that a is an array for this private function
+
+    if a.dtype.kind not in 'fc':
+        return True
+
+    y = np.isnan(a, out=out)
+    y = np.invert(y, out=y)
+    return y
+
+def _replace_nan(a, val):
+    """
+    If `a` is of inexact type, make a copy of `a`, replace NaNs with
+    the `val` value, and return the copy together with a boolean mask
+    marking the locations where NaNs were present. If `a` is not of
+    inexact type, do nothing and return `a` together with a mask of None.
+
+    Note that scalars will end up as array scalars, which is important
+    for using the result as the value of the out argument in some
+    operations.
+
+    Parameters
+    ----------
+    a : array-like
+        Input array.
+    val : float
+        NaN values are set to val before doing the operation.
+
+    Returns
+    -------
+    y : ndarray
+        If `a` is of inexact type, return a copy of `a` with the NaNs
+        replaced by the fill value, otherwise return `a`.
+    mask: {bool, None}
+        If `a` is of inexact type, return a boolean mask marking locations of
+        NaNs, otherwise return None.
+
+    """
+    a = np.asanyarray(a)
+
+    if a.dtype == np.object_:
+        # object arrays do not support `isnan` (gh-9009), so make a guess
+        mask = np.not_equal(a, a, dtype=bool)
+    elif issubclass(a.dtype.type, np.inexact):
+        mask = np.isnan(a)
+    else:
+        mask = None
+
+    if mask is not None:
+        a = np.array(a, subok=True, copy=True)
+        np.copyto(a, val, where=mask)
+
+    return a, mask
+
+
+def _copyto(a, val, mask):
+    """
+    Replace values in `a` with NaN where `mask` is True.  This differs from
+    copyto in that it will deal with the case where `a` is a numpy scalar.
+
+    Parameters
+    ----------
+    a : ndarray or numpy scalar
+        Array or numpy scalar some of whose values are to be replaced
+        by val.
+    val : numpy scalar
+        Value used a replacement.
+    mask : ndarray, scalar
+        Boolean array. Where True the corresponding element of `a` is
+        replaced by `val`. Broadcasts.
+
+    Returns
+    -------
+    res : ndarray, scalar
+        Array with elements replaced or scalar `val`.
+
+    """
+    if isinstance(a, np.ndarray):
+        np.copyto(a, val, where=mask, casting='unsafe')
+    else:
+        a = a.dtype.type(val)
+    return a
+
+
+def _remove_nan_1d(arr1d, overwrite_input=False):
+    """
+    Equivalent to arr1d[~arr1d.isnan()], but in a different order
+
+    Presumably faster as it incurs fewer copies
+
+    Parameters
+    ----------
+    arr1d : ndarray
+        Array to remove nans from
+    overwrite_input : bool
+        True if `arr1d` can be modified in place
+
+    Returns
+    -------
+    res : ndarray
+        Array with nan elements removed
+    overwrite_input : bool
+        True if `res` can be modified in place, given the constraint on the
+        input
+    """
+    if arr1d.dtype == object:
+        # object arrays do not support `isnan` (gh-9009), so make a guess
+        c = np.not_equal(arr1d, arr1d, dtype=bool)
+    else:
+        c = np.isnan(arr1d)
+
+    s = np.nonzero(c)[0]
+    if s.size == arr1d.size:
+        warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                      stacklevel=6)
+        return arr1d[:0], True
+    elif s.size == 0:
+        return arr1d, overwrite_input
+    else:
+        if not overwrite_input:
+            arr1d = arr1d.copy()
+        # select non-nans at end of array
+        enonan = arr1d[-s.size:][~c[-s.size:]]
+        # fill nans in beginning of array with non-nans of end
+        arr1d[s[:enonan.size]] = enonan
+
+        return arr1d[:-s.size], True
+
+
+def _divide_by_count(a, b, out=None):
+    """
+    Compute a/b ignoring invalid results. If `a` is an array the division
+    is done in place. If `a` is a scalar, then its type is preserved in the
+    output. If out is None, then a is used instead so that the division
+    is in place. Note that this is only called with `a` an inexact type.
+
+    Parameters
+    ----------
+    a : {ndarray, numpy scalar}
+        Numerator. Expected to be of inexact type but not checked.
+    b : {ndarray, numpy scalar}
+        Denominator.
+    out : ndarray, optional
+        Alternate 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.
+
+    Returns
+    -------
+    ret : {ndarray, numpy scalar}
+        The return value is a/b. If `a` was an ndarray the division is done
+        in place. If `a` is a numpy scalar, the division preserves its type.
+
+    """
+    with np.errstate(invalid='ignore', divide='ignore'):
+        if isinstance(a, np.ndarray):
+            if out is None:
+                return np.divide(a, b, out=a, casting='unsafe')
+            else:
+                return np.divide(a, b, out=out, casting='unsafe')
+        else:
+            if out is None:
+                # Precaution against reduced object arrays
+                try:
+                    return a.dtype.type(a / b)
+                except AttributeError:
+                    return a / b
+            else:
+                # This is questionable, but currently a numpy scalar can
+                # be output to a zero dimensional array.
+                return np.divide(a, b, out=out, casting='unsafe')
+
+
+def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmin_dispatcher)
+def nanmin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+           where=np._NoValue):
+    """
+    Return 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.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose minimum is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the minimum is computed. The default is to compute
+        the minimum of the flattened array.
+    out : ndarray, optional
+        Alternate 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
+        :ref:`ufuncs-output-type` for more details.
+
+        .. versionadded:: 1.8.0
+    keepdims : bool, optional
+        If 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`.
+
+        If the value is anything but the default, then
+        `keepdims` will be passed through to the `min` method
+        of sub-classes of `ndarray`.  If the sub-classes methods
+        does not implement `keepdims` any exceptions will be raised.
+
+        .. versionadded:: 1.8.0
+    initial : scalar, optional
+        The maximum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    nanmin : ndarray
+        An 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.
+
+    See Also
+    --------
+    nanmax :
+        The maximum value of an array along a given axis, ignoring any NaNs.
+    amin :
+        The minimum value of an array along a given axis, propagating any NaNs.
+    fmin :
+        Element-wise minimum of two arrays, ignoring any NaNs.
+    minimum :
+        Element-wise minimum of two arrays, propagating any NaNs.
+    isnan :
+        Shows which elements are Not a Number (NaN).
+    isfinite:
+        Shows which elements are neither NaN nor infinity.
+
+    amax, fmax, maximum
+
+    Notes
+    -----
+    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.
+
+    If the input has a integer type the function is equivalent to np.min.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, np.nan]])
+    >>> np.nanmin(a)
+    1.0
+    >>> np.nanmin(a, axis=0)
+    array([1.,  2.])
+    >>> np.nanmin(a, axis=1)
+    array([1.,  3.])
+
+    When positive infinity and negative infinity are present:
+
+    >>> np.nanmin([1, 2, np.nan, np.inf])
+    1.0
+    >>> np.nanmin([1, 2, np.nan, np.NINF])
+    -inf
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if initial is not np._NoValue:
+        kwargs['initial'] = initial
+    if where is not np._NoValue:
+        kwargs['where'] = where
+
+    if type(a) is np.ndarray and a.dtype != np.object_:
+        # Fast, but not safe for subclasses of ndarray, or object arrays,
+        # which do not implement isnan (gh-9009), or fmin correctly (gh-8975)
+        res = np.fmin.reduce(a, axis=axis, out=out, **kwargs)
+        if np.isnan(res).any():
+            warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                          stacklevel=2)
+    else:
+        # Slow, but safe for subclasses of ndarray
+        a, mask = _replace_nan(a, +np.inf)
+        res = np.amin(a, axis=axis, out=out, **kwargs)
+        if mask is None:
+            return res
+
+        # Check for all-NaN axis
+        kwargs.pop("initial", None)
+        mask = np.all(mask, axis=axis, **kwargs)
+        if np.any(mask):
+            res = _copyto(res, np.nan, mask)
+            warnings.warn("All-NaN axis encountered", RuntimeWarning,
+                          stacklevel=2)
+    return res
+
+
+def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmax_dispatcher)
+def nanmax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+           where=np._NoValue):
+    """
+    Return 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.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose maximum is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the maximum is computed. The default is to compute
+        the maximum of the flattened array.
+    out : ndarray, optional
+        Alternate 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
+        :ref:`ufuncs-output-type` for more details.
+
+        .. versionadded:: 1.8.0
+    keepdims : bool, optional
+        If 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`.
+
+        If the value is anything but the default, then
+        `keepdims` will be passed through to the `max` method
+        of sub-classes of `ndarray`.  If the sub-classes methods
+        does not implement `keepdims` any exceptions will be raised.
+
+        .. versionadded:: 1.8.0
+    initial : scalar, optional
+        The minimum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    nanmax : ndarray
+        An 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.
+
+    See Also
+    --------
+    nanmin :
+        The minimum value of an array along a given axis, ignoring any NaNs.
+    amax :
+        The maximum value of an array along a given axis, propagating any NaNs.
+    fmax :
+        Element-wise maximum of two arrays, ignoring any NaNs.
+    maximum :
+        Element-wise maximum of two arrays, propagating any NaNs.
+    isnan :
+        Shows which elements are Not a Number (NaN).
+    isfinite:
+        Shows which elements are neither NaN nor infinity.
+
+    amin, fmin, minimum
+
+    Notes
+    -----
+    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.
+
+    If the input has a integer type the function is equivalent to np.max.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2], [3, np.nan]])
+    >>> np.nanmax(a)
+    3.0
+    >>> np.nanmax(a, axis=0)
+    array([3.,  2.])
+    >>> np.nanmax(a, axis=1)
+    array([2.,  3.])
+
+    When positive infinity and negative infinity are present:
+
+    >>> np.nanmax([1, 2, np.nan, np.NINF])
+    2.0
+    >>> np.nanmax([1, 2, np.nan, np.inf])
+    inf
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if initial is not np._NoValue:
+        kwargs['initial'] = initial
+    if where is not np._NoValue:
+        kwargs['where'] = where
+
+    if type(a) is np.ndarray and a.dtype != np.object_:
+        # Fast, but not safe for subclasses of ndarray, or object arrays,
+        # which do not implement isnan (gh-9009), or fmax correctly (gh-8975)
+        res = np.fmax.reduce(a, axis=axis, out=out, **kwargs)
+        if np.isnan(res).any():
+            warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                          stacklevel=2)
+    else:
+        # Slow, but safe for subclasses of ndarray
+        a, mask = _replace_nan(a, -np.inf)
+        res = np.amax(a, axis=axis, out=out, **kwargs)
+        if mask is None:
+            return res
+
+        # Check for all-NaN axis
+        kwargs.pop("initial", None)
+        mask = np.all(mask, axis=axis, **kwargs)
+        if np.any(mask):
+            res = _copyto(res, np.nan, mask)
+            warnings.warn("All-NaN axis encountered", RuntimeWarning,
+                          stacklevel=2)
+    return res
+
+
+def _nanargmin_dispatcher(a, axis=None, out=None, *, keepdims=None):
+    return (a,)
+
+
+@array_function_dispatch(_nanargmin_dispatcher)
+def nanargmin(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Return 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.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int, optional
+        Axis along which to operate.  By default flattened input is used.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+
+        .. versionadded:: 1.22.0
+    keepdims : bool, optional
+        If 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.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray
+        An array of indices or a single index value.
+
+    See Also
+    --------
+    argmin, nanargmax
+
+    Examples
+    --------
+    >>> a = np.array([[np.nan, 4], [2, 3]])
+    >>> np.argmin(a)
+    0
+    >>> np.nanargmin(a)
+    2
+    >>> np.nanargmin(a, axis=0)
+    array([1, 1])
+    >>> np.nanargmin(a, axis=1)
+    array([1, 0])
+
+    """
+    a, mask = _replace_nan(a, np.inf)
+    if mask is not None:
+        mask = np.all(mask, axis=axis)
+        if np.any(mask):
+            raise ValueError("All-NaN slice encountered")
+    res = np.argmin(a, axis=axis, out=out, keepdims=keepdims)
+    return res
+
+
+def _nanargmax_dispatcher(a, axis=None, out=None, *, keepdims=None):
+    return (a,)
+
+
+@array_function_dispatch(_nanargmax_dispatcher)
+def nanargmax(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Return 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.
+
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int, optional
+        Axis along which to operate.  By default flattened input is used.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+
+        .. versionadded:: 1.22.0
+    keepdims : bool, optional
+        If 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.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray
+        An array of indices or a single index value.
+
+    See Also
+    --------
+    argmax, nanargmin
+
+    Examples
+    --------
+    >>> a = np.array([[np.nan, 4], [2, 3]])
+    >>> np.argmax(a)
+    0
+    >>> np.nanargmax(a)
+    1
+    >>> np.nanargmax(a, axis=0)
+    array([1, 0])
+    >>> np.nanargmax(a, axis=1)
+    array([1, 1])
+
+    """
+    a, mask = _replace_nan(a, -np.inf)
+    if mask is not None:
+        mask = np.all(mask, axis=axis)
+        if np.any(mask):
+            raise ValueError("All-NaN slice encountered")
+    res = np.argmax(a, axis=axis, out=out, keepdims=keepdims)
+    return res
+
+
+def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nansum_dispatcher)
+def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+           initial=np._NoValue, where=np._NoValue):
+    """
+    Return the sum of array elements over a given axis treating Not a
+    Numbers (NaNs) as zero.
+
+    In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or
+    empty. In later versions zero is returned.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose sum is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the sum is computed. The default is to compute the
+        sum of the flattened array.
+    dtype : data-type, optional
+        The 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.
+
+        .. versionadded:: 1.8.0
+    out : ndarray, optional
+        Alternate 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
+        :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
+        can yield unexpected results.
+
+        .. versionadded:: 1.8.0
+    keepdims : bool, optional
+        If 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`.
+
+
+        If the value is anything but the default, then
+        `keepdims` will be passed through to the `mean` or `sum` methods
+        of sub-classes of `ndarray`.  If the sub-classes methods
+        does not implement `keepdims` any exceptions will be raised.
+
+        .. versionadded:: 1.8.0
+    initial : scalar, optional
+        Starting value for the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    nansum : ndarray.
+        A 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.
+
+    See Also
+    --------
+    numpy.sum : Sum across array propagating NaNs.
+    isnan : Show which elements are NaN.
+    isfinite : Show which elements are not NaN or +/-inf.
+
+    Notes
+    -----
+    If both positive and negative infinity are present, the sum will be Not
+    A Number (NaN).
+
+    Examples
+    --------
+    >>> np.nansum(1)
+    1
+    >>> np.nansum([1])
+    1
+    >>> np.nansum([1, np.nan])
+    1.0
+    >>> a = np.array([[1, 1], [1, np.nan]])
+    >>> np.nansum(a)
+    3.0
+    >>> np.nansum(a, axis=0)
+    array([2.,  1.])
+    >>> np.nansum([1, np.nan, np.inf])
+    inf
+    >>> np.nansum([1, np.nan, np.NINF])
+    -inf
+    >>> from numpy.testing import suppress_warnings
+    >>> with suppress_warnings() as sup:
+    ...     sup.filter(RuntimeWarning)
+    ...     np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
+    nan
+
+    """
+    a, mask = _replace_nan(a, 0)
+    return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                  initial=initial, where=where)
+
+
+def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                        initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanprod_dispatcher)
+def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+            initial=np._NoValue, where=np._NoValue):
+    """
+    Return the product of array elements over a given axis treating Not a
+    Numbers (NaNs) as ones.
+
+    One is returned for slices that are all-NaN or empty.
+
+    .. versionadded:: 1.10.0
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose product is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the product is computed. The default is to compute
+        the product of the flattened array.
+    dtype : data-type, optional
+        The 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.
+    out : ndarray, optional
+        Alternate 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
+        :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
+        can yield unexpected results.
+    keepdims : bool, optional
+        If 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`.
+    initial : scalar, optional
+        The starting value for this product. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to include in the product. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    nanprod : ndarray
+        A new array holding the result is returned unless `out` is
+        specified, in which case it is returned.
+
+    See Also
+    --------
+    numpy.prod : Product across array propagating NaNs.
+    isnan : Show which elements are NaN.
+
+    Examples
+    --------
+    >>> np.nanprod(1)
+    1
+    >>> np.nanprod([1])
+    1
+    >>> np.nanprod([1, np.nan])
+    1.0
+    >>> a = np.array([[1, 2], [3, np.nan]])
+    >>> np.nanprod(a)
+    6.0
+    >>> np.nanprod(a, axis=0)
+    array([3., 2.])
+
+    """
+    a, mask = _replace_nan(a, 1)
+    return np.prod(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                   initial=initial, where=where)
+
+
+def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nancumsum_dispatcher)
+def nancumsum(a, axis=None, dtype=None, out=None):
+    """
+    Return 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.
+
+    Zeros are returned for slices that are all-NaN or empty.
+
+    .. versionadded:: 1.12.0
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative sum is computed. The default
+        (None) is to compute the cumsum over the flattened array.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed.  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.
+    out : ndarray, optional
+        Alternative 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 :ref:`ufuncs-output-type` for
+        more details.
+
+    Returns
+    -------
+    nancumsum : ndarray.
+        A 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.
+
+    See Also
+    --------
+    numpy.cumsum : Cumulative sum across array propagating NaNs.
+    isnan : Show which elements are NaN.
+
+    Examples
+    --------
+    >>> np.nancumsum(1)
+    array([1])
+    >>> np.nancumsum([1])
+    array([1])
+    >>> np.nancumsum([1, np.nan])
+    array([1.,  1.])
+    >>> a = np.array([[1, 2], [3, np.nan]])
+    >>> np.nancumsum(a)
+    array([1.,  3.,  6.,  6.])
+    >>> np.nancumsum(a, axis=0)
+    array([[1.,  2.],
+           [4.,  2.]])
+    >>> np.nancumsum(a, axis=1)
+    array([[1.,  3.],
+           [3.,  3.]])
+
+    """
+    a, mask = _replace_nan(a, 0)
+    return np.cumsum(a, axis=axis, dtype=dtype, out=out)
+
+
+def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nancumprod_dispatcher)
+def nancumprod(a, axis=None, dtype=None, out=None):
+    """
+    Return 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.
+
+    Ones are returned for slices that are all-NaN or empty.
+
+    .. versionadded:: 1.12.0
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative product is computed.  By default
+        the input is flattened.
+    dtype : dtype, optional
+        Type 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.
+    out : ndarray, optional
+        Alternative 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.
+
+    Returns
+    -------
+    nancumprod : ndarray
+        A new array holding the result is returned unless `out` is
+        specified, in which case it is returned.
+
+    See Also
+    --------
+    numpy.cumprod : Cumulative product across array propagating NaNs.
+    isnan : Show which elements are NaN.
+
+    Examples
+    --------
+    >>> np.nancumprod(1)
+    array([1])
+    >>> np.nancumprod([1])
+    array([1])
+    >>> np.nancumprod([1, np.nan])
+    array([1.,  1.])
+    >>> a = np.array([[1, 2], [3, np.nan]])
+    >>> np.nancumprod(a)
+    array([1.,  2.,  6.,  6.])
+    >>> np.nancumprod(a, axis=0)
+    array([[1.,  2.],
+           [3.,  2.]])
+    >>> np.nancumprod(a, axis=1)
+    array([[1.,  2.],
+           [3.,  3.]])
+
+    """
+    a, mask = _replace_nan(a, 1)
+    return np.cumprod(a, axis=axis, dtype=dtype, out=out)
+
+
+def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                        *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmean_dispatcher)
+def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+            *, where=np._NoValue):
+    """
+    Compute the arithmetic mean along the specified axis, ignoring NaNs.
+
+    Returns the average of the array elements.  The average is taken over
+    the flattened array by default, otherwise over the specified axis.
+    `float64` intermediate and return values are used for integer inputs.
+
+    For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.
+
+    .. versionadded:: 1.8.0
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose mean is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the means are computed. The default is to compute
+        the mean of the flattened array.
+    dtype : data-type, optional
+        Type to use in computing the mean.  For integer inputs, the default
+        is `float64`; for inexact inputs, it is the same as the input
+        dtype.
+    out : ndarray, optional
+        Alternate 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
+        :ref:`ufuncs-output-type` for more details.
+    keepdims : bool, optional
+        If 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`.
+
+        If the value is anything but the default, then
+        `keepdims` will be passed through to the `mean` or `sum` methods
+        of sub-classes of `ndarray`.  If the sub-classes methods
+        does not implement `keepdims` any exceptions will be raised.
+    where : array_like of bool, optional
+        Elements to include in the mean. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    m : ndarray, see dtype parameter above
+        If `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.
+
+    See Also
+    --------
+    average : Weighted average
+    mean : Arithmetic mean taken while not ignoring NaNs
+    var, nanvar
+
+    Notes
+    -----
+    The arithmetic mean is the sum of the non-NaN elements along the axis
+    divided by the number of non-NaN elements.
+
+    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`.  Specifying a
+    higher-precision accumulator using the `dtype` keyword can alleviate
+    this issue.
+
+    Examples
+    --------
+    >>> a = np.array([[1, np.nan], [3, 4]])
+    >>> np.nanmean(a)
+    2.6666666666666665
+    >>> np.nanmean(a, axis=0)
+    array([2.,  4.])
+    >>> np.nanmean(a, axis=1)
+    array([1.,  3.5]) # may vary
+
+    """
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.mean(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                       where=where)
+
+    if dtype is not None:
+        dtype = np.dtype(dtype)
+    if dtype is not None and not issubclass(dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then dtype must be inexact")
+    if out is not None and not issubclass(out.dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then out must be inexact")
+
+    cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=keepdims,
+                 where=where)
+    tot = np.sum(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                 where=where)
+    avg = _divide_by_count(tot, cnt, out=out)
+
+    isbad = (cnt == 0)
+    if isbad.any():
+        warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=2)
+        # NaN is the only possible bad value, so no further
+        # action is needed to handle bad results.
+    return avg
+
+
+def _nanmedian1d(arr1d, overwrite_input=False):
+    """
+    Private function for rank 1 arrays. Compute the median ignoring NaNs.
+    See nanmedian for parameter usage
+    """
+    arr1d_parsed, overwrite_input = _remove_nan_1d(
+        arr1d, overwrite_input=overwrite_input,
+    )
+
+    if arr1d_parsed.size == 0:
+        # Ensure that a nan-esque scalar of the appropriate type (and unit)
+        # is returned for `timedelta64` and `complexfloating`
+        return arr1d[-1]
+
+    return np.median(arr1d_parsed, overwrite_input=overwrite_input)
+
+
+def _nanmedian(a, axis=None, out=None, overwrite_input=False):
+    """
+    Private function that doesn't support extended axis or keepdims.
+    These methods are extended to this function using _ureduce
+    See nanmedian for parameter usage
+
+    """
+    if axis is None or a.ndim == 1:
+        part = a.ravel()
+        if out is None:
+            return _nanmedian1d(part, overwrite_input)
+        else:
+            out[...] = _nanmedian1d(part, overwrite_input)
+            return out
+    else:
+        # for small medians use sort + indexing which is still faster than
+        # apply_along_axis
+        # benchmarked with shuffled (50, 50, x) containing a few NaN
+        if a.shape[axis] < 600:
+            return _nanmedian_small(a, axis, out, overwrite_input)
+        result = np.apply_along_axis(_nanmedian1d, axis, a, overwrite_input)
+        if out is not None:
+            out[...] = result
+        return result
+
+
+def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):
+    """
+    sort + indexing median, faster for small medians along multiple
+    dimensions due to the high overhead of apply_along_axis
+
+    see nanmedian for parameter usage
+    """
+    a = np.ma.masked_array(a, np.isnan(a))
+    m = np.ma.median(a, axis=axis, overwrite_input=overwrite_input)
+    for i in range(np.count_nonzero(m.mask.ravel())):
+        warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                      stacklevel=5)
+
+    fill_value = np.timedelta64("NaT") if m.dtype.kind == "m" else np.nan
+    if out is not None:
+        out[...] = m.filled(fill_value)
+        return out
+    return m.filled(fill_value)
+
+
+def _nanmedian_dispatcher(
+        a, axis=None, out=None, overwrite_input=None, keepdims=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmedian_dispatcher)
+def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):
+    """
+    Compute the median along the specified axis, while ignoring NaNs.
+
+    Returns the median of the array elements.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : {int, sequence of int, None}, optional
+        Axis 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.
+    out : ndarray, optional
+        Alternative 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.
+    overwrite_input : bool, optional
+       If 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. If `overwrite_input` is ``True`` and `a` is not already an
+       `ndarray`, an error will be raised.
+    keepdims : bool, optional
+        If 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`.
+
+        If this is anything but the default value it will be passed
+        through (in the special case of an empty array) to the
+        `mean` function of the underlying array.  If the array is
+        a sub-class and `mean` does not have the kwarg `keepdims` this
+        will raise a RuntimeError.
+
+    Returns
+    -------
+    median : ndarray
+        A 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.
+
+    See Also
+    --------
+    mean, median, percentile
+
+    Notes
+    -----
+    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.
+
+    Examples
+    --------
+    >>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
+    >>> a[0, 1] = np.nan
+    >>> a
+    array([[10., nan,  4.],
+           [ 3.,  2.,  1.]])
+    >>> np.median(a)
+    nan
+    >>> np.nanmedian(a)
+    3.0
+    >>> np.nanmedian(a, axis=0)
+    array([6.5, 2. , 2.5])
+    >>> np.median(a, axis=1)
+    array([nan,  2.])
+    >>> b = a.copy()
+    >>> np.nanmedian(b, axis=1, overwrite_input=True)
+    array([7.,  2.])
+    >>> assert not np.all(a==b)
+    >>> b = a.copy()
+    >>> np.nanmedian(b, axis=None, overwrite_input=True)
+    3.0
+    >>> assert not np.all(a==b)
+
+    """
+    a = np.asanyarray(a)
+    # apply_along_axis in _nanmedian doesn't handle empty arrays well,
+    # so deal them upfront
+    if a.size == 0:
+        return np.nanmean(a, axis, out=out, keepdims=keepdims)
+
+    return function_base._ureduce(a, func=_nanmedian, keepdims=keepdims,
+                                  axis=axis, out=out,
+                                  overwrite_input=overwrite_input)
+
+
+def _nanpercentile_dispatcher(
+        a, q, axis=None, out=None, overwrite_input=None,
+        method=None, keepdims=None, *, interpolation=None):
+    return (a, q, out)
+
+
+@array_function_dispatch(_nanpercentile_dispatcher)
+def nanpercentile(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+        *,
+        interpolation=None,
+):
+    """
+    Compute the qth percentile of the data along the specified axis,
+    while ignoring nan values.
+
+    Returns the qth percentile(s) of the array elements.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array, containing
+        nan values to be ignored.
+    q : array_like of float
+        Percentile or sequence of percentiles to compute, which must be
+        between 0 and 100 inclusive.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the percentiles are computed. The default
+        is to compute the percentile(s) along a flattened version of the
+        array.
+    out : ndarray, optional
+        Alternative 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.
+    overwrite_input : bool, optional
+        If 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.
+    method : str, optional
+        This 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]_ are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        The first three methods are discontinuous.  NumPy further defines the
+        following discontinuous variations of the default 'linear' (7.) option:
+
+        * 'lower'
+        * 'higher',
+        * 'midpoint'
+        * 'nearest'
+
+        .. versionchanged:: 1.22.0
+            This argument was previously called "interpolation" and only
+            offered the "linear" default and last four options.
+
+    keepdims : bool, optional
+        If 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`.
+
+        If this is anything but the default value it will be passed
+        through (in the special case of an empty array) to the
+        `mean` function of the underlying array.  If the array is
+        a sub-class and `mean` does not have the kwarg `keepdims` this
+        will raise a RuntimeError.
+
+    interpolation : str, optional
+        Deprecated name for the method keyword argument.
+
+        .. deprecated:: 1.22.0
+
+    Returns
+    -------
+    percentile : scalar or ndarray
+        If `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.
+
+    See Also
+    --------
+    nanmean
+    nanmedian : equivalent to ``nanpercentile(..., 50)``
+    percentile, median, mean
+    nanquantile : equivalent to nanpercentile, except q in range [0, 1].
+
+    Notes
+    -----
+    For more information please see `numpy.percentile`
+
+    Examples
+    --------
+    >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
+    >>> a[0][1] = np.nan
+    >>> a
+    array([[10.,  nan,   4.],
+          [ 3.,   2.,   1.]])
+    >>> np.percentile(a, 50)
+    nan
+    >>> np.nanpercentile(a, 50)
+    3.0
+    >>> np.nanpercentile(a, 50, axis=0)
+    array([6.5, 2. , 2.5])
+    >>> np.nanpercentile(a, 50, axis=1, keepdims=True)
+    array([[7.],
+           [2.]])
+    >>> m = np.nanpercentile(a, 50, axis=0)
+    >>> out = np.zeros_like(m)
+    >>> np.nanpercentile(a, 50, axis=0, out=out)
+    array([6.5, 2. , 2.5])
+    >>> m
+    array([6.5,  2. ,  2.5])
+
+    >>> b = a.copy()
+    >>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
+    array([7., 2.])
+    >>> assert not np.all(a==b)
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+
+    """
+    if interpolation is not None:
+        method = function_base._check_interpolation_as_method(
+            method, interpolation, "nanpercentile")
+
+    a = np.asanyarray(a)
+    if a.dtype.kind == "c":
+        raise TypeError("a must be an array of real numbers")
+
+    q = np.true_divide(q, 100.0)
+    # undo any decay that the ufunc performed (see gh-13105)
+    q = np.asanyarray(q)
+    if not function_base._quantile_is_valid(q):
+        raise ValueError("Percentiles must be in the range [0, 100]")
+    return _nanquantile_unchecked(
+        a, q, axis, out, overwrite_input, method, keepdims)
+
+
+def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
+                            method=None, keepdims=None, *, interpolation=None):
+    return (a, q, out)
+
+
+@array_function_dispatch(_nanquantile_dispatcher)
+def nanquantile(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+        *,
+        interpolation=None,
+):
+    """
+    Compute the qth quantile of the data along the specified axis,
+    while ignoring nan values.
+    Returns the qth quantile(s) of the array elements.
+
+    .. versionadded:: 1.15.0
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array, containing
+        nan values to be ignored
+    q : array_like of float
+        Probability or sequence of probabilities for the quantiles to compute.
+        Values must be between 0 and 1 inclusive.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the quantiles are computed. The
+        default is to compute the quantile(s) along a flattened
+        version of the array.
+    out : ndarray, optional
+        Alternative 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.
+    overwrite_input : bool, optional
+        If 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.
+    method : str, optional
+        This 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]_ are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        The first three methods are discontinuous.  NumPy further defines the
+        following discontinuous variations of the default 'linear' (7.) option:
+
+        * 'lower'
+        * 'higher',
+        * 'midpoint'
+        * 'nearest'
+
+        .. versionchanged:: 1.22.0
+            This argument was previously called "interpolation" and only
+            offered the "linear" default and last four options.
+
+    keepdims : bool, optional
+        If 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`.
+
+        If this is anything but the default value it will be passed
+        through (in the special case of an empty array) to the
+        `mean` function of the underlying array.  If the array is
+        a sub-class and `mean` does not have the kwarg `keepdims` this
+        will raise a RuntimeError.
+
+    interpolation : str, optional
+        Deprecated name for the method keyword argument.
+
+        .. deprecated:: 1.22.0
+
+    Returns
+    -------
+    quantile : scalar or ndarray
+        If `q` is a single probability and `axis=None`, then the result
+        is a scalar. If multiple probability levels 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.
+
+    See Also
+    --------
+    quantile
+    nanmean, nanmedian
+    nanmedian : equivalent to ``nanquantile(..., 0.5)``
+    nanpercentile : same as nanquantile, but with q in the range [0, 100].
+
+    Notes
+    -----
+    For more information please see `numpy.quantile`
+
+    Examples
+    --------
+    >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
+    >>> a[0][1] = np.nan
+    >>> a
+    array([[10.,  nan,   4.],
+          [ 3.,   2.,   1.]])
+    >>> np.quantile(a, 0.5)
+    nan
+    >>> np.nanquantile(a, 0.5)
+    3.0
+    >>> np.nanquantile(a, 0.5, axis=0)
+    array([6.5, 2. , 2.5])
+    >>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
+    array([[7.],
+           [2.]])
+    >>> m = np.nanquantile(a, 0.5, axis=0)
+    >>> out = np.zeros_like(m)
+    >>> np.nanquantile(a, 0.5, axis=0, out=out)
+    array([6.5, 2. , 2.5])
+    >>> m
+    array([6.5,  2. ,  2.5])
+    >>> b = a.copy()
+    >>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
+    array([7., 2.])
+    >>> assert not np.all(a==b)
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+
+    """
+
+    if interpolation is not None:
+        method = function_base._check_interpolation_as_method(
+            method, interpolation, "nanquantile")
+
+    a = np.asanyarray(a)
+    if a.dtype.kind == "c":
+        raise TypeError("a must be an array of real numbers")
+
+    q = np.asanyarray(q)
+    if not function_base._quantile_is_valid(q):
+        raise ValueError("Quantiles must be in the range [0, 1]")
+    return _nanquantile_unchecked(
+        a, q, axis, out, overwrite_input, method, keepdims)
+
+
+def _nanquantile_unchecked(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+):
+    """Assumes that q is in [0, 1], and is an ndarray"""
+    # apply_along_axis in _nanpercentile doesn't handle empty arrays well,
+    # so deal them upfront
+    if a.size == 0:
+        return np.nanmean(a, axis, out=out, keepdims=keepdims)
+    return function_base._ureduce(a,
+                                  func=_nanquantile_ureduce_func,
+                                  q=q,
+                                  keepdims=keepdims,
+                                  axis=axis,
+                                  out=out,
+                                  overwrite_input=overwrite_input,
+                                  method=method)
+
+
+def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False,
+                              method="linear"):
+    """
+    Private function that doesn't support extended axis or keepdims.
+    These methods are extended to this function using _ureduce
+    See nanpercentile for parameter usage
+    """
+    if axis is None or a.ndim == 1:
+        part = a.ravel()
+        result = _nanquantile_1d(part, q, overwrite_input, method)
+    else:
+        result = np.apply_along_axis(_nanquantile_1d, axis, a, q,
+                                     overwrite_input, method)
+        # apply_along_axis fills in collapsed axis with results.
+        # Move that axis to the beginning to match percentile's
+        # convention.
+        if q.ndim != 0:
+            result = np.moveaxis(result, axis, 0)
+
+    if out is not None:
+        out[...] = result
+    return result
+
+
+def _nanquantile_1d(arr1d, q, overwrite_input=False, method="linear"):
+    """
+    Private function for rank 1 arrays. Compute quantile ignoring NaNs.
+    See nanpercentile for parameter usage
+    """
+    arr1d, overwrite_input = _remove_nan_1d(arr1d,
+        overwrite_input=overwrite_input)
+    if arr1d.size == 0:
+        # convert to scalar
+        return np.full(q.shape, np.nan, dtype=arr1d.dtype)[()]
+
+    return function_base._quantile_unchecked(
+        arr1d, q, overwrite_input=overwrite_input, method=method)
+
+
+def _nanvar_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                       keepdims=None, *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanvar_dispatcher)
+def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
+           *, where=np._NoValue):
+    """
+    Compute the variance along the specified axis, while ignoring NaNs.
+
+    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.
+
+    For all-NaN slices or slices with zero degrees of freedom, NaN is
+    returned and a `RuntimeWarning` is raised.
+
+    .. versionadded:: 1.8.0
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose variance is desired.  If `a` is not an
+        array, a conversion is attempted.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the variance is computed.  The default is to compute
+        the variance of the flattened array.
+    dtype : data-type, optional
+        Type to use in computing the variance.  For arrays of integer type
+        the default is `float64`; for arrays of float types it is the same as
+        the array type.
+    out : ndarray, optional
+        Alternate 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.
+    ddof : int, optional
+        "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.
+    keepdims : bool, optional
+        If 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`.
+    where : array_like of bool, optional
+        Elements to include in the variance. See `~numpy.ufunc.reduce` for
+        details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    variance : ndarray, see dtype parameter above
+        If `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.
+
+    See Also
+    --------
+    std : Standard deviation
+    mean : Average
+    var : Variance while not ignoring NaNs
+    nanstd, nanmean
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    The variance is the average of the squared deviations from the mean,
+    i.e.,  ``var = mean(abs(x - x.mean())**2)``.
+
+    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.
+
+    Note that for complex numbers, the absolute value is taken before
+    squaring, so that the result is always real and nonnegative.
+
+    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` (see example
+    below).  Specifying a higher-accuracy accumulator using the ``dtype``
+    keyword can alleviate this issue.
+
+    For this function to work on sub-classes of ndarray, they must define
+    `sum` with the kwarg `keepdims`
+
+    Examples
+    --------
+    >>> a = np.array([[1, np.nan], [3, 4]])
+    >>> np.nanvar(a)
+    1.5555555555555554
+    >>> np.nanvar(a, axis=0)
+    array([1.,  0.])
+    >>> np.nanvar(a, axis=1)
+    array([0.,  0.25])  # may vary
+
+    """
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.var(arr, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                      keepdims=keepdims, where=where)
+
+    if dtype is not None:
+        dtype = np.dtype(dtype)
+    if dtype is not None and not issubclass(dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then dtype must be inexact")
+    if out is not None and not issubclass(out.dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then out must be inexact")
+
+    # Compute mean
+    if type(arr) is np.matrix:
+        _keepdims = np._NoValue
+    else:
+        _keepdims = True
+    # we need to special case matrix for reverse compatibility
+    # in order for this to work, these sums need to be called with
+    # keepdims=True, however matrix now raises an error in this case, but
+    # the reason that it drops the keepdims kwarg is to force keepdims=True
+    # so this used to work by serendipity.
+    cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=_keepdims,
+                 where=where)
+    avg = np.sum(arr, axis=axis, dtype=dtype, keepdims=_keepdims, where=where)
+    avg = _divide_by_count(avg, cnt)
+
+    # Compute squared deviation from mean.
+    np.subtract(arr, avg, out=arr, casting='unsafe', where=where)
+    arr = _copyto(arr, 0, mask)
+    if issubclass(arr.dtype.type, np.complexfloating):
+        sqr = np.multiply(arr, arr.conj(), out=arr, where=where).real
+    else:
+        sqr = np.multiply(arr, arr, out=arr, where=where)
+
+    # Compute variance.
+    var = np.sum(sqr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                 where=where)
+
+    # Precaution against reduced object arrays
+    try:
+        var_ndim = var.ndim
+    except AttributeError:
+        var_ndim = np.ndim(var)
+    if var_ndim < cnt.ndim:
+        # Subclasses of ndarray may ignore keepdims, so check here.
+        cnt = cnt.squeeze(axis)
+    dof = cnt - ddof
+    var = _divide_by_count(var, dof)
+
+    isbad = (dof <= 0)
+    if np.any(isbad):
+        warnings.warn("Degrees of freedom <= 0 for slice.", RuntimeWarning,
+                      stacklevel=2)
+        # NaN, inf, or negative numbers are all possible bad
+        # values, so explicitly replace them with NaN.
+        var = _copyto(var, np.nan, isbad)
+    return var
+
+
+def _nanstd_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                       keepdims=None, *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanstd_dispatcher)
+def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
+           *, where=np._NoValue):
+    """
+    Compute the standard deviation along the specified axis, while
+    ignoring NaNs.
+
+    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.
+
+    For all-NaN slices or slices with zero degrees of freedom, NaN is
+    returned and a `RuntimeWarning` is raised.
+
+    .. versionadded:: 1.8.0
+
+    Parameters
+    ----------
+    a : array_like
+        Calculate the standard deviation of the non-NaN values.
+    axis : {int, tuple of int, None}, optional
+        Axis or axes along which the standard deviation is computed. The default is
+        to compute the standard deviation of the flattened array.
+    dtype : dtype, optional
+        Type 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.
+    out : ndarray, optional
+        Alternative 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.
+    ddof : int, optional
+        Means 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.
+
+    keepdims : bool, optional
+        If 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`.
+
+        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.
+    where : array_like of bool, optional
+        Elements to include in the standard deviation.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    standard_deviation : ndarray, see dtype parameter above.
+        If `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.
+
+    See Also
+    --------
+    var, mean, std
+    nanvar, nanmean
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    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))``.
+
+    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.
+
+    Note that, for complex numbers, `std` takes the absolute value before
+    squaring, so that the result is always real and nonnegative.
+
+    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`
+    keyword can alleviate this issue.
+
+    Examples
+    --------
+    >>> a = np.array([[1, np.nan], [3, 4]])
+    >>> np.nanstd(a)
+    1.247219128924647
+    >>> np.nanstd(a, axis=0)
+    array([1., 0.])
+    >>> np.nanstd(a, axis=1)
+    array([0.,  0.5]) # may vary
+
+    """
+    var = nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                 keepdims=keepdims, where=where)
+    if isinstance(var, np.ndarray):
+        std = np.sqrt(var, out=var)
+    elif hasattr(var, 'dtype'):
+        std = var.dtype.type(np.sqrt(var))
+    else:
+        std = np.sqrt(var)
+    return std

.venv/lib/python3.11/site-packages/numpy/lib/nanfunctions.pyi

@@ -0,0 +1,38 @@
+from numpy.core.fromnumeric import (
+    amin,
+    amax,
+    argmin,
+    argmax,
+    sum,
+    prod,
+    cumsum,
+    cumprod,
+    mean,
+    var,
+    std
+)
+
+from numpy.lib.function_base import (
+    median,
+    percentile,
+    quantile,
+)
+
+__all__: list[str]
+
+# NOTE: In reaility these functions are not aliases but distinct functions
+# with identical signatures.
+nanmin = amin
+nanmax = amax
+nanargmin = argmin
+nanargmax = argmax
+nansum = sum
+nanprod = prod
+nancumsum = cumsum
+nancumprod = cumprod
+nanmean = mean
+nanvar = var
+nanstd = std
+nanmedian = median
+nanpercentile = percentile
+nanquantile = quantile

.venv/lib/python3.11/site-packages/numpy/lib/polynomial.py

@@ -0,0 +1,1453 @@
+"""
+Functions to operate on polynomials.
+
+"""
+__all__ = ['poly', 'roots', 'polyint', 'polyder', 'polyadd',
+           'polysub', 'polymul', 'polydiv', 'polyval', 'poly1d',
+           'polyfit', 'RankWarning']
+
+import functools
+import re
+import warnings
+
+from .._utils import set_module
+import numpy.core.numeric as NX
+
+from numpy.core import (isscalar, abs, finfo, atleast_1d, hstack, dot, array,
+                        ones)
+from numpy.core import overrides
+from numpy.lib.twodim_base import diag, vander
+from numpy.lib.function_base import trim_zeros
+from numpy.lib.type_check import iscomplex, real, imag, mintypecode
+from numpy.linalg import eigvals, lstsq, inv
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+@set_module('numpy')
+class RankWarning(UserWarning):
+    """
+    Issued by `polyfit` when the Vandermonde matrix is rank deficient.
+
+    For more information, a way to suppress the warning, and an example of
+    `RankWarning` being issued, see `polyfit`.
+
+    """
+    pass
+
+
+def _poly_dispatcher(seq_of_zeros):
+    return seq_of_zeros
+
+
+@array_function_dispatch(_poly_dispatcher)
+def poly(seq_of_zeros):
+    """
+    Find the coefficients of a polynomial with the given sequence of roots.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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.
+
+    Parameters
+    ----------
+    seq_of_zeros : array_like, shape (N,) or (N, N)
+        A sequence of polynomial roots, or a square array or matrix object.
+
+    Returns
+    -------
+    c : ndarray
+        1D array of polynomial coefficients from highest to lowest degree:
+
+        ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]``
+        where c[0] always equals 1.
+
+    Raises
+    ------
+    ValueError
+        If input is the wrong shape (the input must be a 1-D or square
+        2-D array).
+
+    See Also
+    --------
+    polyval : Compute polynomial values.
+    roots : Return the roots of a polynomial.
+    polyfit : Least squares polynomial fit.
+    poly1d : A one-dimensional polynomial class.
+
+    Notes
+    -----
+    Specifying the roots of a polynomial still leaves one degree of
+    freedom, typically represented by an undetermined leading
+    coefficient. [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``.)
+
+    The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n`
+    matrix **A** is given by
+
+        :math:`p_a(t) = \\mathrm{det}(t\\, \\mathbf{I} - \\mathbf{A})`,
+
+    where **I** is the `n`-by-`n` identity matrix. [2]_
+
+    References
+    ----------
+    .. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trigonometry,
+       Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996.
+
+    .. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition,"
+       Academic Press, pg. 182, 1980.
+
+    Examples
+    --------
+    Given a sequence of a polynomial's zeros:
+
+    >>> np.poly((0, 0, 0)) # Multiple root example
+    array([1., 0., 0., 0.])
+
+    The line above represents z**3 + 0*z**2 + 0*z + 0.
+
+    >>> np.poly((-1./2, 0, 1./2))
+    array([ 1.  ,  0.  , -0.25,  0.  ])
+
+    The line above represents z**3 - z/4
+
+    >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))
+    array([ 1.        , -0.77086955,  0.08618131,  0.        ]) # random
+
+    Given a square array object:
+
+    >>> P = np.array([[0, 1./3], [-1./2, 0]])
+    >>> np.poly(P)
+    array([1.        , 0.        , 0.16666667])
+
+    Note how in all cases the leading coefficient is always 1.
+
+    """
+    seq_of_zeros = atleast_1d(seq_of_zeros)
+    sh = seq_of_zeros.shape
+
+    if len(sh) == 2 and sh[0] == sh[1] and sh[0] != 0:
+        seq_of_zeros = eigvals(seq_of_zeros)
+    elif len(sh) == 1:
+        dt = seq_of_zeros.dtype
+        # Let object arrays slip through, e.g. for arbitrary precision
+        if dt != object:
+            seq_of_zeros = seq_of_zeros.astype(mintypecode(dt.char))
+    else:
+        raise ValueError("input must be 1d or non-empty square 2d array.")
+
+    if len(seq_of_zeros) == 0:
+        return 1.0
+    dt = seq_of_zeros.dtype
+    a = ones((1,), dtype=dt)
+    for zero in seq_of_zeros:
+        a = NX.convolve(a, array([1, -zero], dtype=dt), mode='full')
+
+    if issubclass(a.dtype.type, NX.complexfloating):
+        # if complex roots are all complex conjugates, the roots are real.
+        roots = NX.asarray(seq_of_zeros, complex)
+        if NX.all(NX.sort(roots) == NX.sort(roots.conjugate())):
+            a = a.real.copy()
+
+    return a
+
+
+def _roots_dispatcher(p):
+    return p
+
+
+@array_function_dispatch(_roots_dispatcher)
+def roots(p):
+    """
+    Return the roots of a polynomial with coefficients given in p.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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::
+
+      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
+
+    Parameters
+    ----------
+    p : array_like
+        Rank-1 array of polynomial coefficients.
+
+    Returns
+    -------
+    out : ndarray
+        An array containing the roots of the polynomial.
+
+    Raises
+    ------
+    ValueError
+        When `p` cannot be converted to a rank-1 array.
+
+    See also
+    --------
+    poly : Find the coefficients of a polynomial with a given sequence
+           of roots.
+    polyval : Compute polynomial values.
+    polyfit : Least squares polynomial fit.
+    poly1d : A one-dimensional polynomial class.
+
+    Notes
+    -----
+    The algorithm relies on computing the eigenvalues of the
+    companion matrix [1]_.
+
+    References
+    ----------
+    .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*.  Cambridge, UK:
+        Cambridge University Press, 1999, pp. 146-7.
+
+    Examples
+    --------
+    >>> coeff = [3.2, 2, 1]
+    >>> np.roots(coeff)
+    array([-0.3125+0.46351241j, -0.3125-0.46351241j])
+
+    """
+    # If input is scalar, this makes it an array
+    p = atleast_1d(p)
+    if p.ndim != 1:
+        raise ValueError("Input must be a rank-1 array.")
+
+    # find non-zero array entries
+    non_zero = NX.nonzero(NX.ravel(p))[0]
+
+    # Return an empty array if polynomial is all zeros
+    if len(non_zero) == 0:
+        return NX.array([])
+
+    # find the number of trailing zeros -- this is the number of roots at 0.
+    trailing_zeros = len(p) - non_zero[-1] - 1
+
+    # strip leading and trailing zeros
+    p = p[int(non_zero[0]):int(non_zero[-1])+1]
+
+    # casting: if incoming array isn't floating point, make it floating point.
+    if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
+        p = p.astype(float)
+
+    N = len(p)
+    if N > 1:
+        # build companion matrix and find its eigenvalues (the roots)
+        A = diag(NX.ones((N-2,), p.dtype), -1)
+        A[0,:] = -p[1:] / p[0]
+        roots = eigvals(A)
+    else:
+        roots = NX.array([])
+
+    # tack any zeros onto the back of the array
+    roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
+    return roots
+
+
+def _polyint_dispatcher(p, m=None, k=None):
+    return (p,)
+
+
+@array_function_dispatch(_polyint_dispatcher)
+def polyint(p, m=1, k=None):
+    """
+    Return an antiderivative (indefinite integral) of a polynomial.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    The returned order `m` antiderivative `P` of polynomial `p` satisfies
+    :math:`\\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
+
+    .. math:: \\frac{k_{m-1}}{0!} x^0 + \\ldots + \\frac{k_0}{(m-1)!}x^{m-1}
+
+    of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.
+
+    Parameters
+    ----------
+    p : array_like or poly1d
+        Polynomial to integrate.
+        A sequence is interpreted as polynomial coefficients, see `poly1d`.
+    m : int, optional
+        Order of the antiderivative. (Default: 1)
+    k : list of `m` scalars or scalar, optional
+        Integration constants. They are given in the order of integration:
+        those corresponding to highest-order terms come first.
+
+        If ``None`` (default), all constants are assumed to be zero.
+        If `m = 1`, a single scalar can be given instead of a list.
+
+    See Also
+    --------
+    polyder : derivative of a polynomial
+    poly1d.integ : equivalent method
+
+    Examples
+    --------
+    The defining property of the antiderivative:
+
+    >>> p = np.poly1d([1,1,1])
+    >>> P = np.polyint(p)
+    >>> P
+     poly1d([ 0.33333333,  0.5       ,  1.        ,  0.        ]) # may vary
+    >>> np.polyder(P) == p
+    True
+
+    The integration constants default to zero, but can be specified:
+
+    >>> P = np.polyint(p, 3)
+    >>> P(0)
+    0.0
+    >>> np.polyder(P)(0)
+    0.0
+    >>> np.polyder(P, 2)(0)
+    0.0
+    >>> P = np.polyint(p, 3, k=[6,5,3])
+    >>> P
+    poly1d([ 0.01666667,  0.04166667,  0.16666667,  3. ,  5. ,  3. ]) # may vary
+
+    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:
+
+    >>> np.polyder(P, 2)(0)
+    6.0
+    >>> np.polyder(P, 1)(0)
+    5.0
+    >>> P(0)
+    3.0
+
+    """
+    m = int(m)
+    if m < 0:
+        raise ValueError("Order of integral must be positive (see polyder)")
+    if k is None:
+        k = NX.zeros(m, float)
+    k = atleast_1d(k)
+    if len(k) == 1 and m > 1:
+        k = k[0]*NX.ones(m, float)
+    if len(k) < m:
+        raise ValueError(
+              "k must be a scalar or a rank-1 array of length 1 or >m.")
+
+    truepoly = isinstance(p, poly1d)
+    p = NX.asarray(p)
+    if m == 0:
+        if truepoly:
+            return poly1d(p)
+        return p
+    else:
+        # Note: this must work also with object and integer arrays
+        y = NX.concatenate((p.__truediv__(NX.arange(len(p), 0, -1)), [k[0]]))
+        val = polyint(y, m - 1, k=k[1:])
+        if truepoly:
+            return poly1d(val)
+        return val
+
+
+def _polyder_dispatcher(p, m=None):
+    return (p,)
+
+
+@array_function_dispatch(_polyder_dispatcher)
+def polyder(p, m=1):
+    """
+    Return the derivative of the specified order of a polynomial.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    Parameters
+    ----------
+    p : poly1d or sequence
+        Polynomial to differentiate.
+        A sequence is interpreted as polynomial coefficients, see `poly1d`.
+    m : int, optional
+        Order of differentiation (default: 1)
+
+    Returns
+    -------
+    der : poly1d
+        A new polynomial representing the derivative.
+
+    See Also
+    --------
+    polyint : Anti-derivative of a polynomial.
+    poly1d : Class for one-dimensional polynomials.
+
+    Examples
+    --------
+    The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is:
+
+    >>> p = np.poly1d([1,1,1,1])
+    >>> p2 = np.polyder(p)
+    >>> p2
+    poly1d([3, 2, 1])
+
+    which evaluates to:
+
+    >>> p2(2.)
+    17.0
+
+    We can verify this, approximating the derivative with
+    ``(f(x + h) - f(x))/h``:
+
+    >>> (p(2. + 0.001) - p(2.)) / 0.001
+    17.007000999997857
+
+    The fourth-order derivative of a 3rd-order polynomial is zero:
+
+    >>> np.polyder(p, 2)
+    poly1d([6, 2])
+    >>> np.polyder(p, 3)
+    poly1d([6])
+    >>> np.polyder(p, 4)
+    poly1d([0])
+
+    """
+    m = int(m)
+    if m < 0:
+        raise ValueError("Order of derivative must be positive (see polyint)")
+
+    truepoly = isinstance(p, poly1d)
+    p = NX.asarray(p)
+    n = len(p) - 1
+    y = p[:-1] * NX.arange(n, 0, -1)
+    if m == 0:
+        val = p
+    else:
+        val = polyder(y, m - 1)
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+def _polyfit_dispatcher(x, y, deg, rcond=None, full=None, w=None, cov=None):
+    return (x, y, w)
+
+
+@array_function_dispatch(_polyfit_dispatcher)
+def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False):
+    """
+    Least squares polynomial fit.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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`.
+
+    The `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.
+
+    Parameters
+    ----------
+    x : array_like, shape (M,)
+        x-coordinates of the M sample points ``(x[i], y[i])``.
+    y : array_like, shape (M,) or (M, K)
+        y-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.
+    deg : int
+        Degree of the fitting polynomial
+    rcond : float, optional
+        Relative 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.
+    full : bool, optional
+        Switch 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.
+    w : array_like, shape (M,), optional
+        Weights. 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.
+    cov : bool or str, optional
+        If 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.
+
+    Returns
+    -------
+    p : ndarray, shape (deg + 1,) or (deg + 1, K)
+        Polynomial coefficients, highest power first.  If `y` was 2-D, the
+        coefficients for `k`-th data set are in ``p[:,k]``.
+
+    residuals, rank, singular_values, rcond
+        These values are only returned if ``full == True``
+
+        - residuals -- sum of squared residuals of the least squares fit
+        - rank -- the effective rank of the scaled Vandermonde
+           coefficient matrix
+        - singular_values -- singular values of the scaled Vandermonde
+           coefficient matrix
+        - rcond -- value of `rcond`.
+
+        For more details, see `numpy.linalg.lstsq`.
+
+    V : ndarray, shape (M,M) or (M,M,K)
+        Present 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]``
+
+
+    Warns
+    -----
+    RankWarning
+        The 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
+
+        >>> import warnings
+        >>> warnings.simplefilter('ignore', np.RankWarning)
+
+    See Also
+    --------
+    polyval : Compute polynomial values.
+    linalg.lstsq : Computes a least-squares fit.
+    scipy.interpolate.UnivariateSpline : Computes spline fits.
+
+    Notes
+    -----
+    The solution minimizes the squared error
+
+    .. math::
+        E = \\sum_{j=0}^k |p(x_j) - y_j|^2
+
+    in the equations::
+
+        x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]
+        x[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]
+        ...
+        x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]
+
+    The coefficient matrix of the coefficients `p` is a Vandermonde matrix.
+
+    `polyfit` issues a `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.
+
+    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.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Curve fitting",
+           https://en.wikipedia.org/wiki/Curve_fitting
+    .. [2] Wikipedia, "Polynomial interpolation",
+           https://en.wikipedia.org/wiki/Polynomial_interpolation
+
+    Examples
+    --------
+    >>> import warnings
+    >>> x = np.array([0.0, 1.0, 2.0, 3.0,  4.0,  5.0])
+    >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])
+    >>> z = np.polyfit(x, y, 3)
+    >>> z
+    array([ 0.08703704, -0.81349206,  1.69312169, -0.03968254]) # may vary
+
+    It is convenient to use `poly1d` objects for dealing with polynomials:
+
+    >>> p = np.poly1d(z)
+    >>> p(0.5)
+    0.6143849206349179 # may vary
+    >>> p(3.5)
+    -0.34732142857143039 # may vary
+    >>> p(10)
+    22.579365079365115 # may vary
+
+    High-order polynomials may oscillate wildly:
+
+    >>> with warnings.catch_warnings():
+    ...     warnings.simplefilter('ignore', np.RankWarning)
+    ...     p30 = np.poly1d(np.polyfit(x, y, 30))
+    ...
+    >>> p30(4)
+    -0.80000000000000204 # may vary
+    >>> p30(5)
+    -0.99999999999999445 # may vary
+    >>> p30(4.5)
+    -0.10547061179440398 # may vary
+
+    Illustration:
+
+    >>> import matplotlib.pyplot as plt
+    >>> xp = np.linspace(-2, 6, 100)
+    >>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')
+    >>> plt.ylim(-2,2)
+    (-2, 2)
+    >>> plt.show()
+
+    """
+    order = int(deg) + 1
+    x = NX.asarray(x) + 0.0
+    y = NX.asarray(y) + 0.0
+
+    # check arguments.
+    if deg < 0:
+        raise ValueError("expected deg >= 0")
+    if x.ndim != 1:
+        raise TypeError("expected 1D vector for x")
+    if x.size == 0:
+        raise TypeError("expected non-empty vector for x")
+    if y.ndim < 1 or y.ndim > 2:
+        raise TypeError("expected 1D or 2D array for y")
+    if x.shape[0] != y.shape[0]:
+        raise TypeError("expected x and y to have same length")
+
+    # set rcond
+    if rcond is None:
+        rcond = len(x)*finfo(x.dtype).eps
+
+    # set up least squares equation for powers of x
+    lhs = vander(x, order)
+    rhs = y
+
+    # apply weighting
+    if w is not None:
+        w = NX.asarray(w) + 0.0
+        if w.ndim != 1:
+            raise TypeError("expected a 1-d array for weights")
+        if w.shape[0] != y.shape[0]:
+            raise TypeError("expected w and y to have the same length")
+        lhs *= w[:, NX.newaxis]
+        if rhs.ndim == 2:
+            rhs *= w[:, NX.newaxis]
+        else:
+            rhs *= w
+
+    # scale lhs to improve condition number and solve
+    scale = NX.sqrt((lhs*lhs).sum(axis=0))
+    lhs /= scale
+    c, resids, rank, s = lstsq(lhs, rhs, rcond)
+    c = (c.T/scale).T  # broadcast scale coefficients
+
+    # warn on rank reduction, which indicates an ill conditioned matrix
+    if rank != order and not full:
+        msg = "Polyfit may be poorly conditioned"
+        warnings.warn(msg, RankWarning, stacklevel=2)
+
+    if full:
+        return c, resids, rank, s, rcond
+    elif cov:
+        Vbase = inv(dot(lhs.T, lhs))
+        Vbase /= NX.outer(scale, scale)
+        if cov == "unscaled":
+            fac = 1
+        else:
+            if len(x) <= order:
+                raise ValueError("the number of data points must exceed order "
+                                 "to scale the covariance matrix")
+            # note, this used to be: fac = resids / (len(x) - order - 2.0)
+            # it was deciced that the "- 2" (originally justified by "Bayesian
+            # uncertainty analysis") is not what the user expects
+            # (see gh-11196 and gh-11197)
+            fac = resids / (len(x) - order)
+        if y.ndim == 1:
+            return c, Vbase * fac
+        else:
+            return c, Vbase[:,:, NX.newaxis] * fac
+    else:
+        return c
+
+
+def _polyval_dispatcher(p, x):
+    return (p, x)
+
+
+@array_function_dispatch(_polyval_dispatcher)
+def polyval(p, x):
+    """
+    Evaluate a polynomial at specific values.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    If `p` is of length N, this function returns the value:
+
+        ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]``
+
+    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.
+
+    Parameters
+    ----------
+    p : array_like or poly1d object
+       1D array of polynomial coefficients (including coefficients equal
+       to zero) from highest degree to the constant term, or an
+       instance of poly1d.
+    x : array_like or poly1d object
+       A number, an array of numbers, or an instance of poly1d, at
+       which to evaluate `p`.
+
+    Returns
+    -------
+    values : ndarray or poly1d
+       If `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.
+
+    See Also
+    --------
+    poly1d: A polynomial class.
+
+    Notes
+    -----
+    Horner's scheme [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.
+
+    If `x` is a subtype of `ndarray` the return value will be of the same type.
+
+    References
+    ----------
+    .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.
+       trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand
+       Reinhold Co., 1985, pg. 720.
+
+    Examples
+    --------
+    >>> np.polyval([3,0,1], 5)  # 3 * 5**2 + 0 * 5**1 + 1
+    76
+    >>> np.polyval([3,0,1], np.poly1d(5))
+    poly1d([76])
+    >>> np.polyval(np.poly1d([3,0,1]), 5)
+    76
+    >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))
+    poly1d([76])
+
+    """
+    p = NX.asarray(p)
+    if isinstance(x, poly1d):
+        y = 0
+    else:
+        x = NX.asanyarray(x)
+        y = NX.zeros_like(x)
+    for pv in p:
+        y = y * x + pv
+    return y
+
+
+def _binary_op_dispatcher(a1, a2):
+    return (a1, a2)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polyadd(a1, a2):
+    """
+    Find the sum of two polynomials.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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.
+
+    Parameters
+    ----------
+    a1, a2 : array_like or poly1d object
+        Input polynomials.
+
+    Returns
+    -------
+    out : ndarray or poly1d object
+        The 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.
+
+    See Also
+    --------
+    poly1d : A one-dimensional polynomial class.
+    poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval
+
+    Examples
+    --------
+    >>> np.polyadd([1, 2], [9, 5, 4])
+    array([9, 6, 6])
+
+    Using poly1d objects:
+
+    >>> p1 = np.poly1d([1, 2])
+    >>> p2 = np.poly1d([9, 5, 4])
+    >>> print(p1)
+    1 x + 2
+    >>> print(p2)
+       2
+    9 x + 5 x + 4
+    >>> print(np.polyadd(p1, p2))
+       2
+    9 x + 6 x + 6
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1 = atleast_1d(a1)
+    a2 = atleast_1d(a2)
+    diff = len(a2) - len(a1)
+    if diff == 0:
+        val = a1 + a2
+    elif diff > 0:
+        zr = NX.zeros(diff, a1.dtype)
+        val = NX.concatenate((zr, a1)) + a2
+    else:
+        zr = NX.zeros(abs(diff), a2.dtype)
+        val = a1 + NX.concatenate((zr, a2))
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polysub(a1, a2):
+    """
+    Difference (subtraction) of two polynomials.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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` objects.
+
+    Parameters
+    ----------
+    a1, a2 : array_like or poly1d
+        Minuend and subtrahend polynomials, respectively.
+
+    Returns
+    -------
+    out : ndarray or poly1d
+        Array or `poly1d` object of the difference polynomial's coefficients.
+
+    See Also
+    --------
+    polyval, polydiv, polymul, polyadd
+
+    Examples
+    --------
+    .. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2)
+
+    >>> np.polysub([2, 10, -2], [3, 10, -4])
+    array([-1,  0,  2])
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1 = atleast_1d(a1)
+    a2 = atleast_1d(a2)
+    diff = len(a2) - len(a1)
+    if diff == 0:
+        val = a1 - a2
+    elif diff > 0:
+        zr = NX.zeros(diff, a1.dtype)
+        val = NX.concatenate((zr, a1)) - a2
+    else:
+        zr = NX.zeros(abs(diff), a2.dtype)
+        val = a1 - NX.concatenate((zr, a2))
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polymul(a1, a2):
+    """
+    Find the product of two polynomials.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    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.
+
+    Parameters
+    ----------
+    a1, a2 : array_like or poly1d object
+        Input polynomials.
+
+    Returns
+    -------
+    out : ndarray or poly1d object
+        The 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.
+
+    See Also
+    --------
+    poly1d : A one-dimensional polynomial class.
+    poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval
+    convolve : Array convolution. Same output as polymul, but has parameter
+               for overlap mode.
+
+    Examples
+    --------
+    >>> np.polymul([1, 2, 3], [9, 5, 1])
+    array([ 9, 23, 38, 17,  3])
+
+    Using poly1d objects:
+
+    >>> p1 = np.poly1d([1, 2, 3])
+    >>> p2 = np.poly1d([9, 5, 1])
+    >>> print(p1)
+       2
+    1 x + 2 x + 3
+    >>> print(p2)
+       2
+    9 x + 5 x + 1
+    >>> print(np.polymul(p1, p2))
+       4      3      2
+    9 x + 23 x + 38 x + 17 x + 3
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1, a2 = poly1d(a1), poly1d(a2)
+    val = NX.convolve(a1, a2)
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+def _polydiv_dispatcher(u, v):
+    return (u, v)
+
+
+@array_function_dispatch(_polydiv_dispatcher)
+def polydiv(u, v):
+    """
+    Returns the quotient and remainder of polynomial division.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    The input arrays are the coefficients (including any coefficients
+    equal to zero) of the "numerator" (dividend) and "denominator"
+    (divisor) polynomials, respectively.
+
+    Parameters
+    ----------
+    u : array_like or poly1d
+        Dividend polynomial's coefficients.
+
+    v : array_like or poly1d
+        Divisor polynomial's coefficients.
+
+    Returns
+    -------
+    q : ndarray
+        Coefficients, including those equal to zero, of the quotient.
+    r : ndarray
+        Coefficients, including those equal to zero, of the remainder.
+
+    See Also
+    --------
+    poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub
+    polyval
+
+    Notes
+    -----
+    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.
+
+    Examples
+    --------
+    .. math:: \\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25
+
+    >>> x = np.array([3.0, 5.0, 2.0])
+    >>> y = np.array([2.0, 1.0])
+    >>> np.polydiv(x, y)
+    (array([1.5 , 1.75]), array([0.25]))
+
+    """
+    truepoly = (isinstance(u, poly1d) or isinstance(v, poly1d))
+    u = atleast_1d(u) + 0.0
+    v = atleast_1d(v) + 0.0
+    # w has the common type
+    w = u[0] + v[0]
+    m = len(u) - 1
+    n = len(v) - 1
+    scale = 1. / v[0]
+    q = NX.zeros((max(m - n + 1, 1),), w.dtype)
+    r = u.astype(w.dtype)
+    for k in range(0, m-n+1):
+        d = scale * r[k]
+        q[k] = d
+        r[k:k+n+1] -= d*v
+    while NX.allclose(r[0], 0, rtol=1e-14) and (r.shape[-1] > 1):
+        r = r[1:]
+    if truepoly:
+        return poly1d(q), poly1d(r)
+    return q, r
+
+_poly_mat = re.compile(r"\*\*([0-9]*)")
+def _raise_power(astr, wrap=70):
+    n = 0
+    line1 = ''
+    line2 = ''
+    output = ' '
+    while True:
+        mat = _poly_mat.search(astr, n)
+        if mat is None:
+            break
+        span = mat.span()
+        power = mat.groups()[0]
+        partstr = astr[n:span[0]]
+        n = span[1]
+        toadd2 = partstr + ' '*(len(power)-1)
+        toadd1 = ' '*(len(partstr)-1) + power
+        if ((len(line2) + len(toadd2) > wrap) or
+                (len(line1) + len(toadd1) > wrap)):
+            output += line1 + "\n" + line2 + "\n "
+            line1 = toadd1
+            line2 = toadd2
+        else:
+            line2 += partstr + ' '*(len(power)-1)
+            line1 += ' '*(len(partstr)-1) + power
+    output += line1 + "\n" + line2
+    return output + astr[n:]
+
+
+@set_module('numpy')
+class poly1d:
+    """
+    A one-dimensional polynomial class.
+
+    .. note::
+       This forms part of the old polynomial API. Since version 1.4, the
+       new polynomial API defined in `numpy.polynomial` is preferred.
+       A summary of the differences can be found in the
+       :doc:`transition guide </reference/routines.polynomials>`.
+
+    A convenience class, used to encapsulate "natural" operations on
+    polynomials so that said operations may take on their customary
+    form in code (see Examples).
+
+    Parameters
+    ----------
+    c_or_r : array_like
+        The 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
+        :math:`x^2 + 2x + 3`, whereas ``poly1d([1, 2, 3], True)`` returns
+        one that represents :math:`(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6`.
+    r : bool, optional
+        If True, `c_or_r` specifies the polynomial's roots; the default
+        is False.
+    variable : str, optional
+        Changes the variable used when printing `p` from `x` to `variable`
+        (see Examples).
+
+    Examples
+    --------
+    Construct the polynomial :math:`x^2 + 2x + 3`:
+
+    >>> p = np.poly1d([1, 2, 3])
+    >>> print(np.poly1d(p))
+       2
+    1 x + 2 x + 3
+
+    Evaluate the polynomial at :math:`x = 0.5`:
+
+    >>> p(0.5)
+    4.25
+
+    Find the roots:
+
+    >>> p.r
+    array([-1.+1.41421356j, -1.-1.41421356j])
+    >>> p(p.r)
+    array([ -4.44089210e-16+0.j,  -4.44089210e-16+0.j]) # may vary
+
+    These numbers in the previous line represent (0, 0) to machine precision
+
+    Show the coefficients:
+
+    >>> p.c
+    array([1, 2, 3])
+
+    Display the order (the leading zero-coefficients are removed):
+
+    >>> p.order
+    2
+
+    Show the coefficient of the k-th power in the polynomial
+    (which is equivalent to ``p.c[-(i+1)]``):
+
+    >>> p[1]
+    2
+
+    Polynomials can be added, subtracted, multiplied, and divided
+    (returns quotient and remainder):
+
+    >>> p * p
+    poly1d([ 1,  4, 10, 12,  9])
+
+    >>> (p**3 + 4) / p
+    (poly1d([ 1.,  4., 10., 12.,  9.]), poly1d([4.]))
+
+    ``asarray(p)`` gives the coefficient array, so polynomials can be
+    used in all functions that accept arrays:
+
+    >>> p**2 # square of polynomial
+    poly1d([ 1,  4, 10, 12,  9])
+
+    >>> np.square(p) # square of individual coefficients
+    array([1, 4, 9])
+
+    The variable used in the string representation of `p` can be modified,
+    using the `variable` parameter:
+
+    >>> p = np.poly1d([1,2,3], variable='z')
+    >>> print(p)
+       2
+    1 z + 2 z + 3
+
+    Construct a polynomial from its roots:
+
+    >>> np.poly1d([1, 2], True)
+    poly1d([ 1., -3.,  2.])
+
+    This is the same polynomial as obtained by:
+
+    >>> np.poly1d([1, -1]) * np.poly1d([1, -2])
+    poly1d([ 1, -3,  2])
+
+    """
+    __hash__ = None
+
+    @property
+    def coeffs(self):
+        """ The polynomial coefficients """
+        return self._coeffs
+
+    @coeffs.setter
+    def coeffs(self, value):
+        # allowing this makes p.coeffs *= 2 legal
+        if value is not self._coeffs:
+            raise AttributeError("Cannot set attribute")
+
+    @property
+    def variable(self):
+        """ The name of the polynomial variable """
+        return self._variable
+
+    # calculated attributes
+    @property
+    def order(self):
+        """ The order or degree of the polynomial """
+        return len(self._coeffs) - 1
+
+    @property
+    def roots(self):
+        """ The roots of the polynomial, where self(x) == 0 """
+        return roots(self._coeffs)
+
+    # our internal _coeffs property need to be backed by __dict__['coeffs'] for
+    # scipy to work correctly.
+    @property
+    def _coeffs(self):
+        return self.__dict__['coeffs']
+    @_coeffs.setter
+    def _coeffs(self, coeffs):
+        self.__dict__['coeffs'] = coeffs
+
+    # alias attributes
+    r = roots
+    c = coef = coefficients = coeffs
+    o = order
+
+    def __init__(self, c_or_r, r=False, variable=None):
+        if isinstance(c_or_r, poly1d):
+            self._variable = c_or_r._variable
+            self._coeffs = c_or_r._coeffs
+
+            if set(c_or_r.__dict__) - set(self.__dict__):
+                msg = ("In the future extra properties will not be copied "
+                       "across when constructing one poly1d from another")
+                warnings.warn(msg, FutureWarning, stacklevel=2)
+                self.__dict__.update(c_or_r.__dict__)
+
+            if variable is not None:
+                self._variable = variable
+            return
+        if r:
+            c_or_r = poly(c_or_r)
+        c_or_r = atleast_1d(c_or_r)
+        if c_or_r.ndim > 1:
+            raise ValueError("Polynomial must be 1d only.")
+        c_or_r = trim_zeros(c_or_r, trim='f')
+        if len(c_or_r) == 0:
+            c_or_r = NX.array([0], dtype=c_or_r.dtype)
+        self._coeffs = c_or_r
+        if variable is None:
+            variable = 'x'
+        self._variable = variable
+
+    def __array__(self, t=None):
+        if t:
+            return NX.asarray(self.coeffs, t)
+        else:
+            return NX.asarray(self.coeffs)
+
+    def __repr__(self):
+        vals = repr(self.coeffs)
+        vals = vals[6:-1]
+        return "poly1d(%s)" % vals
+
+    def __len__(self):
+        return self.order
+
+    def __str__(self):
+        thestr = "0"
+        var = self.variable
+
+        # Remove leading zeros
+        coeffs = self.coeffs[NX.logical_or.accumulate(self.coeffs != 0)]
+        N = len(coeffs)-1
+
+        def fmt_float(q):
+            s = '%.4g' % q
+            if s.endswith('.0000'):
+                s = s[:-5]
+            return s
+
+        for k, coeff in enumerate(coeffs):
+            if not iscomplex(coeff):
+                coefstr = fmt_float(real(coeff))
+            elif real(coeff) == 0:
+                coefstr = '%sj' % fmt_float(imag(coeff))
+            else:
+                coefstr = '(%s + %sj)' % (fmt_float(real(coeff)),
+                                          fmt_float(imag(coeff)))
+
+            power = (N-k)
+            if power == 0:
+                if coefstr != '0':
+                    newstr = '%s' % (coefstr,)
+                else:
+                    if k == 0:
+                        newstr = '0'
+                    else:
+                        newstr = ''
+            elif power == 1:
+                if coefstr == '0':
+                    newstr = ''
+                elif coefstr == 'b':
+                    newstr = var
+                else:
+                    newstr = '%s %s' % (coefstr, var)
+            else:
+                if coefstr == '0':
+                    newstr = ''
+                elif coefstr == 'b':
+                    newstr = '%s**%d' % (var, power,)
+                else:
+                    newstr = '%s %s**%d' % (coefstr, var, power)
+
+            if k > 0:
+                if newstr != '':
+                    if newstr.startswith('-'):
+                        thestr = "%s - %s" % (thestr, newstr[1:])
+                    else:
+                        thestr = "%s + %s" % (thestr, newstr)
+            else:
+                thestr = newstr
+        return _raise_power(thestr)
+
+    def __call__(self, val):
+        return polyval(self.coeffs, val)
+
+    def __neg__(self):
+        return poly1d(-self.coeffs)
+
+    def __pos__(self):
+        return self
+
+    def __mul__(self, other):
+        if isscalar(other):
+            return poly1d(self.coeffs * other)
+        else:
+            other = poly1d(other)
+            return poly1d(polymul(self.coeffs, other.coeffs))
+
+    def __rmul__(self, other):
+        if isscalar(other):
+            return poly1d(other * self.coeffs)
+        else:
+            other = poly1d(other)
+            return poly1d(polymul(self.coeffs, other.coeffs))
+
+    def __add__(self, other):
+        other = poly1d(other)
+        return poly1d(polyadd(self.coeffs, other.coeffs))
+
+    def __radd__(self, other):
+        other = poly1d(other)
+        return poly1d(polyadd(self.coeffs, other.coeffs))
+
+    def __pow__(self, val):
+        if not isscalar(val) or int(val) != val or val < 0:
+            raise ValueError("Power to non-negative integers only.")
+        res = [1]
+        for _ in range(val):
+            res = polymul(self.coeffs, res)
+        return poly1d(res)
+
+    def __sub__(self, other):
+        other = poly1d(other)
+        return poly1d(polysub(self.coeffs, other.coeffs))
+
+    def __rsub__(self, other):
+        other = poly1d(other)
+        return poly1d(polysub(other.coeffs, self.coeffs))
+
+    def __div__(self, other):
+        if isscalar(other):
+            return poly1d(self.coeffs/other)
+        else:
+            other = poly1d(other)
+            return polydiv(self, other)
+
+    __truediv__ = __div__
+
+    def __rdiv__(self, other):
+        if isscalar(other):
+            return poly1d(other/self.coeffs)
+        else:
+            other = poly1d(other)
+            return polydiv(other, self)
+
+    __rtruediv__ = __rdiv__
+
+    def __eq__(self, other):
+        if not isinstance(other, poly1d):
+            return NotImplemented
+        if self.coeffs.shape != other.coeffs.shape:
+            return False
+        return (self.coeffs == other.coeffs).all()
+
+    def __ne__(self, other):
+        if not isinstance(other, poly1d):
+            return NotImplemented
+        return not self.__eq__(other)
+
+
+    def __getitem__(self, val):
+        ind = self.order - val
+        if val > self.order:
+            return self.coeffs.dtype.type(0)
+        if val < 0:
+            return self.coeffs.dtype.type(0)
+        return self.coeffs[ind]
+
+    def __setitem__(self, key, val):
+        ind = self.order - key
+        if key < 0:
+            raise ValueError("Does not support negative powers.")
+        if key > self.order:
+            zr = NX.zeros(key-self.order, self.coeffs.dtype)
+            self._coeffs = NX.concatenate((zr, self.coeffs))
+            ind = 0
+        self._coeffs[ind] = val
+        return
+
+    def __iter__(self):
+        return iter(self.coeffs)
+
+    def integ(self, m=1, k=0):
+        """
+        Return an antiderivative (indefinite integral) of this polynomial.
+
+        Refer to `polyint` for full documentation.
+
+        See Also
+        --------
+        polyint : equivalent function
+
+        """
+        return poly1d(polyint(self.coeffs, m=m, k=k))
+
+    def deriv(self, m=1):
+        """
+        Return a derivative of this polynomial.
+
+        Refer to `polyder` for full documentation.
+
+        See Also
+        --------
+        polyder : equivalent function
+
+        """
+        return poly1d(polyder(self.coeffs, m=m))
+
+# Stuff to do on module import
+
+warnings.simplefilter('always', RankWarning)

.venv/lib/python3.11/site-packages/numpy/lib/scimath.pyi

@@ -0,0 +1,94 @@
+from typing import overload, Any
+
+from numpy import complexfloating
+
+from numpy._typing import (
+    NDArray,
+    _ArrayLikeFloat_co,
+    _ArrayLikeComplex_co,
+    _ComplexLike_co,
+    _FloatLike_co,
+)
+
+__all__: list[str]
+
+@overload
+def sqrt(x: _FloatLike_co) -> Any: ...
+@overload
+def sqrt(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def sqrt(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def sqrt(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log(x: _FloatLike_co) -> Any: ...
+@overload
+def log(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log10(x: _FloatLike_co) -> Any: ...
+@overload
+def log10(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log10(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log10(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log2(x: _FloatLike_co) -> Any: ...
+@overload
+def log2(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log2(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log2(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def logn(n: _FloatLike_co, x: _FloatLike_co) -> Any: ...
+@overload
+def logn(n: _ComplexLike_co, x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def logn(n: _ArrayLikeFloat_co, x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def logn(n: _ArrayLikeComplex_co, x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def power(x: _FloatLike_co, p: _FloatLike_co) -> Any: ...
+@overload
+def power(x: _ComplexLike_co, p: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def power(x: _ArrayLikeFloat_co, p: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def power(x: _ArrayLikeComplex_co, p: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arccos(x: _FloatLike_co) -> Any: ...
+@overload
+def arccos(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arccos(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arccos(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arcsin(x: _FloatLike_co) -> Any: ...
+@overload
+def arcsin(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arcsin(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arcsin(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arctanh(x: _FloatLike_co) -> Any: ...
+@overload
+def arctanh(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arctanh(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arctanh(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...