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168,590 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _tensorinv_dispatcher(a, ind=None):
return (a,) | null |
168,591 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def inv(a):
"""
Compute the (multiplicative) inverse of a matrix.
Given a square matrix `a`, return the matrix `ainv` satisfying
``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``.
Parameters
----------
a : (..., M, M) array_like
Matrix to be inverted.
Returns
-------
ainv : (..., M, M) ndarray or matrix
(Multiplicative) inverse of the matrix `a`.
Raises
------
LinAlgError
If `a` is not square or inversion fails.
See Also
--------
scipy.linalg.inv : Similar function in SciPy.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
Examples
--------
>>> from numpy.linalg import inv
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = inv(a)
>>> np.allclose(np.dot(a, ainv), np.eye(2))
True
>>> np.allclose(np.dot(ainv, a), np.eye(2))
True
If a is a matrix object, then the return value is a matrix as well:
>>> ainv = inv(np.matrix(a))
>>> ainv
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
Inverses of several matrices can be computed at once:
>>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]])
>>> inv(a)
array([[[-2. , 1. ],
[ 1.5 , -0.5 ]],
[[-1.25, 0.75],
[ 0.75, -0.25]]])
"""
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
signature = 'D->D' if isComplexType(t) else 'd->d'
extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
ainv = _umath_linalg.inv(a, signature=signature, extobj=extobj)
return wrap(ainv.astype(result_t, copy=False))
The provided code snippet includes necessary dependencies for implementing the `tensorinv` function. Write a Python function `def tensorinv(a, ind=2)` to solve the following problem:
Compute the 'inverse' of an N-dimensional array. The result is an inverse for `a` relative to the tensordot operation ``tensordot(a, b, ind)``, i. e., up to floating-point accuracy, ``tensordot(tensorinv(a), a, ind)`` is the "identity" tensor for the tensordot operation. Parameters ---------- a : array_like Tensor to 'invert'. Its shape must be 'square', i. e., ``prod(a.shape[:ind]) == prod(a.shape[ind:])``. ind : int, optional Number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2. Returns ------- b : ndarray `a`'s tensordot inverse, shape ``a.shape[ind:] + a.shape[:ind]``. Raises ------ LinAlgError If `a` is singular or not 'square' (in the above sense). See Also -------- numpy.tensordot, tensorsolve Examples -------- >>> a = np.eye(4*6) >>> a.shape = (4, 6, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=2) >>> ainv.shape (8, 3, 4, 6) >>> b = np.random.randn(4, 6) >>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b)) True >>> a = np.eye(4*6) >>> a.shape = (24, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=1) >>> ainv.shape (8, 3, 24) >>> b = np.random.randn(24) >>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b)) True
Here is the function:
def tensorinv(a, ind=2):
"""
Compute the 'inverse' of an N-dimensional array.
The result is an inverse for `a` relative to the tensordot operation
``tensordot(a, b, ind)``, i. e., up to floating-point accuracy,
``tensordot(tensorinv(a), a, ind)`` is the "identity" tensor for the
tensordot operation.
Parameters
----------
a : array_like
Tensor to 'invert'. Its shape must be 'square', i. e.,
``prod(a.shape[:ind]) == prod(a.shape[ind:])``.
ind : int, optional
Number of first indices that are involved in the inverse sum.
Must be a positive integer, default is 2.
Returns
-------
b : ndarray
`a`'s tensordot inverse, shape ``a.shape[ind:] + a.shape[:ind]``.
Raises
------
LinAlgError
If `a` is singular or not 'square' (in the above sense).
See Also
--------
numpy.tensordot, tensorsolve
Examples
--------
>>> a = np.eye(4*6)
>>> a.shape = (4, 6, 8, 3)
>>> ainv = np.linalg.tensorinv(a, ind=2)
>>> ainv.shape
(8, 3, 4, 6)
>>> b = np.random.randn(4, 6)
>>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b))
True
>>> a = np.eye(4*6)
>>> a.shape = (24, 8, 3)
>>> ainv = np.linalg.tensorinv(a, ind=1)
>>> ainv.shape
(8, 3, 24)
>>> b = np.random.randn(24)
>>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b))
True
"""
a = asarray(a)
oldshape = a.shape
prod = 1
if ind > 0:
invshape = oldshape[ind:] + oldshape[:ind]
for k in oldshape[ind:]:
prod *= k
else:
raise ValueError("Invalid ind argument.")
a = a.reshape(prod, -1)
ia = inv(a)
return ia.reshape(*invshape) | Compute the 'inverse' of an N-dimensional array. The result is an inverse for `a` relative to the tensordot operation ``tensordot(a, b, ind)``, i. e., up to floating-point accuracy, ``tensordot(tensorinv(a), a, ind)`` is the "identity" tensor for the tensordot operation. Parameters ---------- a : array_like Tensor to 'invert'. Its shape must be 'square', i. e., ``prod(a.shape[:ind]) == prod(a.shape[ind:])``. ind : int, optional Number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2. Returns ------- b : ndarray `a`'s tensordot inverse, shape ``a.shape[ind:] + a.shape[:ind]``. Raises ------ LinAlgError If `a` is singular or not 'square' (in the above sense). See Also -------- numpy.tensordot, tensorsolve Examples -------- >>> a = np.eye(4*6) >>> a.shape = (4, 6, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=2) >>> ainv.shape (8, 3, 4, 6) >>> b = np.random.randn(4, 6) >>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b)) True >>> a = np.eye(4*6) >>> a.shape = (24, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=1) >>> ainv.shape (8, 3, 24) >>> b = np.random.randn(24) >>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b)) True |
168,592 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _unary_dispatcher(a):
return (a,) | null |
168,593 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _matrix_power_dispatcher(a, n):
return (a,) | null |
168,594 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
def inv(a):
"""
Compute the (multiplicative) inverse of a matrix.
Given a square matrix `a`, return the matrix `ainv` satisfying
``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``.
Parameters
----------
a : (..., M, M) array_like
Matrix to be inverted.
Returns
-------
ainv : (..., M, M) ndarray or matrix
(Multiplicative) inverse of the matrix `a`.
Raises
------
LinAlgError
If `a` is not square or inversion fails.
See Also
--------
scipy.linalg.inv : Similar function in SciPy.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
Examples
--------
>>> from numpy.linalg import inv
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = inv(a)
>>> np.allclose(np.dot(a, ainv), np.eye(2))
True
>>> np.allclose(np.dot(ainv, a), np.eye(2))
True
If a is a matrix object, then the return value is a matrix as well:
>>> ainv = inv(np.matrix(a))
>>> ainv
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
Inverses of several matrices can be computed at once:
>>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]])
>>> inv(a)
array([[[-2. , 1. ],
[ 1.5 , -0.5 ]],
[[-1.25, 0.75],
[ 0.75, -0.25]]])
"""
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
signature = 'D->D' if isComplexType(t) else 'd->d'
extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
ainv = _umath_linalg.inv(a, signature=signature, extobj=extobj)
return wrap(ainv.astype(result_t, copy=False))
def eye(N, M=None, k=0, dtype=float, order='C', *, like=None):
"""
Return a 2-D array with ones on the diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the output.
M : int, optional
Number of columns in the output. If None, defaults to `N`.
k : int, optional
Index of the diagonal: 0 (the default) refers to the main diagonal,
a positive value refers to an upper diagonal, and a negative value
to a lower diagonal.
dtype : data-type, optional
Data-type of the returned array.
order : {'C', 'F'}, optional
Whether the output should be stored in row-major (C-style) or
column-major (Fortran-style) order in memory.
.. versionadded:: 1.14.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
I : ndarray of shape (N,M)
An array where all elements are equal to zero, except for the `k`-th
diagonal, whose values are equal to one.
See Also
--------
identity : (almost) equivalent function
diag : diagonal 2-D array from a 1-D array specified by the user.
Examples
--------
>>> np.eye(2, dtype=int)
array([[1, 0],
[0, 1]])
>>> np.eye(3, k=1)
array([[0., 1., 0.],
[0., 0., 1.],
[0., 0., 0.]])
"""
if like is not None:
return _eye_with_like(N, M=M, k=k, dtype=dtype, order=order, like=like)
if M is None:
M = N
m = zeros((N, M), dtype=dtype, order=order)
if k >= M:
return m
# Ensure M and k are integers, so we don't get any surprise casting
# results in the expressions `M-k` and `M+1` used below. This avoids
# a problem with inputs with type (for example) np.uint64.
M = operator.index(M)
k = operator.index(k)
if k >= 0:
i = k
else:
i = (-k) * M
m[:M-k].flat[i::M+1] = 1
return m
The provided code snippet includes necessary dependencies for implementing the `matrix_power` function. Write a Python function `def matrix_power(a, n)` to solve the following problem:
Raise a square matrix to the (integer) power `n`. For positive integers `n`, the power is computed by repeated matrix squarings and matrix multiplications. If ``n == 0``, the identity matrix of the same shape as M is returned. If ``n < 0``, the inverse is computed and then raised to the ``abs(n)``. .. note:: Stacks of object matrices are not currently supported. Parameters ---------- a : (..., M, M) array_like Matrix to be "powered". n : int The exponent can be any integer or long integer, positive, negative, or zero. Returns ------- a**n : (..., M, M) ndarray or matrix object The return value is the same shape and type as `M`; if the exponent is positive or zero then the type of the elements is the same as those of `M`. If the exponent is negative the elements are floating-point. Raises ------ LinAlgError For matrices that are not square or that (for negative powers) cannot be inverted numerically. Examples -------- >>> from numpy.linalg import matrix_power >>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit >>> matrix_power(i, 3) # should = -i array([[ 0, -1], [ 1, 0]]) >>> matrix_power(i, 0) array([[1, 0], [0, 1]]) >>> matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements array([[ 0., 1.], [-1., 0.]]) Somewhat more sophisticated example >>> q = np.zeros((4, 4)) >>> q[0:2, 0:2] = -i >>> q[2:4, 2:4] = i >>> q # one of the three quaternion units not equal to 1 array([[ 0., -1., 0., 0.], [ 1., 0., 0., 0.], [ 0., 0., 0., 1.], [ 0., 0., -1., 0.]]) >>> matrix_power(q, 2) # = -np.eye(4) array([[-1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., -1.]])
Here is the function:
def matrix_power(a, n):
"""
Raise a square matrix to the (integer) power `n`.
For positive integers `n`, the power is computed by repeated matrix
squarings and matrix multiplications. If ``n == 0``, the identity matrix
of the same shape as M is returned. If ``n < 0``, the inverse
is computed and then raised to the ``abs(n)``.
.. note:: Stacks of object matrices are not currently supported.
Parameters
----------
a : (..., M, M) array_like
Matrix to be "powered".
n : int
The exponent can be any integer or long integer, positive,
negative, or zero.
Returns
-------
a**n : (..., M, M) ndarray or matrix object
The return value is the same shape and type as `M`;
if the exponent is positive or zero then the type of the
elements is the same as those of `M`. If the exponent is
negative the elements are floating-point.
Raises
------
LinAlgError
For matrices that are not square or that (for negative powers) cannot
be inverted numerically.
Examples
--------
>>> from numpy.linalg import matrix_power
>>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
>>> matrix_power(i, 3) # should = -i
array([[ 0, -1],
[ 1, 0]])
>>> matrix_power(i, 0)
array([[1, 0],
[0, 1]])
>>> matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements
array([[ 0., 1.],
[-1., 0.]])
Somewhat more sophisticated example
>>> q = np.zeros((4, 4))
>>> q[0:2, 0:2] = -i
>>> q[2:4, 2:4] = i
>>> q # one of the three quaternion units not equal to 1
array([[ 0., -1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 0., 0., 1.],
[ 0., 0., -1., 0.]])
>>> matrix_power(q, 2) # = -np.eye(4)
array([[-1., 0., 0., 0.],
[ 0., -1., 0., 0.],
[ 0., 0., -1., 0.],
[ 0., 0., 0., -1.]])
"""
a = asanyarray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
try:
n = operator.index(n)
except TypeError as e:
raise TypeError("exponent must be an integer") from e
# Fall back on dot for object arrays. Object arrays are not supported by
# the current implementation of matmul using einsum
if a.dtype != object:
fmatmul = matmul
elif a.ndim == 2:
fmatmul = dot
else:
raise NotImplementedError(
"matrix_power not supported for stacks of object arrays")
if n == 0:
a = empty_like(a)
a[...] = eye(a.shape[-2], dtype=a.dtype)
return a
elif n < 0:
a = inv(a)
n = abs(n)
# short-cuts.
if n == 1:
return a
elif n == 2:
return fmatmul(a, a)
elif n == 3:
return fmatmul(fmatmul(a, a), a)
# Use binary decomposition to reduce the number of matrix multiplications.
# Here, we iterate over the bits of n, from LSB to MSB, raise `a` to
# increasing powers of 2, and multiply into the result as needed.
z = result = None
while n > 0:
z = a if z is None else fmatmul(z, z)
n, bit = divmod(n, 2)
if bit:
result = z if result is None else fmatmul(result, z)
return result | Raise a square matrix to the (integer) power `n`. For positive integers `n`, the power is computed by repeated matrix squarings and matrix multiplications. If ``n == 0``, the identity matrix of the same shape as M is returned. If ``n < 0``, the inverse is computed and then raised to the ``abs(n)``. .. note:: Stacks of object matrices are not currently supported. Parameters ---------- a : (..., M, M) array_like Matrix to be "powered". n : int The exponent can be any integer or long integer, positive, negative, or zero. Returns ------- a**n : (..., M, M) ndarray or matrix object The return value is the same shape and type as `M`; if the exponent is positive or zero then the type of the elements is the same as those of `M`. If the exponent is negative the elements are floating-point. Raises ------ LinAlgError For matrices that are not square or that (for negative powers) cannot be inverted numerically. Examples -------- >>> from numpy.linalg import matrix_power >>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit >>> matrix_power(i, 3) # should = -i array([[ 0, -1], [ 1, 0]]) >>> matrix_power(i, 0) array([[1, 0], [0, 1]]) >>> matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements array([[ 0., 1.], [-1., 0.]]) Somewhat more sophisticated example >>> q = np.zeros((4, 4)) >>> q[0:2, 0:2] = -i >>> q[2:4, 2:4] = i >>> q # one of the three quaternion units not equal to 1 array([[ 0., -1., 0., 0.], [ 1., 0., 0., 0.], [ 0., 0., 0., 1.], [ 0., 0., -1., 0.]]) >>> matrix_power(q, 2) # = -np.eye(4) array([[-1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., -1.]]) |
168,595 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _raise_linalgerror_nonposdef(err, flag):
raise LinAlgError("Matrix is not positive definite")
def get_linalg_error_extobj(callback):
extobj = list(_linalg_error_extobj) # make a copy
extobj[2] = callback
return extobj
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def isComplexType(t):
return issubclass(t, complexfloating)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
The provided code snippet includes necessary dependencies for implementing the `cholesky` function. Write a Python function `def cholesky(a)` to solve the following problem:
Cholesky decomposition. Return the Cholesky decomposition, `L * L.H`, of the square matrix `a`, where `L` is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if `a` is real-valued). `a` must be Hermitian (symmetric if real-valued) and positive-definite. No checking is performed to verify whether `a` is Hermitian or not. In addition, only the lower-triangular and diagonal elements of `a` are used. Only `L` is actually returned. Parameters ---------- a : (..., M, M) array_like Hermitian (symmetric if all elements are real), positive-definite input matrix. Returns ------- L : (..., M, M) array_like Lower-triangular Cholesky factor of `a`. Returns a matrix object if `a` is a matrix object. Raises ------ LinAlgError If the decomposition fails, for example, if `a` is not positive-definite. See Also -------- scipy.linalg.cholesky : Similar function in SciPy. scipy.linalg.cholesky_banded : Cholesky decompose a banded Hermitian positive-definite matrix. scipy.linalg.cho_factor : Cholesky decomposition of a matrix, to use in `scipy.linalg.cho_solve`. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. The Cholesky decomposition is often used as a fast way of solving .. math:: A \\mathbf{x} = \\mathbf{b} (when `A` is both Hermitian/symmetric and positive-definite). First, we solve for :math:`\\mathbf{y}` in .. math:: L \\mathbf{y} = \\mathbf{b}, and then for :math:`\\mathbf{x}` in .. math:: L.H \\mathbf{x} = \\mathbf{y}. Examples -------- >>> A = np.array([[1,-2j],[2j,5]]) >>> A array([[ 1.+0.j, -0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> L = np.linalg.cholesky(A) >>> L array([[1.+0.j, 0.+0.j], [0.+2.j, 1.+0.j]]) >>> np.dot(L, L.T.conj()) # verify that L * L.H = A array([[1.+0.j, 0.-2.j], [0.+2.j, 5.+0.j]]) >>> A = [[1,-2j],[2j,5]] # what happens if A is only array_like? >>> np.linalg.cholesky(A) # an ndarray object is returned array([[1.+0.j, 0.+0.j], [0.+2.j, 1.+0.j]]) >>> # But a matrix object is returned if A is a matrix object >>> np.linalg.cholesky(np.matrix(A)) matrix([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]])
Here is the function:
def cholesky(a):
"""
Cholesky decomposition.
Return the Cholesky decomposition, `L * L.H`, of the square matrix `a`,
where `L` is lower-triangular and .H is the conjugate transpose operator
(which is the ordinary transpose if `a` is real-valued). `a` must be
Hermitian (symmetric if real-valued) and positive-definite. No
checking is performed to verify whether `a` is Hermitian or not.
In addition, only the lower-triangular and diagonal elements of `a`
are used. Only `L` is actually returned.
Parameters
----------
a : (..., M, M) array_like
Hermitian (symmetric if all elements are real), positive-definite
input matrix.
Returns
-------
L : (..., M, M) array_like
Lower-triangular Cholesky factor of `a`. Returns a matrix object if
`a` is a matrix object.
Raises
------
LinAlgError
If the decomposition fails, for example, if `a` is not
positive-definite.
See Also
--------
scipy.linalg.cholesky : Similar function in SciPy.
scipy.linalg.cholesky_banded : Cholesky decompose a banded Hermitian
positive-definite matrix.
scipy.linalg.cho_factor : Cholesky decomposition of a matrix, to use in
`scipy.linalg.cho_solve`.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
The Cholesky decomposition is often used as a fast way of solving
.. math:: A \\mathbf{x} = \\mathbf{b}
(when `A` is both Hermitian/symmetric and positive-definite).
First, we solve for :math:`\\mathbf{y}` in
.. math:: L \\mathbf{y} = \\mathbf{b},
and then for :math:`\\mathbf{x}` in
.. math:: L.H \\mathbf{x} = \\mathbf{y}.
Examples
--------
>>> A = np.array([[1,-2j],[2j,5]])
>>> A
array([[ 1.+0.j, -0.-2.j],
[ 0.+2.j, 5.+0.j]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[1.+0.j, 0.+0.j],
[0.+2.j, 1.+0.j]])
>>> np.dot(L, L.T.conj()) # verify that L * L.H = A
array([[1.+0.j, 0.-2.j],
[0.+2.j, 5.+0.j]])
>>> A = [[1,-2j],[2j,5]] # what happens if A is only array_like?
>>> np.linalg.cholesky(A) # an ndarray object is returned
array([[1.+0.j, 0.+0.j],
[0.+2.j, 1.+0.j]])
>>> # But a matrix object is returned if A is a matrix object
>>> np.linalg.cholesky(np.matrix(A))
matrix([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
"""
extobj = get_linalg_error_extobj(_raise_linalgerror_nonposdef)
gufunc = _umath_linalg.cholesky_lo
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
signature = 'D->D' if isComplexType(t) else 'd->d'
r = gufunc(a, signature=signature, extobj=extobj)
return wrap(r.astype(result_t, copy=False)) | Cholesky decomposition. Return the Cholesky decomposition, `L * L.H`, of the square matrix `a`, where `L` is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if `a` is real-valued). `a` must be Hermitian (symmetric if real-valued) and positive-definite. No checking is performed to verify whether `a` is Hermitian or not. In addition, only the lower-triangular and diagonal elements of `a` are used. Only `L` is actually returned. Parameters ---------- a : (..., M, M) array_like Hermitian (symmetric if all elements are real), positive-definite input matrix. Returns ------- L : (..., M, M) array_like Lower-triangular Cholesky factor of `a`. Returns a matrix object if `a` is a matrix object. Raises ------ LinAlgError If the decomposition fails, for example, if `a` is not positive-definite. See Also -------- scipy.linalg.cholesky : Similar function in SciPy. scipy.linalg.cholesky_banded : Cholesky decompose a banded Hermitian positive-definite matrix. scipy.linalg.cho_factor : Cholesky decomposition of a matrix, to use in `scipy.linalg.cho_solve`. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. The Cholesky decomposition is often used as a fast way of solving .. math:: A \\mathbf{x} = \\mathbf{b} (when `A` is both Hermitian/symmetric and positive-definite). First, we solve for :math:`\\mathbf{y}` in .. math:: L \\mathbf{y} = \\mathbf{b}, and then for :math:`\\mathbf{x}` in .. math:: L.H \\mathbf{x} = \\mathbf{y}. Examples -------- >>> A = np.array([[1,-2j],[2j,5]]) >>> A array([[ 1.+0.j, -0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> L = np.linalg.cholesky(A) >>> L array([[1.+0.j, 0.+0.j], [0.+2.j, 1.+0.j]]) >>> np.dot(L, L.T.conj()) # verify that L * L.H = A array([[1.+0.j, 0.-2.j], [0.+2.j, 5.+0.j]]) >>> A = [[1,-2j],[2j,5]] # what happens if A is only array_like? >>> np.linalg.cholesky(A) # an ndarray object is returned array([[1.+0.j, 0.+0.j], [0.+2.j, 1.+0.j]]) >>> # But a matrix object is returned if A is a matrix object >>> np.linalg.cholesky(np.matrix(A)) matrix([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]]) |
168,596 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _qr_dispatcher(a, mode=None):
return (a,) | null |
168,597 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _raise_linalgerror_qr(err, flag):
raise LinAlgError("Incorrect argument found while performing "
"QR factorization")
def get_linalg_error_extobj(callback):
extobj = list(_linalg_error_extobj) # make a copy
extobj[2] = callback
return extobj
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def isComplexType(t):
return issubclass(t, complexfloating)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _to_native_byte_order(*arrays):
ret = []
for arr in arrays:
if arr.dtype.byteorder not in ('=', '|'):
ret.append(asarray(arr, dtype=arr.dtype.newbyteorder('=')))
else:
ret.append(arr)
if len(ret) == 1:
return ret[0]
else:
return ret
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def transpose(a):
"""
Transpose each matrix in a stack of matrices.
Unlike np.transpose, this only swaps the last two axes, rather than all of
them
Parameters
----------
a : (...,M,N) array_like
Returns
-------
aT : (...,N,M) ndarray
"""
return swapaxes(a, -1, -2)
def triu(m, k=0):
"""
Upper triangle of an array.
Return a copy of an array with the elements below the `k`-th diagonal
zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the
final two axes.
Please refer to the documentation for `tril` for further details.
See Also
--------
tril : lower triangle of an array
Examples
--------
>>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
>>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))
array([[[ 0, 1, 2, 3, 4],
[ 0, 6, 7, 8, 9],
[ 0, 0, 12, 13, 14],
[ 0, 0, 0, 18, 19]],
[[20, 21, 22, 23, 24],
[ 0, 26, 27, 28, 29],
[ 0, 0, 32, 33, 34],
[ 0, 0, 0, 38, 39]],
[[40, 41, 42, 43, 44],
[ 0, 46, 47, 48, 49],
[ 0, 0, 52, 53, 54],
[ 0, 0, 0, 58, 59]]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k-1, dtype=bool)
return where(mask, zeros(1, m.dtype), m)
The provided code snippet includes necessary dependencies for implementing the `qr` function. Write a Python function `def qr(a, mode='reduced')` to solve the following problem:
Compute the qr factorization of a matrix. Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is upper-triangular. Parameters ---------- a : array_like, shape (..., M, N) An array-like object with the dimensionality of at least 2. mode : {'reduced', 'complete', 'r', 'raw'}, optional If K = min(M, N), then * 'reduced' : returns q, r with dimensions (..., M, K), (..., K, N) (default) * 'complete' : returns q, r with dimensions (..., M, M), (..., M, N) * 'r' : returns r only with dimensions (..., K, N) * 'raw' : returns h, tau with dimensions (..., N, M), (..., K,) The options 'reduced', 'complete, and 'raw' are new in numpy 1.8, see the notes for more information. The default is 'reduced', and to maintain backward compatibility with earlier versions of numpy both it and the old default 'full' can be omitted. Note that array h returned in 'raw' mode is transposed for calling Fortran. The 'economic' mode is deprecated. The modes 'full' and 'economic' may be passed using only the first letter for backwards compatibility, but all others must be spelled out. See the Notes for more explanation. Returns ------- q : ndarray of float or complex, optional A matrix with orthonormal columns. When mode = 'complete' the result is an orthogonal/unitary matrix depending on whether or not a is real/complex. The determinant may be either +/- 1 in that case. In case the number of dimensions in the input array is greater than 2 then a stack of the matrices with above properties is returned. r : ndarray of float or complex, optional The upper-triangular matrix or a stack of upper-triangular matrices if the number of dimensions in the input array is greater than 2. (h, tau) : ndarrays of np.double or np.cdouble, optional The array h contains the Householder reflectors that generate q along with r. The tau array contains scaling factors for the reflectors. In the deprecated 'economic' mode only h is returned. Raises ------ LinAlgError If factoring fails. See Also -------- scipy.linalg.qr : Similar function in SciPy. scipy.linalg.rq : Compute RQ decomposition of a matrix. Notes ----- This is an interface to the LAPACK routines ``dgeqrf``, ``zgeqrf``, ``dorgqr``, and ``zungqr``. For more information on the qr factorization, see for example: https://en.wikipedia.org/wiki/QR_factorization Subclasses of `ndarray` are preserved except for the 'raw' mode. So if `a` is of type `matrix`, all the return values will be matrices too. New 'reduced', 'complete', and 'raw' options for mode were added in NumPy 1.8.0 and the old option 'full' was made an alias of 'reduced'. In addition the options 'full' and 'economic' were deprecated. Because 'full' was the previous default and 'reduced' is the new default, backward compatibility can be maintained by letting `mode` default. The 'raw' option was added so that LAPACK routines that can multiply arrays by q using the Householder reflectors can be used. Note that in this case the returned arrays are of type np.double or np.cdouble and the h array is transposed to be FORTRAN compatible. No routines using the 'raw' return are currently exposed by numpy, but some are available in lapack_lite and just await the necessary work. Examples -------- >>> a = np.random.randn(9, 6) >>> q, r = np.linalg.qr(a) >>> np.allclose(a, np.dot(q, r)) # a does equal qr True >>> r2 = np.linalg.qr(a, mode='r') >>> np.allclose(r, r2) # mode='r' returns the same r as mode='full' True >>> a = np.random.normal(size=(3, 2, 2)) # Stack of 2 x 2 matrices as input >>> q, r = np.linalg.qr(a) >>> q.shape (3, 2, 2) >>> r.shape (3, 2, 2) >>> np.allclose(a, np.matmul(q, r)) True Example illustrating a common use of `qr`: solving of least squares problems What are the least-squares-best `m` and `y0` in ``y = y0 + mx`` for the following data: {(0,1), (1,0), (1,2), (2,1)}. (Graph the points and you'll see that it should be y0 = 0, m = 1.) The answer is provided by solving the over-determined matrix equation ``Ax = b``, where:: A = array([[0, 1], [1, 1], [1, 1], [2, 1]]) x = array([[y0], [m]]) b = array([[1], [0], [2], [1]]) If A = qr such that q is orthonormal (which is always possible via Gram-Schmidt), then ``x = inv(r) * (q.T) * b``. (In numpy practice, however, we simply use `lstsq`.) >>> A = np.array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> A array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> b = np.array([1, 2, 2, 3]) >>> q, r = np.linalg.qr(A) >>> p = np.dot(q.T, b) >>> np.dot(np.linalg.inv(r), p) array([ 1., 1.])
Here is the function:
def qr(a, mode='reduced'):
"""
Compute the qr factorization of a matrix.
Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is
upper-triangular.
Parameters
----------
a : array_like, shape (..., M, N)
An array-like object with the dimensionality of at least 2.
mode : {'reduced', 'complete', 'r', 'raw'}, optional
If K = min(M, N), then
* 'reduced' : returns q, r with dimensions
(..., M, K), (..., K, N) (default)
* 'complete' : returns q, r with dimensions (..., M, M), (..., M, N)
* 'r' : returns r only with dimensions (..., K, N)
* 'raw' : returns h, tau with dimensions (..., N, M), (..., K,)
The options 'reduced', 'complete, and 'raw' are new in numpy 1.8,
see the notes for more information. The default is 'reduced', and to
maintain backward compatibility with earlier versions of numpy both
it and the old default 'full' can be omitted. Note that array h
returned in 'raw' mode is transposed for calling Fortran. The
'economic' mode is deprecated. The modes 'full' and 'economic' may
be passed using only the first letter for backwards compatibility,
but all others must be spelled out. See the Notes for more
explanation.
Returns
-------
q : ndarray of float or complex, optional
A matrix with orthonormal columns. When mode = 'complete' the
result is an orthogonal/unitary matrix depending on whether or not
a is real/complex. The determinant may be either +/- 1 in that
case. In case the number of dimensions in the input array is
greater than 2 then a stack of the matrices with above properties
is returned.
r : ndarray of float or complex, optional
The upper-triangular matrix or a stack of upper-triangular
matrices if the number of dimensions in the input array is greater
than 2.
(h, tau) : ndarrays of np.double or np.cdouble, optional
The array h contains the Householder reflectors that generate q
along with r. The tau array contains scaling factors for the
reflectors. In the deprecated 'economic' mode only h is returned.
Raises
------
LinAlgError
If factoring fails.
See Also
--------
scipy.linalg.qr : Similar function in SciPy.
scipy.linalg.rq : Compute RQ decomposition of a matrix.
Notes
-----
This is an interface to the LAPACK routines ``dgeqrf``, ``zgeqrf``,
``dorgqr``, and ``zungqr``.
For more information on the qr factorization, see for example:
https://en.wikipedia.org/wiki/QR_factorization
Subclasses of `ndarray` are preserved except for the 'raw' mode. So if
`a` is of type `matrix`, all the return values will be matrices too.
New 'reduced', 'complete', and 'raw' options for mode were added in
NumPy 1.8.0 and the old option 'full' was made an alias of 'reduced'. In
addition the options 'full' and 'economic' were deprecated. Because
'full' was the previous default and 'reduced' is the new default,
backward compatibility can be maintained by letting `mode` default.
The 'raw' option was added so that LAPACK routines that can multiply
arrays by q using the Householder reflectors can be used. Note that in
this case the returned arrays are of type np.double or np.cdouble and
the h array is transposed to be FORTRAN compatible. No routines using
the 'raw' return are currently exposed by numpy, but some are available
in lapack_lite and just await the necessary work.
Examples
--------
>>> a = np.random.randn(9, 6)
>>> q, r = np.linalg.qr(a)
>>> np.allclose(a, np.dot(q, r)) # a does equal qr
True
>>> r2 = np.linalg.qr(a, mode='r')
>>> np.allclose(r, r2) # mode='r' returns the same r as mode='full'
True
>>> a = np.random.normal(size=(3, 2, 2)) # Stack of 2 x 2 matrices as input
>>> q, r = np.linalg.qr(a)
>>> q.shape
(3, 2, 2)
>>> r.shape
(3, 2, 2)
>>> np.allclose(a, np.matmul(q, r))
True
Example illustrating a common use of `qr`: solving of least squares
problems
What are the least-squares-best `m` and `y0` in ``y = y0 + mx`` for
the following data: {(0,1), (1,0), (1,2), (2,1)}. (Graph the points
and you'll see that it should be y0 = 0, m = 1.) The answer is provided
by solving the over-determined matrix equation ``Ax = b``, where::
A = array([[0, 1], [1, 1], [1, 1], [2, 1]])
x = array([[y0], [m]])
b = array([[1], [0], [2], [1]])
If A = qr such that q is orthonormal (which is always possible via
Gram-Schmidt), then ``x = inv(r) * (q.T) * b``. (In numpy practice,
however, we simply use `lstsq`.)
>>> A = np.array([[0, 1], [1, 1], [1, 1], [2, 1]])
>>> A
array([[0, 1],
[1, 1],
[1, 1],
[2, 1]])
>>> b = np.array([1, 2, 2, 3])
>>> q, r = np.linalg.qr(A)
>>> p = np.dot(q.T, b)
>>> np.dot(np.linalg.inv(r), p)
array([ 1., 1.])
"""
if mode not in ('reduced', 'complete', 'r', 'raw'):
if mode in ('f', 'full'):
# 2013-04-01, 1.8
msg = "".join((
"The 'full' option is deprecated in favor of 'reduced'.\n",
"For backward compatibility let mode default."))
warnings.warn(msg, DeprecationWarning, stacklevel=3)
mode = 'reduced'
elif mode in ('e', 'economic'):
# 2013-04-01, 1.8
msg = "The 'economic' option is deprecated."
warnings.warn(msg, DeprecationWarning, stacklevel=3)
mode = 'economic'
else:
raise ValueError(f"Unrecognized mode '{mode}'")
a, wrap = _makearray(a)
_assert_stacked_2d(a)
m, n = a.shape[-2:]
t, result_t = _commonType(a)
a = a.astype(t, copy=True)
a = _to_native_byte_order(a)
mn = min(m, n)
if m <= n:
gufunc = _umath_linalg.qr_r_raw_m
else:
gufunc = _umath_linalg.qr_r_raw_n
signature = 'D->D' if isComplexType(t) else 'd->d'
extobj = get_linalg_error_extobj(_raise_linalgerror_qr)
tau = gufunc(a, signature=signature, extobj=extobj)
# handle modes that don't return q
if mode == 'r':
r = triu(a[..., :mn, :])
r = r.astype(result_t, copy=False)
return wrap(r)
if mode == 'raw':
q = transpose(a)
q = q.astype(result_t, copy=False)
tau = tau.astype(result_t, copy=False)
return wrap(q), tau
if mode == 'economic':
a = a.astype(result_t, copy=False)
return wrap(a)
# mc is the number of columns in the resulting q
# matrix. If the mode is complete then it is
# same as number of rows, and if the mode is reduced,
# then it is the minimum of number of rows and columns.
if mode == 'complete' and m > n:
mc = m
gufunc = _umath_linalg.qr_complete
else:
mc = mn
gufunc = _umath_linalg.qr_reduced
signature = 'DD->D' if isComplexType(t) else 'dd->d'
extobj = get_linalg_error_extobj(_raise_linalgerror_qr)
q = gufunc(a, tau, signature=signature, extobj=extobj)
r = triu(a[..., :mc, :])
q = q.astype(result_t, copy=False)
r = r.astype(result_t, copy=False)
return wrap(q), wrap(r) | Compute the qr factorization of a matrix. Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is upper-triangular. Parameters ---------- a : array_like, shape (..., M, N) An array-like object with the dimensionality of at least 2. mode : {'reduced', 'complete', 'r', 'raw'}, optional If K = min(M, N), then * 'reduced' : returns q, r with dimensions (..., M, K), (..., K, N) (default) * 'complete' : returns q, r with dimensions (..., M, M), (..., M, N) * 'r' : returns r only with dimensions (..., K, N) * 'raw' : returns h, tau with dimensions (..., N, M), (..., K,) The options 'reduced', 'complete, and 'raw' are new in numpy 1.8, see the notes for more information. The default is 'reduced', and to maintain backward compatibility with earlier versions of numpy both it and the old default 'full' can be omitted. Note that array h returned in 'raw' mode is transposed for calling Fortran. The 'economic' mode is deprecated. The modes 'full' and 'economic' may be passed using only the first letter for backwards compatibility, but all others must be spelled out. See the Notes for more explanation. Returns ------- q : ndarray of float or complex, optional A matrix with orthonormal columns. When mode = 'complete' the result is an orthogonal/unitary matrix depending on whether or not a is real/complex. The determinant may be either +/- 1 in that case. In case the number of dimensions in the input array is greater than 2 then a stack of the matrices with above properties is returned. r : ndarray of float or complex, optional The upper-triangular matrix or a stack of upper-triangular matrices if the number of dimensions in the input array is greater than 2. (h, tau) : ndarrays of np.double or np.cdouble, optional The array h contains the Householder reflectors that generate q along with r. The tau array contains scaling factors for the reflectors. In the deprecated 'economic' mode only h is returned. Raises ------ LinAlgError If factoring fails. See Also -------- scipy.linalg.qr : Similar function in SciPy. scipy.linalg.rq : Compute RQ decomposition of a matrix. Notes ----- This is an interface to the LAPACK routines ``dgeqrf``, ``zgeqrf``, ``dorgqr``, and ``zungqr``. For more information on the qr factorization, see for example: https://en.wikipedia.org/wiki/QR_factorization Subclasses of `ndarray` are preserved except for the 'raw' mode. So if `a` is of type `matrix`, all the return values will be matrices too. New 'reduced', 'complete', and 'raw' options for mode were added in NumPy 1.8.0 and the old option 'full' was made an alias of 'reduced'. In addition the options 'full' and 'economic' were deprecated. Because 'full' was the previous default and 'reduced' is the new default, backward compatibility can be maintained by letting `mode` default. The 'raw' option was added so that LAPACK routines that can multiply arrays by q using the Householder reflectors can be used. Note that in this case the returned arrays are of type np.double or np.cdouble and the h array is transposed to be FORTRAN compatible. No routines using the 'raw' return are currently exposed by numpy, but some are available in lapack_lite and just await the necessary work. Examples -------- >>> a = np.random.randn(9, 6) >>> q, r = np.linalg.qr(a) >>> np.allclose(a, np.dot(q, r)) # a does equal qr True >>> r2 = np.linalg.qr(a, mode='r') >>> np.allclose(r, r2) # mode='r' returns the same r as mode='full' True >>> a = np.random.normal(size=(3, 2, 2)) # Stack of 2 x 2 matrices as input >>> q, r = np.linalg.qr(a) >>> q.shape (3, 2, 2) >>> r.shape (3, 2, 2) >>> np.allclose(a, np.matmul(q, r)) True Example illustrating a common use of `qr`: solving of least squares problems What are the least-squares-best `m` and `y0` in ``y = y0 + mx`` for the following data: {(0,1), (1,0), (1,2), (2,1)}. (Graph the points and you'll see that it should be y0 = 0, m = 1.) The answer is provided by solving the over-determined matrix equation ``Ax = b``, where:: A = array([[0, 1], [1, 1], [1, 1], [2, 1]]) x = array([[y0], [m]]) b = array([[1], [0], [2], [1]]) If A = qr such that q is orthonormal (which is always possible via Gram-Schmidt), then ``x = inv(r) * (q.T) * b``. (In numpy practice, however, we simply use `lstsq`.) >>> A = np.array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> A array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> b = np.array([1, 2, 2, 3]) >>> q, r = np.linalg.qr(A) >>> p = np.dot(q.T, b) >>> np.dot(np.linalg.inv(r), p) array([ 1., 1.]) |
168,598 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _raise_linalgerror_eigenvalues_nonconvergence(err, flag):
raise LinAlgError("Eigenvalues did not converge")
def get_linalg_error_extobj(callback):
extobj = list(_linalg_error_extobj) # make a copy
extobj[2] = callback
return extobj
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def isComplexType(t):
return issubclass(t, complexfloating)
def _realType(t, default=double):
return _real_types_map.get(t, default)
def _complexType(t, default=cdouble):
return _complex_types_map.get(t, default)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
def _assert_finite(*arrays):
for a in arrays:
if not isfinite(a).all():
raise LinAlgError("Array must not contain infs or NaNs")
The provided code snippet includes necessary dependencies for implementing the `eigvals` function. Write a Python function `def eigvals(a)` to solve the following problem:
Compute the eigenvalues of a general matrix. Main difference between `eigvals` and `eig`: the eigenvectors aren't returned. Parameters ---------- a : (..., M, M) array_like A complex- or real-valued matrix whose eigenvalues will be computed. Returns ------- w : (..., M,) ndarray The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eig : eigenvalues and right eigenvectors of general arrays eigvalsh : eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays. eigh : eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays. scipy.linalg.eigvals : Similar function in SciPy. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the ``_geev`` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. Examples -------- Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, `Q`, and on the right by `Q.T` (the transpose of `Q`), preserves the eigenvalues of the "middle" matrix. In other words, if `Q` is orthogonal, then ``Q * A * Q.T`` has the same eigenvalues as ``A``: >>> from numpy import linalg as LA >>> x = np.random.random() >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]]) >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :]) (1.0, 1.0, 0.0) Now multiply a diagonal matrix by ``Q`` on one side and by ``Q.T`` on the other: >>> D = np.diag((-1,1)) >>> LA.eigvals(D) array([-1., 1.]) >>> A = np.dot(Q, D) >>> A = np.dot(A, Q.T) >>> LA.eigvals(A) array([ 1., -1.]) # random
Here is the function:
def eigvals(a):
"""
Compute the eigenvalues of a general matrix.
Main difference between `eigvals` and `eig`: the eigenvectors aren't
returned.
Parameters
----------
a : (..., M, M) array_like
A complex- or real-valued matrix whose eigenvalues will be computed.
Returns
-------
w : (..., M,) ndarray
The eigenvalues, each repeated according to its multiplicity.
They are not necessarily ordered, nor are they necessarily
real for real matrices.
Raises
------
LinAlgError
If the eigenvalue computation does not converge.
See Also
--------
eig : eigenvalues and right eigenvectors of general arrays
eigvalsh : eigenvalues of real symmetric or complex Hermitian
(conjugate symmetric) arrays.
eigh : eigenvalues and eigenvectors of real symmetric or complex
Hermitian (conjugate symmetric) arrays.
scipy.linalg.eigvals : Similar function in SciPy.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
This is implemented using the ``_geev`` LAPACK routines which compute
the eigenvalues and eigenvectors of general square arrays.
Examples
--------
Illustration, using the fact that the eigenvalues of a diagonal matrix
are its diagonal elements, that multiplying a matrix on the left
by an orthogonal matrix, `Q`, and on the right by `Q.T` (the transpose
of `Q`), preserves the eigenvalues of the "middle" matrix. In other words,
if `Q` is orthogonal, then ``Q * A * Q.T`` has the same eigenvalues as
``A``:
>>> from numpy import linalg as LA
>>> x = np.random.random()
>>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]])
>>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :])
(1.0, 1.0, 0.0)
Now multiply a diagonal matrix by ``Q`` on one side and by ``Q.T`` on the other:
>>> D = np.diag((-1,1))
>>> LA.eigvals(D)
array([-1., 1.])
>>> A = np.dot(Q, D)
>>> A = np.dot(A, Q.T)
>>> LA.eigvals(A)
array([ 1., -1.]) # random
"""
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
_assert_finite(a)
t, result_t = _commonType(a)
extobj = get_linalg_error_extobj(
_raise_linalgerror_eigenvalues_nonconvergence)
signature = 'D->D' if isComplexType(t) else 'd->D'
w = _umath_linalg.eigvals(a, signature=signature, extobj=extobj)
if not isComplexType(t):
if all(w.imag == 0):
w = w.real
result_t = _realType(result_t)
else:
result_t = _complexType(result_t)
return w.astype(result_t, copy=False) | Compute the eigenvalues of a general matrix. Main difference between `eigvals` and `eig`: the eigenvectors aren't returned. Parameters ---------- a : (..., M, M) array_like A complex- or real-valued matrix whose eigenvalues will be computed. Returns ------- w : (..., M,) ndarray The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eig : eigenvalues and right eigenvectors of general arrays eigvalsh : eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays. eigh : eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays. scipy.linalg.eigvals : Similar function in SciPy. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the ``_geev`` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. Examples -------- Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, `Q`, and on the right by `Q.T` (the transpose of `Q`), preserves the eigenvalues of the "middle" matrix. In other words, if `Q` is orthogonal, then ``Q * A * Q.T`` has the same eigenvalues as ``A``: >>> from numpy import linalg as LA >>> x = np.random.random() >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]]) >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :]) (1.0, 1.0, 0.0) Now multiply a diagonal matrix by ``Q`` on one side and by ``Q.T`` on the other: >>> D = np.diag((-1,1)) >>> LA.eigvals(D) array([-1., 1.]) >>> A = np.dot(Q, D) >>> A = np.dot(A, Q.T) >>> LA.eigvals(A) array([ 1., -1.]) # random |
168,599 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _eigvalsh_dispatcher(a, UPLO=None):
return (a,) | null |
168,600 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _convertarray(a):
t, result_t = _commonType(a)
a = a.astype(t).T.copy()
return a, t, result_t | null |
168,601 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _raise_linalgerror_eigenvalues_nonconvergence(err, flag):
raise LinAlgError("Eigenvalues did not converge")
def get_linalg_error_extobj(callback):
extobj = list(_linalg_error_extobj) # make a copy
extobj[2] = callback
return extobj
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def isComplexType(t):
return issubclass(t, complexfloating)
def _realType(t, default=double):
return _real_types_map.get(t, default)
def _complexType(t, default=cdouble):
return _complex_types_map.get(t, default)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
def _assert_finite(*arrays):
for a in arrays:
if not isfinite(a).all():
raise LinAlgError("Array must not contain infs or NaNs")
The provided code snippet includes necessary dependencies for implementing the `eig` function. Write a Python function `def eig(a)` to solve the following problem:
Compute the eigenvalues and right eigenvectors of a square array. Parameters ---------- a : (..., M, M) array Matrices for which the eigenvalues and right eigenvectors will be computed Returns ------- w : (..., M) array The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be of complex type, unless the imaginary part is zero in which case it will be cast to a real type. When `a` is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs v : (..., M, M) array The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]``. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eigvals : eigenvalues of a non-symmetric array. eigh : eigenvalues and eigenvectors of a real symmetric or complex Hermitian (conjugate symmetric) array. eigvalsh : eigenvalues of a real symmetric or complex Hermitian (conjugate symmetric) array. scipy.linalg.eig : Similar function in SciPy that also solves the generalized eigenvalue problem. scipy.linalg.schur : Best choice for unitary and other non-Hermitian normal matrices. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the ``_geev`` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. The number `w` is an eigenvalue of `a` if there exists a vector `v` such that ``a @ v = w * v``. Thus, the arrays `a`, `w`, and `v` satisfy the equations ``a @ v[:,i] = w[i] * v[:,i]`` for :math:`i \\in \\{0,...,M-1\\}`. The array `v` of eigenvectors may not be of maximum rank, that is, some of the columns may be linearly dependent, although round-off error may obscure that fact. If the eigenvalues are all different, then theoretically the eigenvectors are linearly independent and `a` can be diagonalized by a similarity transformation using `v`, i.e, ``inv(v) @ a @ v`` is diagonal. For non-Hermitian normal matrices the SciPy function `scipy.linalg.schur` is preferred because the matrix `v` is guaranteed to be unitary, which is not the case when using `eig`. The Schur factorization produces an upper triangular matrix rather than a diagonal matrix, but for normal matrices only the diagonal of the upper triangular matrix is needed, the rest is roundoff error. Finally, it is emphasized that `v` consists of the *right* (as in right-hand side) eigenvectors of `a`. A vector `y` satisfying ``y.T @ a = z * y.T`` for some number `z` is called a *left* eigenvector of `a`, and, in general, the left and right eigenvectors of a matrix are not necessarily the (perhaps conjugate) transposes of each other. References ---------- G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, Various pp. Examples -------- >>> from numpy import linalg as LA (Almost) trivial example with real e-values and e-vectors. >>> w, v = LA.eig(np.diag((1, 2, 3))) >>> w; v array([1., 2., 3.]) array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) Real matrix possessing complex e-values and e-vectors; note that the e-values are complex conjugates of each other. >>> w, v = LA.eig(np.array([[1, -1], [1, 1]])) >>> w; v array([1.+1.j, 1.-1.j]) array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]]) Complex-valued matrix with real e-values (but complex-valued e-vectors); note that ``a.conj().T == a``, i.e., `a` is Hermitian. >>> a = np.array([[1, 1j], [-1j, 1]]) >>> w, v = LA.eig(a) >>> w; v array([2.+0.j, 0.+0.j]) array([[ 0. +0.70710678j, 0.70710678+0.j ], # may vary [ 0.70710678+0.j , -0. +0.70710678j]]) Be careful about round-off error! >>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]]) >>> # Theor. e-values are 1 +/- 1e-9 >>> w, v = LA.eig(a) >>> w; v array([1., 1.]) array([[1., 0.], [0., 1.]])
Here is the function:
def eig(a):
"""
Compute the eigenvalues and right eigenvectors of a square array.
Parameters
----------
a : (..., M, M) array
Matrices for which the eigenvalues and right eigenvectors will
be computed
Returns
-------
w : (..., M) array
The eigenvalues, each repeated according to its multiplicity.
The eigenvalues are not necessarily ordered. The resulting
array will be of complex type, unless the imaginary part is
zero in which case it will be cast to a real type. When `a`
is real the resulting eigenvalues will be real (0 imaginary
part) or occur in conjugate pairs
v : (..., M, M) array
The normalized (unit "length") eigenvectors, such that the
column ``v[:,i]`` is the eigenvector corresponding to the
eigenvalue ``w[i]``.
Raises
------
LinAlgError
If the eigenvalue computation does not converge.
See Also
--------
eigvals : eigenvalues of a non-symmetric array.
eigh : eigenvalues and eigenvectors of a real symmetric or complex
Hermitian (conjugate symmetric) array.
eigvalsh : eigenvalues of a real symmetric or complex Hermitian
(conjugate symmetric) array.
scipy.linalg.eig : Similar function in SciPy that also solves the
generalized eigenvalue problem.
scipy.linalg.schur : Best choice for unitary and other non-Hermitian
normal matrices.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
This is implemented using the ``_geev`` LAPACK routines which compute
the eigenvalues and eigenvectors of general square arrays.
The number `w` is an eigenvalue of `a` if there exists a vector
`v` such that ``a @ v = w * v``. Thus, the arrays `a`, `w`, and
`v` satisfy the equations ``a @ v[:,i] = w[i] * v[:,i]``
for :math:`i \\in \\{0,...,M-1\\}`.
The array `v` of eigenvectors may not be of maximum rank, that is, some
of the columns may be linearly dependent, although round-off error may
obscure that fact. If the eigenvalues are all different, then theoretically
the eigenvectors are linearly independent and `a` can be diagonalized by
a similarity transformation using `v`, i.e, ``inv(v) @ a @ v`` is diagonal.
For non-Hermitian normal matrices the SciPy function `scipy.linalg.schur`
is preferred because the matrix `v` is guaranteed to be unitary, which is
not the case when using `eig`. The Schur factorization produces an
upper triangular matrix rather than a diagonal matrix, but for normal
matrices only the diagonal of the upper triangular matrix is needed, the
rest is roundoff error.
Finally, it is emphasized that `v` consists of the *right* (as in
right-hand side) eigenvectors of `a`. A vector `y` satisfying
``y.T @ a = z * y.T`` for some number `z` is called a *left*
eigenvector of `a`, and, in general, the left and right eigenvectors
of a matrix are not necessarily the (perhaps conjugate) transposes
of each other.
References
----------
G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL,
Academic Press, Inc., 1980, Various pp.
Examples
--------
>>> from numpy import linalg as LA
(Almost) trivial example with real e-values and e-vectors.
>>> w, v = LA.eig(np.diag((1, 2, 3)))
>>> w; v
array([1., 2., 3.])
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
Real matrix possessing complex e-values and e-vectors; note that the
e-values are complex conjugates of each other.
>>> w, v = LA.eig(np.array([[1, -1], [1, 1]]))
>>> w; v
array([1.+1.j, 1.-1.j])
array([[0.70710678+0.j , 0.70710678-0.j ],
[0. -0.70710678j, 0. +0.70710678j]])
Complex-valued matrix with real e-values (but complex-valued e-vectors);
note that ``a.conj().T == a``, i.e., `a` is Hermitian.
>>> a = np.array([[1, 1j], [-1j, 1]])
>>> w, v = LA.eig(a)
>>> w; v
array([2.+0.j, 0.+0.j])
array([[ 0. +0.70710678j, 0.70710678+0.j ], # may vary
[ 0.70710678+0.j , -0. +0.70710678j]])
Be careful about round-off error!
>>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]])
>>> # Theor. e-values are 1 +/- 1e-9
>>> w, v = LA.eig(a)
>>> w; v
array([1., 1.])
array([[1., 0.],
[0., 1.]])
"""
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
_assert_finite(a)
t, result_t = _commonType(a)
extobj = get_linalg_error_extobj(
_raise_linalgerror_eigenvalues_nonconvergence)
signature = 'D->DD' if isComplexType(t) else 'd->DD'
w, vt = _umath_linalg.eig(a, signature=signature, extobj=extobj)
if not isComplexType(t) and all(w.imag == 0.0):
w = w.real
vt = vt.real
result_t = _realType(result_t)
else:
result_t = _complexType(result_t)
vt = vt.astype(result_t, copy=False)
return w.astype(result_t, copy=False), wrap(vt) | Compute the eigenvalues and right eigenvectors of a square array. Parameters ---------- a : (..., M, M) array Matrices for which the eigenvalues and right eigenvectors will be computed Returns ------- w : (..., M) array The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be of complex type, unless the imaginary part is zero in which case it will be cast to a real type. When `a` is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs v : (..., M, M) array The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]``. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eigvals : eigenvalues of a non-symmetric array. eigh : eigenvalues and eigenvectors of a real symmetric or complex Hermitian (conjugate symmetric) array. eigvalsh : eigenvalues of a real symmetric or complex Hermitian (conjugate symmetric) array. scipy.linalg.eig : Similar function in SciPy that also solves the generalized eigenvalue problem. scipy.linalg.schur : Best choice for unitary and other non-Hermitian normal matrices. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the ``_geev`` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. The number `w` is an eigenvalue of `a` if there exists a vector `v` such that ``a @ v = w * v``. Thus, the arrays `a`, `w`, and `v` satisfy the equations ``a @ v[:,i] = w[i] * v[:,i]`` for :math:`i \\in \\{0,...,M-1\\}`. The array `v` of eigenvectors may not be of maximum rank, that is, some of the columns may be linearly dependent, although round-off error may obscure that fact. If the eigenvalues are all different, then theoretically the eigenvectors are linearly independent and `a` can be diagonalized by a similarity transformation using `v`, i.e, ``inv(v) @ a @ v`` is diagonal. For non-Hermitian normal matrices the SciPy function `scipy.linalg.schur` is preferred because the matrix `v` is guaranteed to be unitary, which is not the case when using `eig`. The Schur factorization produces an upper triangular matrix rather than a diagonal matrix, but for normal matrices only the diagonal of the upper triangular matrix is needed, the rest is roundoff error. Finally, it is emphasized that `v` consists of the *right* (as in right-hand side) eigenvectors of `a`. A vector `y` satisfying ``y.T @ a = z * y.T`` for some number `z` is called a *left* eigenvector of `a`, and, in general, the left and right eigenvectors of a matrix are not necessarily the (perhaps conjugate) transposes of each other. References ---------- G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, Various pp. Examples -------- >>> from numpy import linalg as LA (Almost) trivial example with real e-values and e-vectors. >>> w, v = LA.eig(np.diag((1, 2, 3))) >>> w; v array([1., 2., 3.]) array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) Real matrix possessing complex e-values and e-vectors; note that the e-values are complex conjugates of each other. >>> w, v = LA.eig(np.array([[1, -1], [1, 1]])) >>> w; v array([1.+1.j, 1.-1.j]) array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]]) Complex-valued matrix with real e-values (but complex-valued e-vectors); note that ``a.conj().T == a``, i.e., `a` is Hermitian. >>> a = np.array([[1, 1j], [-1j, 1]]) >>> w, v = LA.eig(a) >>> w; v array([2.+0.j, 0.+0.j]) array([[ 0. +0.70710678j, 0.70710678+0.j ], # may vary [ 0.70710678+0.j , -0. +0.70710678j]]) Be careful about round-off error! >>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]]) >>> # Theor. e-values are 1 +/- 1e-9 >>> w, v = LA.eig(a) >>> w; v array([1., 1.]) array([[1., 0.], [0., 1.]]) |
168,602 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _svd_dispatcher(a, full_matrices=None, compute_uv=None, hermitian=None):
return (a,) | null |
168,603 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _cond_dispatcher(x, p=None):
return (x,) | null |
168,604 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
class LinAlgError(Exception):
"""
Generic Python-exception-derived object raised by linalg functions.
General purpose exception class, derived from Python's exception.Exception
class, programmatically raised in linalg functions when a Linear
Algebra-related condition would prevent further correct execution of the
function.
Parameters
----------
None
Examples
--------
>>> from numpy import linalg as LA
>>> LA.inv(np.zeros((2,2)))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "...linalg.py", line 350,
in inv return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
File "...linalg.py", line 249,
in solve
raise LinAlgError('Singular matrix')
numpy.linalg.LinAlgError: Singular matrix
"""
def isComplexType(t):
return issubclass(t, complexfloating)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
def _is_empty_2d(arr):
# check size first for efficiency
return arr.size == 0 and product(arr.shape[-2:]) == 0
def inv(a):
"""
Compute the (multiplicative) inverse of a matrix.
Given a square matrix `a`, return the matrix `ainv` satisfying
``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``.
Parameters
----------
a : (..., M, M) array_like
Matrix to be inverted.
Returns
-------
ainv : (..., M, M) ndarray or matrix
(Multiplicative) inverse of the matrix `a`.
Raises
------
LinAlgError
If `a` is not square or inversion fails.
See Also
--------
scipy.linalg.inv : Similar function in SciPy.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
Examples
--------
>>> from numpy.linalg import inv
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = inv(a)
>>> np.allclose(np.dot(a, ainv), np.eye(2))
True
>>> np.allclose(np.dot(ainv, a), np.eye(2))
True
If a is a matrix object, then the return value is a matrix as well:
>>> ainv = inv(np.matrix(a))
>>> ainv
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
Inverses of several matrices can be computed at once:
>>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]])
>>> inv(a)
array([[[-2. , 1. ],
[ 1.5 , -0.5 ]],
[[-1.25, 0.75],
[ 0.75, -0.25]]])
"""
a, wrap = _makearray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
signature = 'D->D' if isComplexType(t) else 'd->d'
extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
ainv = _umath_linalg.inv(a, signature=signature, extobj=extobj)
return wrap(ainv.astype(result_t, copy=False))
def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
"""
Singular Value Decomposition.
When `a` is a 2D array, and ``full_matrices=False``, then it is
factorized as ``u @ np.diag(s) @ vh = (u * s) @ vh``, where
`u` and the Hermitian transpose of `vh` are 2D arrays with
orthonormal columns and `s` is a 1D array of `a`'s singular
values. When `a` is higher-dimensional, SVD is applied in
stacked mode as explained below.
Parameters
----------
a : (..., M, N) array_like
A real or complex array with ``a.ndim >= 2``.
full_matrices : bool, optional
If True (default), `u` and `vh` have the shapes ``(..., M, M)`` and
``(..., N, N)``, respectively. Otherwise, the shapes are
``(..., M, K)`` and ``(..., K, N)``, respectively, where
``K = min(M, N)``.
compute_uv : bool, optional
Whether or not to compute `u` and `vh` in addition to `s`. True
by default.
hermitian : bool, optional
If True, `a` is assumed to be Hermitian (symmetric if real-valued),
enabling a more efficient method for finding singular values.
Defaults to False.
.. versionadded:: 1.17.0
Returns
-------
u : { (..., M, M), (..., M, K) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
s : (..., K) array
Vector(s) with the singular values, within each vector sorted in
descending order. The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`.
vh : { (..., N, N), (..., K, N) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
Raises
------
LinAlgError
If SVD computation does not converge.
See Also
--------
scipy.linalg.svd : Similar function in SciPy.
scipy.linalg.svdvals : Compute singular values of a matrix.
Notes
-----
.. versionchanged:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
The decomposition is performed using LAPACK routine ``_gesdd``.
SVD is usually described for the factorization of a 2D matrix :math:`A`.
The higher-dimensional case will be discussed below. In the 2D case, SVD is
written as :math:`A = U S V^H`, where :math:`A = a`, :math:`U= u`,
:math:`S= \\mathtt{np.diag}(s)` and :math:`V^H = vh`. The 1D array `s`
contains the singular values of `a` and `u` and `vh` are unitary. The rows
of `vh` are the eigenvectors of :math:`A^H A` and the columns of `u` are
the eigenvectors of :math:`A A^H`. In both cases the corresponding
(possibly non-zero) eigenvalues are given by ``s**2``.
If `a` has more than two dimensions, then broadcasting rules apply, as
explained in :ref:`routines.linalg-broadcasting`. This means that SVD is
working in "stacked" mode: it iterates over all indices of the first
``a.ndim - 2`` dimensions and for each combination SVD is applied to the
last two indices. The matrix `a` can be reconstructed from the
decomposition with either ``(u * s[..., None, :]) @ vh`` or
``u @ (s[..., None] * vh)``. (The ``@`` operator can be replaced by the
function ``np.matmul`` for python versions below 3.5.)
If `a` is a ``matrix`` object (as opposed to an ``ndarray``), then so are
all the return values.
Examples
--------
>>> a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6)
>>> b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3)
Reconstruction based on full SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((9, 9), (6,), (6, 6))
>>> np.allclose(a, np.dot(u[:, :6] * s, vh))
True
>>> smat = np.zeros((9, 6), dtype=complex)
>>> smat[:6, :6] = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on reduced SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((9, 6), (6,), (6, 6))
>>> np.allclose(a, np.dot(u * s, vh))
True
>>> smat = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on full SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u[..., :3] * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u[..., :3], s[..., None] * vh))
True
Reconstruction based on reduced SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u, s[..., None] * vh))
True
"""
import numpy as _nx
a, wrap = _makearray(a)
if hermitian:
# note: lapack svd returns eigenvalues with s ** 2 sorted descending,
# but eig returns s sorted ascending, so we re-order the eigenvalues
# and related arrays to have the correct order
if compute_uv:
s, u = eigh(a)
sgn = sign(s)
s = abs(s)
sidx = argsort(s)[..., ::-1]
sgn = _nx.take_along_axis(sgn, sidx, axis=-1)
s = _nx.take_along_axis(s, sidx, axis=-1)
u = _nx.take_along_axis(u, sidx[..., None, :], axis=-1)
# singular values are unsigned, move the sign into v
vt = transpose(u * sgn[..., None, :]).conjugate()
return wrap(u), s, wrap(vt)
else:
s = eigvalsh(a)
s = abs(s)
return sort(s)[..., ::-1]
_assert_stacked_2d(a)
t, result_t = _commonType(a)
extobj = get_linalg_error_extobj(_raise_linalgerror_svd_nonconvergence)
m, n = a.shape[-2:]
if compute_uv:
if full_matrices:
if m < n:
gufunc = _umath_linalg.svd_m_f
else:
gufunc = _umath_linalg.svd_n_f
else:
if m < n:
gufunc = _umath_linalg.svd_m_s
else:
gufunc = _umath_linalg.svd_n_s
signature = 'D->DdD' if isComplexType(t) else 'd->ddd'
u, s, vh = gufunc(a, signature=signature, extobj=extobj)
u = u.astype(result_t, copy=False)
s = s.astype(_realType(result_t), copy=False)
vh = vh.astype(result_t, copy=False)
return wrap(u), s, wrap(vh)
else:
if m < n:
gufunc = _umath_linalg.svd_m
else:
gufunc = _umath_linalg.svd_n
signature = 'D->d' if isComplexType(t) else 'd->d'
s = gufunc(a, signature=signature, extobj=extobj)
s = s.astype(_realType(result_t), copy=False)
return s
def norm(x, ord=None, axis=None, keepdims=False):
"""
Matrix or vector norm.
This function is able to return one of eight different matrix norms,
or one of an infinite number of vector norms (described below), depending
on the value of the ``ord`` parameter.
Parameters
----------
x : array_like
Input array. If `axis` is None, `x` must be 1-D or 2-D, unless `ord`
is None. If both `axis` and `ord` are None, the 2-norm of
``x.ravel`` will be returned.
ord : {non-zero int, inf, -inf, 'fro', 'nuc'}, optional
Order of the norm (see table under ``Notes``). inf means numpy's
`inf` object. The default is None.
axis : {None, int, 2-tuple of ints}, optional.
If `axis` is an integer, it specifies the axis of `x` along which to
compute the vector norms. If `axis` is a 2-tuple, it specifies the
axes that hold 2-D matrices, and the matrix norms of these matrices
are computed. If `axis` is None then either a vector norm (when `x`
is 1-D) or a matrix norm (when `x` is 2-D) is returned. The default
is None.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are normed over are left in the
result as dimensions with size one. With this option the result will
broadcast correctly against the original `x`.
.. versionadded:: 1.10.0
Returns
-------
n : float or ndarray
Norm of the matrix or vector(s).
See Also
--------
scipy.linalg.norm : Similar function in SciPy.
Notes
-----
For values of ``ord < 1``, the result is, strictly speaking, not a
mathematical 'norm', but it may still be useful for various numerical
purposes.
The following norms can be calculated:
===== ============================ ==========================
ord norm for matrices norm for vectors
===== ============================ ==========================
None Frobenius norm 2-norm
'fro' Frobenius norm --
'nuc' nuclear norm --
inf max(sum(abs(x), axis=1)) max(abs(x))
-inf min(sum(abs(x), axis=1)) min(abs(x))
0 -- sum(x != 0)
1 max(sum(abs(x), axis=0)) as below
-1 min(sum(abs(x), axis=0)) as below
2 2-norm (largest sing. value) as below
-2 smallest singular value as below
other -- sum(abs(x)**ord)**(1./ord)
===== ============================ ==========================
The Frobenius norm is given by [1]_:
:math:`||A||_F = [\\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
The nuclear norm is the sum of the singular values.
Both the Frobenius and nuclear norm orders are only defined for
matrices and raise a ValueError when ``x.ndim != 2``.
References
----------
.. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15
Examples
--------
>>> from numpy import linalg as LA
>>> a = np.arange(9) - 4
>>> a
array([-4, -3, -2, ..., 2, 3, 4])
>>> b = a.reshape((3, 3))
>>> b
array([[-4, -3, -2],
[-1, 0, 1],
[ 2, 3, 4]])
>>> LA.norm(a)
7.745966692414834
>>> LA.norm(b)
7.745966692414834
>>> LA.norm(b, 'fro')
7.745966692414834
>>> LA.norm(a, np.inf)
4.0
>>> LA.norm(b, np.inf)
9.0
>>> LA.norm(a, -np.inf)
0.0
>>> LA.norm(b, -np.inf)
2.0
>>> LA.norm(a, 1)
20.0
>>> LA.norm(b, 1)
7.0
>>> LA.norm(a, -1)
-4.6566128774142013e-010
>>> LA.norm(b, -1)
6.0
>>> LA.norm(a, 2)
7.745966692414834
>>> LA.norm(b, 2)
7.3484692283495345
>>> LA.norm(a, -2)
0.0
>>> LA.norm(b, -2)
1.8570331885190563e-016 # may vary
>>> LA.norm(a, 3)
5.8480354764257312 # may vary
>>> LA.norm(a, -3)
0.0
Using the `axis` argument to compute vector norms:
>>> c = np.array([[ 1, 2, 3],
... [-1, 1, 4]])
>>> LA.norm(c, axis=0)
array([ 1.41421356, 2.23606798, 5. ])
>>> LA.norm(c, axis=1)
array([ 3.74165739, 4.24264069])
>>> LA.norm(c, ord=1, axis=1)
array([ 6., 6.])
Using the `axis` argument to compute matrix norms:
>>> m = np.arange(8).reshape(2,2,2)
>>> LA.norm(m, axis=(1,2))
array([ 3.74165739, 11.22497216])
>>> LA.norm(m[0, :, :]), LA.norm(m[1, :, :])
(3.7416573867739413, 11.224972160321824)
"""
x = asarray(x)
if not issubclass(x.dtype.type, (inexact, object_)):
x = x.astype(float)
# Immediately handle some default, simple, fast, and common cases.
if axis is None:
ndim = x.ndim
if ((ord is None) or
(ord in ('f', 'fro') and ndim == 2) or
(ord == 2 and ndim == 1)):
x = x.ravel(order='K')
if isComplexType(x.dtype.type):
x_real = x.real
x_imag = x.imag
sqnorm = x_real.dot(x_real) + x_imag.dot(x_imag)
else:
sqnorm = x.dot(x)
ret = sqrt(sqnorm)
if keepdims:
ret = ret.reshape(ndim*[1])
return ret
# Normalize the `axis` argument to a tuple.
nd = x.ndim
if axis is None:
axis = tuple(range(nd))
elif not isinstance(axis, tuple):
try:
axis = int(axis)
except Exception as e:
raise TypeError("'axis' must be None, an integer or a tuple of integers") from e
axis = (axis,)
if len(axis) == 1:
if ord == Inf:
return abs(x).max(axis=axis, keepdims=keepdims)
elif ord == -Inf:
return abs(x).min(axis=axis, keepdims=keepdims)
elif ord == 0:
# Zero norm
return (x != 0).astype(x.real.dtype).sum(axis=axis, keepdims=keepdims)
elif ord == 1:
# special case for speedup
return add.reduce(abs(x), axis=axis, keepdims=keepdims)
elif ord is None or ord == 2:
# special case for speedup
s = (x.conj() * x).real
return sqrt(add.reduce(s, axis=axis, keepdims=keepdims))
# None of the str-type keywords for ord ('fro', 'nuc')
# are valid for vectors
elif isinstance(ord, str):
raise ValueError(f"Invalid norm order '{ord}' for vectors")
else:
absx = abs(x)
absx **= ord
ret = add.reduce(absx, axis=axis, keepdims=keepdims)
ret **= reciprocal(ord, dtype=ret.dtype)
return ret
elif len(axis) == 2:
row_axis, col_axis = axis
row_axis = normalize_axis_index(row_axis, nd)
col_axis = normalize_axis_index(col_axis, nd)
if row_axis == col_axis:
raise ValueError('Duplicate axes given.')
if ord == 2:
ret = _multi_svd_norm(x, row_axis, col_axis, amax)
elif ord == -2:
ret = _multi_svd_norm(x, row_axis, col_axis, amin)
elif ord == 1:
if col_axis > row_axis:
col_axis -= 1
ret = add.reduce(abs(x), axis=row_axis).max(axis=col_axis)
elif ord == Inf:
if row_axis > col_axis:
row_axis -= 1
ret = add.reduce(abs(x), axis=col_axis).max(axis=row_axis)
elif ord == -1:
if col_axis > row_axis:
col_axis -= 1
ret = add.reduce(abs(x), axis=row_axis).min(axis=col_axis)
elif ord == -Inf:
if row_axis > col_axis:
row_axis -= 1
ret = add.reduce(abs(x), axis=col_axis).min(axis=row_axis)
elif ord in [None, 'fro', 'f']:
ret = sqrt(add.reduce((x.conj() * x).real, axis=axis))
elif ord == 'nuc':
ret = _multi_svd_norm(x, row_axis, col_axis, sum)
else:
raise ValueError("Invalid norm order for matrices.")
if keepdims:
ret_shape = list(x.shape)
ret_shape[axis[0]] = 1
ret_shape[axis[1]] = 1
ret = ret.reshape(ret_shape)
return ret
else:
raise ValueError("Improper number of dimensions to norm.")
The provided code snippet includes necessary dependencies for implementing the `cond` function. Write a Python function `def cond(x, p=None)` to solve the following problem:
Compute the condition number of a matrix. This function is capable of returning the condition number using one of seven different norms, depending on the value of `p` (see Parameters below). Parameters ---------- x : (..., M, N) array_like The matrix whose condition number is sought. p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional Order of the norm used in the condition number computation: ===== ============================ p norm for matrices ===== ============================ None 2-norm, computed directly using the ``SVD`` 'fro' Frobenius norm inf max(sum(abs(x), axis=1)) -inf min(sum(abs(x), axis=1)) 1 max(sum(abs(x), axis=0)) -1 min(sum(abs(x), axis=0)) 2 2-norm (largest sing. value) -2 smallest singular value ===== ============================ inf means the `numpy.inf` object, and the Frobenius norm is the root-of-sum-of-squares norm. Returns ------- c : {float, inf} The condition number of the matrix. May be infinite. See Also -------- numpy.linalg.norm Notes ----- The condition number of `x` is defined as the norm of `x` times the norm of the inverse of `x` [1]_; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms. References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL, Academic Press, Inc., 1980, pg. 285. Examples -------- >>> from numpy import linalg as LA >>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]]) >>> a array([[ 1, 0, -1], [ 0, 1, 0], [ 1, 0, 1]]) >>> LA.cond(a) 1.4142135623730951 >>> LA.cond(a, 'fro') 3.1622776601683795 >>> LA.cond(a, np.inf) 2.0 >>> LA.cond(a, -np.inf) 1.0 >>> LA.cond(a, 1) 2.0 >>> LA.cond(a, -1) 1.0 >>> LA.cond(a, 2) 1.4142135623730951 >>> LA.cond(a, -2) 0.70710678118654746 # may vary >>> min(LA.svd(a, compute_uv=False))*min(LA.svd(LA.inv(a), compute_uv=False)) 0.70710678118654746 # may vary
Here is the function:
def cond(x, p=None):
"""
Compute the condition number of a matrix.
This function is capable of returning the condition number using
one of seven different norms, depending on the value of `p` (see
Parameters below).
Parameters
----------
x : (..., M, N) array_like
The matrix whose condition number is sought.
p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional
Order of the norm used in the condition number computation:
===== ============================
p norm for matrices
===== ============================
None 2-norm, computed directly using the ``SVD``
'fro' Frobenius norm
inf max(sum(abs(x), axis=1))
-inf min(sum(abs(x), axis=1))
1 max(sum(abs(x), axis=0))
-1 min(sum(abs(x), axis=0))
2 2-norm (largest sing. value)
-2 smallest singular value
===== ============================
inf means the `numpy.inf` object, and the Frobenius norm is
the root-of-sum-of-squares norm.
Returns
-------
c : {float, inf}
The condition number of the matrix. May be infinite.
See Also
--------
numpy.linalg.norm
Notes
-----
The condition number of `x` is defined as the norm of `x` times the
norm of the inverse of `x` [1]_; the norm can be the usual L2-norm
(root-of-sum-of-squares) or one of a number of other matrix norms.
References
----------
.. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL,
Academic Press, Inc., 1980, pg. 285.
Examples
--------
>>> from numpy import linalg as LA
>>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
>>> a
array([[ 1, 0, -1],
[ 0, 1, 0],
[ 1, 0, 1]])
>>> LA.cond(a)
1.4142135623730951
>>> LA.cond(a, 'fro')
3.1622776601683795
>>> LA.cond(a, np.inf)
2.0
>>> LA.cond(a, -np.inf)
1.0
>>> LA.cond(a, 1)
2.0
>>> LA.cond(a, -1)
1.0
>>> LA.cond(a, 2)
1.4142135623730951
>>> LA.cond(a, -2)
0.70710678118654746 # may vary
>>> min(LA.svd(a, compute_uv=False))*min(LA.svd(LA.inv(a), compute_uv=False))
0.70710678118654746 # may vary
"""
x = asarray(x) # in case we have a matrix
if _is_empty_2d(x):
raise LinAlgError("cond is not defined on empty arrays")
if p is None or p == 2 or p == -2:
s = svd(x, compute_uv=False)
with errstate(all='ignore'):
if p == -2:
r = s[..., -1] / s[..., 0]
else:
r = s[..., 0] / s[..., -1]
else:
# Call inv(x) ignoring errors. The result array will
# contain nans in the entries where inversion failed.
_assert_stacked_2d(x)
_assert_stacked_square(x)
t, result_t = _commonType(x)
signature = 'D->D' if isComplexType(t) else 'd->d'
with errstate(all='ignore'):
invx = _umath_linalg.inv(x, signature=signature)
r = norm(x, p, axis=(-2, -1)) * norm(invx, p, axis=(-2, -1))
r = r.astype(result_t, copy=False)
# Convert nans to infs unless the original array had nan entries
r = asarray(r)
nan_mask = isnan(r)
if nan_mask.any():
nan_mask &= ~isnan(x).any(axis=(-2, -1))
if r.ndim > 0:
r[nan_mask] = Inf
elif nan_mask:
r[()] = Inf
# Convention is to return scalars instead of 0d arrays
if r.ndim == 0:
r = r[()]
return r | Compute the condition number of a matrix. This function is capable of returning the condition number using one of seven different norms, depending on the value of `p` (see Parameters below). Parameters ---------- x : (..., M, N) array_like The matrix whose condition number is sought. p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional Order of the norm used in the condition number computation: ===== ============================ p norm for matrices ===== ============================ None 2-norm, computed directly using the ``SVD`` 'fro' Frobenius norm inf max(sum(abs(x), axis=1)) -inf min(sum(abs(x), axis=1)) 1 max(sum(abs(x), axis=0)) -1 min(sum(abs(x), axis=0)) 2 2-norm (largest sing. value) -2 smallest singular value ===== ============================ inf means the `numpy.inf` object, and the Frobenius norm is the root-of-sum-of-squares norm. Returns ------- c : {float, inf} The condition number of the matrix. May be infinite. See Also -------- numpy.linalg.norm Notes ----- The condition number of `x` is defined as the norm of `x` times the norm of the inverse of `x` [1]_; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms. References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL, Academic Press, Inc., 1980, pg. 285. Examples -------- >>> from numpy import linalg as LA >>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]]) >>> a array([[ 1, 0, -1], [ 0, 1, 0], [ 1, 0, 1]]) >>> LA.cond(a) 1.4142135623730951 >>> LA.cond(a, 'fro') 3.1622776601683795 >>> LA.cond(a, np.inf) 2.0 >>> LA.cond(a, -np.inf) 1.0 >>> LA.cond(a, 1) 2.0 >>> LA.cond(a, -1) 1.0 >>> LA.cond(a, 2) 1.4142135623730951 >>> LA.cond(a, -2) 0.70710678118654746 # may vary >>> min(LA.svd(a, compute_uv=False))*min(LA.svd(LA.inv(a), compute_uv=False)) 0.70710678118654746 # may vary |
168,605 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _matrix_rank_dispatcher(A, tol=None, hermitian=None):
return (A,) | null |
168,606 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
"""
Singular Value Decomposition.
When `a` is a 2D array, and ``full_matrices=False``, then it is
factorized as ``u @ np.diag(s) @ vh = (u * s) @ vh``, where
`u` and the Hermitian transpose of `vh` are 2D arrays with
orthonormal columns and `s` is a 1D array of `a`'s singular
values. When `a` is higher-dimensional, SVD is applied in
stacked mode as explained below.
Parameters
----------
a : (..., M, N) array_like
A real or complex array with ``a.ndim >= 2``.
full_matrices : bool, optional
If True (default), `u` and `vh` have the shapes ``(..., M, M)`` and
``(..., N, N)``, respectively. Otherwise, the shapes are
``(..., M, K)`` and ``(..., K, N)``, respectively, where
``K = min(M, N)``.
compute_uv : bool, optional
Whether or not to compute `u` and `vh` in addition to `s`. True
by default.
hermitian : bool, optional
If True, `a` is assumed to be Hermitian (symmetric if real-valued),
enabling a more efficient method for finding singular values.
Defaults to False.
.. versionadded:: 1.17.0
Returns
-------
u : { (..., M, M), (..., M, K) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
s : (..., K) array
Vector(s) with the singular values, within each vector sorted in
descending order. The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`.
vh : { (..., N, N), (..., K, N) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
Raises
------
LinAlgError
If SVD computation does not converge.
See Also
--------
scipy.linalg.svd : Similar function in SciPy.
scipy.linalg.svdvals : Compute singular values of a matrix.
Notes
-----
.. versionchanged:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
The decomposition is performed using LAPACK routine ``_gesdd``.
SVD is usually described for the factorization of a 2D matrix :math:`A`.
The higher-dimensional case will be discussed below. In the 2D case, SVD is
written as :math:`A = U S V^H`, where :math:`A = a`, :math:`U= u`,
:math:`S= \\mathtt{np.diag}(s)` and :math:`V^H = vh`. The 1D array `s`
contains the singular values of `a` and `u` and `vh` are unitary. The rows
of `vh` are the eigenvectors of :math:`A^H A` and the columns of `u` are
the eigenvectors of :math:`A A^H`. In both cases the corresponding
(possibly non-zero) eigenvalues are given by ``s**2``.
If `a` has more than two dimensions, then broadcasting rules apply, as
explained in :ref:`routines.linalg-broadcasting`. This means that SVD is
working in "stacked" mode: it iterates over all indices of the first
``a.ndim - 2`` dimensions and for each combination SVD is applied to the
last two indices. The matrix `a` can be reconstructed from the
decomposition with either ``(u * s[..., None, :]) @ vh`` or
``u @ (s[..., None] * vh)``. (The ``@`` operator can be replaced by the
function ``np.matmul`` for python versions below 3.5.)
If `a` is a ``matrix`` object (as opposed to an ``ndarray``), then so are
all the return values.
Examples
--------
>>> a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6)
>>> b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3)
Reconstruction based on full SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((9, 9), (6,), (6, 6))
>>> np.allclose(a, np.dot(u[:, :6] * s, vh))
True
>>> smat = np.zeros((9, 6), dtype=complex)
>>> smat[:6, :6] = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on reduced SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((9, 6), (6,), (6, 6))
>>> np.allclose(a, np.dot(u * s, vh))
True
>>> smat = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on full SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u[..., :3] * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u[..., :3], s[..., None] * vh))
True
Reconstruction based on reduced SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u, s[..., None] * vh))
True
"""
import numpy as _nx
a, wrap = _makearray(a)
if hermitian:
# note: lapack svd returns eigenvalues with s ** 2 sorted descending,
# but eig returns s sorted ascending, so we re-order the eigenvalues
# and related arrays to have the correct order
if compute_uv:
s, u = eigh(a)
sgn = sign(s)
s = abs(s)
sidx = argsort(s)[..., ::-1]
sgn = _nx.take_along_axis(sgn, sidx, axis=-1)
s = _nx.take_along_axis(s, sidx, axis=-1)
u = _nx.take_along_axis(u, sidx[..., None, :], axis=-1)
# singular values are unsigned, move the sign into v
vt = transpose(u * sgn[..., None, :]).conjugate()
return wrap(u), s, wrap(vt)
else:
s = eigvalsh(a)
s = abs(s)
return sort(s)[..., ::-1]
_assert_stacked_2d(a)
t, result_t = _commonType(a)
extobj = get_linalg_error_extobj(_raise_linalgerror_svd_nonconvergence)
m, n = a.shape[-2:]
if compute_uv:
if full_matrices:
if m < n:
gufunc = _umath_linalg.svd_m_f
else:
gufunc = _umath_linalg.svd_n_f
else:
if m < n:
gufunc = _umath_linalg.svd_m_s
else:
gufunc = _umath_linalg.svd_n_s
signature = 'D->DdD' if isComplexType(t) else 'd->ddd'
u, s, vh = gufunc(a, signature=signature, extobj=extobj)
u = u.astype(result_t, copy=False)
s = s.astype(_realType(result_t), copy=False)
vh = vh.astype(result_t, copy=False)
return wrap(u), s, wrap(vh)
else:
if m < n:
gufunc = _umath_linalg.svd_m
else:
gufunc = _umath_linalg.svd_n
signature = 'D->d' if isComplexType(t) else 'd->d'
s = gufunc(a, signature=signature, extobj=extobj)
s = s.astype(_realType(result_t), copy=False)
return s
The provided code snippet includes necessary dependencies for implementing the `matrix_rank` function. Write a Python function `def matrix_rank(A, tol=None, hermitian=False)` to solve the following problem:
Return matrix rank of array using SVD method Rank of the array is the number of singular values of the array that are greater than `tol`. .. versionchanged:: 1.14 Can now operate on stacks of matrices Parameters ---------- A : {(M,), (..., M, N)} array_like Input vector or stack of matrices. tol : (...) array_like, float, optional Threshold below which SVD values are considered zero. If `tol` is None, and ``S`` is an array with singular values for `M`, and ``eps`` is the epsilon value for datatype of ``S``, then `tol` is set to ``S.max() * max(M, N) * eps``. .. versionchanged:: 1.14 Broadcasted against the stack of matrices hermitian : bool, optional If True, `A` is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Defaults to False. .. versionadded:: 1.14 Returns ------- rank : (...) array_like Rank of A. Notes ----- The default threshold to detect rank deficiency is a test on the magnitude of the singular values of `A`. By default, we identify singular values less than ``S.max() * max(M, N) * eps`` as indicating rank deficiency (with the symbols defined above). This is the algorithm MATLAB uses [1]. It also appears in *Numerical recipes* in the discussion of SVD solutions for linear least squares [2]. This default threshold is designed to detect rank deficiency accounting for the numerical errors of the SVD computation. Imagine that there is a column in `A` that is an exact (in floating point) linear combination of other columns in `A`. Computing the SVD on `A` will not produce a singular value exactly equal to 0 in general: any difference of the smallest SVD value from 0 will be caused by numerical imprecision in the calculation of the SVD. Our threshold for small SVD values takes this numerical imprecision into account, and the default threshold will detect such numerical rank deficiency. The threshold may declare a matrix `A` rank deficient even if the linear combination of some columns of `A` is not exactly equal to another column of `A` but only numerically very close to another column of `A`. We chose our default threshold because it is in wide use. Other thresholds are possible. For example, elsewhere in the 2007 edition of *Numerical recipes* there is an alternative threshold of ``S.max() * np.finfo(A.dtype).eps / 2. * np.sqrt(m + n + 1.)``. The authors describe this threshold as being based on "expected roundoff error" (p 71). The thresholds above deal with floating point roundoff error in the calculation of the SVD. However, you may have more information about the sources of error in `A` that would make you consider other tolerance values to detect *effective* rank deficiency. The most useful measure of the tolerance depends on the operations you intend to use on your matrix. For example, if your data come from uncertain measurements with uncertainties greater than floating point epsilon, choosing a tolerance near that uncertainty may be preferable. The tolerance may be absolute if the uncertainties are absolute rather than relative. References ---------- .. [1] MATLAB reference documentation, "Rank" https://www.mathworks.com/help/techdoc/ref/rank.html .. [2] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes (3rd edition)", Cambridge University Press, 2007, page 795. Examples -------- >>> from numpy.linalg import matrix_rank >>> matrix_rank(np.eye(4)) # Full rank matrix 4 >>> I=np.eye(4); I[-1,-1] = 0. # rank deficient matrix >>> matrix_rank(I) 3 >>> matrix_rank(np.ones((4,))) # 1 dimension - rank 1 unless all 0 1 >>> matrix_rank(np.zeros((4,))) 0
Here is the function:
def matrix_rank(A, tol=None, hermitian=False):
"""
Return matrix rank of array using SVD method
Rank of the array is the number of singular values of the array that are
greater than `tol`.
.. versionchanged:: 1.14
Can now operate on stacks of matrices
Parameters
----------
A : {(M,), (..., M, N)} array_like
Input vector or stack of matrices.
tol : (...) array_like, float, optional
Threshold below which SVD values are considered zero. If `tol` is
None, and ``S`` is an array with singular values for `M`, and
``eps`` is the epsilon value for datatype of ``S``, then `tol` is
set to ``S.max() * max(M, N) * eps``.
.. versionchanged:: 1.14
Broadcasted against the stack of matrices
hermitian : bool, optional
If True, `A` is assumed to be Hermitian (symmetric if real-valued),
enabling a more efficient method for finding singular values.
Defaults to False.
.. versionadded:: 1.14
Returns
-------
rank : (...) array_like
Rank of A.
Notes
-----
The default threshold to detect rank deficiency is a test on the magnitude
of the singular values of `A`. By default, we identify singular values less
than ``S.max() * max(M, N) * eps`` as indicating rank deficiency (with
the symbols defined above). This is the algorithm MATLAB uses [1]. It also
appears in *Numerical recipes* in the discussion of SVD solutions for linear
least squares [2].
This default threshold is designed to detect rank deficiency accounting for
the numerical errors of the SVD computation. Imagine that there is a column
in `A` that is an exact (in floating point) linear combination of other
columns in `A`. Computing the SVD on `A` will not produce a singular value
exactly equal to 0 in general: any difference of the smallest SVD value from
0 will be caused by numerical imprecision in the calculation of the SVD.
Our threshold for small SVD values takes this numerical imprecision into
account, and the default threshold will detect such numerical rank
deficiency. The threshold may declare a matrix `A` rank deficient even if
the linear combination of some columns of `A` is not exactly equal to
another column of `A` but only numerically very close to another column of
`A`.
We chose our default threshold because it is in wide use. Other thresholds
are possible. For example, elsewhere in the 2007 edition of *Numerical
recipes* there is an alternative threshold of ``S.max() *
np.finfo(A.dtype).eps / 2. * np.sqrt(m + n + 1.)``. The authors describe
this threshold as being based on "expected roundoff error" (p 71).
The thresholds above deal with floating point roundoff error in the
calculation of the SVD. However, you may have more information about the
sources of error in `A` that would make you consider other tolerance values
to detect *effective* rank deficiency. The most useful measure of the
tolerance depends on the operations you intend to use on your matrix. For
example, if your data come from uncertain measurements with uncertainties
greater than floating point epsilon, choosing a tolerance near that
uncertainty may be preferable. The tolerance may be absolute if the
uncertainties are absolute rather than relative.
References
----------
.. [1] MATLAB reference documentation, "Rank"
https://www.mathworks.com/help/techdoc/ref/rank.html
.. [2] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery,
"Numerical Recipes (3rd edition)", Cambridge University Press, 2007,
page 795.
Examples
--------
>>> from numpy.linalg import matrix_rank
>>> matrix_rank(np.eye(4)) # Full rank matrix
4
>>> I=np.eye(4); I[-1,-1] = 0. # rank deficient matrix
>>> matrix_rank(I)
3
>>> matrix_rank(np.ones((4,))) # 1 dimension - rank 1 unless all 0
1
>>> matrix_rank(np.zeros((4,)))
0
"""
A = asarray(A)
if A.ndim < 2:
return int(not all(A==0))
S = svd(A, compute_uv=False, hermitian=hermitian)
if tol is None:
tol = S.max(axis=-1, keepdims=True) * max(A.shape[-2:]) * finfo(S.dtype).eps
else:
tol = asarray(tol)[..., newaxis]
return count_nonzero(S > tol, axis=-1) | Return matrix rank of array using SVD method Rank of the array is the number of singular values of the array that are greater than `tol`. .. versionchanged:: 1.14 Can now operate on stacks of matrices Parameters ---------- A : {(M,), (..., M, N)} array_like Input vector or stack of matrices. tol : (...) array_like, float, optional Threshold below which SVD values are considered zero. If `tol` is None, and ``S`` is an array with singular values for `M`, and ``eps`` is the epsilon value for datatype of ``S``, then `tol` is set to ``S.max() * max(M, N) * eps``. .. versionchanged:: 1.14 Broadcasted against the stack of matrices hermitian : bool, optional If True, `A` is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Defaults to False. .. versionadded:: 1.14 Returns ------- rank : (...) array_like Rank of A. Notes ----- The default threshold to detect rank deficiency is a test on the magnitude of the singular values of `A`. By default, we identify singular values less than ``S.max() * max(M, N) * eps`` as indicating rank deficiency (with the symbols defined above). This is the algorithm MATLAB uses [1]. It also appears in *Numerical recipes* in the discussion of SVD solutions for linear least squares [2]. This default threshold is designed to detect rank deficiency accounting for the numerical errors of the SVD computation. Imagine that there is a column in `A` that is an exact (in floating point) linear combination of other columns in `A`. Computing the SVD on `A` will not produce a singular value exactly equal to 0 in general: any difference of the smallest SVD value from 0 will be caused by numerical imprecision in the calculation of the SVD. Our threshold for small SVD values takes this numerical imprecision into account, and the default threshold will detect such numerical rank deficiency. The threshold may declare a matrix `A` rank deficient even if the linear combination of some columns of `A` is not exactly equal to another column of `A` but only numerically very close to another column of `A`. We chose our default threshold because it is in wide use. Other thresholds are possible. For example, elsewhere in the 2007 edition of *Numerical recipes* there is an alternative threshold of ``S.max() * np.finfo(A.dtype).eps / 2. * np.sqrt(m + n + 1.)``. The authors describe this threshold as being based on "expected roundoff error" (p 71). The thresholds above deal with floating point roundoff error in the calculation of the SVD. However, you may have more information about the sources of error in `A` that would make you consider other tolerance values to detect *effective* rank deficiency. The most useful measure of the tolerance depends on the operations you intend to use on your matrix. For example, if your data come from uncertain measurements with uncertainties greater than floating point epsilon, choosing a tolerance near that uncertainty may be preferable. The tolerance may be absolute if the uncertainties are absolute rather than relative. References ---------- .. [1] MATLAB reference documentation, "Rank" https://www.mathworks.com/help/techdoc/ref/rank.html .. [2] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes (3rd edition)", Cambridge University Press, 2007, page 795. Examples -------- >>> from numpy.linalg import matrix_rank >>> matrix_rank(np.eye(4)) # Full rank matrix 4 >>> I=np.eye(4); I[-1,-1] = 0. # rank deficient matrix >>> matrix_rank(I) 3 >>> matrix_rank(np.ones((4,))) # 1 dimension - rank 1 unless all 0 1 >>> matrix_rank(np.zeros((4,))) 0 |
168,607 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _pinv_dispatcher(a, rcond=None, hermitian=None):
return (a,) | null |
168,608 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def _is_empty_2d(arr):
# check size first for efficiency
return arr.size == 0 and product(arr.shape[-2:]) == 0
def transpose(a):
"""
Transpose each matrix in a stack of matrices.
Unlike np.transpose, this only swaps the last two axes, rather than all of
them
Parameters
----------
a : (...,M,N) array_like
Returns
-------
aT : (...,N,M) ndarray
"""
return swapaxes(a, -1, -2)
def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
"""
Singular Value Decomposition.
When `a` is a 2D array, and ``full_matrices=False``, then it is
factorized as ``u @ np.diag(s) @ vh = (u * s) @ vh``, where
`u` and the Hermitian transpose of `vh` are 2D arrays with
orthonormal columns and `s` is a 1D array of `a`'s singular
values. When `a` is higher-dimensional, SVD is applied in
stacked mode as explained below.
Parameters
----------
a : (..., M, N) array_like
A real or complex array with ``a.ndim >= 2``.
full_matrices : bool, optional
If True (default), `u` and `vh` have the shapes ``(..., M, M)`` and
``(..., N, N)``, respectively. Otherwise, the shapes are
``(..., M, K)`` and ``(..., K, N)``, respectively, where
``K = min(M, N)``.
compute_uv : bool, optional
Whether or not to compute `u` and `vh` in addition to `s`. True
by default.
hermitian : bool, optional
If True, `a` is assumed to be Hermitian (symmetric if real-valued),
enabling a more efficient method for finding singular values.
Defaults to False.
.. versionadded:: 1.17.0
Returns
-------
u : { (..., M, M), (..., M, K) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
s : (..., K) array
Vector(s) with the singular values, within each vector sorted in
descending order. The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`.
vh : { (..., N, N), (..., K, N) } array
Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
size as those of the input `a`. The size of the last two dimensions
depends on the value of `full_matrices`. Only returned when
`compute_uv` is True.
Raises
------
LinAlgError
If SVD computation does not converge.
See Also
--------
scipy.linalg.svd : Similar function in SciPy.
scipy.linalg.svdvals : Compute singular values of a matrix.
Notes
-----
.. versionchanged:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
The decomposition is performed using LAPACK routine ``_gesdd``.
SVD is usually described for the factorization of a 2D matrix :math:`A`.
The higher-dimensional case will be discussed below. In the 2D case, SVD is
written as :math:`A = U S V^H`, where :math:`A = a`, :math:`U= u`,
:math:`S= \\mathtt{np.diag}(s)` and :math:`V^H = vh`. The 1D array `s`
contains the singular values of `a` and `u` and `vh` are unitary. The rows
of `vh` are the eigenvectors of :math:`A^H A` and the columns of `u` are
the eigenvectors of :math:`A A^H`. In both cases the corresponding
(possibly non-zero) eigenvalues are given by ``s**2``.
If `a` has more than two dimensions, then broadcasting rules apply, as
explained in :ref:`routines.linalg-broadcasting`. This means that SVD is
working in "stacked" mode: it iterates over all indices of the first
``a.ndim - 2`` dimensions and for each combination SVD is applied to the
last two indices. The matrix `a` can be reconstructed from the
decomposition with either ``(u * s[..., None, :]) @ vh`` or
``u @ (s[..., None] * vh)``. (The ``@`` operator can be replaced by the
function ``np.matmul`` for python versions below 3.5.)
If `a` is a ``matrix`` object (as opposed to an ``ndarray``), then so are
all the return values.
Examples
--------
>>> a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6)
>>> b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3)
Reconstruction based on full SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((9, 9), (6,), (6, 6))
>>> np.allclose(a, np.dot(u[:, :6] * s, vh))
True
>>> smat = np.zeros((9, 6), dtype=complex)
>>> smat[:6, :6] = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on reduced SVD, 2D case:
>>> u, s, vh = np.linalg.svd(a, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((9, 6), (6,), (6, 6))
>>> np.allclose(a, np.dot(u * s, vh))
True
>>> smat = np.diag(s)
>>> np.allclose(a, np.dot(u, np.dot(smat, vh)))
True
Reconstruction based on full SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=True)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u[..., :3] * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u[..., :3], s[..., None] * vh))
True
Reconstruction based on reduced SVD, 4D case:
>>> u, s, vh = np.linalg.svd(b, full_matrices=False)
>>> u.shape, s.shape, vh.shape
((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))
>>> np.allclose(b, np.matmul(u * s[..., None, :], vh))
True
>>> np.allclose(b, np.matmul(u, s[..., None] * vh))
True
"""
import numpy as _nx
a, wrap = _makearray(a)
if hermitian:
# note: lapack svd returns eigenvalues with s ** 2 sorted descending,
# but eig returns s sorted ascending, so we re-order the eigenvalues
# and related arrays to have the correct order
if compute_uv:
s, u = eigh(a)
sgn = sign(s)
s = abs(s)
sidx = argsort(s)[..., ::-1]
sgn = _nx.take_along_axis(sgn, sidx, axis=-1)
s = _nx.take_along_axis(s, sidx, axis=-1)
u = _nx.take_along_axis(u, sidx[..., None, :], axis=-1)
# singular values are unsigned, move the sign into v
vt = transpose(u * sgn[..., None, :]).conjugate()
return wrap(u), s, wrap(vt)
else:
s = eigvalsh(a)
s = abs(s)
return sort(s)[..., ::-1]
_assert_stacked_2d(a)
t, result_t = _commonType(a)
extobj = get_linalg_error_extobj(_raise_linalgerror_svd_nonconvergence)
m, n = a.shape[-2:]
if compute_uv:
if full_matrices:
if m < n:
gufunc = _umath_linalg.svd_m_f
else:
gufunc = _umath_linalg.svd_n_f
else:
if m < n:
gufunc = _umath_linalg.svd_m_s
else:
gufunc = _umath_linalg.svd_n_s
signature = 'D->DdD' if isComplexType(t) else 'd->ddd'
u, s, vh = gufunc(a, signature=signature, extobj=extobj)
u = u.astype(result_t, copy=False)
s = s.astype(_realType(result_t), copy=False)
vh = vh.astype(result_t, copy=False)
return wrap(u), s, wrap(vh)
else:
if m < n:
gufunc = _umath_linalg.svd_m
else:
gufunc = _umath_linalg.svd_n
signature = 'D->d' if isComplexType(t) else 'd->d'
s = gufunc(a, signature=signature, extobj=extobj)
s = s.astype(_realType(result_t), copy=False)
return s
The provided code snippet includes necessary dependencies for implementing the `pinv` function. Write a Python function `def pinv(a, rcond=1e-15, hermitian=False)` to solve the following problem:
Compute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all *large* singular values. .. versionchanged:: 1.14 Can now operate on stacks of matrices Parameters ---------- a : (..., M, N) array_like Matrix or stack of matrices to be pseudo-inverted. rcond : (...) array_like of float Cutoff for small singular values. Singular values less than or equal to ``rcond * largest_singular_value`` are set to zero. Broadcasts against the stack of matrices. hermitian : bool, optional If True, `a` is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Defaults to False. .. versionadded:: 1.17.0 Returns ------- B : (..., N, M) ndarray The pseudo-inverse of `a`. If `a` is a `matrix` instance, then so is `B`. Raises ------ LinAlgError If the SVD computation does not converge. See Also -------- scipy.linalg.pinv : Similar function in SciPy. scipy.linalg.pinvh : Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix. Notes ----- The pseudo-inverse of a matrix A, denoted :math:`A^+`, is defined as: "the matrix that 'solves' [the least-squares problem] :math:`Ax = b`," i.e., if :math:`\\bar{x}` is said solution, then :math:`A^+` is that matrix such that :math:`\\bar{x} = A^+b`. It can be shown that if :math:`Q_1 \\Sigma Q_2^T = A` is the singular value decomposition of A, then :math:`A^+ = Q_2 \\Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are orthogonal matrices, :math:`\\Sigma` is a diagonal matrix consisting of A's so-called singular values, (followed, typically, by zeros), and then :math:`\\Sigma^+` is simply the diagonal matrix consisting of the reciprocals of A's singular values (again, followed by zeros). [1]_ References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142. Examples -------- The following example checks that ``a * a+ * a == a`` and ``a+ * a * a+ == a+``: >>> a = np.random.randn(9, 6) >>> B = np.linalg.pinv(a) >>> np.allclose(a, np.dot(a, np.dot(B, a))) True >>> np.allclose(B, np.dot(B, np.dot(a, B))) True
Here is the function:
def pinv(a, rcond=1e-15, hermitian=False):
"""
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate the generalized inverse of a matrix using its
singular-value decomposition (SVD) and including all
*large* singular values.
.. versionchanged:: 1.14
Can now operate on stacks of matrices
Parameters
----------
a : (..., M, N) array_like
Matrix or stack of matrices to be pseudo-inverted.
rcond : (...) array_like of float
Cutoff for small singular values.
Singular values less than or equal to
``rcond * largest_singular_value`` are set to zero.
Broadcasts against the stack of matrices.
hermitian : bool, optional
If True, `a` is assumed to be Hermitian (symmetric if real-valued),
enabling a more efficient method for finding singular values.
Defaults to False.
.. versionadded:: 1.17.0
Returns
-------
B : (..., N, M) ndarray
The pseudo-inverse of `a`. If `a` is a `matrix` instance, then so
is `B`.
Raises
------
LinAlgError
If the SVD computation does not converge.
See Also
--------
scipy.linalg.pinv : Similar function in SciPy.
scipy.linalg.pinvh : Compute the (Moore-Penrose) pseudo-inverse of a
Hermitian matrix.
Notes
-----
The pseudo-inverse of a matrix A, denoted :math:`A^+`, is
defined as: "the matrix that 'solves' [the least-squares problem]
:math:`Ax = b`," i.e., if :math:`\\bar{x}` is said solution, then
:math:`A^+` is that matrix such that :math:`\\bar{x} = A^+b`.
It can be shown that if :math:`Q_1 \\Sigma Q_2^T = A` is the singular
value decomposition of A, then
:math:`A^+ = Q_2 \\Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are
orthogonal matrices, :math:`\\Sigma` is a diagonal matrix consisting
of A's so-called singular values, (followed, typically, by
zeros), and then :math:`\\Sigma^+` is simply the diagonal matrix
consisting of the reciprocals of A's singular values
(again, followed by zeros). [1]_
References
----------
.. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando,
FL, Academic Press, Inc., 1980, pp. 139-142.
Examples
--------
The following example checks that ``a * a+ * a == a`` and
``a+ * a * a+ == a+``:
>>> a = np.random.randn(9, 6)
>>> B = np.linalg.pinv(a)
>>> np.allclose(a, np.dot(a, np.dot(B, a)))
True
>>> np.allclose(B, np.dot(B, np.dot(a, B)))
True
"""
a, wrap = _makearray(a)
rcond = asarray(rcond)
if _is_empty_2d(a):
m, n = a.shape[-2:]
res = empty(a.shape[:-2] + (n, m), dtype=a.dtype)
return wrap(res)
a = a.conjugate()
u, s, vt = svd(a, full_matrices=False, hermitian=hermitian)
# discard small singular values
cutoff = rcond[..., newaxis] * amax(s, axis=-1, keepdims=True)
large = s > cutoff
s = divide(1, s, where=large, out=s)
s[~large] = 0
res = matmul(transpose(vt), multiply(s[..., newaxis], transpose(u)))
return wrap(res) | Compute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all *large* singular values. .. versionchanged:: 1.14 Can now operate on stacks of matrices Parameters ---------- a : (..., M, N) array_like Matrix or stack of matrices to be pseudo-inverted. rcond : (...) array_like of float Cutoff for small singular values. Singular values less than or equal to ``rcond * largest_singular_value`` are set to zero. Broadcasts against the stack of matrices. hermitian : bool, optional If True, `a` is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Defaults to False. .. versionadded:: 1.17.0 Returns ------- B : (..., N, M) ndarray The pseudo-inverse of `a`. If `a` is a `matrix` instance, then so is `B`. Raises ------ LinAlgError If the SVD computation does not converge. See Also -------- scipy.linalg.pinv : Similar function in SciPy. scipy.linalg.pinvh : Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix. Notes ----- The pseudo-inverse of a matrix A, denoted :math:`A^+`, is defined as: "the matrix that 'solves' [the least-squares problem] :math:`Ax = b`," i.e., if :math:`\\bar{x}` is said solution, then :math:`A^+` is that matrix such that :math:`\\bar{x} = A^+b`. It can be shown that if :math:`Q_1 \\Sigma Q_2^T = A` is the singular value decomposition of A, then :math:`A^+ = Q_2 \\Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are orthogonal matrices, :math:`\\Sigma` is a diagonal matrix consisting of A's so-called singular values, (followed, typically, by zeros), and then :math:`\\Sigma^+` is simply the diagonal matrix consisting of the reciprocals of A's singular values (again, followed by zeros). [1]_ References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142. Examples -------- The following example checks that ``a * a+ * a == a`` and ``a+ * a * a+ == a+``: >>> a = np.random.randn(9, 6) >>> B = np.linalg.pinv(a) >>> np.allclose(a, np.dot(a, np.dot(B, a))) True >>> np.allclose(B, np.dot(B, np.dot(a, B))) True |
168,609 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def isComplexType(t):
return issubclass(t, complexfloating)
def _realType(t, default=double):
return _real_types_map.get(t, default)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
The provided code snippet includes necessary dependencies for implementing the `slogdet` function. Write a Python function `def slogdet(a)` to solve the following problem:
Compute the sign and (natural) logarithm of the determinant of an array. If an array has a very small or very large determinant, then a call to `det` may overflow or underflow. This routine is more robust against such issues, because it computes the logarithm of the determinant rather than the determinant itself. Parameters ---------- a : (..., M, M) array_like Input array, has to be a square 2-D array. Returns ------- sign : (...) array_like A number representing the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1 (i.e., it is on the unit circle), or else 0. logdet : (...) array_like The natural log of the absolute value of the determinant. If the determinant is zero, then `sign` will be 0 and `logdet` will be -Inf. In all cases, the determinant is equal to ``sign * np.exp(logdet)``. See Also -------- det Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. .. versionadded:: 1.6.0 The determinant is computed via LU factorization using the LAPACK routine ``z/dgetrf``. Examples -------- The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``: >>> a = np.array([[1, 2], [3, 4]]) >>> (sign, logdet) = np.linalg.slogdet(a) >>> (sign, logdet) (-1, 0.69314718055994529) # may vary >>> sign * np.exp(logdet) -2.0 Computing log-determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (3, 2, 2) >>> sign, logdet = np.linalg.slogdet(a) >>> (sign, logdet) (array([-1., -1., -1.]), array([ 0.69314718, 1.09861229, 2.07944154])) >>> sign * np.exp(logdet) array([-2., -3., -8.]) This routine succeeds where ordinary `det` does not: >>> np.linalg.det(np.eye(500) * 0.1) 0.0 >>> np.linalg.slogdet(np.eye(500) * 0.1) (1, -1151.2925464970228)
Here is the function:
def slogdet(a):
"""
Compute the sign and (natural) logarithm of the determinant of an array.
If an array has a very small or very large determinant, then a call to
`det` may overflow or underflow. This routine is more robust against such
issues, because it computes the logarithm of the determinant rather than
the determinant itself.
Parameters
----------
a : (..., M, M) array_like
Input array, has to be a square 2-D array.
Returns
-------
sign : (...) array_like
A number representing the sign of the determinant. For a real matrix,
this is 1, 0, or -1. For a complex matrix, this is a complex number
with absolute value 1 (i.e., it is on the unit circle), or else 0.
logdet : (...) array_like
The natural log of the absolute value of the determinant.
If the determinant is zero, then `sign` will be 0 and `logdet` will be
-Inf. In all cases, the determinant is equal to ``sign * np.exp(logdet)``.
See Also
--------
det
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
.. versionadded:: 1.6.0
The determinant is computed via LU factorization using the LAPACK
routine ``z/dgetrf``.
Examples
--------
The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``:
>>> a = np.array([[1, 2], [3, 4]])
>>> (sign, logdet) = np.linalg.slogdet(a)
>>> (sign, logdet)
(-1, 0.69314718055994529) # may vary
>>> sign * np.exp(logdet)
-2.0
Computing log-determinants for a stack of matrices:
>>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
>>> a.shape
(3, 2, 2)
>>> sign, logdet = np.linalg.slogdet(a)
>>> (sign, logdet)
(array([-1., -1., -1.]), array([ 0.69314718, 1.09861229, 2.07944154]))
>>> sign * np.exp(logdet)
array([-2., -3., -8.])
This routine succeeds where ordinary `det` does not:
>>> np.linalg.det(np.eye(500) * 0.1)
0.0
>>> np.linalg.slogdet(np.eye(500) * 0.1)
(1, -1151.2925464970228)
"""
a = asarray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
real_t = _realType(result_t)
signature = 'D->Dd' if isComplexType(t) else 'd->dd'
sign, logdet = _umath_linalg.slogdet(a, signature=signature)
sign = sign.astype(result_t, copy=False)
logdet = logdet.astype(real_t, copy=False)
return sign, logdet | Compute the sign and (natural) logarithm of the determinant of an array. If an array has a very small or very large determinant, then a call to `det` may overflow or underflow. This routine is more robust against such issues, because it computes the logarithm of the determinant rather than the determinant itself. Parameters ---------- a : (..., M, M) array_like Input array, has to be a square 2-D array. Returns ------- sign : (...) array_like A number representing the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1 (i.e., it is on the unit circle), or else 0. logdet : (...) array_like The natural log of the absolute value of the determinant. If the determinant is zero, then `sign` will be 0 and `logdet` will be -Inf. In all cases, the determinant is equal to ``sign * np.exp(logdet)``. See Also -------- det Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. .. versionadded:: 1.6.0 The determinant is computed via LU factorization using the LAPACK routine ``z/dgetrf``. Examples -------- The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``: >>> a = np.array([[1, 2], [3, 4]]) >>> (sign, logdet) = np.linalg.slogdet(a) >>> (sign, logdet) (-1, 0.69314718055994529) # may vary >>> sign * np.exp(logdet) -2.0 Computing log-determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (3, 2, 2) >>> sign, logdet = np.linalg.slogdet(a) >>> (sign, logdet) (array([-1., -1., -1.]), array([ 0.69314718, 1.09861229, 2.07944154])) >>> sign * np.exp(logdet) array([-2., -3., -8.]) This routine succeeds where ordinary `det` does not: >>> np.linalg.det(np.eye(500) * 0.1) 0.0 >>> np.linalg.slogdet(np.eye(500) * 0.1) (1, -1151.2925464970228) |
168,610 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def isComplexType(t):
return issubclass(t, complexfloating)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'at least two-dimensional' % a.ndim)
def _assert_stacked_square(*arrays):
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise LinAlgError('Last 2 dimensions of the array must be square')
The provided code snippet includes necessary dependencies for implementing the `det` function. Write a Python function `def det(a)` to solve the following problem:
Compute the determinant of an array. Parameters ---------- a : (..., M, M) array_like Input array to compute determinants for. Returns ------- det : (...) array_like Determinant of `a`. See Also -------- slogdet : Another way to represent the determinant, more suitable for large matrices where underflow/overflow may occur. scipy.linalg.det : Similar function in SciPy. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. The determinant is computed via LU factorization using the LAPACK routine ``z/dgetrf``. Examples -------- The determinant of a 2-D array [[a, b], [c, d]] is ad - bc: >>> a = np.array([[1, 2], [3, 4]]) >>> np.linalg.det(a) -2.0 # may vary Computing determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (3, 2, 2) >>> np.linalg.det(a) array([-2., -3., -8.])
Here is the function:
def det(a):
"""
Compute the determinant of an array.
Parameters
----------
a : (..., M, M) array_like
Input array to compute determinants for.
Returns
-------
det : (...) array_like
Determinant of `a`.
See Also
--------
slogdet : Another way to represent the determinant, more suitable
for large matrices where underflow/overflow may occur.
scipy.linalg.det : Similar function in SciPy.
Notes
-----
.. versionadded:: 1.8.0
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.
The determinant is computed via LU factorization using the LAPACK
routine ``z/dgetrf``.
Examples
--------
The determinant of a 2-D array [[a, b], [c, d]] is ad - bc:
>>> a = np.array([[1, 2], [3, 4]])
>>> np.linalg.det(a)
-2.0 # may vary
Computing determinants for a stack of matrices:
>>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
>>> a.shape
(3, 2, 2)
>>> np.linalg.det(a)
array([-2., -3., -8.])
"""
a = asarray(a)
_assert_stacked_2d(a)
_assert_stacked_square(a)
t, result_t = _commonType(a)
signature = 'D->D' if isComplexType(t) else 'd->d'
r = _umath_linalg.det(a, signature=signature)
r = r.astype(result_t, copy=False)
return r | Compute the determinant of an array. Parameters ---------- a : (..., M, M) array_like Input array to compute determinants for. Returns ------- det : (...) array_like Determinant of `a`. See Also -------- slogdet : Another way to represent the determinant, more suitable for large matrices where underflow/overflow may occur. scipy.linalg.det : Similar function in SciPy. Notes ----- .. versionadded:: 1.8.0 Broadcasting rules apply, see the `numpy.linalg` documentation for details. The determinant is computed via LU factorization using the LAPACK routine ``z/dgetrf``. Examples -------- The determinant of a 2-D array [[a, b], [c, d]] is ad - bc: >>> a = np.array([[1, 2], [3, 4]]) >>> np.linalg.det(a) -2.0 # may vary Computing determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (3, 2, 2) >>> np.linalg.det(a) array([-2., -3., -8.]) |
168,611 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _lstsq_dispatcher(a, b, rcond=None):
return (a, b) | null |
168,612 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
class LinAlgError(Exception):
"""
Generic Python-exception-derived object raised by linalg functions.
General purpose exception class, derived from Python's exception.Exception
class, programmatically raised in linalg functions when a Linear
Algebra-related condition would prevent further correct execution of the
function.
Parameters
----------
None
Examples
--------
>>> from numpy import linalg as LA
>>> LA.inv(np.zeros((2,2)))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "...linalg.py", line 350,
in inv return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
File "...linalg.py", line 249,
in solve
raise LinAlgError('Singular matrix')
numpy.linalg.LinAlgError: Singular matrix
"""
def _raise_linalgerror_lstsq(err, flag):
raise LinAlgError("SVD did not converge in Linear Least Squares")
def get_linalg_error_extobj(callback):
extobj = list(_linalg_error_extobj) # make a copy
extobj[2] = callback
return extobj
def _makearray(a):
new = asarray(a)
wrap = getattr(a, "__array_prepare__", new.__array_wrap__)
return new, wrap
def isComplexType(t):
return issubclass(t, complexfloating)
def _realType(t, default=double):
return _real_types_map.get(t, default)
def _commonType(*arrays):
# in lite version, use higher precision (always double or cdouble)
result_type = single
is_complex = False
for a in arrays:
if issubclass(a.dtype.type, inexact):
if isComplexType(a.dtype.type):
is_complex = True
rt = _realType(a.dtype.type, default=None)
if rt is None:
# unsupported inexact scalar
raise TypeError("array type %s is unsupported in linalg" %
(a.dtype.name,))
else:
rt = double
if rt is double:
result_type = double
if is_complex:
t = cdouble
result_type = _complex_types_map[result_type]
else:
t = double
return t, result_type
def _assert_2d(*arrays):
for a in arrays:
if a.ndim != 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'two-dimensional' % a.ndim)
The provided code snippet includes necessary dependencies for implementing the `lstsq` function. Write a Python function `def lstsq(a, b, rcond="warn")` to solve the following problem:
r""" Return the least-squares solution to a linear matrix equation. Computes the vector `x` that approximately solves the equation ``a @ x = b``. The equation may be under-, well-, or over-determined (i.e., the number of linearly independent rows of `a` can be less than, equal to, or greater than its number of linearly independent columns). If `a` is square and of full rank, then `x` (but for round-off error) is the "exact" solution of the equation. Else, `x` minimizes the Euclidean 2-norm :math:`||b - ax||`. If there are multiple minimizing solutions, the one with the smallest 2-norm :math:`||x||` is returned. Parameters ---------- a : (M, N) array_like "Coefficient" matrix. b : {(M,), (M, K)} array_like Ordinate or "dependent variable" values. If `b` is two-dimensional, the least-squares solution is calculated for each of the `K` columns of `b`. rcond : float, optional Cut-off ratio for small singular values of `a`. For the purposes of rank determination, singular values are treated as zero if they are smaller than `rcond` times the largest singular value of `a`. .. versionchanged:: 1.14.0 If not set, a FutureWarning is given. The previous default of ``-1`` will use the machine precision as `rcond` parameter, the new default will use the machine precision times `max(M, N)`. To silence the warning and use the new default, use ``rcond=None``, to keep using the old behavior, use ``rcond=-1``. Returns ------- x : {(N,), (N, K)} ndarray Least-squares solution. If `b` is two-dimensional, the solutions are in the `K` columns of `x`. residuals : {(1,), (K,), (0,)} ndarray Sums of squared residuals: Squared Euclidean 2-norm for each column in ``b - a @ x``. If the rank of `a` is < N or M <= N, this is an empty array. If `b` is 1-dimensional, this is a (1,) shape array. Otherwise the shape is (K,). rank : int Rank of matrix `a`. s : (min(M, N),) ndarray Singular values of `a`. Raises ------ LinAlgError If computation does not converge. See Also -------- scipy.linalg.lstsq : Similar function in SciPy. Notes ----- If `b` is a matrix, then all array results are returned as matrices. Examples -------- Fit a line, ``y = mx + c``, through some noisy data-points: >>> x = np.array([0, 1, 2, 3]) >>> y = np.array([-1, 0.2, 0.9, 2.1]) By examining the coefficients, we see that the line should have a gradient of roughly 1 and cut the y-axis at, more or less, -1. We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]`` and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`: >>> A = np.vstack([x, np.ones(len(x))]).T >>> A array([[ 0., 1.], [ 1., 1.], [ 2., 1.], [ 3., 1.]]) >>> m, c = np.linalg.lstsq(A, y, rcond=None)[0] >>> m, c (1.0 -0.95) # may vary Plot the data along with the fitted line: >>> import matplotlib.pyplot as plt >>> _ = plt.plot(x, y, 'o', label='Original data', markersize=10) >>> _ = plt.plot(x, m*x + c, 'r', label='Fitted line') >>> _ = plt.legend() >>> plt.show()
Here is the function:
def lstsq(a, b, rcond="warn"):
r"""
Return the least-squares solution to a linear matrix equation.
Computes the vector `x` that approximately solves the equation
``a @ x = b``. The equation may be under-, well-, or over-determined
(i.e., the number of linearly independent rows of `a` can be less than,
equal to, or greater than its number of linearly independent columns).
If `a` is square and of full rank, then `x` (but for round-off error)
is the "exact" solution of the equation. Else, `x` minimizes the
Euclidean 2-norm :math:`||b - ax||`. If there are multiple minimizing
solutions, the one with the smallest 2-norm :math:`||x||` is returned.
Parameters
----------
a : (M, N) array_like
"Coefficient" matrix.
b : {(M,), (M, K)} array_like
Ordinate or "dependent variable" values. If `b` is two-dimensional,
the least-squares solution is calculated for each of the `K` columns
of `b`.
rcond : float, optional
Cut-off ratio for small singular values of `a`.
For the purposes of rank determination, singular values are treated
as zero if they are smaller than `rcond` times the largest singular
value of `a`.
.. versionchanged:: 1.14.0
If not set, a FutureWarning is given. The previous default
of ``-1`` will use the machine precision as `rcond` parameter,
the new default will use the machine precision times `max(M, N)`.
To silence the warning and use the new default, use ``rcond=None``,
to keep using the old behavior, use ``rcond=-1``.
Returns
-------
x : {(N,), (N, K)} ndarray
Least-squares solution. If `b` is two-dimensional,
the solutions are in the `K` columns of `x`.
residuals : {(1,), (K,), (0,)} ndarray
Sums of squared residuals: Squared Euclidean 2-norm for each column in
``b - a @ x``.
If the rank of `a` is < N or M <= N, this is an empty array.
If `b` is 1-dimensional, this is a (1,) shape array.
Otherwise the shape is (K,).
rank : int
Rank of matrix `a`.
s : (min(M, N),) ndarray
Singular values of `a`.
Raises
------
LinAlgError
If computation does not converge.
See Also
--------
scipy.linalg.lstsq : Similar function in SciPy.
Notes
-----
If `b` is a matrix, then all array results are returned as matrices.
Examples
--------
Fit a line, ``y = mx + c``, through some noisy data-points:
>>> x = np.array([0, 1, 2, 3])
>>> y = np.array([-1, 0.2, 0.9, 2.1])
By examining the coefficients, we see that the line should have a
gradient of roughly 1 and cut the y-axis at, more or less, -1.
We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]``
and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`:
>>> A = np.vstack([x, np.ones(len(x))]).T
>>> A
array([[ 0., 1.],
[ 1., 1.],
[ 2., 1.],
[ 3., 1.]])
>>> m, c = np.linalg.lstsq(A, y, rcond=None)[0]
>>> m, c
(1.0 -0.95) # may vary
Plot the data along with the fitted line:
>>> import matplotlib.pyplot as plt
>>> _ = plt.plot(x, y, 'o', label='Original data', markersize=10)
>>> _ = plt.plot(x, m*x + c, 'r', label='Fitted line')
>>> _ = plt.legend()
>>> plt.show()
"""
a, _ = _makearray(a)
b, wrap = _makearray(b)
is_1d = b.ndim == 1
if is_1d:
b = b[:, newaxis]
_assert_2d(a, b)
m, n = a.shape[-2:]
m2, n_rhs = b.shape[-2:]
if m != m2:
raise LinAlgError('Incompatible dimensions')
t, result_t = _commonType(a, b)
result_real_t = _realType(result_t)
# Determine default rcond value
if rcond == "warn":
# 2017-08-19, 1.14.0
warnings.warn("`rcond` parameter will change to the default of "
"machine precision times ``max(M, N)`` where M and N "
"are the input matrix dimensions.\n"
"To use the future default and silence this warning "
"we advise to pass `rcond=None`, to keep using the old, "
"explicitly pass `rcond=-1`.",
FutureWarning, stacklevel=3)
rcond = -1
if rcond is None:
rcond = finfo(t).eps * max(n, m)
if m <= n:
gufunc = _umath_linalg.lstsq_m
else:
gufunc = _umath_linalg.lstsq_n
signature = 'DDd->Ddid' if isComplexType(t) else 'ddd->ddid'
extobj = get_linalg_error_extobj(_raise_linalgerror_lstsq)
if n_rhs == 0:
# lapack can't handle n_rhs = 0 - so allocate the array one larger in that axis
b = zeros(b.shape[:-2] + (m, n_rhs + 1), dtype=b.dtype)
x, resids, rank, s = gufunc(a, b, rcond, signature=signature, extobj=extobj)
if m == 0:
x[...] = 0
if n_rhs == 0:
# remove the item we added
x = x[..., :n_rhs]
resids = resids[..., :n_rhs]
# remove the axis we added
if is_1d:
x = x.squeeze(axis=-1)
# we probably should squeeze resids too, but we can't
# without breaking compatibility.
# as documented
if rank != n or m <= n:
resids = array([], result_real_t)
# coerce output arrays
s = s.astype(result_real_t, copy=False)
resids = resids.astype(result_real_t, copy=False)
x = x.astype(result_t, copy=True) # Copying lets the memory in r_parts be freed
return wrap(x), wrap(resids), rank, s | r""" Return the least-squares solution to a linear matrix equation. Computes the vector `x` that approximately solves the equation ``a @ x = b``. The equation may be under-, well-, or over-determined (i.e., the number of linearly independent rows of `a` can be less than, equal to, or greater than its number of linearly independent columns). If `a` is square and of full rank, then `x` (but for round-off error) is the "exact" solution of the equation. Else, `x` minimizes the Euclidean 2-norm :math:`||b - ax||`. If there are multiple minimizing solutions, the one with the smallest 2-norm :math:`||x||` is returned. Parameters ---------- a : (M, N) array_like "Coefficient" matrix. b : {(M,), (M, K)} array_like Ordinate or "dependent variable" values. If `b` is two-dimensional, the least-squares solution is calculated for each of the `K` columns of `b`. rcond : float, optional Cut-off ratio for small singular values of `a`. For the purposes of rank determination, singular values are treated as zero if they are smaller than `rcond` times the largest singular value of `a`. .. versionchanged:: 1.14.0 If not set, a FutureWarning is given. The previous default of ``-1`` will use the machine precision as `rcond` parameter, the new default will use the machine precision times `max(M, N)`. To silence the warning and use the new default, use ``rcond=None``, to keep using the old behavior, use ``rcond=-1``. Returns ------- x : {(N,), (N, K)} ndarray Least-squares solution. If `b` is two-dimensional, the solutions are in the `K` columns of `x`. residuals : {(1,), (K,), (0,)} ndarray Sums of squared residuals: Squared Euclidean 2-norm for each column in ``b - a @ x``. If the rank of `a` is < N or M <= N, this is an empty array. If `b` is 1-dimensional, this is a (1,) shape array. Otherwise the shape is (K,). rank : int Rank of matrix `a`. s : (min(M, N),) ndarray Singular values of `a`. Raises ------ LinAlgError If computation does not converge. See Also -------- scipy.linalg.lstsq : Similar function in SciPy. Notes ----- If `b` is a matrix, then all array results are returned as matrices. Examples -------- Fit a line, ``y = mx + c``, through some noisy data-points: >>> x = np.array([0, 1, 2, 3]) >>> y = np.array([-1, 0.2, 0.9, 2.1]) By examining the coefficients, we see that the line should have a gradient of roughly 1 and cut the y-axis at, more or less, -1. We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]`` and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`: >>> A = np.vstack([x, np.ones(len(x))]).T >>> A array([[ 0., 1.], [ 1., 1.], [ 2., 1.], [ 3., 1.]]) >>> m, c = np.linalg.lstsq(A, y, rcond=None)[0] >>> m, c (1.0 -0.95) # may vary Plot the data along with the fitted line: >>> import matplotlib.pyplot as plt >>> _ = plt.plot(x, y, 'o', label='Original data', markersize=10) >>> _ = plt.plot(x, m*x + c, 'r', label='Fitted line') >>> _ = plt.legend() >>> plt.show() |
168,613 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _norm_dispatcher(x, ord=None, axis=None, keepdims=None):
return (x,) | null |
168,614 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _multidot_dispatcher(arrays, *, out=None):
yield from arrays
yield out | null |
168,615 | import functools
import operator
import warnings
from numpy.core import (
array, asarray, zeros, empty, empty_like, intc, single, double,
csingle, cdouble, inexact, complexfloating, newaxis, all, Inf, dot,
add, multiply, sqrt, sum, isfinite,
finfo, errstate, geterrobj, moveaxis, amin, amax, product, abs,
atleast_2d, intp, asanyarray, object_, matmul,
swapaxes, divide, count_nonzero, isnan, sign, argsort, sort,
reciprocal
)
from numpy.core.multiarray import normalize_axis_index
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.lib.twodim_base import triu, eye
from numpy.linalg import _umath_linalg
def _assert_2d(*arrays):
for a in arrays:
if a.ndim != 2:
raise LinAlgError('%d-dimensional array given. Array must be '
'two-dimensional' % a.ndim)
def _multi_dot_three(A, B, C, out=None):
"""
Find the best order for three arrays and do the multiplication.
For three arguments `_multi_dot_three` is approximately 15 times faster
than `_multi_dot_matrix_chain_order`
"""
a0, a1b0 = A.shape
b1c0, c1 = C.shape
# cost1 = cost((AB)C) = a0*a1b0*b1c0 + a0*b1c0*c1
cost1 = a0 * b1c0 * (a1b0 + c1)
# cost2 = cost(A(BC)) = a1b0*b1c0*c1 + a0*a1b0*c1
cost2 = a1b0 * c1 * (a0 + b1c0)
if cost1 < cost2:
return dot(dot(A, B), C, out=out)
else:
return dot(A, dot(B, C), out=out)
def _multi_dot_matrix_chain_order(arrays, return_costs=False):
"""
Return a np.array that encodes the optimal order of mutiplications.
The optimal order array is then used by `_multi_dot()` to do the
multiplication.
Also return the cost matrix if `return_costs` is `True`
The implementation CLOSELY follows Cormen, "Introduction to Algorithms",
Chapter 15.2, p. 370-378. Note that Cormen uses 1-based indices.
cost[i, j] = min([
cost[prefix] + cost[suffix] + cost_mult(prefix, suffix)
for k in range(i, j)])
"""
n = len(arrays)
# p stores the dimensions of the matrices
# Example for p: A_{10x100}, B_{100x5}, C_{5x50} --> p = [10, 100, 5, 50]
p = [a.shape[0] for a in arrays] + [arrays[-1].shape[1]]
# m is a matrix of costs of the subproblems
# m[i,j]: min number of scalar multiplications needed to compute A_{i..j}
m = zeros((n, n), dtype=double)
# s is the actual ordering
# s[i, j] is the value of k at which we split the product A_i..A_j
s = empty((n, n), dtype=intp)
for l in range(1, n):
for i in range(n - l):
j = i + l
m[i, j] = Inf
for k in range(i, j):
q = m[i, k] + m[k+1, j] + p[i]*p[k+1]*p[j+1]
if q < m[i, j]:
m[i, j] = q
s[i, j] = k # Note that Cormen uses 1-based index
return (s, m) if return_costs else s
def _multi_dot(arrays, order, i, j, out=None):
"""Actually do the multiplication with the given order."""
if i == j:
# the initial call with non-None out should never get here
assert out is None
return arrays[i]
else:
return dot(_multi_dot(arrays, order, i, order[i, j]),
_multi_dot(arrays, order, order[i, j] + 1, j),
out=out)
The provided code snippet includes necessary dependencies for implementing the `multi_dot` function. Write a Python function `def multi_dot(arrays, *, out=None)` to solve the following problem:
Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order. `multi_dot` chains `numpy.dot` and uses optimal parenthesization of the matrices [1]_ [2]_. Depending on the shapes of the matrices, this can speed up the multiplication a lot. If the first argument is 1-D it is treated as a row vector. If the last argument is 1-D it is treated as a column vector. The other arguments must be 2-D. Think of `multi_dot` as:: def multi_dot(arrays): return functools.reduce(np.dot, arrays) Parameters ---------- arrays : sequence of array_like If the first argument is 1-D it is treated as row vector. If the last argument is 1-D it is treated as column vector. The other arguments must be 2-D. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a, b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. .. versionadded:: 1.19.0 Returns ------- output : ndarray Returns the dot product of the supplied arrays. See Also -------- numpy.dot : dot multiplication with two arguments. References ---------- .. [1] Cormen, "Introduction to Algorithms", Chapter 15.2, p. 370-378 .. [2] https://en.wikipedia.org/wiki/Matrix_chain_multiplication Examples -------- `multi_dot` allows you to write:: >>> from numpy.linalg import multi_dot >>> # Prepare some data >>> A = np.random.random((10000, 100)) >>> B = np.random.random((100, 1000)) >>> C = np.random.random((1000, 5)) >>> D = np.random.random((5, 333)) >>> # the actual dot multiplication >>> _ = multi_dot([A, B, C, D]) instead of:: >>> _ = np.dot(np.dot(np.dot(A, B), C), D) >>> # or >>> _ = A.dot(B).dot(C).dot(D) Notes ----- The cost for a matrix multiplication can be calculated with the following function:: def cost(A, B): return A.shape[0] * A.shape[1] * B.shape[1] Assume we have three matrices :math:`A_{10x100}, B_{100x5}, C_{5x50}`. The costs for the two different parenthesizations are as follows:: cost((AB)C) = 10*100*5 + 10*5*50 = 5000 + 2500 = 7500 cost(A(BC)) = 10*100*50 + 100*5*50 = 50000 + 25000 = 75000
Here is the function:
def multi_dot(arrays, *, out=None):
"""
Compute the dot product of two or more arrays in a single function call,
while automatically selecting the fastest evaluation order.
`multi_dot` chains `numpy.dot` and uses optimal parenthesization
of the matrices [1]_ [2]_. Depending on the shapes of the matrices,
this can speed up the multiplication a lot.
If the first argument is 1-D it is treated as a row vector.
If the last argument is 1-D it is treated as a column vector.
The other arguments must be 2-D.
Think of `multi_dot` as::
def multi_dot(arrays): return functools.reduce(np.dot, arrays)
Parameters
----------
arrays : sequence of array_like
If the first argument is 1-D it is treated as row vector.
If the last argument is 1-D it is treated as column vector.
The other arguments must be 2-D.
out : ndarray, optional
Output argument. This must have the exact kind that would be returned
if it was not used. In particular, it must have the right type, must be
C-contiguous, and its dtype must be the dtype that would be returned
for `dot(a, b)`. This is a performance feature. Therefore, if these
conditions are not met, an exception is raised, instead of attempting
to be flexible.
.. versionadded:: 1.19.0
Returns
-------
output : ndarray
Returns the dot product of the supplied arrays.
See Also
--------
numpy.dot : dot multiplication with two arguments.
References
----------
.. [1] Cormen, "Introduction to Algorithms", Chapter 15.2, p. 370-378
.. [2] https://en.wikipedia.org/wiki/Matrix_chain_multiplication
Examples
--------
`multi_dot` allows you to write::
>>> from numpy.linalg import multi_dot
>>> # Prepare some data
>>> A = np.random.random((10000, 100))
>>> B = np.random.random((100, 1000))
>>> C = np.random.random((1000, 5))
>>> D = np.random.random((5, 333))
>>> # the actual dot multiplication
>>> _ = multi_dot([A, B, C, D])
instead of::
>>> _ = np.dot(np.dot(np.dot(A, B), C), D)
>>> # or
>>> _ = A.dot(B).dot(C).dot(D)
Notes
-----
The cost for a matrix multiplication can be calculated with the
following function::
def cost(A, B):
return A.shape[0] * A.shape[1] * B.shape[1]
Assume we have three matrices
:math:`A_{10x100}, B_{100x5}, C_{5x50}`.
The costs for the two different parenthesizations are as follows::
cost((AB)C) = 10*100*5 + 10*5*50 = 5000 + 2500 = 7500
cost(A(BC)) = 10*100*50 + 100*5*50 = 50000 + 25000 = 75000
"""
n = len(arrays)
# optimization only makes sense for len(arrays) > 2
if n < 2:
raise ValueError("Expecting at least two arrays.")
elif n == 2:
return dot(arrays[0], arrays[1], out=out)
arrays = [asanyarray(a) for a in arrays]
# save original ndim to reshape the result array into the proper form later
ndim_first, ndim_last = arrays[0].ndim, arrays[-1].ndim
# Explicitly convert vectors to 2D arrays to keep the logic of the internal
# _multi_dot_* functions as simple as possible.
if arrays[0].ndim == 1:
arrays[0] = atleast_2d(arrays[0])
if arrays[-1].ndim == 1:
arrays[-1] = atleast_2d(arrays[-1]).T
_assert_2d(*arrays)
# _multi_dot_three is much faster than _multi_dot_matrix_chain_order
if n == 3:
result = _multi_dot_three(arrays[0], arrays[1], arrays[2], out=out)
else:
order = _multi_dot_matrix_chain_order(arrays)
result = _multi_dot(arrays, order, 0, n - 1, out=out)
# return proper shape
if ndim_first == 1 and ndim_last == 1:
return result[0, 0] # scalar
elif ndim_first == 1 or ndim_last == 1:
return result.ravel() # 1-D
else:
return result | Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order. `multi_dot` chains `numpy.dot` and uses optimal parenthesization of the matrices [1]_ [2]_. Depending on the shapes of the matrices, this can speed up the multiplication a lot. If the first argument is 1-D it is treated as a row vector. If the last argument is 1-D it is treated as a column vector. The other arguments must be 2-D. Think of `multi_dot` as:: def multi_dot(arrays): return functools.reduce(np.dot, arrays) Parameters ---------- arrays : sequence of array_like If the first argument is 1-D it is treated as row vector. If the last argument is 1-D it is treated as column vector. The other arguments must be 2-D. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a, b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. .. versionadded:: 1.19.0 Returns ------- output : ndarray Returns the dot product of the supplied arrays. See Also -------- numpy.dot : dot multiplication with two arguments. References ---------- .. [1] Cormen, "Introduction to Algorithms", Chapter 15.2, p. 370-378 .. [2] https://en.wikipedia.org/wiki/Matrix_chain_multiplication Examples -------- `multi_dot` allows you to write:: >>> from numpy.linalg import multi_dot >>> # Prepare some data >>> A = np.random.random((10000, 100)) >>> B = np.random.random((100, 1000)) >>> C = np.random.random((1000, 5)) >>> D = np.random.random((5, 333)) >>> # the actual dot multiplication >>> _ = multi_dot([A, B, C, D]) instead of:: >>> _ = np.dot(np.dot(np.dot(A, B), C), D) >>> # or >>> _ = A.dot(B).dot(C).dot(D) Notes ----- The cost for a matrix multiplication can be calculated with the following function:: def cost(A, B): return A.shape[0] * A.shape[1] * B.shape[1] Assume we have three matrices :math:`A_{10x100}, B_{100x5}, C_{5x50}`. The costs for the two different parenthesizations are as follows:: cost((AB)C) = 10*100*5 + 10*5*50 = 5000 + 2500 = 7500 cost(A(BC)) = 10*100*50 + 100*5*50 = 50000 + 25000 = 75000 |
168,646 |
class Configuration:
_list_keys = ['packages', 'ext_modules', 'data_files', 'include_dirs',
'libraries', 'headers', 'scripts', 'py_modules',
'installed_libraries', 'define_macros']
_dict_keys = ['package_dir', 'installed_pkg_config']
_extra_keys = ['name', 'version']
numpy_include_dirs = []
def __init__(self,
package_name=None,
parent_name=None,
top_path=None,
package_path=None,
caller_level=1,
setup_name='setup.py',
**attrs):
"""Construct configuration instance of a package.
package_name -- name of the package
Ex.: 'distutils'
parent_name -- name of the parent package
Ex.: 'numpy'
top_path -- directory of the toplevel package
Ex.: the directory where the numpy package source sits
package_path -- directory of package. Will be computed by magic from the
directory of the caller module if not specified
Ex.: the directory where numpy.distutils is
caller_level -- frame level to caller namespace, internal parameter.
"""
self.name = dot_join(parent_name, package_name)
self.version = None
caller_frame = get_frame(caller_level)
self.local_path = get_path_from_frame(caller_frame, top_path)
# local_path -- directory of a file (usually setup.py) that
# defines a configuration() function.
# local_path -- directory of a file (usually setup.py) that
# defines a configuration() function.
if top_path is None:
top_path = self.local_path
self.local_path = ''
if package_path is None:
package_path = self.local_path
elif os.path.isdir(njoin(self.local_path, package_path)):
package_path = njoin(self.local_path, package_path)
if not os.path.isdir(package_path or '.'):
raise ValueError("%r is not a directory" % (package_path,))
self.top_path = top_path
self.package_path = package_path
# this is the relative path in the installed package
self.path_in_package = os.path.join(*self.name.split('.'))
self.list_keys = self._list_keys[:]
self.dict_keys = self._dict_keys[:]
for n in self.list_keys:
v = copy.copy(attrs.get(n, []))
setattr(self, n, as_list(v))
for n in self.dict_keys:
v = copy.copy(attrs.get(n, {}))
setattr(self, n, v)
known_keys = self.list_keys + self.dict_keys
self.extra_keys = self._extra_keys[:]
for n in attrs.keys():
if n in known_keys:
continue
a = attrs[n]
setattr(self, n, a)
if isinstance(a, list):
self.list_keys.append(n)
elif isinstance(a, dict):
self.dict_keys.append(n)
else:
self.extra_keys.append(n)
if os.path.exists(njoin(package_path, '__init__.py')):
self.packages.append(self.name)
self.package_dir[self.name] = package_path
self.options = dict(
ignore_setup_xxx_py = False,
assume_default_configuration = False,
delegate_options_to_subpackages = False,
quiet = False,
)
caller_instance = None
for i in range(1, 3):
try:
f = get_frame(i)
except ValueError:
break
try:
caller_instance = eval('self', f.f_globals, f.f_locals)
break
except NameError:
pass
if isinstance(caller_instance, self.__class__):
if caller_instance.options['delegate_options_to_subpackages']:
self.set_options(**caller_instance.options)
self.setup_name = setup_name
def todict(self):
"""
Return a dictionary compatible with the keyword arguments of distutils
setup function.
Examples
--------
>>> setup(**config.todict()) #doctest: +SKIP
"""
self._optimize_data_files()
d = {}
known_keys = self.list_keys + self.dict_keys + self.extra_keys
for n in known_keys:
a = getattr(self, n)
if a:
d[n] = a
return d
def info(self, message):
if not self.options['quiet']:
print(message)
def warn(self, message):
sys.stderr.write('Warning: %s\n' % (message,))
def set_options(self, **options):
"""
Configure Configuration instance.
The following options are available:
- ignore_setup_xxx_py
- assume_default_configuration
- delegate_options_to_subpackages
- quiet
"""
for key, value in options.items():
if key in self.options:
self.options[key] = value
else:
raise ValueError('Unknown option: '+key)
def get_distribution(self):
"""Return the distutils distribution object for self."""
from numpy.distutils.core import get_distribution
return get_distribution()
def _wildcard_get_subpackage(self, subpackage_name,
parent_name,
caller_level = 1):
l = subpackage_name.split('.')
subpackage_path = njoin([self.local_path]+l)
dirs = [_m for _m in sorted_glob(subpackage_path) if os.path.isdir(_m)]
config_list = []
for d in dirs:
if not os.path.isfile(njoin(d, '__init__.py')):
continue
if 'build' in d.split(os.sep):
continue
n = '.'.join(d.split(os.sep)[-len(l):])
c = self.get_subpackage(n,
parent_name = parent_name,
caller_level = caller_level+1)
config_list.extend(c)
return config_list
def _get_configuration_from_setup_py(self, setup_py,
subpackage_name,
subpackage_path,
parent_name,
caller_level = 1):
# In case setup_py imports local modules:
sys.path.insert(0, os.path.dirname(setup_py))
try:
setup_name = os.path.splitext(os.path.basename(setup_py))[0]
n = dot_join(self.name, subpackage_name, setup_name)
setup_module = exec_mod_from_location(
'_'.join(n.split('.')), setup_py)
if not hasattr(setup_module, 'configuration'):
if not self.options['assume_default_configuration']:
self.warn('Assuming default configuration '\
'(%s does not define configuration())'\
% (setup_module))
config = Configuration(subpackage_name, parent_name,
self.top_path, subpackage_path,
caller_level = caller_level + 1)
else:
pn = dot_join(*([parent_name] + subpackage_name.split('.')[:-1]))
args = (pn,)
if setup_module.configuration.__code__.co_argcount > 1:
args = args + (self.top_path,)
config = setup_module.configuration(*args)
if config.name!=dot_join(parent_name, subpackage_name):
self.warn('Subpackage %r configuration returned as %r' % \
(dot_join(parent_name, subpackage_name), config.name))
finally:
del sys.path[0]
return config
def get_subpackage(self,subpackage_name,
subpackage_path=None,
parent_name=None,
caller_level = 1):
"""Return list of subpackage configurations.
Parameters
----------
subpackage_name : str or None
Name of the subpackage to get the configuration. '*' in
subpackage_name is handled as a wildcard.
subpackage_path : str
If None, then the path is assumed to be the local path plus the
subpackage_name. If a setup.py file is not found in the
subpackage_path, then a default configuration is used.
parent_name : str
Parent name.
"""
if subpackage_name is None:
if subpackage_path is None:
raise ValueError(
"either subpackage_name or subpackage_path must be specified")
subpackage_name = os.path.basename(subpackage_path)
# handle wildcards
l = subpackage_name.split('.')
if subpackage_path is None and '*' in subpackage_name:
return self._wildcard_get_subpackage(subpackage_name,
parent_name,
caller_level = caller_level+1)
assert '*' not in subpackage_name, repr((subpackage_name, subpackage_path, parent_name))
if subpackage_path is None:
subpackage_path = njoin([self.local_path] + l)
else:
subpackage_path = njoin([subpackage_path] + l[:-1])
subpackage_path = self.paths([subpackage_path])[0]
setup_py = njoin(subpackage_path, self.setup_name)
if not self.options['ignore_setup_xxx_py']:
if not os.path.isfile(setup_py):
setup_py = njoin(subpackage_path,
'setup_%s.py' % (subpackage_name))
if not os.path.isfile(setup_py):
if not self.options['assume_default_configuration']:
self.warn('Assuming default configuration '\
'(%s/{setup_%s,setup}.py was not found)' \
% (os.path.dirname(setup_py), subpackage_name))
config = Configuration(subpackage_name, parent_name,
self.top_path, subpackage_path,
caller_level = caller_level+1)
else:
config = self._get_configuration_from_setup_py(
setup_py,
subpackage_name,
subpackage_path,
parent_name,
caller_level = caller_level + 1)
if config:
return [config]
else:
return []
def add_subpackage(self,subpackage_name,
subpackage_path=None,
standalone = False):
"""Add a sub-package to the current Configuration instance.
This is useful in a setup.py script for adding sub-packages to a
package.
Parameters
----------
subpackage_name : str
name of the subpackage
subpackage_path : str
if given, the subpackage path such as the subpackage is in
subpackage_path / subpackage_name. If None,the subpackage is
assumed to be located in the local path / subpackage_name.
standalone : bool
"""
if standalone:
parent_name = None
else:
parent_name = self.name
config_list = self.get_subpackage(subpackage_name, subpackage_path,
parent_name = parent_name,
caller_level = 2)
if not config_list:
self.warn('No configuration returned, assuming unavailable.')
for config in config_list:
d = config
if isinstance(config, Configuration):
d = config.todict()
assert isinstance(d, dict), repr(type(d))
self.info('Appending %s configuration to %s' \
% (d.get('name'), self.name))
self.dict_append(**d)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add a subpackage '+ subpackage_name)
def add_data_dir(self, data_path):
"""Recursively add files under data_path to data_files list.
Recursively add files under data_path to the list of data_files to be
installed (and distributed). The data_path can be either a relative
path-name, or an absolute path-name, or a 2-tuple where the first
argument shows where in the install directory the data directory
should be installed to.
Parameters
----------
data_path : seq or str
Argument can be either
* 2-sequence (<datadir suffix>, <path to data directory>)
* path to data directory where python datadir suffix defaults
to package dir.
Notes
-----
Rules for installation paths::
foo/bar -> (foo/bar, foo/bar) -> parent/foo/bar
(gun, foo/bar) -> parent/gun
foo/* -> (foo/a, foo/a), (foo/b, foo/b) -> parent/foo/a, parent/foo/b
(gun, foo/*) -> (gun, foo/a), (gun, foo/b) -> gun
(gun/*, foo/*) -> parent/gun/a, parent/gun/b
/foo/bar -> (bar, /foo/bar) -> parent/bar
(gun, /foo/bar) -> parent/gun
(fun/*/gun/*, sun/foo/bar) -> parent/fun/foo/gun/bar
Examples
--------
For example suppose the source directory contains fun/foo.dat and
fun/bar/car.dat:
>>> self.add_data_dir('fun') #doctest: +SKIP
>>> self.add_data_dir(('sun', 'fun')) #doctest: +SKIP
>>> self.add_data_dir(('gun', '/full/path/to/fun'))#doctest: +SKIP
Will install data-files to the locations::
<package install directory>/
fun/
foo.dat
bar/
car.dat
sun/
foo.dat
bar/
car.dat
gun/
foo.dat
car.dat
"""
if is_sequence(data_path):
d, data_path = data_path
else:
d = None
if is_sequence(data_path):
[self.add_data_dir((d, p)) for p in data_path]
return
if not is_string(data_path):
raise TypeError("not a string: %r" % (data_path,))
if d is None:
if os.path.isabs(data_path):
return self.add_data_dir((os.path.basename(data_path), data_path))
return self.add_data_dir((data_path, data_path))
paths = self.paths(data_path, include_non_existing=False)
if is_glob_pattern(data_path):
if is_glob_pattern(d):
pattern_list = allpath(d).split(os.sep)
pattern_list.reverse()
# /a/*//b/ -> /a/*/b
rl = list(range(len(pattern_list)-1)); rl.reverse()
for i in rl:
if not pattern_list[i]:
del pattern_list[i]
#
for path in paths:
if not os.path.isdir(path):
print('Not a directory, skipping', path)
continue
rpath = rel_path(path, self.local_path)
path_list = rpath.split(os.sep)
path_list.reverse()
target_list = []
i = 0
for s in pattern_list:
if is_glob_pattern(s):
if i>=len(path_list):
raise ValueError('cannot fill pattern %r with %r' \
% (d, path))
target_list.append(path_list[i])
else:
assert s==path_list[i], repr((s, path_list[i], data_path, d, path, rpath))
target_list.append(s)
i += 1
if path_list[i:]:
self.warn('mismatch of pattern_list=%s and path_list=%s'\
% (pattern_list, path_list))
target_list.reverse()
self.add_data_dir((os.sep.join(target_list), path))
else:
for path in paths:
self.add_data_dir((d, path))
return
assert not is_glob_pattern(d), repr(d)
dist = self.get_distribution()
if dist is not None and dist.data_files is not None:
data_files = dist.data_files
else:
data_files = self.data_files
for path in paths:
for d1, f in list(general_source_directories_files(path)):
target_path = os.path.join(self.path_in_package, d, d1)
data_files.append((target_path, f))
def _optimize_data_files(self):
data_dict = {}
for p, files in self.data_files:
if p not in data_dict:
data_dict[p] = set()
for f in files:
data_dict[p].add(f)
self.data_files[:] = [(p, list(files)) for p, files in data_dict.items()]
def add_data_files(self,*files):
"""Add data files to configuration data_files.
Parameters
----------
files : sequence
Argument(s) can be either
* 2-sequence (<datadir prefix>,<path to data file(s)>)
* paths to data files where python datadir prefix defaults
to package dir.
Notes
-----
The form of each element of the files sequence is very flexible
allowing many combinations of where to get the files from the package
and where they should ultimately be installed on the system. The most
basic usage is for an element of the files argument sequence to be a
simple filename. This will cause that file from the local path to be
installed to the installation path of the self.name package (package
path). The file argument can also be a relative path in which case the
entire relative path will be installed into the package directory.
Finally, the file can be an absolute path name in which case the file
will be found at the absolute path name but installed to the package
path.
This basic behavior can be augmented by passing a 2-tuple in as the
file argument. The first element of the tuple should specify the
relative path (under the package install directory) where the
remaining sequence of files should be installed to (it has nothing to
do with the file-names in the source distribution). The second element
of the tuple is the sequence of files that should be installed. The
files in this sequence can be filenames, relative paths, or absolute
paths. For absolute paths the file will be installed in the top-level
package installation directory (regardless of the first argument).
Filenames and relative path names will be installed in the package
install directory under the path name given as the first element of
the tuple.
Rules for installation paths:
#. file.txt -> (., file.txt)-> parent/file.txt
#. foo/file.txt -> (foo, foo/file.txt) -> parent/foo/file.txt
#. /foo/bar/file.txt -> (., /foo/bar/file.txt) -> parent/file.txt
#. ``*``.txt -> parent/a.txt, parent/b.txt
#. foo/``*``.txt`` -> parent/foo/a.txt, parent/foo/b.txt
#. ``*/*.txt`` -> (``*``, ``*``/``*``.txt) -> parent/c/a.txt, parent/d/b.txt
#. (sun, file.txt) -> parent/sun/file.txt
#. (sun, bar/file.txt) -> parent/sun/file.txt
#. (sun, /foo/bar/file.txt) -> parent/sun/file.txt
#. (sun, ``*``.txt) -> parent/sun/a.txt, parent/sun/b.txt
#. (sun, bar/``*``.txt) -> parent/sun/a.txt, parent/sun/b.txt
#. (sun/``*``, ``*``/``*``.txt) -> parent/sun/c/a.txt, parent/d/b.txt
An additional feature is that the path to a data-file can actually be
a function that takes no arguments and returns the actual path(s) to
the data-files. This is useful when the data files are generated while
building the package.
Examples
--------
Add files to the list of data_files to be included with the package.
>>> self.add_data_files('foo.dat',
... ('fun', ['gun.dat', 'nun/pun.dat', '/tmp/sun.dat']),
... 'bar/cat.dat',
... '/full/path/to/can.dat') #doctest: +SKIP
will install these data files to::
<package install directory>/
foo.dat
fun/
gun.dat
nun/
pun.dat
sun.dat
bar/
car.dat
can.dat
where <package install directory> is the package (or sub-package)
directory such as '/usr/lib/python2.4/site-packages/mypackage' ('C:
\\Python2.4 \\Lib \\site-packages \\mypackage') or
'/usr/lib/python2.4/site- packages/mypackage/mysubpackage' ('C:
\\Python2.4 \\Lib \\site-packages \\mypackage \\mysubpackage').
"""
if len(files)>1:
for f in files:
self.add_data_files(f)
return
assert len(files)==1
if is_sequence(files[0]):
d, files = files[0]
else:
d = None
if is_string(files):
filepat = files
elif is_sequence(files):
if len(files)==1:
filepat = files[0]
else:
for f in files:
self.add_data_files((d, f))
return
else:
raise TypeError(repr(type(files)))
if d is None:
if hasattr(filepat, '__call__'):
d = ''
elif os.path.isabs(filepat):
d = ''
else:
d = os.path.dirname(filepat)
self.add_data_files((d, files))
return
paths = self.paths(filepat, include_non_existing=False)
if is_glob_pattern(filepat):
if is_glob_pattern(d):
pattern_list = d.split(os.sep)
pattern_list.reverse()
for path in paths:
path_list = path.split(os.sep)
path_list.reverse()
path_list.pop() # filename
target_list = []
i = 0
for s in pattern_list:
if is_glob_pattern(s):
target_list.append(path_list[i])
i += 1
else:
target_list.append(s)
target_list.reverse()
self.add_data_files((os.sep.join(target_list), path))
else:
self.add_data_files((d, paths))
return
assert not is_glob_pattern(d), repr((d, filepat))
dist = self.get_distribution()
if dist is not None and dist.data_files is not None:
data_files = dist.data_files
else:
data_files = self.data_files
data_files.append((os.path.join(self.path_in_package, d), paths))
### XXX Implement add_py_modules
def add_define_macros(self, macros):
"""Add define macros to configuration
Add the given sequence of macro name and value duples to the beginning
of the define_macros list This list will be visible to all extension
modules of the current package.
"""
dist = self.get_distribution()
if dist is not None:
if not hasattr(dist, 'define_macros'):
dist.define_macros = []
dist.define_macros.extend(macros)
else:
self.define_macros.extend(macros)
def add_include_dirs(self,*paths):
"""Add paths to configuration include directories.
Add the given sequence of paths to the beginning of the include_dirs
list. This list will be visible to all extension modules of the
current package.
"""
include_dirs = self.paths(paths)
dist = self.get_distribution()
if dist is not None:
if dist.include_dirs is None:
dist.include_dirs = []
dist.include_dirs.extend(include_dirs)
else:
self.include_dirs.extend(include_dirs)
def add_headers(self,*files):
"""Add installable headers to configuration.
Add the given sequence of files to the beginning of the headers list.
By default, headers will be installed under <python-
include>/<self.name.replace('.','/')>/ directory. If an item of files
is a tuple, then its first argument specifies the actual installation
location relative to the <python-include> path.
Parameters
----------
files : str or seq
Argument(s) can be either:
* 2-sequence (<includedir suffix>,<path to header file(s)>)
* path(s) to header file(s) where python includedir suffix will
default to package name.
"""
headers = []
for path in files:
if is_string(path):
[headers.append((self.name, p)) for p in self.paths(path)]
else:
if not isinstance(path, (tuple, list)) or len(path) != 2:
raise TypeError(repr(path))
[headers.append((path[0], p)) for p in self.paths(path[1])]
dist = self.get_distribution()
if dist is not None:
if dist.headers is None:
dist.headers = []
dist.headers.extend(headers)
else:
self.headers.extend(headers)
def paths(self,*paths,**kws):
"""Apply glob to paths and prepend local_path if needed.
Applies glob.glob(...) to each path in the sequence (if needed) and
pre-pends the local_path if needed. Because this is called on all
source lists, this allows wildcard characters to be specified in lists
of sources for extension modules and libraries and scripts and allows
path-names be relative to the source directory.
"""
include_non_existing = kws.get('include_non_existing', True)
return gpaths(paths,
local_path = self.local_path,
include_non_existing=include_non_existing)
def _fix_paths_dict(self, kw):
for k in kw.keys():
v = kw[k]
if k in ['sources', 'depends', 'include_dirs', 'library_dirs',
'module_dirs', 'extra_objects']:
new_v = self.paths(v)
kw[k] = new_v
def add_extension(self,name,sources,**kw):
"""Add extension to configuration.
Create and add an Extension instance to the ext_modules list. This
method also takes the following optional keyword arguments that are
passed on to the Extension constructor.
Parameters
----------
name : str
name of the extension
sources : seq
list of the sources. The list of sources may contain functions
(called source generators) which must take an extension instance
and a build directory as inputs and return a source file or list of
source files or None. If None is returned then no sources are
generated. If the Extension instance has no sources after
processing all source generators, then no extension module is
built.
include_dirs :
define_macros :
undef_macros :
library_dirs :
libraries :
runtime_library_dirs :
extra_objects :
extra_compile_args :
extra_link_args :
extra_f77_compile_args :
extra_f90_compile_args :
export_symbols :
swig_opts :
depends :
The depends list contains paths to files or directories that the
sources of the extension module depend on. If any path in the
depends list is newer than the extension module, then the module
will be rebuilt.
language :
f2py_options :
module_dirs :
extra_info : dict or list
dict or list of dict of keywords to be appended to keywords.
Notes
-----
The self.paths(...) method is applied to all lists that may contain
paths.
"""
ext_args = copy.copy(kw)
ext_args['name'] = dot_join(self.name, name)
ext_args['sources'] = sources
if 'extra_info' in ext_args:
extra_info = ext_args['extra_info']
del ext_args['extra_info']
if isinstance(extra_info, dict):
extra_info = [extra_info]
for info in extra_info:
assert isinstance(info, dict), repr(info)
dict_append(ext_args,**info)
self._fix_paths_dict(ext_args)
# Resolve out-of-tree dependencies
libraries = ext_args.get('libraries', [])
libnames = []
ext_args['libraries'] = []
for libname in libraries:
if isinstance(libname, tuple):
self._fix_paths_dict(libname[1])
# Handle library names of the form libname@relative/path/to/library
if '@' in libname:
lname, lpath = libname.split('@', 1)
lpath = os.path.abspath(njoin(self.local_path, lpath))
if os.path.isdir(lpath):
c = self.get_subpackage(None, lpath,
caller_level = 2)
if isinstance(c, Configuration):
c = c.todict()
for l in [l[0] for l in c.get('libraries', [])]:
llname = l.split('__OF__', 1)[0]
if llname == lname:
c.pop('name', None)
dict_append(ext_args,**c)
break
continue
libnames.append(libname)
ext_args['libraries'] = libnames + ext_args['libraries']
ext_args['define_macros'] = \
self.define_macros + ext_args.get('define_macros', [])
from numpy.distutils.core import Extension
ext = Extension(**ext_args)
self.ext_modules.append(ext)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add an extension '+name)
return ext
def add_library(self,name,sources,**build_info):
"""
Add library to configuration.
Parameters
----------
name : str
Name of the extension.
sources : sequence
List of the sources. The list of sources may contain functions
(called source generators) which must take an extension instance
and a build directory as inputs and return a source file or list of
source files or None. If None is returned then no sources are
generated. If the Extension instance has no sources after
processing all source generators, then no extension module is
built.
build_info : dict, optional
The following keys are allowed:
* depends
* macros
* include_dirs
* extra_compiler_args
* extra_f77_compile_args
* extra_f90_compile_args
* f2py_options
* language
"""
self._add_library(name, sources, None, build_info)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add a library '+ name)
def _add_library(self, name, sources, install_dir, build_info):
"""Common implementation for add_library and add_installed_library. Do
not use directly"""
build_info = copy.copy(build_info)
build_info['sources'] = sources
# Sometimes, depends is not set up to an empty list by default, and if
# depends is not given to add_library, distutils barfs (#1134)
if not 'depends' in build_info:
build_info['depends'] = []
self._fix_paths_dict(build_info)
# Add to libraries list so that it is build with build_clib
self.libraries.append((name, build_info))
def add_installed_library(self, name, sources, install_dir, build_info=None):
"""
Similar to add_library, but the specified library is installed.
Most C libraries used with `distutils` are only used to build python
extensions, but libraries built through this method will be installed
so that they can be reused by third-party packages.
Parameters
----------
name : str
Name of the installed library.
sources : sequence
List of the library's source files. See `add_library` for details.
install_dir : str
Path to install the library, relative to the current sub-package.
build_info : dict, optional
The following keys are allowed:
* depends
* macros
* include_dirs
* extra_compiler_args
* extra_f77_compile_args
* extra_f90_compile_args
* f2py_options
* language
Returns
-------
None
See Also
--------
add_library, add_npy_pkg_config, get_info
Notes
-----
The best way to encode the options required to link against the specified
C libraries is to use a "libname.ini" file, and use `get_info` to
retrieve the required options (see `add_npy_pkg_config` for more
information).
"""
if not build_info:
build_info = {}
install_dir = os.path.join(self.package_path, install_dir)
self._add_library(name, sources, install_dir, build_info)
self.installed_libraries.append(InstallableLib(name, build_info, install_dir))
def add_npy_pkg_config(self, template, install_dir, subst_dict=None):
"""
Generate and install a npy-pkg config file from a template.
The config file generated from `template` is installed in the
given install directory, using `subst_dict` for variable substitution.
Parameters
----------
template : str
The path of the template, relatively to the current package path.
install_dir : str
Where to install the npy-pkg config file, relatively to the current
package path.
subst_dict : dict, optional
If given, any string of the form ``@key@`` will be replaced by
``subst_dict[key]`` in the template file when installed. The install
prefix is always available through the variable ``@prefix@``, since the
install prefix is not easy to get reliably from setup.py.
See also
--------
add_installed_library, get_info
Notes
-----
This works for both standard installs and in-place builds, i.e. the
``@prefix@`` refer to the source directory for in-place builds.
Examples
--------
::
config.add_npy_pkg_config('foo.ini.in', 'lib', {'foo': bar})
Assuming the foo.ini.in file has the following content::
[meta]
Name=@foo@
Version=1.0
Description=dummy description
[default]
Cflags=-I@prefix@/include
Libs=
The generated file will have the following content::
[meta]
Name=bar
Version=1.0
Description=dummy description
[default]
Cflags=-Iprefix_dir/include
Libs=
and will be installed as foo.ini in the 'lib' subpath.
When cross-compiling with numpy distutils, it might be necessary to
use modified npy-pkg-config files. Using the default/generated files
will link with the host libraries (i.e. libnpymath.a). For
cross-compilation you of-course need to link with target libraries,
while using the host Python installation.
You can copy out the numpy/core/lib/npy-pkg-config directory, add a
pkgdir value to the .ini files and set NPY_PKG_CONFIG_PATH environment
variable to point to the directory with the modified npy-pkg-config
files.
Example npymath.ini modified for cross-compilation::
[meta]
Name=npymath
Description=Portable, core math library implementing C99 standard
Version=0.1
[variables]
pkgname=numpy.core
pkgdir=/build/arm-linux-gnueabi/sysroot/usr/lib/python3.7/site-packages/numpy/core
prefix=${pkgdir}
libdir=${prefix}/lib
includedir=${prefix}/include
[default]
Libs=-L${libdir} -lnpymath
Cflags=-I${includedir}
Requires=mlib
[msvc]
Libs=/LIBPATH:${libdir} npymath.lib
Cflags=/INCLUDE:${includedir}
Requires=mlib
"""
if subst_dict is None:
subst_dict = {}
template = os.path.join(self.package_path, template)
if self.name in self.installed_pkg_config:
self.installed_pkg_config[self.name].append((template, install_dir,
subst_dict))
else:
self.installed_pkg_config[self.name] = [(template, install_dir,
subst_dict)]
def add_scripts(self,*files):
"""Add scripts to configuration.
Add the sequence of files to the beginning of the scripts list.
Scripts will be installed under the <prefix>/bin/ directory.
"""
scripts = self.paths(files)
dist = self.get_distribution()
if dist is not None:
if dist.scripts is None:
dist.scripts = []
dist.scripts.extend(scripts)
else:
self.scripts.extend(scripts)
def dict_append(self,**dict):
for key in self.list_keys:
a = getattr(self, key)
a.extend(dict.get(key, []))
for key in self.dict_keys:
a = getattr(self, key)
a.update(dict.get(key, {}))
known_keys = self.list_keys + self.dict_keys + self.extra_keys
for key in dict.keys():
if key not in known_keys:
a = getattr(self, key, None)
if a and a==dict[key]: continue
self.warn('Inheriting attribute %r=%r from %r' \
% (key, dict[key], dict.get('name', '?')))
setattr(self, key, dict[key])
self.extra_keys.append(key)
elif key in self.extra_keys:
self.info('Ignoring attempt to set %r (from %r to %r)' \
% (key, getattr(self, key), dict[key]))
elif key in known_keys:
# key is already processed above
pass
else:
raise ValueError("Don't know about key=%r" % (key))
def __str__(self):
from pprint import pformat
known_keys = self.list_keys + self.dict_keys + self.extra_keys
s = '<'+5*'-' + '\n'
s += 'Configuration of '+self.name+':\n'
known_keys.sort()
for k in known_keys:
a = getattr(self, k, None)
if a:
s += '%s = %s\n' % (k, pformat(a))
s += 5*'-' + '>'
return s
def get_config_cmd(self):
"""
Returns the numpy.distutils config command instance.
"""
cmd = get_cmd('config')
cmd.ensure_finalized()
cmd.dump_source = 0
cmd.noisy = 0
old_path = os.environ.get('PATH')
if old_path:
path = os.pathsep.join(['.', old_path])
os.environ['PATH'] = path
return cmd
def get_build_temp_dir(self):
"""
Return a path to a temporary directory where temporary files should be
placed.
"""
cmd = get_cmd('build')
cmd.ensure_finalized()
return cmd.build_temp
def have_f77c(self):
"""Check for availability of Fortran 77 compiler.
Use it inside source generating function to ensure that
setup distribution instance has been initialized.
Notes
-----
True if a Fortran 77 compiler is available (because a simple Fortran 77
code was able to be compiled successfully).
"""
simple_fortran_subroutine = '''
subroutine simple
end
'''
config_cmd = self.get_config_cmd()
flag = config_cmd.try_compile(simple_fortran_subroutine, lang='f77')
return flag
def have_f90c(self):
"""Check for availability of Fortran 90 compiler.
Use it inside source generating function to ensure that
setup distribution instance has been initialized.
Notes
-----
True if a Fortran 90 compiler is available (because a simple Fortran
90 code was able to be compiled successfully)
"""
simple_fortran_subroutine = '''
subroutine simple
end
'''
config_cmd = self.get_config_cmd()
flag = config_cmd.try_compile(simple_fortran_subroutine, lang='f90')
return flag
def append_to(self, extlib):
"""Append libraries, include_dirs to extension or library item.
"""
if is_sequence(extlib):
lib_name, build_info = extlib
dict_append(build_info,
libraries=self.libraries,
include_dirs=self.include_dirs)
else:
from numpy.distutils.core import Extension
assert isinstance(extlib, Extension), repr(extlib)
extlib.libraries.extend(self.libraries)
extlib.include_dirs.extend(self.include_dirs)
def _get_svn_revision(self, path):
"""Return path's SVN revision number.
"""
try:
output = subprocess.check_output(['svnversion'], cwd=path)
except (subprocess.CalledProcessError, OSError):
pass
else:
m = re.match(rb'(?P<revision>\d+)', output)
if m:
return int(m.group('revision'))
if sys.platform=='win32' and os.environ.get('SVN_ASP_DOT_NET_HACK', None):
entries = njoin(path, '_svn', 'entries')
else:
entries = njoin(path, '.svn', 'entries')
if os.path.isfile(entries):
with open(entries) as f:
fstr = f.read()
if fstr[:5] == '<?xml': # pre 1.4
m = re.search(r'revision="(?P<revision>\d+)"', fstr)
if m:
return int(m.group('revision'))
else: # non-xml entries file --- check to be sure that
m = re.search(r'dir[\n\r]+(?P<revision>\d+)', fstr)
if m:
return int(m.group('revision'))
return None
def _get_hg_revision(self, path):
"""Return path's Mercurial revision number.
"""
try:
output = subprocess.check_output(
['hg', 'identify', '--num'], cwd=path)
except (subprocess.CalledProcessError, OSError):
pass
else:
m = re.match(rb'(?P<revision>\d+)', output)
if m:
return int(m.group('revision'))
branch_fn = njoin(path, '.hg', 'branch')
branch_cache_fn = njoin(path, '.hg', 'branch.cache')
if os.path.isfile(branch_fn):
branch0 = None
with open(branch_fn) as f:
revision0 = f.read().strip()
branch_map = {}
with open(branch_cache_fn, 'r') as f:
for line in f:
branch1, revision1 = line.split()[:2]
if revision1==revision0:
branch0 = branch1
try:
revision1 = int(revision1)
except ValueError:
continue
branch_map[branch1] = revision1
return branch_map.get(branch0)
return None
def get_version(self, version_file=None, version_variable=None):
"""Try to get version string of a package.
Return a version string of the current package or None if the version
information could not be detected.
Notes
-----
This method scans files named
__version__.py, <packagename>_version.py, version.py, and
__svn_version__.py for string variables version, __version__, and
<packagename>_version, until a version number is found.
"""
version = getattr(self, 'version', None)
if version is not None:
return version
# Get version from version file.
if version_file is None:
files = ['__version__.py',
self.name.split('.')[-1]+'_version.py',
'version.py',
'__svn_version__.py',
'__hg_version__.py']
else:
files = [version_file]
if version_variable is None:
version_vars = ['version',
'__version__',
self.name.split('.')[-1]+'_version']
else:
version_vars = [version_variable]
for f in files:
fn = njoin(self.local_path, f)
if os.path.isfile(fn):
info = ('.py', 'U', 1)
name = os.path.splitext(os.path.basename(fn))[0]
n = dot_join(self.name, name)
try:
version_module = exec_mod_from_location(
'_'.join(n.split('.')), fn)
except ImportError as e:
self.warn(str(e))
version_module = None
if version_module is None:
continue
for a in version_vars:
version = getattr(version_module, a, None)
if version is not None:
break
# Try if versioneer module
try:
version = version_module.get_versions()['version']
except AttributeError:
pass
if version is not None:
break
if version is not None:
self.version = version
return version
# Get version as SVN or Mercurial revision number
revision = self._get_svn_revision(self.local_path)
if revision is None:
revision = self._get_hg_revision(self.local_path)
if revision is not None:
version = str(revision)
self.version = version
return version
def make_svn_version_py(self, delete=True):
"""Appends a data function to the data_files list that will generate
__svn_version__.py file to the current package directory.
Generate package __svn_version__.py file from SVN revision number,
it will be removed after python exits but will be available
when sdist, etc commands are executed.
Notes
-----
If __svn_version__.py existed before, nothing is done.
This is
intended for working with source directories that are in an SVN
repository.
"""
target = njoin(self.local_path, '__svn_version__.py')
revision = self._get_svn_revision(self.local_path)
if os.path.isfile(target) or revision is None:
return
else:
def generate_svn_version_py():
if not os.path.isfile(target):
version = str(revision)
self.info('Creating %s (version=%r)' % (target, version))
with open(target, 'w') as f:
f.write('version = %r\n' % (version))
def rm_file(f=target,p=self.info):
if delete:
try: os.remove(f); p('removed '+f)
except OSError: pass
try: os.remove(f+'c'); p('removed '+f+'c')
except OSError: pass
atexit.register(rm_file)
return target
self.add_data_files(('', generate_svn_version_py()))
def make_hg_version_py(self, delete=True):
"""Appends a data function to the data_files list that will generate
__hg_version__.py file to the current package directory.
Generate package __hg_version__.py file from Mercurial revision,
it will be removed after python exits but will be available
when sdist, etc commands are executed.
Notes
-----
If __hg_version__.py existed before, nothing is done.
This is intended for working with source directories that are
in an Mercurial repository.
"""
target = njoin(self.local_path, '__hg_version__.py')
revision = self._get_hg_revision(self.local_path)
if os.path.isfile(target) or revision is None:
return
else:
def generate_hg_version_py():
if not os.path.isfile(target):
version = str(revision)
self.info('Creating %s (version=%r)' % (target, version))
with open(target, 'w') as f:
f.write('version = %r\n' % (version))
def rm_file(f=target,p=self.info):
if delete:
try: os.remove(f); p('removed '+f)
except OSError: pass
try: os.remove(f+'c'); p('removed '+f+'c')
except OSError: pass
atexit.register(rm_file)
return target
self.add_data_files(('', generate_hg_version_py()))
def make_config_py(self,name='__config__'):
"""Generate package __config__.py file containing system_info
information used during building the package.
This file is installed to the
package installation directory.
"""
self.py_modules.append((self.name, name, generate_config_py))
def get_info(self,*names):
"""Get resources information.
Return information (from system_info.get_info) for all of the names in
the argument list in a single dictionary.
"""
from .system_info import get_info, dict_append
info_dict = {}
for a in names:
dict_append(info_dict,**get_info(a))
return info_dict
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration('lib', parent_package, top_path)
config.add_subpackage('tests')
config.add_data_dir('tests/data')
config.add_data_files('*.pyi')
return config | null |
168,647 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _unary_dispatcher(x):
return (x,) | null |
168,648 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_lt_zero(x):
"""Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `sqrt` function. Write a Python function `def sqrt(x)` to solve the following problem:
Compute the square root of x. For negative input elements, a complex value is returned (unlike `numpy.sqrt` which returns NaN). Parameters ---------- x : array_like The input value(s). Returns ------- out : ndarray or scalar The square root of `x`. If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.sqrt Examples -------- For real, non-negative inputs this works just like `numpy.sqrt`: >>> np.emath.sqrt(1) 1.0 >>> np.emath.sqrt([1, 4]) array([1., 2.]) But it automatically handles negative inputs: >>> np.emath.sqrt(-1) 1j >>> np.emath.sqrt([-1,4]) array([0.+1.j, 2.+0.j]) Different results are expected because: floating point 0.0 and -0.0 are distinct. For more control, explicitly use complex() as follows: >>> np.emath.sqrt(complex(-4.0, 0.0)) 2j >>> np.emath.sqrt(complex(-4.0, -0.0)) -2j
Here is the function:
def sqrt(x):
"""
Compute the square root of x.
For negative input elements, a complex value is returned
(unlike `numpy.sqrt` which returns NaN).
Parameters
----------
x : array_like
The input value(s).
Returns
-------
out : ndarray or scalar
The square root of `x`. If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.sqrt
Examples
--------
For real, non-negative inputs this works just like `numpy.sqrt`:
>>> np.emath.sqrt(1)
1.0
>>> np.emath.sqrt([1, 4])
array([1., 2.])
But it automatically handles negative inputs:
>>> np.emath.sqrt(-1)
1j
>>> np.emath.sqrt([-1,4])
array([0.+1.j, 2.+0.j])
Different results are expected because:
floating point 0.0 and -0.0 are distinct.
For more control, explicitly use complex() as follows:
>>> np.emath.sqrt(complex(-4.0, 0.0))
2j
>>> np.emath.sqrt(complex(-4.0, -0.0))
-2j
"""
x = _fix_real_lt_zero(x)
return nx.sqrt(x) | Compute the square root of x. For negative input elements, a complex value is returned (unlike `numpy.sqrt` which returns NaN). Parameters ---------- x : array_like The input value(s). Returns ------- out : ndarray or scalar The square root of `x`. If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.sqrt Examples -------- For real, non-negative inputs this works just like `numpy.sqrt`: >>> np.emath.sqrt(1) 1.0 >>> np.emath.sqrt([1, 4]) array([1., 2.]) But it automatically handles negative inputs: >>> np.emath.sqrt(-1) 1j >>> np.emath.sqrt([-1,4]) array([0.+1.j, 2.+0.j]) Different results are expected because: floating point 0.0 and -0.0 are distinct. For more control, explicitly use complex() as follows: >>> np.emath.sqrt(complex(-4.0, 0.0)) 2j >>> np.emath.sqrt(complex(-4.0, -0.0)) -2j |
168,649 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_lt_zero(x):
"""Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `log10` function. Write a Python function `def log10(x)` to solve the following problem:
Compute the logarithm base 10 of `x`. Return the "principal value" (for a description of this, see `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose log base 10 is (are) required. Returns ------- out : ndarray or scalar The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.log10 Notes ----- For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10` (note, however, that otherwise `numpy.log10` and this `log10` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- (We set the printing precision so the example can be auto-tested) >>> np.set_printoptions(precision=4) >>> np.emath.log10(10**1) 1.0 >>> np.emath.log10([-10**1, -10**2, 10**2]) array([1.+1.3644j, 2.+1.3644j, 2.+0.j ])
Here is the function:
def log10(x):
"""
Compute the logarithm base 10 of `x`.
Return the "principal value" (for a description of this, see
`numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this
is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)``
returns ``inf``). Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like or scalar
The value(s) whose log base 10 is (are) required.
Returns
-------
out : ndarray or scalar
The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array object is returned.
See Also
--------
numpy.log10
Notes
-----
For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10`
(note, however, that otherwise `numpy.log10` and this `log10` are
identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
and, notably, the complex principle value if ``x.imag != 0``).
Examples
--------
(We set the printing precision so the example can be auto-tested)
>>> np.set_printoptions(precision=4)
>>> np.emath.log10(10**1)
1.0
>>> np.emath.log10([-10**1, -10**2, 10**2])
array([1.+1.3644j, 2.+1.3644j, 2.+0.j ])
"""
x = _fix_real_lt_zero(x)
return nx.log10(x) | Compute the logarithm base 10 of `x`. Return the "principal value" (for a description of this, see `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose log base 10 is (are) required. Returns ------- out : ndarray or scalar The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.log10 Notes ----- For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10` (note, however, that otherwise `numpy.log10` and this `log10` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- (We set the printing precision so the example can be auto-tested) >>> np.set_printoptions(precision=4) >>> np.emath.log10(10**1) 1.0 >>> np.emath.log10([-10**1, -10**2, 10**2]) array([1.+1.3644j, 2.+1.3644j, 2.+0.j ]) |
168,650 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _logn_dispatcher(n, x):
return (n, x,) | null |
168,651 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_lt_zero(x):
"""Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = _tocomplex(x)
return x
def log(x):
"""
Compute the natural logarithm of `x`.
Return the "principal value" (for a description of this, see `numpy.log`)
of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)``
returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the
complex principle value is returned.
Parameters
----------
x : array_like
The value(s) whose log is (are) required.
Returns
-------
out : ndarray or scalar
The log of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.log
Notes
-----
For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log`
(note, however, that otherwise `numpy.log` and this `log` are identical,
i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and,
notably, the complex principle value if ``x.imag != 0``).
Examples
--------
>>> np.emath.log(np.exp(1))
1.0
Negative arguments are handled "correctly" (recall that
``exp(log(x)) == x`` does *not* hold for real ``x < 0``):
>>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j)
True
"""
x = _fix_real_lt_zero(x)
return nx.log(x)
The provided code snippet includes necessary dependencies for implementing the `logn` function. Write a Python function `def logn(n, x)` to solve the following problem:
Take log base n of x. If `x` contains negative inputs, the answer is computed and returned in the complex domain. Parameters ---------- n : array_like The integer base(s) in which the log is taken. x : array_like The value(s) whose log base `n` is (are) required. Returns ------- out : ndarray or scalar The log base `n` of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.logn(2, [4, 8]) array([2., 3.]) >>> np.emath.logn(2, [-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
Here is the function:
def logn(n, x):
"""
Take log base n of x.
If `x` contains negative inputs, the answer is computed and returned in the
complex domain.
Parameters
----------
n : array_like
The integer base(s) in which the log is taken.
x : array_like
The value(s) whose log base `n` is (are) required.
Returns
-------
out : ndarray or scalar
The log base `n` of the `x` value(s). If `x` was a scalar, so is
`out`, otherwise an array is returned.
Examples
--------
>>> np.set_printoptions(precision=4)
>>> np.emath.logn(2, [4, 8])
array([2., 3.])
>>> np.emath.logn(2, [-4, -8, 8])
array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
"""
x = _fix_real_lt_zero(x)
n = _fix_real_lt_zero(n)
return nx.log(x)/nx.log(n) | Take log base n of x. If `x` contains negative inputs, the answer is computed and returned in the complex domain. Parameters ---------- n : array_like The integer base(s) in which the log is taken. x : array_like The value(s) whose log base `n` is (are) required. Returns ------- out : ndarray or scalar The log base `n` of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.logn(2, [4, 8]) array([2., 3.]) >>> np.emath.logn(2, [-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ]) |
168,652 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_lt_zero(x):
"""Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `log2` function. Write a Python function `def log2(x)` to solve the following problem:
Compute the logarithm base 2 of `x`. Return the "principal value" (for a description of this, see `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log base 2 is (are) required. Returns ------- out : ndarray or scalar The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log2 Notes ----- For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2` (note, however, that otherwise `numpy.log2` and this `log2` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- We set the printing precision so the example can be auto-tested: >>> np.set_printoptions(precision=4) >>> np.emath.log2(8) 3.0 >>> np.emath.log2([-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
Here is the function:
def log2(x):
"""
Compute the logarithm base 2 of `x`.
Return the "principal value" (for a description of this, see
`numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is
a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns
``inf``). Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like
The value(s) whose log base 2 is (are) required.
Returns
-------
out : ndarray or scalar
The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.log2
Notes
-----
For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2`
(note, however, that otherwise `numpy.log2` and this `log2` are
identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
and, notably, the complex principle value if ``x.imag != 0``).
Examples
--------
We set the printing precision so the example can be auto-tested:
>>> np.set_printoptions(precision=4)
>>> np.emath.log2(8)
3.0
>>> np.emath.log2([-4, -8, 8])
array([2.+4.5324j, 3.+4.5324j, 3.+0.j ])
"""
x = _fix_real_lt_zero(x)
return nx.log2(x) | Compute the logarithm base 2 of `x`. Return the "principal value" (for a description of this, see `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log base 2 is (are) required. Returns ------- out : ndarray or scalar The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log2 Notes ----- For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2` (note, however, that otherwise `numpy.log2` and this `log2` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- We set the printing precision so the example can be auto-tested: >>> np.set_printoptions(precision=4) >>> np.emath.log2(8) 3.0 >>> np.emath.log2([-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ]) |
168,653 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _power_dispatcher(x, p):
return (x, p) | null |
168,654 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_lt_zero(x):
"""Convert `x` to complex if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_real_lt_zero([-1,2])
array([-1.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = _tocomplex(x)
return x
def _fix_int_lt_zero(x):
"""Convert `x` to double if it has real, negative components.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_int_lt_zero([1,2])
array([1, 2])
>>> np.lib.scimath._fix_int_lt_zero([-1,2])
array([-1., 2.])
"""
x = asarray(x)
if any(isreal(x) & (x < 0)):
x = x * 1.0
return x
The provided code snippet includes necessary dependencies for implementing the `power` function. Write a Python function `def power(x, p)` to solve the following problem:
Return x to the power p, (x**p). If `x` contains negative values, the output is converted to the complex domain. Parameters ---------- x : array_like The input value(s). p : array_like of ints The power(s) to which `x` is raised. If `x` contains multiple values, `p` has to either be a scalar, or contain the same number of values as `x`. In the latter case, the result is ``x[0]**p[0], x[1]**p[1], ...``. Returns ------- out : ndarray or scalar The result of ``x**p``. If `x` and `p` are scalars, so is `out`, otherwise an array is returned. See Also -------- numpy.power Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.power([2, 4], 2) array([ 4, 16]) >>> np.emath.power([2, 4], -2) array([0.25 , 0.0625]) >>> np.emath.power([-2, 4], 2) array([ 4.-0.j, 16.+0.j])
Here is the function:
def power(x, p):
"""
Return x to the power p, (x**p).
If `x` contains negative values, the output is converted to the
complex domain.
Parameters
----------
x : array_like
The input value(s).
p : array_like of ints
The power(s) to which `x` is raised. If `x` contains multiple values,
`p` has to either be a scalar, or contain the same number of values
as `x`. In the latter case, the result is
``x[0]**p[0], x[1]**p[1], ...``.
Returns
-------
out : ndarray or scalar
The result of ``x**p``. If `x` and `p` are scalars, so is `out`,
otherwise an array is returned.
See Also
--------
numpy.power
Examples
--------
>>> np.set_printoptions(precision=4)
>>> np.emath.power([2, 4], 2)
array([ 4, 16])
>>> np.emath.power([2, 4], -2)
array([0.25 , 0.0625])
>>> np.emath.power([-2, 4], 2)
array([ 4.-0.j, 16.+0.j])
"""
x = _fix_real_lt_zero(x)
p = _fix_int_lt_zero(p)
return nx.power(x, p) | Return x to the power p, (x**p). If `x` contains negative values, the output is converted to the complex domain. Parameters ---------- x : array_like The input value(s). p : array_like of ints The power(s) to which `x` is raised. If `x` contains multiple values, `p` has to either be a scalar, or contain the same number of values as `x`. In the latter case, the result is ``x[0]**p[0], x[1]**p[1], ...``. Returns ------- out : ndarray or scalar The result of ``x**p``. If `x` and `p` are scalars, so is `out`, otherwise an array is returned. See Also -------- numpy.power Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.power([2, 4], 2) array([ 4, 16]) >>> np.emath.power([2, 4], -2) array([0.25 , 0.0625]) >>> np.emath.power([-2, 4], 2) array([ 4.-0.j, 16.+0.j]) |
168,655 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_abs_gt_1(x):
"""Convert `x` to complex if it has real components x_i with abs(x_i)>1.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_abs_gt_1([0,1])
array([0, 1])
>>> np.lib.scimath._fix_real_abs_gt_1([0,2])
array([0.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (abs(x) > 1)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `arccos` function. Write a Python function `def arccos(x)` to solve the following problem:
Compute the inverse cosine of x. Return the "principal value" (for a description of this, see `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[0, \\pi]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arccos is (are) required. Returns ------- out : ndarray or scalar The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arccos Notes ----- For an arccos() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arccos`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arccos(1) # a scalar is returned 0.0 >>> np.emath.arccos([1,2]) array([0.-0.j , 0.-1.317j])
Here is the function:
def arccos(x):
"""
Compute the inverse cosine of x.
Return the "principal value" (for a description of this, see
`numpy.arccos`) of the inverse cosine of `x`. For real `x` such that
`abs(x) <= 1`, this is a real number in the closed interval
:math:`[0, \\pi]`. Otherwise, the complex principle value is returned.
Parameters
----------
x : array_like or scalar
The value(s) whose arccos is (are) required.
Returns
-------
out : ndarray or scalar
The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so
is `out`, otherwise an array object is returned.
See Also
--------
numpy.arccos
Notes
-----
For an arccos() that returns ``NAN`` when real `x` is not in the
interval ``[-1,1]``, use `numpy.arccos`.
Examples
--------
>>> np.set_printoptions(precision=4)
>>> np.emath.arccos(1) # a scalar is returned
0.0
>>> np.emath.arccos([1,2])
array([0.-0.j , 0.-1.317j])
"""
x = _fix_real_abs_gt_1(x)
return nx.arccos(x) | Compute the inverse cosine of x. Return the "principal value" (for a description of this, see `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[0, \\pi]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arccos is (are) required. Returns ------- out : ndarray or scalar The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arccos Notes ----- For an arccos() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arccos`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arccos(1) # a scalar is returned 0.0 >>> np.emath.arccos([1,2]) array([0.-0.j , 0.-1.317j]) |
168,656 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_abs_gt_1(x):
"""Convert `x` to complex if it has real components x_i with abs(x_i)>1.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_abs_gt_1([0,1])
array([0, 1])
>>> np.lib.scimath._fix_real_abs_gt_1([0,2])
array([0.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (abs(x) > 1)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `arcsin` function. Write a Python function `def arcsin(x)` to solve the following problem:
Compute the inverse sine of x. Return the "principal value" (for a description of this, see `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[-\\pi/2, \\pi/2]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arcsin is (are) required. Returns ------- out : ndarray or scalar The inverse sine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arcsin Notes ----- For an arcsin() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arcsin`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([0. , 1.5708])
Here is the function:
def arcsin(x):
"""
Compute the inverse sine of x.
Return the "principal value" (for a description of this, see
`numpy.arcsin`) of the inverse sine of `x`. For real `x` such that
`abs(x) <= 1`, this is a real number in the closed interval
:math:`[-\\pi/2, \\pi/2]`. Otherwise, the complex principle value is
returned.
Parameters
----------
x : array_like or scalar
The value(s) whose arcsin is (are) required.
Returns
-------
out : ndarray or scalar
The inverse sine(s) of the `x` value(s). If `x` was a scalar, so
is `out`, otherwise an array object is returned.
See Also
--------
numpy.arcsin
Notes
-----
For an arcsin() that returns ``NAN`` when real `x` is not in the
interval ``[-1,1]``, use `numpy.arcsin`.
Examples
--------
>>> np.set_printoptions(precision=4)
>>> np.emath.arcsin(0)
0.0
>>> np.emath.arcsin([0,1])
array([0. , 1.5708])
"""
x = _fix_real_abs_gt_1(x)
return nx.arcsin(x) | Compute the inverse sine of x. Return the "principal value" (for a description of this, see `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[-\\pi/2, \\pi/2]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arcsin is (are) required. Returns ------- out : ndarray or scalar The inverse sine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arcsin Notes ----- For an arcsin() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arcsin`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([0. , 1.5708]) |
168,657 | import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal
def _fix_real_abs_gt_1(x):
"""Convert `x` to complex if it has real components x_i with abs(x_i)>1.
Otherwise, output is just the array version of the input (via asarray).
Parameters
----------
x : array_like
Returns
-------
array
Examples
--------
>>> np.lib.scimath._fix_real_abs_gt_1([0,1])
array([0, 1])
>>> np.lib.scimath._fix_real_abs_gt_1([0,2])
array([0.+0.j, 2.+0.j])
"""
x = asarray(x)
if any(isreal(x) & (abs(x) > 1)):
x = _tocomplex(x)
return x
The provided code snippet includes necessary dependencies for implementing the `arctanh` function. Write a Python function `def arctanh(x)` to solve the following problem:
Compute the inverse hyperbolic tangent of `x`. Return the "principal value" (for a description of this, see `numpy.arctanh`) of ``arctanh(x)``. For real `x` such that ``abs(x) < 1``, this is a real number. If `abs(x) > 1`, or if `x` is complex, the result is complex. Finally, `x = 1` returns``inf`` and ``x=-1`` returns ``-inf``. Parameters ---------- x : array_like The value(s) whose arctanh is (are) required. Returns ------- out : ndarray or scalar The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was a scalar so is `out`, otherwise an array is returned. See Also -------- numpy.arctanh Notes ----- For an arctanh() that returns ``NAN`` when real `x` is not in the interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does return +/-inf for ``x = +/-1``). Examples -------- >>> np.set_printoptions(precision=4) >>> from numpy.testing import suppress_warnings >>> with suppress_warnings() as sup: ... sup.filter(RuntimeWarning) ... np.emath.arctanh(np.eye(2)) array([[inf, 0.], [ 0., inf]]) >>> np.emath.arctanh([1j]) array([0.+0.7854j])
Here is the function:
def arctanh(x):
"""
Compute the inverse hyperbolic tangent of `x`.
Return the "principal value" (for a description of this, see
`numpy.arctanh`) of ``arctanh(x)``. For real `x` such that
``abs(x) < 1``, this is a real number. If `abs(x) > 1`, or if `x` is
complex, the result is complex. Finally, `x = 1` returns``inf`` and
``x=-1`` returns ``-inf``.
Parameters
----------
x : array_like
The value(s) whose arctanh is (are) required.
Returns
-------
out : ndarray or scalar
The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was
a scalar so is `out`, otherwise an array is returned.
See Also
--------
numpy.arctanh
Notes
-----
For an arctanh() that returns ``NAN`` when real `x` is not in the
interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does
return +/-inf for ``x = +/-1``).
Examples
--------
>>> np.set_printoptions(precision=4)
>>> from numpy.testing import suppress_warnings
>>> with suppress_warnings() as sup:
... sup.filter(RuntimeWarning)
... np.emath.arctanh(np.eye(2))
array([[inf, 0.],
[ 0., inf]])
>>> np.emath.arctanh([1j])
array([0.+0.7854j])
"""
x = _fix_real_abs_gt_1(x)
return nx.arctanh(x) | Compute the inverse hyperbolic tangent of `x`. Return the "principal value" (for a description of this, see `numpy.arctanh`) of ``arctanh(x)``. For real `x` such that ``abs(x) < 1``, this is a real number. If `abs(x) > 1`, or if `x` is complex, the result is complex. Finally, `x = 1` returns``inf`` and ``x=-1`` returns ``-inf``. Parameters ---------- x : array_like The value(s) whose arctanh is (are) required. Returns ------- out : ndarray or scalar The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was a scalar so is `out`, otherwise an array is returned. See Also -------- numpy.arctanh Notes ----- For an arctanh() that returns ``NAN`` when real `x` is not in the interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does return +/-inf for ``x = +/-1``). Examples -------- >>> np.set_printoptions(precision=4) >>> from numpy.testing import suppress_warnings >>> with suppress_warnings() as sup: ... sup.filter(RuntimeWarning) ... np.emath.arctanh(np.eye(2)) array([[inf, 0.], [ 0., inf]]) >>> np.emath.arctanh([1j]) array([0.+0.7854j]) |
168,658 | import numpy as np
import numpy.core.numeric as nx
from numpy.compat import asbytes, asunicode
The provided code snippet includes necessary dependencies for implementing the `_is_bytes_like` function. Write a Python function `def _is_bytes_like(obj)` to solve the following problem:
Check whether obj behaves like a bytes object.
Here is the function:
def _is_bytes_like(obj):
"""
Check whether obj behaves like a bytes object.
"""
try:
obj + b''
except (TypeError, ValueError):
return False
return True | Check whether obj behaves like a bytes object. |
168,659 | import numpy as np
import numpy.core.numeric as nx
from numpy.compat import asbytes, asunicode
The provided code snippet includes necessary dependencies for implementing the `str2bool` function. Write a Python function `def str2bool(value)` to solve the following problem:
Tries to transform a string supposed to represent a boolean to a boolean. Parameters ---------- value : str The string that is transformed to a boolean. Returns ------- boolval : bool The boolean representation of `value`. Raises ------ ValueError If the string is not 'True' or 'False' (case independent) Examples -------- >>> np.lib._iotools.str2bool('TRUE') True >>> np.lib._iotools.str2bool('false') False
Here is the function:
def str2bool(value):
"""
Tries to transform a string supposed to represent a boolean to a boolean.
Parameters
----------
value : str
The string that is transformed to a boolean.
Returns
-------
boolval : bool
The boolean representation of `value`.
Raises
------
ValueError
If the string is not 'True' or 'False' (case independent)
Examples
--------
>>> np.lib._iotools.str2bool('TRUE')
True
>>> np.lib._iotools.str2bool('false')
False
"""
value = value.upper()
if value == 'TRUE':
return True
elif value == 'FALSE':
return False
else:
raise ValueError("Invalid boolean") | Tries to transform a string supposed to represent a boolean to a boolean. Parameters ---------- value : str The string that is transformed to a boolean. Returns ------- boolval : bool The boolean representation of `value`. Raises ------ ValueError If the string is not 'True' or 'False' (case independent) Examples -------- >>> np.lib._iotools.str2bool('TRUE') True >>> np.lib._iotools.str2bool('false') False |
168,660 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `show_runtime` function. Write a Python function `def show_runtime()` to solve the following problem:
Print information about various resources in the system including available intrinsic support and BLAS/LAPACK library in use See Also -------- show_config : Show libraries in the system on which NumPy was built. Notes ----- 1. Information is derived with the help of `threadpoolctl <https://pypi.org/project/threadpoolctl/>`_ library. 2. SIMD related information is derived from ``__cpu_features__``, ``__cpu_baseline__`` and ``__cpu_dispatch__`` Examples -------- >>> import numpy as np >>> np.show_runtime() [{'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'], 'found': ['SSSE3', 'SSE41', 'POPCNT', 'SSE42', 'AVX', 'F16C', 'FMA3', 'AVX2'], 'not_found': ['AVX512F', 'AVX512CD', 'AVX512_KNL', 'AVX512_KNM', 'AVX512_SKX', 'AVX512_CLX', 'AVX512_CNL', 'AVX512_ICL']}}, {'architecture': 'Zen', 'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so', 'internal_api': 'openblas', 'num_threads': 12, 'prefix': 'libopenblas', 'threading_layer': 'pthreads', 'user_api': 'blas', 'version': '0.3.20'}]
Here is the function:
def show_runtime():
"""
Print information about various resources in the system
including available intrinsic support and BLAS/LAPACK library
in use
See Also
--------
show_config : Show libraries in the system on which NumPy was built.
Notes
-----
1. Information is derived with the help of `threadpoolctl <https://pypi.org/project/threadpoolctl/>`_
library.
2. SIMD related information is derived from ``__cpu_features__``,
``__cpu_baseline__`` and ``__cpu_dispatch__``
Examples
--------
>>> import numpy as np
>>> np.show_runtime()
[{'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],
'found': ['SSSE3',
'SSE41',
'POPCNT',
'SSE42',
'AVX',
'F16C',
'FMA3',
'AVX2'],
'not_found': ['AVX512F',
'AVX512CD',
'AVX512_KNL',
'AVX512_KNM',
'AVX512_SKX',
'AVX512_CLX',
'AVX512_CNL',
'AVX512_ICL']}},
{'architecture': 'Zen',
'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so',
'internal_api': 'openblas',
'num_threads': 12,
'prefix': 'libopenblas',
'threading_layer': 'pthreads',
'user_api': 'blas',
'version': '0.3.20'}]
"""
from numpy.core._multiarray_umath import (
__cpu_features__, __cpu_baseline__, __cpu_dispatch__
)
from pprint import pprint
config_found = []
features_found, features_not_found = [], []
for feature in __cpu_dispatch__:
if __cpu_features__[feature]:
features_found.append(feature)
else:
features_not_found.append(feature)
config_found.append({
"simd_extensions": {
"baseline": __cpu_baseline__,
"found": features_found,
"not_found": features_not_found
}
})
try:
from threadpoolctl import threadpool_info
config_found.extend(threadpool_info())
except ImportError:
print("WARNING: `threadpoolctl` not found in system!"
" Install it by `pip install threadpoolctl`."
" Once installed, try `np.show_runtime` again"
" for more detailed build information")
pprint(config_found) | Print information about various resources in the system including available intrinsic support and BLAS/LAPACK library in use See Also -------- show_config : Show libraries in the system on which NumPy was built. Notes ----- 1. Information is derived with the help of `threadpoolctl <https://pypi.org/project/threadpoolctl/>`_ library. 2. SIMD related information is derived from ``__cpu_features__``, ``__cpu_baseline__`` and ``__cpu_dispatch__`` Examples -------- >>> import numpy as np >>> np.show_runtime() [{'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'], 'found': ['SSSE3', 'SSE41', 'POPCNT', 'SSE42', 'AVX', 'F16C', 'FMA3', 'AVX2'], 'not_found': ['AVX512F', 'AVX512CD', 'AVX512_KNL', 'AVX512_KNM', 'AVX512_SKX', 'AVX512_CLX', 'AVX512_CNL', 'AVX512_ICL']}}, {'architecture': 'Zen', 'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so', 'internal_api': 'openblas', 'num_threads': 12, 'prefix': 'libopenblas', 'threading_layer': 'pthreads', 'user_api': 'blas', 'version': '0.3.20'}] |
168,661 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `get_include` function. Write a Python function `def get_include()` to solve the following problem:
Return the directory that contains the NumPy \\*.h header files. Extension modules that need to compile against NumPy should use this function to locate the appropriate include directory. Notes ----- When using ``distutils``, for example in ``setup.py``:: import numpy as np ... Extension('extension_name', ... include_dirs=[np.get_include()]) ...
Here is the function:
def get_include():
"""
Return the directory that contains the NumPy \\*.h header files.
Extension modules that need to compile against NumPy should use this
function to locate the appropriate include directory.
Notes
-----
When using ``distutils``, for example in ``setup.py``::
import numpy as np
...
Extension('extension_name', ...
include_dirs=[np.get_include()])
...
"""
import numpy
if numpy.show_config is None:
# running from numpy source directory
d = os.path.join(os.path.dirname(numpy.__file__), 'core', 'include')
else:
# using installed numpy core headers
import numpy.core as core
d = os.path.join(os.path.dirname(core.__file__), 'include')
return d | Return the directory that contains the NumPy \\*.h header files. Extension modules that need to compile against NumPy should use this function to locate the appropriate include directory. Notes ----- When using ``distutils``, for example in ``setup.py``:: import numpy as np ... Extension('extension_name', ... include_dirs=[np.get_include()]) ... |
168,662 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `_get_indent` function. Write a Python function `def _get_indent(lines)` to solve the following problem:
Determines the leading whitespace that could be removed from all the lines.
Here is the function:
def _get_indent(lines):
"""
Determines the leading whitespace that could be removed from all the lines.
"""
indent = sys.maxsize
for line in lines:
content = len(line.lstrip())
if content:
indent = min(indent, len(line) - content)
if indent == sys.maxsize:
indent = 0
return indent | Determines the leading whitespace that could be removed from all the lines. |
168,663 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
class _Deprecate:
"""
Decorator class to deprecate old functions.
Refer to `deprecate` for details.
See Also
--------
deprecate
"""
def __init__(self, old_name=None, new_name=None, message=None):
self.old_name = old_name
self.new_name = new_name
self.message = message
def __call__(self, func, *args, **kwargs):
"""
Decorator call. Refer to ``decorate``.
"""
old_name = self.old_name
new_name = self.new_name
message = self.message
if old_name is None:
old_name = func.__name__
if new_name is None:
depdoc = "`%s` is deprecated!" % old_name
else:
depdoc = "`%s` is deprecated, use `%s` instead!" % \
(old_name, new_name)
if message is not None:
depdoc += "\n" + message
def newfunc(*args, **kwds):
warnings.warn(depdoc, DeprecationWarning, stacklevel=2)
return func(*args, **kwds)
newfunc.__name__ = old_name
doc = func.__doc__
if doc is None:
doc = depdoc
else:
lines = doc.expandtabs().split('\n')
indent = _get_indent(lines[1:])
if lines[0].lstrip():
# Indent the original first line to let inspect.cleandoc()
# dedent the docstring despite the deprecation notice.
doc = indent * ' ' + doc
else:
# Remove the same leading blank lines as cleandoc() would.
skip = len(lines[0]) + 1
for line in lines[1:]:
if len(line) > indent:
break
skip += len(line) + 1
doc = doc[skip:]
depdoc = textwrap.indent(depdoc, ' ' * indent)
doc = '\n\n'.join([depdoc, doc])
newfunc.__doc__ = doc
return newfunc
The provided code snippet includes necessary dependencies for implementing the `deprecate` function. Write a Python function `def deprecate(*args, **kwargs)` to solve the following problem:
Issues a DeprecationWarning, adds warning to `old_name`'s docstring, rebinds ``old_name.__name__`` and returns the new function object. This function may also be used as a decorator. Parameters ---------- func : function The function to be deprecated. old_name : str, optional The name of the function to be deprecated. Default is None, in which case the name of `func` is used. new_name : str, optional The new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead. message : str, optional Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- old_func : function The deprecated function. Examples -------- Note that ``olduint`` returns a value after printing Deprecation Warning: >>> olduint = np.deprecate(np.uint) DeprecationWarning: `uint64` is deprecated! # may vary >>> olduint(6) 6
Here is the function:
def deprecate(*args, **kwargs):
"""
Issues a DeprecationWarning, adds warning to `old_name`'s
docstring, rebinds ``old_name.__name__`` and returns the new
function object.
This function may also be used as a decorator.
Parameters
----------
func : function
The function to be deprecated.
old_name : str, optional
The name of the function to be deprecated. Default is None, in
which case the name of `func` is used.
new_name : str, optional
The new name for the function. Default is None, in which case the
deprecation message is that `old_name` is deprecated. If given, the
deprecation message is that `old_name` is deprecated and `new_name`
should be used instead.
message : str, optional
Additional explanation of the deprecation. Displayed in the
docstring after the warning.
Returns
-------
old_func : function
The deprecated function.
Examples
--------
Note that ``olduint`` returns a value after printing Deprecation
Warning:
>>> olduint = np.deprecate(np.uint)
DeprecationWarning: `uint64` is deprecated! # may vary
>>> olduint(6)
6
"""
# Deprecate may be run as a function or as a decorator
# If run as a function, we initialise the decorator class
# and execute its __call__ method.
if args:
fn = args[0]
args = args[1:]
return _Deprecate(*args, **kwargs)(fn)
else:
return _Deprecate(*args, **kwargs) | Issues a DeprecationWarning, adds warning to `old_name`'s docstring, rebinds ``old_name.__name__`` and returns the new function object. This function may also be used as a decorator. Parameters ---------- func : function The function to be deprecated. old_name : str, optional The name of the function to be deprecated. Default is None, in which case the name of `func` is used. new_name : str, optional The new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead. message : str, optional Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- old_func : function The deprecated function. Examples -------- Note that ``olduint`` returns a value after printing Deprecation Warning: >>> olduint = np.deprecate(np.uint) DeprecationWarning: `uint64` is deprecated! # may vary >>> olduint(6) 6 |
168,664 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
class _Deprecate:
"""
Decorator class to deprecate old functions.
Refer to `deprecate` for details.
See Also
--------
deprecate
"""
def __init__(self, old_name=None, new_name=None, message=None):
self.old_name = old_name
self.new_name = new_name
self.message = message
def __call__(self, func, *args, **kwargs):
"""
Decorator call. Refer to ``decorate``.
"""
old_name = self.old_name
new_name = self.new_name
message = self.message
if old_name is None:
old_name = func.__name__
if new_name is None:
depdoc = "`%s` is deprecated!" % old_name
else:
depdoc = "`%s` is deprecated, use `%s` instead!" % \
(old_name, new_name)
if message is not None:
depdoc += "\n" + message
def newfunc(*args, **kwds):
warnings.warn(depdoc, DeprecationWarning, stacklevel=2)
return func(*args, **kwds)
newfunc.__name__ = old_name
doc = func.__doc__
if doc is None:
doc = depdoc
else:
lines = doc.expandtabs().split('\n')
indent = _get_indent(lines[1:])
if lines[0].lstrip():
# Indent the original first line to let inspect.cleandoc()
# dedent the docstring despite the deprecation notice.
doc = indent * ' ' + doc
else:
# Remove the same leading blank lines as cleandoc() would.
skip = len(lines[0]) + 1
for line in lines[1:]:
if len(line) > indent:
break
skip += len(line) + 1
doc = doc[skip:]
depdoc = textwrap.indent(depdoc, ' ' * indent)
doc = '\n\n'.join([depdoc, doc])
newfunc.__doc__ = doc
return newfunc
The provided code snippet includes necessary dependencies for implementing the `deprecate_with_doc` function. Write a Python function `def deprecate_with_doc(msg)` to solve the following problem:
Deprecates a function and includes the deprecation in its docstring. This function is used as a decorator. It returns an object that can be used to issue a DeprecationWarning, by passing the to-be decorated function as argument, this adds warning to the to-be decorated function's docstring and returns the new function object. See Also -------- deprecate : Decorate a function such that it issues a `DeprecationWarning` Parameters ---------- msg : str Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- obj : object
Here is the function:
def deprecate_with_doc(msg):
"""
Deprecates a function and includes the deprecation in its docstring.
This function is used as a decorator. It returns an object that can be
used to issue a DeprecationWarning, by passing the to-be decorated
function as argument, this adds warning to the to-be decorated function's
docstring and returns the new function object.
See Also
--------
deprecate : Decorate a function such that it issues a `DeprecationWarning`
Parameters
----------
msg : str
Additional explanation of the deprecation. Displayed in the
docstring after the warning.
Returns
-------
obj : object
"""
return _Deprecate(message=msg) | Deprecates a function and includes the deprecation in its docstring. This function is used as a decorator. It returns an object that can be used to issue a DeprecationWarning, by passing the to-be decorated function as argument, this adds warning to the to-be decorated function's docstring and returns the new function object. See Also -------- deprecate : Decorate a function such that it issues a `DeprecationWarning` Parameters ---------- msg : str Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- obj : object |
168,665 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `byte_bounds` function. Write a Python function `def byte_bounds(a)` to solve the following problem:
Returns pointers to the end-points of an array. Parameters ---------- a : ndarray Input array. It must conform to the Python-side of the array interface. Returns ------- (low, high) : tuple of 2 integers The first integer is the first byte of the array, the second integer is just past the last byte of the array. If `a` is not contiguous it will not use every byte between the (`low`, `high`) values. Examples -------- >>> I = np.eye(2, dtype='f'); I.dtype dtype('float32') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True >>> I = np.eye(2); I.dtype dtype('float64') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True
Here is the function:
def byte_bounds(a):
"""
Returns pointers to the end-points of an array.
Parameters
----------
a : ndarray
Input array. It must conform to the Python-side of the array
interface.
Returns
-------
(low, high) : tuple of 2 integers
The first integer is the first byte of the array, the second
integer is just past the last byte of the array. If `a` is not
contiguous it will not use every byte between the (`low`, `high`)
values.
Examples
--------
>>> I = np.eye(2, dtype='f'); I.dtype
dtype('float32')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
>>> I = np.eye(2); I.dtype
dtype('float64')
>>> low, high = np.byte_bounds(I)
>>> high - low == I.size*I.itemsize
True
"""
ai = a.__array_interface__
a_data = ai['data'][0]
astrides = ai['strides']
ashape = ai['shape']
bytes_a = asarray(a).dtype.itemsize
a_low = a_high = a_data
if astrides is None:
# contiguous case
a_high += a.size * bytes_a
else:
for shape, stride in zip(ashape, astrides):
if stride < 0:
a_low += (shape-1)*stride
else:
a_high += (shape-1)*stride
a_high += bytes_a
return a_low, a_high | Returns pointers to the end-points of an array. Parameters ---------- a : ndarray Input array. It must conform to the Python-side of the array interface. Returns ------- (low, high) : tuple of 2 integers The first integer is the first byte of the array, the second integer is just past the last byte of the array. If `a` is not contiguous it will not use every byte between the (`low`, `high`) values. Examples -------- >>> I = np.eye(2, dtype='f'); I.dtype dtype('float32') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True >>> I = np.eye(2); I.dtype dtype('float64') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True |
168,666 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `who` function. Write a Python function `def who(vardict=None)` to solve the following problem:
Print the NumPy arrays in the given dictionary. If there is no dictionary passed in or `vardict` is None then returns NumPy arrays in the globals() dictionary (all NumPy arrays in the namespace). Parameters ---------- vardict : dict, optional A dictionary possibly containing ndarrays. Default is globals(). Returns ------- out : None Returns 'None'. Notes ----- Prints out the name, shape, bytes and type of all of the ndarrays present in `vardict`. Examples -------- >>> a = np.arange(10) >>> b = np.ones(20) >>> np.who() Name Shape Bytes Type =========================================================== a 10 80 int64 b 20 160 float64 Upper bound on total bytes = 240 >>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str', ... 'idx':5} >>> np.who(d) Name Shape Bytes Type =========================================================== x 2 16 float64 y 3 24 float64 Upper bound on total bytes = 40
Here is the function:
def who(vardict=None):
"""
Print the NumPy arrays in the given dictionary.
If there is no dictionary passed in or `vardict` is None then returns
NumPy arrays in the globals() dictionary (all NumPy arrays in the
namespace).
Parameters
----------
vardict : dict, optional
A dictionary possibly containing ndarrays. Default is globals().
Returns
-------
out : None
Returns 'None'.
Notes
-----
Prints out the name, shape, bytes and type of all of the ndarrays
present in `vardict`.
Examples
--------
>>> a = np.arange(10)
>>> b = np.ones(20)
>>> np.who()
Name Shape Bytes Type
===========================================================
a 10 80 int64
b 20 160 float64
Upper bound on total bytes = 240
>>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str',
... 'idx':5}
>>> np.who(d)
Name Shape Bytes Type
===========================================================
x 2 16 float64
y 3 24 float64
Upper bound on total bytes = 40
"""
if vardict is None:
frame = sys._getframe().f_back
vardict = frame.f_globals
sta = []
cache = {}
for name in vardict.keys():
if isinstance(vardict[name], ndarray):
var = vardict[name]
idv = id(var)
if idv in cache.keys():
namestr = name + " (%s)" % cache[idv]
original = 0
else:
cache[idv] = name
namestr = name
original = 1
shapestr = " x ".join(map(str, var.shape))
bytestr = str(var.nbytes)
sta.append([namestr, shapestr, bytestr, var.dtype.name,
original])
maxname = 0
maxshape = 0
maxbyte = 0
totalbytes = 0
for val in sta:
if maxname < len(val[0]):
maxname = len(val[0])
if maxshape < len(val[1]):
maxshape = len(val[1])
if maxbyte < len(val[2]):
maxbyte = len(val[2])
if val[4]:
totalbytes += int(val[2])
if len(sta) > 0:
sp1 = max(10, maxname)
sp2 = max(10, maxshape)
sp3 = max(10, maxbyte)
prval = "Name %s Shape %s Bytes %s Type" % (sp1*' ', sp2*' ', sp3*' ')
print(prval + "\n" + "="*(len(prval)+5) + "\n")
for val in sta:
print("%s %s %s %s %s %s %s" % (val[0], ' '*(sp1-len(val[0])+4),
val[1], ' '*(sp2-len(val[1])+5),
val[2], ' '*(sp3-len(val[2])+5),
val[3]))
print("\nUpper bound on total bytes = %d" % totalbytes)
return | Print the NumPy arrays in the given dictionary. If there is no dictionary passed in or `vardict` is None then returns NumPy arrays in the globals() dictionary (all NumPy arrays in the namespace). Parameters ---------- vardict : dict, optional A dictionary possibly containing ndarrays. Default is globals(). Returns ------- out : None Returns 'None'. Notes ----- Prints out the name, shape, bytes and type of all of the ndarrays present in `vardict`. Examples -------- >>> a = np.arange(10) >>> b = np.ones(20) >>> np.who() Name Shape Bytes Type =========================================================== a 10 80 int64 b 20 160 float64 Upper bound on total bytes = 240 >>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str', ... 'idx':5} >>> np.who(d) Name Shape Bytes Type =========================================================== x 2 16 float64 y 3 24 float64 Upper bound on total bytes = 40 |
168,667 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
def _split_line(name, arguments, width):
firstwidth = len(name)
k = firstwidth
newstr = name
sepstr = ", "
arglist = arguments.split(sepstr)
for argument in arglist:
if k == firstwidth:
addstr = ""
else:
addstr = sepstr
k = k + len(argument) + len(addstr)
if k > width:
k = firstwidth + 1 + len(argument)
newstr = newstr + ",\n" + " "*(firstwidth+2) + argument
else:
newstr = newstr + addstr + argument
return newstr
_namedict = None
_dictlist = None
def _makenamedict(module='numpy'):
module = __import__(module, globals(), locals(), [])
thedict = {module.__name__:module.__dict__}
dictlist = [module.__name__]
totraverse = [module.__dict__]
while True:
if len(totraverse) == 0:
break
thisdict = totraverse.pop(0)
for x in thisdict.keys():
if isinstance(thisdict[x], types.ModuleType):
modname = thisdict[x].__name__
if modname not in dictlist:
moddict = thisdict[x].__dict__
dictlist.append(modname)
totraverse.append(moddict)
thedict[modname] = moddict
return thedict, dictlist
def _info(obj, output=None):
"""Provide information about ndarray obj.
Parameters
----------
obj : ndarray
Must be ndarray, not checked.
output
Where printed output goes.
Notes
-----
Copied over from the numarray module prior to its removal.
Adapted somewhat as only numpy is an option now.
Called by info.
"""
extra = ""
tic = ""
bp = lambda x: x
cls = getattr(obj, '__class__', type(obj))
nm = getattr(cls, '__name__', cls)
strides = obj.strides
endian = obj.dtype.byteorder
if output is None:
output = sys.stdout
print("class: ", nm, file=output)
print("shape: ", obj.shape, file=output)
print("strides: ", strides, file=output)
print("itemsize: ", obj.itemsize, file=output)
print("aligned: ", bp(obj.flags.aligned), file=output)
print("contiguous: ", bp(obj.flags.contiguous), file=output)
print("fortran: ", obj.flags.fortran, file=output)
print(
"data pointer: %s%s" % (hex(obj.ctypes._as_parameter_.value), extra),
file=output
)
print("byteorder: ", end=' ', file=output)
if endian in ['|', '=']:
print("%s%s%s" % (tic, sys.byteorder, tic), file=output)
byteswap = False
elif endian == '>':
print("%sbig%s" % (tic, tic), file=output)
byteswap = sys.byteorder != "big"
else:
print("%slittle%s" % (tic, tic), file=output)
byteswap = sys.byteorder != "little"
print("byteswap: ", bp(byteswap), file=output)
print("type: %s" % obj.dtype, file=output)
The provided code snippet includes necessary dependencies for implementing the `info` function. Write a Python function `def info(object=None, maxwidth=76, output=None, toplevel='numpy')` to solve the following problem:
Get help information for a function, class, or module. Parameters ---------- object : object or str, optional Input object or name to get information about. If `object` is a numpy object, its docstring is given. If it is a string, available modules are searched for matching objects. If None, information about `info` itself is returned. maxwidth : int, optional Printing width. output : file like object, optional File like object that the output is written to, default is ``None``, in which case ``sys.stdout`` will be used. The object has to be opened in 'w' or 'a' mode. toplevel : str, optional Start search at this level. See Also -------- source, lookfor Notes ----- When used interactively with an object, ``np.info(obj)`` is equivalent to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython prompt. Examples -------- >>> np.info(np.polyval) # doctest: +SKIP polyval(p, x) Evaluate the polynomial p at x. ... When using a string for `object` it is possible to get multiple results. >>> np.info('fft') # doctest: +SKIP *** Found in numpy *** Core FFT routines ... *** Found in numpy.fft *** fft(a, n=None, axis=-1) ... *** Repeat reference found in numpy.fft.fftpack *** *** Total of 3 references found. ***
Here is the function:
def info(object=None, maxwidth=76, output=None, toplevel='numpy'):
"""
Get help information for a function, class, or module.
Parameters
----------
object : object or str, optional
Input object or name to get information about. If `object` is a
numpy object, its docstring is given. If it is a string, available
modules are searched for matching objects. If None, information
about `info` itself is returned.
maxwidth : int, optional
Printing width.
output : file like object, optional
File like object that the output is written to, default is
``None``, in which case ``sys.stdout`` will be used.
The object has to be opened in 'w' or 'a' mode.
toplevel : str, optional
Start search at this level.
See Also
--------
source, lookfor
Notes
-----
When used interactively with an object, ``np.info(obj)`` is equivalent
to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython
prompt.
Examples
--------
>>> np.info(np.polyval) # doctest: +SKIP
polyval(p, x)
Evaluate the polynomial p at x.
...
When using a string for `object` it is possible to get multiple results.
>>> np.info('fft') # doctest: +SKIP
*** Found in numpy ***
Core FFT routines
...
*** Found in numpy.fft ***
fft(a, n=None, axis=-1)
...
*** Repeat reference found in numpy.fft.fftpack ***
*** Total of 3 references found. ***
"""
global _namedict, _dictlist
# Local import to speed up numpy's import time.
import pydoc
import inspect
if (hasattr(object, '_ppimport_importer') or
hasattr(object, '_ppimport_module')):
object = object._ppimport_module
elif hasattr(object, '_ppimport_attr'):
object = object._ppimport_attr
if output is None:
output = sys.stdout
if object is None:
info(info)
elif isinstance(object, ndarray):
_info(object, output=output)
elif isinstance(object, str):
if _namedict is None:
_namedict, _dictlist = _makenamedict(toplevel)
numfound = 0
objlist = []
for namestr in _dictlist:
try:
obj = _namedict[namestr][object]
if id(obj) in objlist:
print("\n "
"*** Repeat reference found in %s *** " % namestr,
file=output
)
else:
objlist.append(id(obj))
print(" *** Found in %s ***" % namestr, file=output)
info(obj)
print("-"*maxwidth, file=output)
numfound += 1
except KeyError:
pass
if numfound == 0:
print("Help for %s not found." % object, file=output)
else:
print("\n "
"*** Total of %d references found. ***" % numfound,
file=output
)
elif inspect.isfunction(object) or inspect.ismethod(object):
name = object.__name__
try:
arguments = str(inspect.signature(object))
except Exception:
arguments = "()"
if len(name+arguments) > maxwidth:
argstr = _split_line(name, arguments, maxwidth)
else:
argstr = name + arguments
print(" " + argstr + "\n", file=output)
print(inspect.getdoc(object), file=output)
elif inspect.isclass(object):
name = object.__name__
try:
arguments = str(inspect.signature(object))
except Exception:
arguments = "()"
if len(name+arguments) > maxwidth:
argstr = _split_line(name, arguments, maxwidth)
else:
argstr = name + arguments
print(" " + argstr + "\n", file=output)
doc1 = inspect.getdoc(object)
if doc1 is None:
if hasattr(object, '__init__'):
print(inspect.getdoc(object.__init__), file=output)
else:
print(inspect.getdoc(object), file=output)
methods = pydoc.allmethods(object)
public_methods = [meth for meth in methods if meth[0] != '_']
if public_methods:
print("\n\nMethods:\n", file=output)
for meth in public_methods:
thisobj = getattr(object, meth, None)
if thisobj is not None:
methstr, other = pydoc.splitdoc(
inspect.getdoc(thisobj) or "None"
)
print(" %s -- %s" % (meth, methstr), file=output)
elif hasattr(object, '__doc__'):
print(inspect.getdoc(object), file=output) | Get help information for a function, class, or module. Parameters ---------- object : object or str, optional Input object or name to get information about. If `object` is a numpy object, its docstring is given. If it is a string, available modules are searched for matching objects. If None, information about `info` itself is returned. maxwidth : int, optional Printing width. output : file like object, optional File like object that the output is written to, default is ``None``, in which case ``sys.stdout`` will be used. The object has to be opened in 'w' or 'a' mode. toplevel : str, optional Start search at this level. See Also -------- source, lookfor Notes ----- When used interactively with an object, ``np.info(obj)`` is equivalent to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython prompt. Examples -------- >>> np.info(np.polyval) # doctest: +SKIP polyval(p, x) Evaluate the polynomial p at x. ... When using a string for `object` it is possible to get multiple results. >>> np.info('fft') # doctest: +SKIP *** Found in numpy *** Core FFT routines ... *** Found in numpy.fft *** fft(a, n=None, axis=-1) ... *** Repeat reference found in numpy.fft.fftpack *** *** Total of 3 references found. *** |
168,668 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `source` function. Write a Python function `def source(object, output=sys.stdout)` to solve the following problem:
Print or write to a file the source code for a NumPy object. The source code is only returned for objects written in Python. Many functions and classes are defined in C and will therefore not return useful information. Parameters ---------- object : numpy object Input object. This can be any object (function, class, module, ...). output : file object, optional If `output` not supplied then source code is printed to screen (sys.stdout). File object must be created with either write 'w' or append 'a' modes. See Also -------- lookfor, info Examples -------- >>> np.source(np.interp) #doctest: +SKIP In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py def interp(x, xp, fp, left=None, right=None): \"\"\".... (full docstring printed)\"\"\" if isinstance(x, (float, int, number)): return compiled_interp([x], xp, fp, left, right).item() else: return compiled_interp(x, xp, fp, left, right) The source code is only returned for objects written in Python. >>> np.source(np.array) #doctest: +SKIP Not available for this object.
Here is the function:
def source(object, output=sys.stdout):
"""
Print or write to a file the source code for a NumPy object.
The source code is only returned for objects written in Python. Many
functions and classes are defined in C and will therefore not return
useful information.
Parameters
----------
object : numpy object
Input object. This can be any object (function, class, module,
...).
output : file object, optional
If `output` not supplied then source code is printed to screen
(sys.stdout). File object must be created with either write 'w' or
append 'a' modes.
See Also
--------
lookfor, info
Examples
--------
>>> np.source(np.interp) #doctest: +SKIP
In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py
def interp(x, xp, fp, left=None, right=None):
\"\"\".... (full docstring printed)\"\"\"
if isinstance(x, (float, int, number)):
return compiled_interp([x], xp, fp, left, right).item()
else:
return compiled_interp(x, xp, fp, left, right)
The source code is only returned for objects written in Python.
>>> np.source(np.array) #doctest: +SKIP
Not available for this object.
"""
# Local import to speed up numpy's import time.
import inspect
try:
print("In file: %s\n" % inspect.getsourcefile(object), file=output)
print(inspect.getsource(object), file=output)
except Exception:
print("Not available for this object.", file=output) | Print or write to a file the source code for a NumPy object. The source code is only returned for objects written in Python. Many functions and classes are defined in C and will therefore not return useful information. Parameters ---------- object : numpy object Input object. This can be any object (function, class, module, ...). output : file object, optional If `output` not supplied then source code is printed to screen (sys.stdout). File object must be created with either write 'w' or append 'a' modes. See Also -------- lookfor, info Examples -------- >>> np.source(np.interp) #doctest: +SKIP In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py def interp(x, xp, fp, left=None, right=None): \"\"\".... (full docstring printed)\"\"\" if isinstance(x, (float, int, number)): return compiled_interp([x], xp, fp, left, right).item() else: return compiled_interp(x, xp, fp, left, right) The source code is only returned for objects written in Python. >>> np.source(np.array) #doctest: +SKIP Not available for this object. |
168,669 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
_function_signature_re = re.compile(r"[a-z0-9_]+\(.*[,=].*\)", re.I)
def _lookfor_generate_cache(module, import_modules, regenerate):
"""
Generate docstring cache for given module.
Parameters
----------
module : str, None, module
Module for which to generate docstring cache
import_modules : bool
Whether to import sub-modules in packages.
regenerate : bool
Re-generate the docstring cache
Returns
-------
cache : dict {obj_full_name: (docstring, kind, index), ...}
Docstring cache for the module, either cached one (regenerate=False)
or newly generated.
"""
# Local import to speed up numpy's import time.
import inspect
from io import StringIO
if module is None:
module = "numpy"
if isinstance(module, str):
try:
__import__(module)
except ImportError:
return {}
module = sys.modules[module]
elif isinstance(module, list) or isinstance(module, tuple):
cache = {}
for mod in module:
cache.update(_lookfor_generate_cache(mod, import_modules,
regenerate))
return cache
if id(module) in _lookfor_caches and not regenerate:
return _lookfor_caches[id(module)]
# walk items and collect docstrings
cache = {}
_lookfor_caches[id(module)] = cache
seen = {}
index = 0
stack = [(module.__name__, module)]
while stack:
name, item = stack.pop(0)
if id(item) in seen:
continue
seen[id(item)] = True
index += 1
kind = "object"
if inspect.ismodule(item):
kind = "module"
try:
_all = item.__all__
except AttributeError:
_all = None
# import sub-packages
if import_modules and hasattr(item, '__path__'):
for pth in item.__path__:
for mod_path in os.listdir(pth):
this_py = os.path.join(pth, mod_path)
init_py = os.path.join(pth, mod_path, '__init__.py')
if (os.path.isfile(this_py) and
mod_path.endswith('.py')):
to_import = mod_path[:-3]
elif os.path.isfile(init_py):
to_import = mod_path
else:
continue
if to_import == '__init__':
continue
try:
old_stdout = sys.stdout
old_stderr = sys.stderr
try:
sys.stdout = StringIO()
sys.stderr = StringIO()
__import__("%s.%s" % (name, to_import))
finally:
sys.stdout = old_stdout
sys.stderr = old_stderr
except KeyboardInterrupt:
# Assume keyboard interrupt came from a user
raise
except BaseException:
# Ignore also SystemExit and pytests.importorskip
# `Skipped` (these are BaseExceptions; gh-22345)
continue
for n, v in _getmembers(item):
try:
item_name = getattr(v, '__name__', "%s.%s" % (name, n))
mod_name = getattr(v, '__module__', None)
except NameError:
# ref. SWIG's global cvars
# NameError: Unknown C global variable
item_name = "%s.%s" % (name, n)
mod_name = None
if '.' not in item_name and mod_name:
item_name = "%s.%s" % (mod_name, item_name)
if not item_name.startswith(name + '.'):
# don't crawl "foreign" objects
if isinstance(v, ufunc):
# ... unless they are ufuncs
pass
else:
continue
elif not (inspect.ismodule(v) or _all is None or n in _all):
continue
stack.append(("%s.%s" % (name, n), v))
elif inspect.isclass(item):
kind = "class"
for n, v in _getmembers(item):
stack.append(("%s.%s" % (name, n), v))
elif hasattr(item, "__call__"):
kind = "func"
try:
doc = inspect.getdoc(item)
except NameError:
# ref SWIG's NameError: Unknown C global variable
doc = None
if doc is not None:
cache[name] = (doc, kind, index)
return cache
The provided code snippet includes necessary dependencies for implementing the `lookfor` function. Write a Python function `def lookfor(what, module=None, import_modules=True, regenerate=False, output=None)` to solve the following problem:
Do a keyword search on docstrings. A list of objects that matched the search is displayed, sorted by relevance. All given keywords need to be found in the docstring for it to be returned as a result, but the order does not matter. Parameters ---------- what : str String containing words to look for. module : str or list, optional Name of module(s) whose docstrings to go through. import_modules : bool, optional Whether to import sub-modules in packages. Default is True. regenerate : bool, optional Whether to re-generate the docstring cache. Default is False. output : file-like, optional File-like object to write the output to. If omitted, use a pager. See Also -------- source, info Notes ----- Relevance is determined only roughly, by checking if the keywords occur in the function name, at the start of a docstring, etc. Examples -------- >>> np.lookfor('binary representation') # doctest: +SKIP Search results for 'binary representation' ------------------------------------------ numpy.binary_repr Return the binary representation of the input number as a string. numpy.core.setup_common.long_double_representation Given a binary dump as given by GNU od -b, look for long double numpy.base_repr Return a string representation of a number in the given base system. ...
Here is the function:
def lookfor(what, module=None, import_modules=True, regenerate=False,
output=None):
"""
Do a keyword search on docstrings.
A list of objects that matched the search is displayed,
sorted by relevance. All given keywords need to be found in the
docstring for it to be returned as a result, but the order does
not matter.
Parameters
----------
what : str
String containing words to look for.
module : str or list, optional
Name of module(s) whose docstrings to go through.
import_modules : bool, optional
Whether to import sub-modules in packages. Default is True.
regenerate : bool, optional
Whether to re-generate the docstring cache. Default is False.
output : file-like, optional
File-like object to write the output to. If omitted, use a pager.
See Also
--------
source, info
Notes
-----
Relevance is determined only roughly, by checking if the keywords occur
in the function name, at the start of a docstring, etc.
Examples
--------
>>> np.lookfor('binary representation') # doctest: +SKIP
Search results for 'binary representation'
------------------------------------------
numpy.binary_repr
Return the binary representation of the input number as a string.
numpy.core.setup_common.long_double_representation
Given a binary dump as given by GNU od -b, look for long double
numpy.base_repr
Return a string representation of a number in the given base system.
...
"""
import pydoc
# Cache
cache = _lookfor_generate_cache(module, import_modules, regenerate)
# Search
# XXX: maybe using a real stemming search engine would be better?
found = []
whats = str(what).lower().split()
if not whats:
return
for name, (docstring, kind, index) in cache.items():
if kind in ('module', 'object'):
# don't show modules or objects
continue
doc = docstring.lower()
if all(w in doc for w in whats):
found.append(name)
# Relevance sort
# XXX: this is full Harrison-Stetson heuristics now,
# XXX: it probably could be improved
kind_relevance = {'func': 1000, 'class': 1000,
'module': -1000, 'object': -1000}
def relevance(name, docstr, kind, index):
r = 0
# do the keywords occur within the start of the docstring?
first_doc = "\n".join(docstr.lower().strip().split("\n")[:3])
r += sum([200 for w in whats if w in first_doc])
# do the keywords occur in the function name?
r += sum([30 for w in whats if w in name])
# is the full name long?
r += -len(name) * 5
# is the object of bad type?
r += kind_relevance.get(kind, -1000)
# is the object deep in namespace hierarchy?
r += -name.count('.') * 10
r += max(-index / 100, -100)
return r
def relevance_value(a):
return relevance(a, *cache[a])
found.sort(key=relevance_value)
# Pretty-print
s = "Search results for '%s'" % (' '.join(whats))
help_text = [s, "-"*len(s)]
for name in found[::-1]:
doc, kind, ix = cache[name]
doclines = [line.strip() for line in doc.strip().split("\n")
if line.strip()]
# find a suitable short description
try:
first_doc = doclines[0].strip()
if _function_signature_re.search(first_doc):
first_doc = doclines[1].strip()
except IndexError:
first_doc = ""
help_text.append("%s\n %s" % (name, first_doc))
if not found:
help_text.append("Nothing found.")
# Output
if output is not None:
output.write("\n".join(help_text))
elif len(help_text) > 10:
pager = pydoc.getpager()
pager("\n".join(help_text))
else:
print("\n".join(help_text)) | Do a keyword search on docstrings. A list of objects that matched the search is displayed, sorted by relevance. All given keywords need to be found in the docstring for it to be returned as a result, but the order does not matter. Parameters ---------- what : str String containing words to look for. module : str or list, optional Name of module(s) whose docstrings to go through. import_modules : bool, optional Whether to import sub-modules in packages. Default is True. regenerate : bool, optional Whether to re-generate the docstring cache. Default is False. output : file-like, optional File-like object to write the output to. If omitted, use a pager. See Also -------- source, info Notes ----- Relevance is determined only roughly, by checking if the keywords occur in the function name, at the start of a docstring, etc. Examples -------- >>> np.lookfor('binary representation') # doctest: +SKIP Search results for 'binary representation' ------------------------------------------ numpy.binary_repr Return the binary representation of the input number as a string. numpy.core.setup_common.long_double_representation Given a binary dump as given by GNU od -b, look for long double numpy.base_repr Return a string representation of a number in the given base system. ... |
168,670 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `_median_nancheck` function. Write a Python function `def _median_nancheck(data, result, axis)` to solve the following problem:
Utility function to check median result from data for NaN values at the end and return NaN in that case. Input result can also be a MaskedArray. Parameters ---------- data : array Sorted input data to median function result : Array or MaskedArray Result of median function. axis : int Axis along which the median was computed. Returns ------- result : scalar or ndarray Median or NaN in axes which contained NaN in the input. If the input was an array, NaN will be inserted in-place. If a scalar, either the input itself or a scalar NaN.
Here is the function:
def _median_nancheck(data, result, axis):
"""
Utility function to check median result from data for NaN values at the end
and return NaN in that case. Input result can also be a MaskedArray.
Parameters
----------
data : array
Sorted input data to median function
result : Array or MaskedArray
Result of median function.
axis : int
Axis along which the median was computed.
Returns
-------
result : scalar or ndarray
Median or NaN in axes which contained NaN in the input. If the input
was an array, NaN will be inserted in-place. If a scalar, either the
input itself or a scalar NaN.
"""
if data.size == 0:
return result
n = np.isnan(data.take(-1, axis=axis))
# masked NaN values are ok
if np.ma.isMaskedArray(n):
n = n.filled(False)
if np.count_nonzero(n.ravel()) > 0:
# Without given output, it is possible that the current result is a
# numpy scalar, which is not writeable. If so, just return nan.
if isinstance(result, np.generic):
return data.dtype.type(np.nan)
result[n] = np.nan
return result | Utility function to check median result from data for NaN values at the end and return NaN in that case. Input result can also be a MaskedArray. Parameters ---------- data : array Sorted input data to median function result : Array or MaskedArray Result of median function. axis : int Axis along which the median was computed. Returns ------- result : scalar or ndarray Median or NaN in axes which contained NaN in the input. If the input was an array, NaN will be inserted in-place. If a scalar, either the input itself or a scalar NaN. |
168,671 | import os
import sys
import textwrap
import types
import re
import warnings
import functools
from numpy.core.numerictypes import issubclass_, issubsctype, issubdtype
from numpy.core.overrides import set_module
from numpy.core import ndarray, ufunc, asarray
import numpy as np
The provided code snippet includes necessary dependencies for implementing the `_opt_info` function. Write a Python function `def _opt_info()` to solve the following problem:
Returns a string contains the supported CPU features by the current build. The string format can be explained as follows: - dispatched features that are supported by the running machine end with `*`. - dispatched features that are "not" supported by the running machine end with `?`. - remained features are representing the baseline.
Here is the function:
def _opt_info():
"""
Returns a string contains the supported CPU features by the current build.
The string format can be explained as follows:
- dispatched features that are supported by the running machine
end with `*`.
- dispatched features that are "not" supported by the running machine
end with `?`.
- remained features are representing the baseline.
"""
from numpy.core._multiarray_umath import (
__cpu_features__, __cpu_baseline__, __cpu_dispatch__
)
if len(__cpu_baseline__) == 0 and len(__cpu_dispatch__) == 0:
return ''
enabled_features = ' '.join(__cpu_baseline__)
for feature in __cpu_dispatch__:
if __cpu_features__[feature]:
enabled_features += f" {feature}*"
else:
enabled_features += f" {feature}?"
return enabled_features | Returns a string contains the supported CPU features by the current build. The string format can be explained as follows: - dispatched features that are supported by the running machine end with `*`. - dispatched features that are "not" supported by the running machine end with `?`. - remained features are representing the baseline. |
168,672 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _flip_dispatcher(m):
return (m,) | null |
168,673 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
The provided code snippet includes necessary dependencies for implementing the `fliplr` function. Write a Python function `def fliplr(m)` to solve the following problem:
Reverse the order of elements along axis 1 (left/right). For a 2-D array, this flips the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array, must be at least 2-D. Returns ------- f : ndarray A view of `m` with the columns reversed. Since a view is returned, this operation is :math:`\\mathcal O(1)`. See Also -------- flipud : Flip array in the up/down direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``. Requires the array to be at least 2-D. Examples -------- >>> A = np.diag([1.,2.,3.]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.fliplr(A) array([[0., 0., 1.], [0., 2., 0.], [3., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A) == A[:,::-1,...]) True
Here is the function:
def fliplr(m):
"""
Reverse the order of elements along axis 1 (left/right).
For a 2-D array, this flips the entries in each row in the left/right
direction. Columns are preserved, but appear in a different order than
before.
Parameters
----------
m : array_like
Input array, must be at least 2-D.
Returns
-------
f : ndarray
A view of `m` with the columns reversed. Since a view
is returned, this operation is :math:`\\mathcal O(1)`.
See Also
--------
flipud : Flip array in the up/down direction.
flip : Flip array in one or more dimensions.
rot90 : Rotate array counterclockwise.
Notes
-----
Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``.
Requires the array to be at least 2-D.
Examples
--------
>>> A = np.diag([1.,2.,3.])
>>> A
array([[1., 0., 0.],
[0., 2., 0.],
[0., 0., 3.]])
>>> np.fliplr(A)
array([[0., 0., 1.],
[0., 2., 0.],
[3., 0., 0.]])
>>> A = np.random.randn(2,3,5)
>>> np.all(np.fliplr(A) == A[:,::-1,...])
True
"""
m = asanyarray(m)
if m.ndim < 2:
raise ValueError("Input must be >= 2-d.")
return m[:, ::-1] | Reverse the order of elements along axis 1 (left/right). For a 2-D array, this flips the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array, must be at least 2-D. Returns ------- f : ndarray A view of `m` with the columns reversed. Since a view is returned, this operation is :math:`\\mathcal O(1)`. See Also -------- flipud : Flip array in the up/down direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``. Requires the array to be at least 2-D. Examples -------- >>> A = np.diag([1.,2.,3.]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.fliplr(A) array([[0., 0., 1.], [0., 2., 0.], [3., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A) == A[:,::-1,...]) True |
168,674 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
The provided code snippet includes necessary dependencies for implementing the `flipud` function. Write a Python function `def flipud(m)` to solve the following problem:
Reverse the order of elements along axis 0 (up/down). For a 2-D array, this flips the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- out : array_like A view of `m` with the rows reversed. Since a view is returned, this operation is :math:`\\mathcal O(1)`. See Also -------- fliplr : Flip array in the left/right direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``. Requires the array to be at least 1-D. Examples -------- >>> A = np.diag([1.0, 2, 3]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.flipud(A) array([[0., 0., 3.], [0., 2., 0.], [1., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A) == A[::-1,...]) True >>> np.flipud([1,2]) array([2, 1])
Here is the function:
def flipud(m):
"""
Reverse the order of elements along axis 0 (up/down).
For a 2-D array, this flips the entries in each column in the up/down
direction. Rows are preserved, but appear in a different order than before.
Parameters
----------
m : array_like
Input array.
Returns
-------
out : array_like
A view of `m` with the rows reversed. Since a view is
returned, this operation is :math:`\\mathcal O(1)`.
See Also
--------
fliplr : Flip array in the left/right direction.
flip : Flip array in one or more dimensions.
rot90 : Rotate array counterclockwise.
Notes
-----
Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``.
Requires the array to be at least 1-D.
Examples
--------
>>> A = np.diag([1.0, 2, 3])
>>> A
array([[1., 0., 0.],
[0., 2., 0.],
[0., 0., 3.]])
>>> np.flipud(A)
array([[0., 0., 3.],
[0., 2., 0.],
[1., 0., 0.]])
>>> A = np.random.randn(2,3,5)
>>> np.all(np.flipud(A) == A[::-1,...])
True
>>> np.flipud([1,2])
array([2, 1])
"""
m = asanyarray(m)
if m.ndim < 1:
raise ValueError("Input must be >= 1-d.")
return m[::-1, ...] | Reverse the order of elements along axis 0 (up/down). For a 2-D array, this flips the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- out : array_like A view of `m` with the rows reversed. Since a view is returned, this operation is :math:`\\mathcal O(1)`. See Also -------- fliplr : Flip array in the left/right direction. flip : Flip array in one or more dimensions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``. Requires the array to be at least 1-D. Examples -------- >>> A = np.diag([1.0, 2, 3]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.flipud(A) array([[0., 0., 3.], [0., 2., 0.], [1., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A) == A[::-1,...]) True >>> np.flipud([1,2]) array([2, 1]) |
168,675 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _eye_dispatcher(N, M=None, k=None, dtype=None, order=None, *, like=None):
return (like,) | null |
168,676 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _diag_dispatcher(v, k=None):
return (v,) | null |
168,677 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
The provided code snippet includes necessary dependencies for implementing the `diagflat` function. Write a Python function `def diagflat(v, k=0)` to solve the following problem:
Create a two-dimensional array with the flattened input as a diagonal. Parameters ---------- v : array_like Input data, which is flattened and set as the `k`-th diagonal of the output. k : int, optional Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive (negative) `k` giving the number of the diagonal above (below) the main. Returns ------- out : ndarray The 2-D output array. See Also -------- diag : MATLAB work-alike for 1-D and 2-D arrays. diagonal : Return specified diagonals. trace : Sum along diagonals. Examples -------- >>> np.diagflat([[1,2], [3,4]]) array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) >>> np.diagflat([1,2], 1) array([[0, 1, 0], [0, 0, 2], [0, 0, 0]])
Here is the function:
def diagflat(v, k=0):
"""
Create a two-dimensional array with the flattened input as a diagonal.
Parameters
----------
v : array_like
Input data, which is flattened and set as the `k`-th
diagonal of the output.
k : int, optional
Diagonal to set; 0, the default, corresponds to the "main" diagonal,
a positive (negative) `k` giving the number of the diagonal above
(below) the main.
Returns
-------
out : ndarray
The 2-D output array.
See Also
--------
diag : MATLAB work-alike for 1-D and 2-D arrays.
diagonal : Return specified diagonals.
trace : Sum along diagonals.
Examples
--------
>>> np.diagflat([[1,2], [3,4]])
array([[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]])
>>> np.diagflat([1,2], 1)
array([[0, 1, 0],
[0, 0, 2],
[0, 0, 0]])
"""
try:
wrap = v.__array_wrap__
except AttributeError:
wrap = None
v = asarray(v).ravel()
s = len(v)
n = s + abs(k)
res = zeros((n, n), v.dtype)
if (k >= 0):
i = arange(0, n-k, dtype=intp)
fi = i+k+i*n
else:
i = arange(0, n+k, dtype=intp)
fi = i+(i-k)*n
res.flat[fi] = v
if not wrap:
return res
return wrap(res) | Create a two-dimensional array with the flattened input as a diagonal. Parameters ---------- v : array_like Input data, which is flattened and set as the `k`-th diagonal of the output. k : int, optional Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive (negative) `k` giving the number of the diagonal above (below) the main. Returns ------- out : ndarray The 2-D output array. See Also -------- diag : MATLAB work-alike for 1-D and 2-D arrays. diagonal : Return specified diagonals. trace : Sum along diagonals. Examples -------- >>> np.diagflat([[1,2], [3,4]]) array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) >>> np.diagflat([1,2], 1) array([[0, 1, 0], [0, 0, 2], [0, 0, 0]]) |
168,678 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _tri_dispatcher(N, M=None, k=None, dtype=None, *, like=None):
return (like,) | null |
168,679 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _trilu_dispatcher(m, k=None):
return (m,) | null |
168,680 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def tri(N, M=None, k=0, dtype=float, *, like=None):
"""
An array with ones at and below the given diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the array.
M : int, optional
Number of columns in the array.
By default, `M` is taken equal to `N`.
k : int, optional
The sub-diagonal at and below which the array is filled.
`k` = 0 is the main diagonal, while `k` < 0 is below it,
and `k` > 0 is above. The default is 0.
dtype : dtype, optional
Data type of the returned array. The default is float.
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
tri : ndarray of shape (N, M)
Array with its lower triangle filled with ones and zero elsewhere;
in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise.
Examples
--------
>>> np.tri(3, 5, 2, dtype=int)
array([[1, 1, 1, 0, 0],
[1, 1, 1, 1, 0],
[1, 1, 1, 1, 1]])
>>> np.tri(3, 5, -1)
array([[0., 0., 0., 0., 0.],
[1., 0., 0., 0., 0.],
[1., 1., 0., 0., 0.]])
"""
if like is not None:
return _tri_with_like(N, M=M, k=k, dtype=dtype, like=like)
if M is None:
M = N
m = greater_equal.outer(arange(N, dtype=_min_int(0, N)),
arange(-k, M-k, dtype=_min_int(-k, M - k)))
# Avoid making a copy if the requested type is already bool
m = m.astype(dtype, copy=False)
return m
The provided code snippet includes necessary dependencies for implementing the `tril` function. Write a Python function `def tril(m, k=0)` to solve the following problem:
Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two axes. Parameters ---------- m : array_like, shape (..., M, N) Input array. k : int, optional Diagonal above which to zero elements. `k = 0` (the default) is the main diagonal, `k < 0` is below it and `k > 0` is above. Returns ------- tril : ndarray, shape (..., M, N) Lower triangle of `m`, of same shape and data-type as `m`. See Also -------- triu : same thing, only for the upper triangle Examples -------- >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]]) >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5)) array([[[ 0, 0, 0, 0, 0], [ 5, 6, 0, 0, 0], [10, 11, 12, 0, 0], [15, 16, 17, 18, 0]], [[20, 0, 0, 0, 0], [25, 26, 0, 0, 0], [30, 31, 32, 0, 0], [35, 36, 37, 38, 0]], [[40, 0, 0, 0, 0], [45, 46, 0, 0, 0], [50, 51, 52, 0, 0], [55, 56, 57, 58, 0]]])
Here is the function:
def tril(m, k=0):
"""
Lower triangle of an array.
Return a copy of an array with elements above the `k`-th diagonal zeroed.
For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two
axes.
Parameters
----------
m : array_like, shape (..., M, N)
Input array.
k : int, optional
Diagonal above which to zero elements. `k = 0` (the default) is the
main diagonal, `k < 0` is below it and `k > 0` is above.
Returns
-------
tril : ndarray, shape (..., M, N)
Lower triangle of `m`, of same shape and data-type as `m`.
See Also
--------
triu : same thing, only for the upper triangle
Examples
--------
>>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
>>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))
array([[[ 0, 0, 0, 0, 0],
[ 5, 6, 0, 0, 0],
[10, 11, 12, 0, 0],
[15, 16, 17, 18, 0]],
[[20, 0, 0, 0, 0],
[25, 26, 0, 0, 0],
[30, 31, 32, 0, 0],
[35, 36, 37, 38, 0]],
[[40, 0, 0, 0, 0],
[45, 46, 0, 0, 0],
[50, 51, 52, 0, 0],
[55, 56, 57, 58, 0]]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k, dtype=bool)
return where(mask, m, zeros(1, m.dtype)) | Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two axes. Parameters ---------- m : array_like, shape (..., M, N) Input array. k : int, optional Diagonal above which to zero elements. `k = 0` (the default) is the main diagonal, `k < 0` is below it and `k > 0` is above. Returns ------- tril : ndarray, shape (..., M, N) Lower triangle of `m`, of same shape and data-type as `m`. See Also -------- triu : same thing, only for the upper triangle Examples -------- >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]]) >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5)) array([[[ 0, 0, 0, 0, 0], [ 5, 6, 0, 0, 0], [10, 11, 12, 0, 0], [15, 16, 17, 18, 0]], [[20, 0, 0, 0, 0], [25, 26, 0, 0, 0], [30, 31, 32, 0, 0], [35, 36, 37, 38, 0]], [[40, 0, 0, 0, 0], [45, 46, 0, 0, 0], [50, 51, 52, 0, 0], [55, 56, 57, 58, 0]]]) |
168,681 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _vander_dispatcher(x, N=None, increasing=None):
return (x,) | null |
168,682 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _histogram2d_dispatcher(x, y, bins=None, range=None, density=None,
weights=None):
yield x
yield y
# This terrible logic is adapted from the checks in histogram2d
try:
N = len(bins)
except TypeError:
N = 1
if N == 2:
yield from bins # bins=[x, y]
else:
yield bins
yield weights | null |
168,683 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
The provided code snippet includes necessary dependencies for implementing the `histogram2d` function. Write a Python function `def histogram2d(x, y, bins=10, range=None, density=None, weights=None)` to solve the following problem:
Compute the bi-dimensional histogram of two data samples. Parameters ---------- x : array_like, shape (N,) An array containing the x coordinates of the points to be histogrammed. y : array_like, shape (N,) An array containing the y coordinates of the points to be histogrammed. bins : int or array_like or [int, int] or [array, array], optional The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [int, int], the number of bins in each dimension (nx, ny = bins). * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins). * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges. range : array_like, shape(2,2), optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. density : bool, optional If False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, ``bin_count / sample_count / bin_area``. weights : array_like, shape(N,), optional An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights are normalized to 1 if `density` is True. If `density` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray, shape(nx, ny) The bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension. xedges : ndarray, shape(nx+1,) The bin edges along the first dimension. yedges : ndarray, shape(ny+1,) The bin edges along the second dimension. See Also -------- histogram : 1D histogram histogramdd : Multidimensional histogram Notes ----- When `density` is True, then the returned histogram is the sample density, defined such that the sum over bins of the product ``bin_value * bin_area`` is 1. Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with `histogramdd`. Examples -------- >>> from matplotlib.image import NonUniformImage >>> import matplotlib.pyplot as plt Construct a 2-D histogram with variable bin width. First define the bin edges: >>> xedges = [0, 1, 3, 5] >>> yedges = [0, 2, 3, 4, 6] Next we create a histogram H with random bin content: >>> x = np.random.normal(2, 1, 100) >>> y = np.random.normal(1, 1, 100) >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges)) >>> # Histogram does not follow Cartesian convention (see Notes), >>> # therefore transpose H for visualization purposes. >>> H = H.T :func:`imshow <matplotlib.pyplot.imshow>` can only display square bins: >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131, title='imshow: square bins') >>> plt.imshow(H, interpolation='nearest', origin='lower', ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) <matplotlib.image.AxesImage object at 0x...> :func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges: >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges', ... aspect='equal') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) <matplotlib.collections.QuadMesh object at 0x...> :class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to display actual bin edges with interpolation: >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated', ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]]) >>> im = NonUniformImage(ax, interpolation='bilinear') >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 >>> im.set_data(xcenters, ycenters, H) >>> ax.images.append(im) >>> plt.show() It is also possible to construct a 2-D histogram without specifying bin edges: >>> # Generate non-symmetric test data >>> n = 10000 >>> x = np.linspace(1, 100, n) >>> y = 2*np.log(x) + np.random.rand(n) - 0.5 >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges >>> H, yedges, xedges = np.histogram2d(y, x, bins=20) Now we can plot the histogram using :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison. >>> # Plot histogram using pcolormesh >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True) >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow') >>> ax1.plot(x, 2*np.log(x), 'k-') >>> ax1.set_xlim(x.min(), x.max()) >>> ax1.set_ylim(y.min(), y.max()) >>> ax1.set_xlabel('x') >>> ax1.set_ylabel('y') >>> ax1.set_title('histogram2d') >>> ax1.grid() >>> # Create hexbin plot for comparison >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow') >>> ax2.plot(x, 2*np.log(x), 'k-') >>> ax2.set_title('hexbin') >>> ax2.set_xlim(x.min(), x.max()) >>> ax2.set_xlabel('x') >>> ax2.grid() >>> plt.show()
Here is the function:
def histogram2d(x, y, bins=10, range=None, density=None, weights=None):
"""
Compute the bi-dimensional histogram of two data samples.
Parameters
----------
x : array_like, shape (N,)
An array containing the x coordinates of the points to be
histogrammed.
y : array_like, shape (N,)
An array containing the y coordinates of the points to be
histogrammed.
bins : int or array_like or [int, int] or [array, array], optional
The bin specification:
* If int, the number of bins for the two dimensions (nx=ny=bins).
* If array_like, the bin edges for the two dimensions
(x_edges=y_edges=bins).
* If [int, int], the number of bins in each dimension
(nx, ny = bins).
* If [array, array], the bin edges in each dimension
(x_edges, y_edges = bins).
* A combination [int, array] or [array, int], where int
is the number of bins and array is the bin edges.
range : array_like, shape(2,2), optional
The leftmost and rightmost edges of the bins along each dimension
(if not specified explicitly in the `bins` parameters):
``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range
will be considered outliers and not tallied in the histogram.
density : bool, optional
If False, the default, returns the number of samples in each bin.
If True, returns the probability *density* function at the bin,
``bin_count / sample_count / bin_area``.
weights : array_like, shape(N,), optional
An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.
Weights are normalized to 1 if `density` is True. If `density` is
False, the values of the returned histogram are equal to the sum of
the weights belonging to the samples falling into each bin.
Returns
-------
H : ndarray, shape(nx, ny)
The bi-dimensional histogram of samples `x` and `y`. Values in `x`
are histogrammed along the first dimension and values in `y` are
histogrammed along the second dimension.
xedges : ndarray, shape(nx+1,)
The bin edges along the first dimension.
yedges : ndarray, shape(ny+1,)
The bin edges along the second dimension.
See Also
--------
histogram : 1D histogram
histogramdd : Multidimensional histogram
Notes
-----
When `density` is True, then the returned histogram is the sample
density, defined such that the sum over bins of the product
``bin_value * bin_area`` is 1.
Please note that the histogram does not follow the Cartesian convention
where `x` values are on the abscissa and `y` values on the ordinate
axis. Rather, `x` is histogrammed along the first dimension of the
array (vertical), and `y` along the second dimension of the array
(horizontal). This ensures compatibility with `histogramdd`.
Examples
--------
>>> from matplotlib.image import NonUniformImage
>>> import matplotlib.pyplot as plt
Construct a 2-D histogram with variable bin width. First define the bin
edges:
>>> xedges = [0, 1, 3, 5]
>>> yedges = [0, 2, 3, 4, 6]
Next we create a histogram H with random bin content:
>>> x = np.random.normal(2, 1, 100)
>>> y = np.random.normal(1, 1, 100)
>>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges))
>>> # Histogram does not follow Cartesian convention (see Notes),
>>> # therefore transpose H for visualization purposes.
>>> H = H.T
:func:`imshow <matplotlib.pyplot.imshow>` can only display square bins:
>>> fig = plt.figure(figsize=(7, 3))
>>> ax = fig.add_subplot(131, title='imshow: square bins')
>>> plt.imshow(H, interpolation='nearest', origin='lower',
... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])
<matplotlib.image.AxesImage object at 0x...>
:func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges:
>>> ax = fig.add_subplot(132, title='pcolormesh: actual edges',
... aspect='equal')
>>> X, Y = np.meshgrid(xedges, yedges)
>>> ax.pcolormesh(X, Y, H)
<matplotlib.collections.QuadMesh object at 0x...>
:class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to
display actual bin edges with interpolation:
>>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated',
... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]])
>>> im = NonUniformImage(ax, interpolation='bilinear')
>>> xcenters = (xedges[:-1] + xedges[1:]) / 2
>>> ycenters = (yedges[:-1] + yedges[1:]) / 2
>>> im.set_data(xcenters, ycenters, H)
>>> ax.images.append(im)
>>> plt.show()
It is also possible to construct a 2-D histogram without specifying bin
edges:
>>> # Generate non-symmetric test data
>>> n = 10000
>>> x = np.linspace(1, 100, n)
>>> y = 2*np.log(x) + np.random.rand(n) - 0.5
>>> # Compute 2d histogram. Note the order of x/y and xedges/yedges
>>> H, yedges, xedges = np.histogram2d(y, x, bins=20)
Now we can plot the histogram using
:func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a
:func:`hexbin <matplotlib.pyplot.hexbin>` for comparison.
>>> # Plot histogram using pcolormesh
>>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)
>>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow')
>>> ax1.plot(x, 2*np.log(x), 'k-')
>>> ax1.set_xlim(x.min(), x.max())
>>> ax1.set_ylim(y.min(), y.max())
>>> ax1.set_xlabel('x')
>>> ax1.set_ylabel('y')
>>> ax1.set_title('histogram2d')
>>> ax1.grid()
>>> # Create hexbin plot for comparison
>>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow')
>>> ax2.plot(x, 2*np.log(x), 'k-')
>>> ax2.set_title('hexbin')
>>> ax2.set_xlim(x.min(), x.max())
>>> ax2.set_xlabel('x')
>>> ax2.grid()
>>> plt.show()
"""
from numpy import histogramdd
if len(x) != len(y):
raise ValueError('x and y must have the same length.')
try:
N = len(bins)
except TypeError:
N = 1
if N != 1 and N != 2:
xedges = yedges = asarray(bins)
bins = [xedges, yedges]
hist, edges = histogramdd([x, y], bins, range, density, weights)
return hist, edges[0], edges[1] | Compute the bi-dimensional histogram of two data samples. Parameters ---------- x : array_like, shape (N,) An array containing the x coordinates of the points to be histogrammed. y : array_like, shape (N,) An array containing the y coordinates of the points to be histogrammed. bins : int or array_like or [int, int] or [array, array], optional The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [int, int], the number of bins in each dimension (nx, ny = bins). * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins). * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges. range : array_like, shape(2,2), optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. density : bool, optional If False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, ``bin_count / sample_count / bin_area``. weights : array_like, shape(N,), optional An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights are normalized to 1 if `density` is True. If `density` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray, shape(nx, ny) The bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension. xedges : ndarray, shape(nx+1,) The bin edges along the first dimension. yedges : ndarray, shape(ny+1,) The bin edges along the second dimension. See Also -------- histogram : 1D histogram histogramdd : Multidimensional histogram Notes ----- When `density` is True, then the returned histogram is the sample density, defined such that the sum over bins of the product ``bin_value * bin_area`` is 1. Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with `histogramdd`. Examples -------- >>> from matplotlib.image import NonUniformImage >>> import matplotlib.pyplot as plt Construct a 2-D histogram with variable bin width. First define the bin edges: >>> xedges = [0, 1, 3, 5] >>> yedges = [0, 2, 3, 4, 6] Next we create a histogram H with random bin content: >>> x = np.random.normal(2, 1, 100) >>> y = np.random.normal(1, 1, 100) >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges)) >>> # Histogram does not follow Cartesian convention (see Notes), >>> # therefore transpose H for visualization purposes. >>> H = H.T :func:`imshow <matplotlib.pyplot.imshow>` can only display square bins: >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131, title='imshow: square bins') >>> plt.imshow(H, interpolation='nearest', origin='lower', ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) <matplotlib.image.AxesImage object at 0x...> :func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges: >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges', ... aspect='equal') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) <matplotlib.collections.QuadMesh object at 0x...> :class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to display actual bin edges with interpolation: >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated', ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]]) >>> im = NonUniformImage(ax, interpolation='bilinear') >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 >>> im.set_data(xcenters, ycenters, H) >>> ax.images.append(im) >>> plt.show() It is also possible to construct a 2-D histogram without specifying bin edges: >>> # Generate non-symmetric test data >>> n = 10000 >>> x = np.linspace(1, 100, n) >>> y = 2*np.log(x) + np.random.rand(n) - 0.5 >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges >>> H, yedges, xedges = np.histogram2d(y, x, bins=20) Now we can plot the histogram using :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison. >>> # Plot histogram using pcolormesh >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True) >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow') >>> ax1.plot(x, 2*np.log(x), 'k-') >>> ax1.set_xlim(x.min(), x.max()) >>> ax1.set_ylim(y.min(), y.max()) >>> ax1.set_xlabel('x') >>> ax1.set_ylabel('y') >>> ax1.set_title('histogram2d') >>> ax1.grid() >>> # Create hexbin plot for comparison >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow') >>> ax2.plot(x, 2*np.log(x), 'k-') >>> ax2.set_title('hexbin') >>> ax2.set_xlim(x.min(), x.max()) >>> ax2.set_xlabel('x') >>> ax2.grid() >>> plt.show() |
168,684 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def ones(shape, dtype=None, order='C', *, like=None):
"""
Return a new array of given shape and type, filled with ones.
Parameters
----------
shape : int or sequence of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
order : {'C', 'F'}, optional, default: C
Whether to store multi-dimensional data in row-major
(C-style) or column-major (Fortran-style) order in
memory.
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Array of ones with the given shape, dtype, and order.
See Also
--------
ones_like : Return an array of ones with shape and type of input.
empty : Return a new uninitialized array.
zeros : Return a new array setting values to zero.
full : Return a new array of given shape filled with value.
Examples
--------
>>> np.ones(5)
array([1., 1., 1., 1., 1.])
>>> np.ones((5,), dtype=int)
array([1, 1, 1, 1, 1])
>>> np.ones((2, 1))
array([[1.],
[1.]])
>>> s = (2,2)
>>> np.ones(s)
array([[1., 1.],
[1., 1.]])
"""
if like is not None:
return _ones_with_like(shape, dtype=dtype, order=order, like=like)
a = empty(shape, dtype, order)
multiarray.copyto(a, 1, casting='unsafe')
return a
The provided code snippet includes necessary dependencies for implementing the `mask_indices` function. Write a Python function `def mask_indices(n, mask_func, k=0)` to solve the following problem:
Return the indices to access (n, n) arrays, given a masking function. Assume `mask_func` is a function that, for a square array a of size ``(n, n)`` with a possible offset argument `k`, when called as ``mask_func(a, k)`` returns a new array with zeros in certain locations (functions like `triu` or `tril` do precisely this). Then this function returns the indices where the non-zero values would be located. Parameters ---------- n : int The returned indices will be valid to access arrays of shape (n, n). mask_func : callable A function whose call signature is similar to that of `triu`, `tril`. That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`. `k` is an optional argument to the function. k : scalar An optional argument which is passed through to `mask_func`. Functions like `triu`, `tril` take a second argument that is interpreted as an offset. Returns ------- indices : tuple of arrays. The `n` arrays of indices corresponding to the locations where ``mask_func(np.ones((n, n)), k)`` is True. See Also -------- triu, tril, triu_indices, tril_indices Notes ----- .. versionadded:: 1.4.0 Examples -------- These are the indices that would allow you to access the upper triangular part of any 3x3 array: >>> iu = np.mask_indices(3, np.triu) For example, if `a` is a 3x3 array: >>> a = np.arange(9).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> a[iu] array([0, 1, 2, 4, 5, 8]) An offset can be passed also to the masking function. This gets us the indices starting on the first diagonal right of the main one: >>> iu1 = np.mask_indices(3, np.triu, 1) with which we now extract only three elements: >>> a[iu1] array([1, 2, 5])
Here is the function:
def mask_indices(n, mask_func, k=0):
"""
Return the indices to access (n, n) arrays, given a masking function.
Assume `mask_func` is a function that, for a square array a of size
``(n, n)`` with a possible offset argument `k`, when called as
``mask_func(a, k)`` returns a new array with zeros in certain locations
(functions like `triu` or `tril` do precisely this). Then this function
returns the indices where the non-zero values would be located.
Parameters
----------
n : int
The returned indices will be valid to access arrays of shape (n, n).
mask_func : callable
A function whose call signature is similar to that of `triu`, `tril`.
That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
`k` is an optional argument to the function.
k : scalar
An optional argument which is passed through to `mask_func`. Functions
like `triu`, `tril` take a second argument that is interpreted as an
offset.
Returns
-------
indices : tuple of arrays.
The `n` arrays of indices corresponding to the locations where
``mask_func(np.ones((n, n)), k)`` is True.
See Also
--------
triu, tril, triu_indices, tril_indices
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
These are the indices that would allow you to access the upper triangular
part of any 3x3 array:
>>> iu = np.mask_indices(3, np.triu)
For example, if `a` is a 3x3 array:
>>> a = np.arange(9).reshape(3, 3)
>>> a
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> a[iu]
array([0, 1, 2, 4, 5, 8])
An offset can be passed also to the masking function. This gets us the
indices starting on the first diagonal right of the main one:
>>> iu1 = np.mask_indices(3, np.triu, 1)
with which we now extract only three elements:
>>> a[iu1]
array([1, 2, 5])
"""
m = ones((n, n), int)
a = mask_func(m, k)
return nonzero(a != 0) | Return the indices to access (n, n) arrays, given a masking function. Assume `mask_func` is a function that, for a square array a of size ``(n, n)`` with a possible offset argument `k`, when called as ``mask_func(a, k)`` returns a new array with zeros in certain locations (functions like `triu` or `tril` do precisely this). Then this function returns the indices where the non-zero values would be located. Parameters ---------- n : int The returned indices will be valid to access arrays of shape (n, n). mask_func : callable A function whose call signature is similar to that of `triu`, `tril`. That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`. `k` is an optional argument to the function. k : scalar An optional argument which is passed through to `mask_func`. Functions like `triu`, `tril` take a second argument that is interpreted as an offset. Returns ------- indices : tuple of arrays. The `n` arrays of indices corresponding to the locations where ``mask_func(np.ones((n, n)), k)`` is True. See Also -------- triu, tril, triu_indices, tril_indices Notes ----- .. versionadded:: 1.4.0 Examples -------- These are the indices that would allow you to access the upper triangular part of any 3x3 array: >>> iu = np.mask_indices(3, np.triu) For example, if `a` is a 3x3 array: >>> a = np.arange(9).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> a[iu] array([0, 1, 2, 4, 5, 8]) An offset can be passed also to the masking function. This gets us the indices starting on the first diagonal right of the main one: >>> iu1 = np.mask_indices(3, np.triu, 1) with which we now extract only three elements: >>> a[iu1] array([1, 2, 5]) |
168,685 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def _trilu_indices_form_dispatcher(arr, k=None):
return (arr,) | null |
168,686 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def tril_indices(n, k=0, m=None):
"""
Return the indices for the lower-triangle of an (n, m) array.
Parameters
----------
n : int
The row dimension of the arrays for which the returned
indices will be valid.
k : int, optional
Diagonal offset (see `tril` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple of arrays
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array.
See also
--------
triu_indices : similar function, for upper-triangular.
mask_indices : generic function accepting an arbitrary mask function.
tril, triu
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
lower triangular part starting at the main diagonal, and one starting two
diagonals further right:
>>> il1 = np.tril_indices(4)
>>> il2 = np.tril_indices(4, 2)
Here is how they can be used with a sample array:
>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
>>> a[il1]
array([ 0, 4, 5, ..., 13, 14, 15])
And for assigning values:
>>> a[il1] = -1
>>> a
array([[-1, 1, 2, 3],
[-1, -1, 6, 7],
[-1, -1, -1, 11],
[-1, -1, -1, -1]])
These cover almost the whole array (two diagonals right of the main one):
>>> a[il2] = -10
>>> a
array([[-10, -10, -10, 3],
[-10, -10, -10, -10],
[-10, -10, -10, -10],
[-10, -10, -10, -10]])
"""
tri_ = tri(n, m, k=k, dtype=bool)
return tuple(broadcast_to(inds, tri_.shape)[tri_]
for inds in indices(tri_.shape, sparse=True))
The provided code snippet includes necessary dependencies for implementing the `tril_indices_from` function. Write a Python function `def tril_indices_from(arr, k=0)` to solve the following problem:
Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). See Also -------- tril_indices, tril Notes ----- .. versionadded:: 1.4.0
Here is the function:
def tril_indices_from(arr, k=0):
"""
Return the indices for the lower-triangle of arr.
See `tril_indices` for full details.
Parameters
----------
arr : array_like
The indices will be valid for square arrays whose dimensions are
the same as arr.
k : int, optional
Diagonal offset (see `tril` for details).
See Also
--------
tril_indices, tril
Notes
-----
.. versionadded:: 1.4.0
"""
if arr.ndim != 2:
raise ValueError("input array must be 2-d")
return tril_indices(arr.shape[-2], k=k, m=arr.shape[-1]) | Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). See Also -------- tril_indices, tril Notes ----- .. versionadded:: 1.4.0 |
168,687 | import functools
import operator
from numpy.core.numeric import (
asanyarray, arange, zeros, greater_equal, multiply, ones,
asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
diagonal, nonzero, indices
)
from numpy.core.overrides import set_array_function_like_doc, set_module
from numpy.core import overrides
from numpy.core import iinfo
from numpy.lib.stride_tricks import broadcast_to
def triu_indices(n, k=0, m=None):
"""
Return the indices for the upper-triangle of an (n, m) array.
Parameters
----------
n : int
The size of the arrays for which the returned indices will
be valid.
k : int, optional
Diagonal offset (see `triu` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple, shape(2) of ndarrays, shape(`n`)
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array. Can be used
to slice a ndarray of shape(`n`, `n`).
See also
--------
tril_indices : similar function, for lower-triangular.
mask_indices : generic function accepting an arbitrary mask function.
triu, tril
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
upper triangular part starting at the main diagonal, and one starting two
diagonals further right:
>>> iu1 = np.triu_indices(4)
>>> iu2 = np.triu_indices(4, 2)
Here is how they can be used with a sample array:
>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
>>> a[iu1]
array([ 0, 1, 2, ..., 10, 11, 15])
And for assigning values:
>>> a[iu1] = -1
>>> a
array([[-1, -1, -1, -1],
[ 4, -1, -1, -1],
[ 8, 9, -1, -1],
[12, 13, 14, -1]])
These cover only a small part of the whole array (two diagonals right
of the main one):
>>> a[iu2] = -10
>>> a
array([[ -1, -1, -10, -10],
[ 4, -1, -1, -10],
[ 8, 9, -1, -1],
[ 12, 13, 14, -1]])
"""
tri_ = ~tri(n, m, k=k - 1, dtype=bool)
return tuple(broadcast_to(inds, tri_.shape)[tri_]
for inds in indices(tri_.shape, sparse=True))
The provided code snippet includes necessary dependencies for implementing the `triu_indices_from` function. Write a Python function `def triu_indices_from(arr, k=0)` to solve the following problem:
Return the indices for the upper-triangle of arr. See `triu_indices` for full details. Parameters ---------- arr : ndarray, shape(N, N) The indices will be valid for square arrays. k : int, optional Diagonal offset (see `triu` for details). Returns ------- triu_indices_from : tuple, shape(2) of ndarray, shape(N) Indices for the upper-triangle of `arr`. See Also -------- triu_indices, triu Notes ----- .. versionadded:: 1.4.0
Here is the function:
def triu_indices_from(arr, k=0):
"""
Return the indices for the upper-triangle of arr.
See `triu_indices` for full details.
Parameters
----------
arr : ndarray, shape(N, N)
The indices will be valid for square arrays.
k : int, optional
Diagonal offset (see `triu` for details).
Returns
-------
triu_indices_from : tuple, shape(2) of ndarray, shape(N)
Indices for the upper-triangle of `arr`.
See Also
--------
triu_indices, triu
Notes
-----
.. versionadded:: 1.4.0
"""
if arr.ndim != 2:
raise ValueError("input array must be 2-d")
return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1]) | Return the indices for the upper-triangle of arr. See `triu_indices` for full details. Parameters ---------- arr : ndarray, shape(N, N) The indices will be valid for square arrays. k : int, optional Diagonal offset (see `triu` for details). Returns ------- triu_indices_from : tuple, shape(2) of ndarray, shape(N) Indices for the upper-triangle of `arr`. See Also -------- triu_indices, triu Notes ----- .. versionadded:: 1.4.0 |
168,699 | from numpy.core import umath as um
def _binary_method(ufunc, name):
"""Implement a forward binary method with a ufunc, e.g., __add__."""
def func(self, other):
if _disables_array_ufunc(other):
return NotImplemented
return ufunc(self, other)
func.__name__ = '__{}__'.format(name)
return func
def _reflected_binary_method(ufunc, name):
"""Implement a reflected binary method with a ufunc, e.g., __radd__."""
def func(self, other):
if _disables_array_ufunc(other):
return NotImplemented
return ufunc(other, self)
func.__name__ = '__r{}__'.format(name)
return func
def _inplace_binary_method(ufunc, name):
"""Implement an in-place binary method with a ufunc, e.g., __iadd__."""
def func(self, other):
return ufunc(self, other, out=(self,))
func.__name__ = '__i{}__'.format(name)
return func
The provided code snippet includes necessary dependencies for implementing the `_numeric_methods` function. Write a Python function `def _numeric_methods(ufunc, name)` to solve the following problem:
Implement forward, reflected and inplace binary methods with a ufunc.
Here is the function:
def _numeric_methods(ufunc, name):
"""Implement forward, reflected and inplace binary methods with a ufunc."""
return (_binary_method(ufunc, name),
_reflected_binary_method(ufunc, name),
_inplace_binary_method(ufunc, name)) | Implement forward, reflected and inplace binary methods with a ufunc. |
168,700 | from numpy.core import umath as um
The provided code snippet includes necessary dependencies for implementing the `_unary_method` function. Write a Python function `def _unary_method(ufunc, name)` to solve the following problem:
Implement a unary special method with a ufunc.
Here is the function:
def _unary_method(ufunc, name):
"""Implement a unary special method with a ufunc."""
def func(self):
return ufunc(self)
func.__name__ = '__{}__'.format(name)
return func | Implement a unary special method with a ufunc. |
168,701 | import functools
import numpy as np
from numpy.core import overrides
def _ediff1d_dispatcher(ary, to_end=None, to_begin=None):
return (ary, to_end, to_begin) | null |
168,702 | import functools
import numpy as np
from numpy.core import overrides
The provided code snippet includes necessary dependencies for implementing the `ediff1d` function. Write a Python function `def ediff1d(ary, to_end=None, to_begin=None)` to solve the following problem:
The differences between consecutive elements of an array. Parameters ---------- ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. Returns ------- ediff1d : ndarray The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``. See Also -------- diff, gradient Notes ----- When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used. Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, -7]) >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99])) array([-99, 1, 2, ..., -7, 88, 99]) The returned array is always 1D. >>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, -3, 5, 18])
Here is the function:
def ediff1d(ary, to_end=None, to_begin=None):
"""
The differences between consecutive elements of an array.
Parameters
----------
ary : array_like
If necessary, will be flattened before the differences are taken.
to_end : array_like, optional
Number(s) to append at the end of the returned differences.
to_begin : array_like, optional
Number(s) to prepend at the beginning of the returned differences.
Returns
-------
ediff1d : ndarray
The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.
See Also
--------
diff, gradient
Notes
-----
When applied to masked arrays, this function drops the mask information
if the `to_begin` and/or `to_end` parameters are used.
Examples
--------
>>> x = np.array([1, 2, 4, 7, 0])
>>> np.ediff1d(x)
array([ 1, 2, 3, -7])
>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
array([-99, 1, 2, ..., -7, 88, 99])
The returned array is always 1D.
>>> y = [[1, 2, 4], [1, 6, 24]]
>>> np.ediff1d(y)
array([ 1, 2, -3, 5, 18])
"""
# force a 1d array
ary = np.asanyarray(ary).ravel()
# enforce that the dtype of `ary` is used for the output
dtype_req = ary.dtype
# fast track default case
if to_begin is None and to_end is None:
return ary[1:] - ary[:-1]
if to_begin is None:
l_begin = 0
else:
to_begin = np.asanyarray(to_begin)
if not np.can_cast(to_begin, dtype_req, casting="same_kind"):
raise TypeError("dtype of `to_begin` must be compatible "
"with input `ary` under the `same_kind` rule.")
to_begin = to_begin.ravel()
l_begin = len(to_begin)
if to_end is None:
l_end = 0
else:
to_end = np.asanyarray(to_end)
if not np.can_cast(to_end, dtype_req, casting="same_kind"):
raise TypeError("dtype of `to_end` must be compatible "
"with input `ary` under the `same_kind` rule.")
to_end = to_end.ravel()
l_end = len(to_end)
# do the calculation in place and copy to_begin and to_end
l_diff = max(len(ary) - 1, 0)
result = np.empty(l_diff + l_begin + l_end, dtype=ary.dtype)
result = ary.__array_wrap__(result)
if l_begin > 0:
result[:l_begin] = to_begin
if l_end > 0:
result[l_begin + l_diff:] = to_end
np.subtract(ary[1:], ary[:-1], result[l_begin:l_begin + l_diff])
return result | The differences between consecutive elements of an array. Parameters ---------- ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. Returns ------- ediff1d : ndarray The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``. See Also -------- diff, gradient Notes ----- When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used. Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, -7]) >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99])) array([-99, 1, 2, ..., -7, 88, 99]) The returned array is always 1D. >>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, -3, 5, 18]) |
168,703 | import functools
import numpy as np
from numpy.core import overrides
def _unique_dispatcher(ar, return_index=None, return_inverse=None,
return_counts=None, axis=None, *, equal_nan=None):
return (ar,) | null |
168,704 | import functools
import numpy as np
from numpy.core import overrides
def _intersect1d_dispatcher(
ar1, ar2, assume_unique=None, return_indices=None):
return (ar1, ar2) | null |
168,705 | import functools
import numpy as np
from numpy.core import overrides
def unique(ar, return_index=False, return_inverse=False,
return_counts=False, axis=None, *, equal_nan=True):
"""
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements:
* the indices of the input array that give the unique values
* the indices of the unique array that reconstruct the input array
* the number of times each unique value comes up in the input array
Parameters
----------
ar : array_like
Input array. Unless `axis` is specified, this will be flattened if it
is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` (along the specified axis,
if provided, or in the flattened array) that result in the unique array.
return_inverse : bool, optional
If True, also return the indices of the unique array (for the specified
axis, if provided) that can be used to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique item appears
in `ar`.
axis : int or None, optional
The axis to operate on. If None, `ar` will be flattened. If an integer,
the subarrays indexed by the given axis will be flattened and treated
as the elements of a 1-D array with the dimension of the given axis,
see the notes for more details. Object arrays or structured arrays
that contain objects are not supported if the `axis` kwarg is used. The
default is None.
.. versionadded:: 1.13.0
equal_nan : bool, optional
If True, collapses multiple NaN values in the return array into one.
.. versionadded:: 1.24
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
.. versionadded:: 1.9.0
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
repeat : Repeat elements of an array.
Notes
-----
When an axis is specified the subarrays indexed by the axis are sorted.
This is done by making the specified axis the first dimension of the array
(move the axis to the first dimension to keep the order of the other axes)
and then flattening the subarrays in C order. The flattened subarrays are
then viewed as a structured type with each element given a label, with the
effect that we end up with a 1-D array of structured types that can be
treated in the same way as any other 1-D array. The result is that the
flattened subarrays are sorted in lexicographic order starting with the
first element.
.. versionchanged: NumPy 1.21
If nan values are in the input array, a single nan is put
to the end of the sorted unique values.
Also for complex arrays all NaN values are considered equivalent
(no matter whether the NaN is in the real or imaginary part).
As the representant for the returned array the smallest one in the
lexicographical order is chosen - see np.sort for how the lexicographical
order is defined for complex arrays.
Examples
--------
>>> np.unique([1, 1, 2, 2, 3, 3])
array([1, 2, 3])
>>> a = np.array([[1, 1], [2, 3]])
>>> np.unique(a)
array([1, 2, 3])
Return the unique rows of a 2D array
>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
>>> np.unique(a, axis=0)
array([[1, 0, 0], [2, 3, 4]])
Return the indices of the original array that give the unique values:
>>> a = np.array(['a', 'b', 'b', 'c', 'a'])
>>> u, indices = np.unique(a, return_index=True)
>>> u
array(['a', 'b', 'c'], dtype='<U1')
>>> indices
array([0, 1, 3])
>>> a[indices]
array(['a', 'b', 'c'], dtype='<U1')
Reconstruct the input array from the unique values and inverse:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_inverse=True)
>>> u
array([1, 2, 3, 4, 6])
>>> indices
array([0, 1, 4, 3, 1, 2, 1])
>>> u[indices]
array([1, 2, 6, 4, 2, 3, 2])
Reconstruct the input values from the unique values and counts:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> values, counts = np.unique(a, return_counts=True)
>>> values
array([1, 2, 3, 4, 6])
>>> counts
array([1, 3, 1, 1, 1])
>>> np.repeat(values, counts)
array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved
"""
ar = np.asanyarray(ar)
if axis is None:
ret = _unique1d(ar, return_index, return_inverse, return_counts,
equal_nan=equal_nan)
return _unpack_tuple(ret)
# axis was specified and not None
try:
ar = np.moveaxis(ar, axis, 0)
except np.AxisError:
# this removes the "axis1" or "axis2" prefix from the error message
raise np.AxisError(axis, ar.ndim) from None
# Must reshape to a contiguous 2D array for this to work...
orig_shape, orig_dtype = ar.shape, ar.dtype
ar = ar.reshape(orig_shape[0], np.prod(orig_shape[1:], dtype=np.intp))
ar = np.ascontiguousarray(ar)
dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
# At this point, `ar` has shape `(n, m)`, and `dtype` is a structured
# data type with `m` fields where each field has the data type of `ar`.
# In the following, we create the array `consolidated`, which has
# shape `(n,)` with data type `dtype`.
try:
if ar.shape[1] > 0:
consolidated = ar.view(dtype)
else:
# If ar.shape[1] == 0, then dtype will be `np.dtype([])`, which is
# a data type with itemsize 0, and the call `ar.view(dtype)` will
# fail. Instead, we'll use `np.empty` to explicitly create the
# array with shape `(len(ar),)`. Because `dtype` in this case has
# itemsize 0, the total size of the result is still 0 bytes.
consolidated = np.empty(len(ar), dtype=dtype)
except TypeError as e:
# There's no good way to do this for object arrays, etc...
msg = 'The axis argument to unique is not supported for dtype {dt}'
raise TypeError(msg.format(dt=ar.dtype)) from e
def reshape_uniq(uniq):
n = len(uniq)
uniq = uniq.view(orig_dtype)
uniq = uniq.reshape(n, *orig_shape[1:])
uniq = np.moveaxis(uniq, 0, axis)
return uniq
output = _unique1d(consolidated, return_index,
return_inverse, return_counts, equal_nan=equal_nan)
output = (reshape_uniq(output[0]),) + output[1:]
return _unpack_tuple(output)
The provided code snippet includes necessary dependencies for implementing the `intersect1d` function. Write a Python function `def intersect1d(ar1, ar2, assume_unique=False, return_indices=False)` to solve the following problem:
Find the intersection of two arrays. Return the sorted, unique values that are in both of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. Will be flattened if not already 1D. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. If True but ``ar1`` or ``ar2`` are not unique, incorrect results and out-of-bounds indices could result. Default is False. return_indices : bool If True, the indices which correspond to the intersection of the two arrays are returned. The first instance of a value is used if there are multiple. Default is False. .. versionadded:: 1.15.0 Returns ------- intersect1d : ndarray Sorted 1D array of common and unique elements. comm1 : ndarray The indices of the first occurrences of the common values in `ar1`. Only provided if `return_indices` is True. comm2 : ndarray The indices of the first occurrences of the common values in `ar2`. Only provided if `return_indices` is True. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1]) array([1, 3]) To intersect more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([3]) To return the indices of the values common to the input arrays along with the intersected values: >>> x = np.array([1, 1, 2, 3, 4]) >>> y = np.array([2, 1, 4, 6]) >>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True) >>> x_ind, y_ind (array([0, 2, 4]), array([1, 0, 2])) >>> xy, x[x_ind], y[y_ind] (array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))
Here is the function:
def intersect1d(ar1, ar2, assume_unique=False, return_indices=False):
"""
Find the intersection of two arrays.
Return the sorted, unique values that are in both of the input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays. Will be flattened if not already 1D.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. If True but ``ar1`` or ``ar2`` are not
unique, incorrect results and out-of-bounds indices could result.
Default is False.
return_indices : bool
If True, the indices which correspond to the intersection of the two
arrays are returned. The first instance of a value is used if there are
multiple. Default is False.
.. versionadded:: 1.15.0
Returns
-------
intersect1d : ndarray
Sorted 1D array of common and unique elements.
comm1 : ndarray
The indices of the first occurrences of the common values in `ar1`.
Only provided if `return_indices` is True.
comm2 : ndarray
The indices of the first occurrences of the common values in `ar2`.
Only provided if `return_indices` is True.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
>>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])
array([1, 3])
To intersect more than two arrays, use functools.reduce:
>>> from functools import reduce
>>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
array([3])
To return the indices of the values common to the input arrays
along with the intersected values:
>>> x = np.array([1, 1, 2, 3, 4])
>>> y = np.array([2, 1, 4, 6])
>>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True)
>>> x_ind, y_ind
(array([0, 2, 4]), array([1, 0, 2]))
>>> xy, x[x_ind], y[y_ind]
(array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))
"""
ar1 = np.asanyarray(ar1)
ar2 = np.asanyarray(ar2)
if not assume_unique:
if return_indices:
ar1, ind1 = unique(ar1, return_index=True)
ar2, ind2 = unique(ar2, return_index=True)
else:
ar1 = unique(ar1)
ar2 = unique(ar2)
else:
ar1 = ar1.ravel()
ar2 = ar2.ravel()
aux = np.concatenate((ar1, ar2))
if return_indices:
aux_sort_indices = np.argsort(aux, kind='mergesort')
aux = aux[aux_sort_indices]
else:
aux.sort()
mask = aux[1:] == aux[:-1]
int1d = aux[:-1][mask]
if return_indices:
ar1_indices = aux_sort_indices[:-1][mask]
ar2_indices = aux_sort_indices[1:][mask] - ar1.size
if not assume_unique:
ar1_indices = ind1[ar1_indices]
ar2_indices = ind2[ar2_indices]
return int1d, ar1_indices, ar2_indices
else:
return int1d | Find the intersection of two arrays. Return the sorted, unique values that are in both of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. Will be flattened if not already 1D. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. If True but ``ar1`` or ``ar2`` are not unique, incorrect results and out-of-bounds indices could result. Default is False. return_indices : bool If True, the indices which correspond to the intersection of the two arrays are returned. The first instance of a value is used if there are multiple. Default is False. .. versionadded:: 1.15.0 Returns ------- intersect1d : ndarray Sorted 1D array of common and unique elements. comm1 : ndarray The indices of the first occurrences of the common values in `ar1`. Only provided if `return_indices` is True. comm2 : ndarray The indices of the first occurrences of the common values in `ar2`. Only provided if `return_indices` is True. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1]) array([1, 3]) To intersect more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([3]) To return the indices of the values common to the input arrays along with the intersected values: >>> x = np.array([1, 1, 2, 3, 4]) >>> y = np.array([2, 1, 4, 6]) >>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True) >>> x_ind, y_ind (array([0, 2, 4]), array([1, 0, 2])) >>> xy, x[x_ind], y[y_ind] (array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4])) |
168,706 | import functools
import numpy as np
from numpy.core import overrides
def _setxor1d_dispatcher(ar1, ar2, assume_unique=None):
return (ar1, ar2) | null |
168,707 | import functools
import numpy as np
from numpy.core import overrides
def unique(ar, return_index=False, return_inverse=False,
return_counts=False, axis=None, *, equal_nan=True):
"""
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements:
* the indices of the input array that give the unique values
* the indices of the unique array that reconstruct the input array
* the number of times each unique value comes up in the input array
Parameters
----------
ar : array_like
Input array. Unless `axis` is specified, this will be flattened if it
is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` (along the specified axis,
if provided, or in the flattened array) that result in the unique array.
return_inverse : bool, optional
If True, also return the indices of the unique array (for the specified
axis, if provided) that can be used to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique item appears
in `ar`.
axis : int or None, optional
The axis to operate on. If None, `ar` will be flattened. If an integer,
the subarrays indexed by the given axis will be flattened and treated
as the elements of a 1-D array with the dimension of the given axis,
see the notes for more details. Object arrays or structured arrays
that contain objects are not supported if the `axis` kwarg is used. The
default is None.
.. versionadded:: 1.13.0
equal_nan : bool, optional
If True, collapses multiple NaN values in the return array into one.
.. versionadded:: 1.24
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
.. versionadded:: 1.9.0
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
repeat : Repeat elements of an array.
Notes
-----
When an axis is specified the subarrays indexed by the axis are sorted.
This is done by making the specified axis the first dimension of the array
(move the axis to the first dimension to keep the order of the other axes)
and then flattening the subarrays in C order. The flattened subarrays are
then viewed as a structured type with each element given a label, with the
effect that we end up with a 1-D array of structured types that can be
treated in the same way as any other 1-D array. The result is that the
flattened subarrays are sorted in lexicographic order starting with the
first element.
.. versionchanged: NumPy 1.21
If nan values are in the input array, a single nan is put
to the end of the sorted unique values.
Also for complex arrays all NaN values are considered equivalent
(no matter whether the NaN is in the real or imaginary part).
As the representant for the returned array the smallest one in the
lexicographical order is chosen - see np.sort for how the lexicographical
order is defined for complex arrays.
Examples
--------
>>> np.unique([1, 1, 2, 2, 3, 3])
array([1, 2, 3])
>>> a = np.array([[1, 1], [2, 3]])
>>> np.unique(a)
array([1, 2, 3])
Return the unique rows of a 2D array
>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
>>> np.unique(a, axis=0)
array([[1, 0, 0], [2, 3, 4]])
Return the indices of the original array that give the unique values:
>>> a = np.array(['a', 'b', 'b', 'c', 'a'])
>>> u, indices = np.unique(a, return_index=True)
>>> u
array(['a', 'b', 'c'], dtype='<U1')
>>> indices
array([0, 1, 3])
>>> a[indices]
array(['a', 'b', 'c'], dtype='<U1')
Reconstruct the input array from the unique values and inverse:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_inverse=True)
>>> u
array([1, 2, 3, 4, 6])
>>> indices
array([0, 1, 4, 3, 1, 2, 1])
>>> u[indices]
array([1, 2, 6, 4, 2, 3, 2])
Reconstruct the input values from the unique values and counts:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> values, counts = np.unique(a, return_counts=True)
>>> values
array([1, 2, 3, 4, 6])
>>> counts
array([1, 3, 1, 1, 1])
>>> np.repeat(values, counts)
array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved
"""
ar = np.asanyarray(ar)
if axis is None:
ret = _unique1d(ar, return_index, return_inverse, return_counts,
equal_nan=equal_nan)
return _unpack_tuple(ret)
# axis was specified and not None
try:
ar = np.moveaxis(ar, axis, 0)
except np.AxisError:
# this removes the "axis1" or "axis2" prefix from the error message
raise np.AxisError(axis, ar.ndim) from None
# Must reshape to a contiguous 2D array for this to work...
orig_shape, orig_dtype = ar.shape, ar.dtype
ar = ar.reshape(orig_shape[0], np.prod(orig_shape[1:], dtype=np.intp))
ar = np.ascontiguousarray(ar)
dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
# At this point, `ar` has shape `(n, m)`, and `dtype` is a structured
# data type with `m` fields where each field has the data type of `ar`.
# In the following, we create the array `consolidated`, which has
# shape `(n,)` with data type `dtype`.
try:
if ar.shape[1] > 0:
consolidated = ar.view(dtype)
else:
# If ar.shape[1] == 0, then dtype will be `np.dtype([])`, which is
# a data type with itemsize 0, and the call `ar.view(dtype)` will
# fail. Instead, we'll use `np.empty` to explicitly create the
# array with shape `(len(ar),)`. Because `dtype` in this case has
# itemsize 0, the total size of the result is still 0 bytes.
consolidated = np.empty(len(ar), dtype=dtype)
except TypeError as e:
# There's no good way to do this for object arrays, etc...
msg = 'The axis argument to unique is not supported for dtype {dt}'
raise TypeError(msg.format(dt=ar.dtype)) from e
def reshape_uniq(uniq):
n = len(uniq)
uniq = uniq.view(orig_dtype)
uniq = uniq.reshape(n, *orig_shape[1:])
uniq = np.moveaxis(uniq, 0, axis)
return uniq
output = _unique1d(consolidated, return_index,
return_inverse, return_counts, equal_nan=equal_nan)
output = (reshape_uniq(output[0]),) + output[1:]
return _unpack_tuple(output)
The provided code snippet includes necessary dependencies for implementing the `setxor1d` function. Write a Python function `def setxor1d(ar1, ar2, assume_unique=False)` to solve the following problem:
Find the set exclusive-or of two arrays. Return the sorted, unique values that are in only one (not both) of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setxor1d : ndarray Sorted 1D array of unique values that are in only one of the input arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4]) >>> b = np.array([2, 3, 5, 7, 5]) >>> np.setxor1d(a,b) array([1, 4, 5, 7])
Here is the function:
def setxor1d(ar1, ar2, assume_unique=False):
"""
Find the set exclusive-or of two arrays.
Return the sorted, unique values that are in only one (not both) of the
input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
Returns
-------
setxor1d : ndarray
Sorted 1D array of unique values that are in only one of the input
arrays.
Examples
--------
>>> a = np.array([1, 2, 3, 2, 4])
>>> b = np.array([2, 3, 5, 7, 5])
>>> np.setxor1d(a,b)
array([1, 4, 5, 7])
"""
if not assume_unique:
ar1 = unique(ar1)
ar2 = unique(ar2)
aux = np.concatenate((ar1, ar2))
if aux.size == 0:
return aux
aux.sort()
flag = np.concatenate(([True], aux[1:] != aux[:-1], [True]))
return aux[flag[1:] & flag[:-1]] | Find the set exclusive-or of two arrays. Return the sorted, unique values that are in only one (not both) of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setxor1d : ndarray Sorted 1D array of unique values that are in only one of the input arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4]) >>> b = np.array([2, 3, 5, 7, 5]) >>> np.setxor1d(a,b) array([1, 4, 5, 7]) |
168,708 | import functools
import numpy as np
from numpy.core import overrides
def _in1d_dispatcher(ar1, ar2, assume_unique=None, invert=None, *,
kind=None):
return (ar1, ar2) | null |
168,709 | import functools
import numpy as np
from numpy.core import overrides
def _isin_dispatcher(element, test_elements, assume_unique=None, invert=None,
*, kind=None):
return (element, test_elements) | null |
168,710 | import functools
import numpy as np
from numpy.core import overrides
def in1d(ar1, ar2, assume_unique=False, invert=False, *, kind=None):
"""
Test whether each element of a 1-D array is also present in a second array.
Returns a boolean array the same length as `ar1` that is True
where an element of `ar1` is in `ar2` and False otherwise.
We recommend using :func:`isin` instead of `in1d` for new code.
Parameters
----------
ar1 : (M,) array_like
Input array.
ar2 : array_like
The values against which to test each value of `ar1`.
assume_unique : bool, optional
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
invert : bool, optional
If True, the values in the returned array are inverted (that is,
False where an element of `ar1` is in `ar2` and True otherwise).
Default is False. ``np.in1d(a, b, invert=True)`` is equivalent
to (but is faster than) ``np.invert(in1d(a, b))``.
kind : {None, 'sort', 'table'}, optional
The algorithm to use. This will not affect the final result,
but will affect the speed and memory use. The default, None,
will select automatically based on memory considerations.
* If 'sort', will use a mergesort-based approach. This will have
a memory usage of roughly 6 times the sum of the sizes of
`ar1` and `ar2`, not accounting for size of dtypes.
* If 'table', will use a lookup table approach similar
to a counting sort. This is only available for boolean and
integer arrays. This will have a memory usage of the
size of `ar1` plus the max-min value of `ar2`. `assume_unique`
has no effect when the 'table' option is used.
* If None, will automatically choose 'table' if
the required memory allocation is less than or equal to
6 times the sum of the sizes of `ar1` and `ar2`,
otherwise will use 'sort'. This is done to not use
a large amount of memory by default, even though
'table' may be faster in most cases. If 'table' is chosen,
`assume_unique` will have no effect.
.. versionadded:: 1.8.0
Returns
-------
in1d : (M,) ndarray, bool
The values `ar1[in1d]` are in `ar2`.
See Also
--------
isin : Version of this function that preserves the
shape of ar1.
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Notes
-----
`in1d` can be considered as an element-wise function version of the
python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly
equivalent to ``np.array([item in b for item in a])``.
However, this idea fails if `ar2` is a set, or similar (non-sequence)
container: As ``ar2`` is converted to an array, in those cases
``asarray(ar2)`` is an object array rather than the expected array of
contained values.
Using ``kind='table'`` tends to be faster than `kind='sort'` if the
following relationship is true:
``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
but may use greater memory. The default value for `kind` will
be automatically selected based only on memory usage, so one may
manually set ``kind='table'`` if memory constraints can be relaxed.
.. versionadded:: 1.4.0
Examples
--------
>>> test = np.array([0, 1, 2, 5, 0])
>>> states = [0, 2]
>>> mask = np.in1d(test, states)
>>> mask
array([ True, False, True, False, True])
>>> test[mask]
array([0, 2, 0])
>>> mask = np.in1d(test, states, invert=True)
>>> mask
array([False, True, False, True, False])
>>> test[mask]
array([1, 5])
"""
# Ravel both arrays, behavior for the first array could be different
ar1 = np.asarray(ar1).ravel()
ar2 = np.asarray(ar2).ravel()
# Ensure that iteration through object arrays yields size-1 arrays
if ar2.dtype == object:
ar2 = ar2.reshape(-1, 1)
if kind not in {None, 'sort', 'table'}:
raise ValueError(
f"Invalid kind: '{kind}'. Please use None, 'sort' or 'table'.")
# Can use the table method if all arrays are integers or boolean:
is_int_arrays = all(ar.dtype.kind in ("u", "i", "b") for ar in (ar1, ar2))
use_table_method = is_int_arrays and kind in {None, 'table'}
if use_table_method:
if ar2.size == 0:
if invert:
return np.ones_like(ar1, dtype=bool)
else:
return np.zeros_like(ar1, dtype=bool)
# Convert booleans to uint8 so we can use the fast integer algorithm
if ar1.dtype == bool:
ar1 = ar1.astype(np.uint8)
if ar2.dtype == bool:
ar2 = ar2.astype(np.uint8)
ar2_min = np.min(ar2)
ar2_max = np.max(ar2)
ar2_range = int(ar2_max) - int(ar2_min)
# Constraints on whether we can actually use the table method:
# 1. Assert memory usage is not too large
below_memory_constraint = ar2_range <= 6 * (ar1.size + ar2.size)
# 2. Check overflows for (ar2 - ar2_min); dtype=ar2.dtype
range_safe_from_overflow = ar2_range <= np.iinfo(ar2.dtype).max
# 3. Check overflows for (ar1 - ar2_min); dtype=ar1.dtype
if ar1.size > 0:
ar1_min = np.min(ar1)
ar1_max = np.max(ar1)
# After masking, the range of ar1 is guaranteed to be
# within the range of ar2:
ar1_upper = min(int(ar1_max), int(ar2_max))
ar1_lower = max(int(ar1_min), int(ar2_min))
range_safe_from_overflow &= all((
ar1_upper - int(ar2_min) <= np.iinfo(ar1.dtype).max,
ar1_lower - int(ar2_min) >= np.iinfo(ar1.dtype).min
))
# Optimal performance is for approximately
# log10(size) > (log10(range) - 2.27) / 0.927.
# However, here we set the requirement that by default
# the intermediate array can only be 6x
# the combined memory allocation of the original
# arrays. See discussion on
# https://github.com/numpy/numpy/pull/12065.
if (
range_safe_from_overflow and
(below_memory_constraint or kind == 'table')
):
if invert:
outgoing_array = np.ones_like(ar1, dtype=bool)
else:
outgoing_array = np.zeros_like(ar1, dtype=bool)
# Make elements 1 where the integer exists in ar2
if invert:
isin_helper_ar = np.ones(ar2_range + 1, dtype=bool)
isin_helper_ar[ar2 - ar2_min] = 0
else:
isin_helper_ar = np.zeros(ar2_range + 1, dtype=bool)
isin_helper_ar[ar2 - ar2_min] = 1
# Mask out elements we know won't work
basic_mask = (ar1 <= ar2_max) & (ar1 >= ar2_min)
outgoing_array[basic_mask] = isin_helper_ar[ar1[basic_mask] -
ar2_min]
return outgoing_array
elif kind == 'table': # not range_safe_from_overflow
raise RuntimeError(
"You have specified kind='table', "
"but the range of values in `ar2` or `ar1` exceed the "
"maximum integer of the datatype. "
"Please set `kind` to None or 'sort'."
)
elif kind == 'table':
raise ValueError(
"The 'table' method is only "
"supported for boolean or integer arrays. "
"Please select 'sort' or None for kind."
)
# Check if one of the arrays may contain arbitrary objects
contains_object = ar1.dtype.hasobject or ar2.dtype.hasobject
# This code is run when
# a) the first condition is true, making the code significantly faster
# b) the second condition is true (i.e. `ar1` or `ar2` may contain
# arbitrary objects), since then sorting is not guaranteed to work
if len(ar2) < 10 * len(ar1) ** 0.145 or contains_object:
if invert:
mask = np.ones(len(ar1), dtype=bool)
for a in ar2:
mask &= (ar1 != a)
else:
mask = np.zeros(len(ar1), dtype=bool)
for a in ar2:
mask |= (ar1 == a)
return mask
# Otherwise use sorting
if not assume_unique:
ar1, rev_idx = np.unique(ar1, return_inverse=True)
ar2 = np.unique(ar2)
ar = np.concatenate((ar1, ar2))
# We need this to be a stable sort, so always use 'mergesort'
# here. The values from the first array should always come before
# the values from the second array.
order = ar.argsort(kind='mergesort')
sar = ar[order]
if invert:
bool_ar = (sar[1:] != sar[:-1])
else:
bool_ar = (sar[1:] == sar[:-1])
flag = np.concatenate((bool_ar, [invert]))
ret = np.empty(ar.shape, dtype=bool)
ret[order] = flag
if assume_unique:
return ret[:len(ar1)]
else:
return ret[rev_idx]
The provided code snippet includes necessary dependencies for implementing the `isin` function. Write a Python function `def isin(element, test_elements, assume_unique=False, invert=False, *, kind=None)` to solve the following problem:
Calculates ``element in test_elements``, broadcasting over `element` only. Returns a boolean array of the same shape as `element` that is True where an element of `element` is in `test_elements` and False otherwise. Parameters ---------- element : array_like Input array. test_elements : array_like The values against which to test each value of `element`. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted, as if calculating `element not in test_elements`. Default is False. ``np.isin(a, b, invert=True)`` is equivalent to (but faster than) ``np.invert(np.isin(a, b))``. kind : {None, 'sort', 'table'}, optional The algorithm to use. This will not affect the final result, but will affect the speed and memory use. The default, None, will select automatically based on memory considerations. * If 'sort', will use a mergesort-based approach. This will have a memory usage of roughly 6 times the sum of the sizes of `ar1` and `ar2`, not accounting for size of dtypes. * If 'table', will use a lookup table approach similar to a counting sort. This is only available for boolean and integer arrays. This will have a memory usage of the size of `ar1` plus the max-min value of `ar2`. `assume_unique` has no effect when the 'table' option is used. * If None, will automatically choose 'table' if the required memory allocation is less than or equal to 6 times the sum of the sizes of `ar1` and `ar2`, otherwise will use 'sort'. This is done to not use a large amount of memory by default, even though 'table' may be faster in most cases. If 'table' is chosen, `assume_unique` will have no effect. Returns ------- isin : ndarray, bool Has the same shape as `element`. The values `element[isin]` are in `test_elements`. See Also -------- in1d : Flattened version of this function. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `isin` is an element-wise function version of the python keyword `in`. ``isin(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences. `element` and `test_elements` are converted to arrays if they are not already. If `test_elements` is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in `test_elements`. This is a consequence of the `array` constructor's way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior. Using ``kind='table'`` tends to be faster than `kind='sort'` if the following relationship is true: ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``, but may use greater memory. The default value for `kind` will be automatically selected based only on memory usage, so one may manually set ``kind='table'`` if memory constraints can be relaxed. .. versionadded:: 1.13.0 Examples -------- >>> element = 2*np.arange(4).reshape((2, 2)) >>> element array([[0, 2], [4, 6]]) >>> test_elements = [1, 2, 4, 8] >>> mask = np.isin(element, test_elements) >>> mask array([[False, True], [ True, False]]) >>> element[mask] array([2, 4]) The indices of the matched values can be obtained with `nonzero`: >>> np.nonzero(mask) (array([0, 1]), array([1, 0])) The test can also be inverted: >>> mask = np.isin(element, test_elements, invert=True) >>> mask array([[ True, False], [False, True]]) >>> element[mask] array([0, 6]) Because of how `array` handles sets, the following does not work as expected: >>> test_set = {1, 2, 4, 8} >>> np.isin(element, test_set) array([[False, False], [False, False]]) Casting the set to a list gives the expected result: >>> np.isin(element, list(test_set)) array([[False, True], [ True, False]])
Here is the function:
def isin(element, test_elements, assume_unique=False, invert=False, *,
kind=None):
"""
Calculates ``element in test_elements``, broadcasting over `element` only.
Returns a boolean array of the same shape as `element` that is True
where an element of `element` is in `test_elements` and False otherwise.
Parameters
----------
element : array_like
Input array.
test_elements : array_like
The values against which to test each value of `element`.
This argument is flattened if it is an array or array_like.
See notes for behavior with non-array-like parameters.
assume_unique : bool, optional
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
invert : bool, optional
If True, the values in the returned array are inverted, as if
calculating `element not in test_elements`. Default is False.
``np.isin(a, b, invert=True)`` is equivalent to (but faster
than) ``np.invert(np.isin(a, b))``.
kind : {None, 'sort', 'table'}, optional
The algorithm to use. This will not affect the final result,
but will affect the speed and memory use. The default, None,
will select automatically based on memory considerations.
* If 'sort', will use a mergesort-based approach. This will have
a memory usage of roughly 6 times the sum of the sizes of
`ar1` and `ar2`, not accounting for size of dtypes.
* If 'table', will use a lookup table approach similar
to a counting sort. This is only available for boolean and
integer arrays. This will have a memory usage of the
size of `ar1` plus the max-min value of `ar2`. `assume_unique`
has no effect when the 'table' option is used.
* If None, will automatically choose 'table' if
the required memory allocation is less than or equal to
6 times the sum of the sizes of `ar1` and `ar2`,
otherwise will use 'sort'. This is done to not use
a large amount of memory by default, even though
'table' may be faster in most cases. If 'table' is chosen,
`assume_unique` will have no effect.
Returns
-------
isin : ndarray, bool
Has the same shape as `element`. The values `element[isin]`
are in `test_elements`.
See Also
--------
in1d : Flattened version of this function.
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Notes
-----
`isin` is an element-wise function version of the python keyword `in`.
``isin(a, b)`` is roughly equivalent to
``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences.
`element` and `test_elements` are converted to arrays if they are not
already. If `test_elements` is a set (or other non-sequence collection)
it will be converted to an object array with one element, rather than an
array of the values contained in `test_elements`. This is a consequence
of the `array` constructor's way of handling non-sequence collections.
Converting the set to a list usually gives the desired behavior.
Using ``kind='table'`` tends to be faster than `kind='sort'` if the
following relationship is true:
``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
but may use greater memory. The default value for `kind` will
be automatically selected based only on memory usage, so one may
manually set ``kind='table'`` if memory constraints can be relaxed.
.. versionadded:: 1.13.0
Examples
--------
>>> element = 2*np.arange(4).reshape((2, 2))
>>> element
array([[0, 2],
[4, 6]])
>>> test_elements = [1, 2, 4, 8]
>>> mask = np.isin(element, test_elements)
>>> mask
array([[False, True],
[ True, False]])
>>> element[mask]
array([2, 4])
The indices of the matched values can be obtained with `nonzero`:
>>> np.nonzero(mask)
(array([0, 1]), array([1, 0]))
The test can also be inverted:
>>> mask = np.isin(element, test_elements, invert=True)
>>> mask
array([[ True, False],
[False, True]])
>>> element[mask]
array([0, 6])
Because of how `array` handles sets, the following does not
work as expected:
>>> test_set = {1, 2, 4, 8}
>>> np.isin(element, test_set)
array([[False, False],
[False, False]])
Casting the set to a list gives the expected result:
>>> np.isin(element, list(test_set))
array([[False, True],
[ True, False]])
"""
element = np.asarray(element)
return in1d(element, test_elements, assume_unique=assume_unique,
invert=invert, kind=kind).reshape(element.shape) | Calculates ``element in test_elements``, broadcasting over `element` only. Returns a boolean array of the same shape as `element` that is True where an element of `element` is in `test_elements` and False otherwise. Parameters ---------- element : array_like Input array. test_elements : array_like The values against which to test each value of `element`. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted, as if calculating `element not in test_elements`. Default is False. ``np.isin(a, b, invert=True)`` is equivalent to (but faster than) ``np.invert(np.isin(a, b))``. kind : {None, 'sort', 'table'}, optional The algorithm to use. This will not affect the final result, but will affect the speed and memory use. The default, None, will select automatically based on memory considerations. * If 'sort', will use a mergesort-based approach. This will have a memory usage of roughly 6 times the sum of the sizes of `ar1` and `ar2`, not accounting for size of dtypes. * If 'table', will use a lookup table approach similar to a counting sort. This is only available for boolean and integer arrays. This will have a memory usage of the size of `ar1` plus the max-min value of `ar2`. `assume_unique` has no effect when the 'table' option is used. * If None, will automatically choose 'table' if the required memory allocation is less than or equal to 6 times the sum of the sizes of `ar1` and `ar2`, otherwise will use 'sort'. This is done to not use a large amount of memory by default, even though 'table' may be faster in most cases. If 'table' is chosen, `assume_unique` will have no effect. Returns ------- isin : ndarray, bool Has the same shape as `element`. The values `element[isin]` are in `test_elements`. See Also -------- in1d : Flattened version of this function. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `isin` is an element-wise function version of the python keyword `in`. ``isin(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences. `element` and `test_elements` are converted to arrays if they are not already. If `test_elements` is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in `test_elements`. This is a consequence of the `array` constructor's way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior. Using ``kind='table'`` tends to be faster than `kind='sort'` if the following relationship is true: ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``, but may use greater memory. The default value for `kind` will be automatically selected based only on memory usage, so one may manually set ``kind='table'`` if memory constraints can be relaxed. .. versionadded:: 1.13.0 Examples -------- >>> element = 2*np.arange(4).reshape((2, 2)) >>> element array([[0, 2], [4, 6]]) >>> test_elements = [1, 2, 4, 8] >>> mask = np.isin(element, test_elements) >>> mask array([[False, True], [ True, False]]) >>> element[mask] array([2, 4]) The indices of the matched values can be obtained with `nonzero`: >>> np.nonzero(mask) (array([0, 1]), array([1, 0])) The test can also be inverted: >>> mask = np.isin(element, test_elements, invert=True) >>> mask array([[ True, False], [False, True]]) >>> element[mask] array([0, 6]) Because of how `array` handles sets, the following does not work as expected: >>> test_set = {1, 2, 4, 8} >>> np.isin(element, test_set) array([[False, False], [False, False]]) Casting the set to a list gives the expected result: >>> np.isin(element, list(test_set)) array([[False, True], [ True, False]]) |
168,711 | import functools
import numpy as np
from numpy.core import overrides
def _union1d_dispatcher(ar1, ar2):
return (ar1, ar2) | null |
168,712 | import functools
import numpy as np
from numpy.core import overrides
def unique(ar, return_index=False, return_inverse=False,
return_counts=False, axis=None, *, equal_nan=True):
"""
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements:
* the indices of the input array that give the unique values
* the indices of the unique array that reconstruct the input array
* the number of times each unique value comes up in the input array
Parameters
----------
ar : array_like
Input array. Unless `axis` is specified, this will be flattened if it
is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` (along the specified axis,
if provided, or in the flattened array) that result in the unique array.
return_inverse : bool, optional
If True, also return the indices of the unique array (for the specified
axis, if provided) that can be used to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique item appears
in `ar`.
axis : int or None, optional
The axis to operate on. If None, `ar` will be flattened. If an integer,
the subarrays indexed by the given axis will be flattened and treated
as the elements of a 1-D array with the dimension of the given axis,
see the notes for more details. Object arrays or structured arrays
that contain objects are not supported if the `axis` kwarg is used. The
default is None.
.. versionadded:: 1.13.0
equal_nan : bool, optional
If True, collapses multiple NaN values in the return array into one.
.. versionadded:: 1.24
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
.. versionadded:: 1.9.0
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
repeat : Repeat elements of an array.
Notes
-----
When an axis is specified the subarrays indexed by the axis are sorted.
This is done by making the specified axis the first dimension of the array
(move the axis to the first dimension to keep the order of the other axes)
and then flattening the subarrays in C order. The flattened subarrays are
then viewed as a structured type with each element given a label, with the
effect that we end up with a 1-D array of structured types that can be
treated in the same way as any other 1-D array. The result is that the
flattened subarrays are sorted in lexicographic order starting with the
first element.
.. versionchanged: NumPy 1.21
If nan values are in the input array, a single nan is put
to the end of the sorted unique values.
Also for complex arrays all NaN values are considered equivalent
(no matter whether the NaN is in the real or imaginary part).
As the representant for the returned array the smallest one in the
lexicographical order is chosen - see np.sort for how the lexicographical
order is defined for complex arrays.
Examples
--------
>>> np.unique([1, 1, 2, 2, 3, 3])
array([1, 2, 3])
>>> a = np.array([[1, 1], [2, 3]])
>>> np.unique(a)
array([1, 2, 3])
Return the unique rows of a 2D array
>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
>>> np.unique(a, axis=0)
array([[1, 0, 0], [2, 3, 4]])
Return the indices of the original array that give the unique values:
>>> a = np.array(['a', 'b', 'b', 'c', 'a'])
>>> u, indices = np.unique(a, return_index=True)
>>> u
array(['a', 'b', 'c'], dtype='<U1')
>>> indices
array([0, 1, 3])
>>> a[indices]
array(['a', 'b', 'c'], dtype='<U1')
Reconstruct the input array from the unique values and inverse:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_inverse=True)
>>> u
array([1, 2, 3, 4, 6])
>>> indices
array([0, 1, 4, 3, 1, 2, 1])
>>> u[indices]
array([1, 2, 6, 4, 2, 3, 2])
Reconstruct the input values from the unique values and counts:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> values, counts = np.unique(a, return_counts=True)
>>> values
array([1, 2, 3, 4, 6])
>>> counts
array([1, 3, 1, 1, 1])
>>> np.repeat(values, counts)
array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved
"""
ar = np.asanyarray(ar)
if axis is None:
ret = _unique1d(ar, return_index, return_inverse, return_counts,
equal_nan=equal_nan)
return _unpack_tuple(ret)
# axis was specified and not None
try:
ar = np.moveaxis(ar, axis, 0)
except np.AxisError:
# this removes the "axis1" or "axis2" prefix from the error message
raise np.AxisError(axis, ar.ndim) from None
# Must reshape to a contiguous 2D array for this to work...
orig_shape, orig_dtype = ar.shape, ar.dtype
ar = ar.reshape(orig_shape[0], np.prod(orig_shape[1:], dtype=np.intp))
ar = np.ascontiguousarray(ar)
dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
# At this point, `ar` has shape `(n, m)`, and `dtype` is a structured
# data type with `m` fields where each field has the data type of `ar`.
# In the following, we create the array `consolidated`, which has
# shape `(n,)` with data type `dtype`.
try:
if ar.shape[1] > 0:
consolidated = ar.view(dtype)
else:
# If ar.shape[1] == 0, then dtype will be `np.dtype([])`, which is
# a data type with itemsize 0, and the call `ar.view(dtype)` will
# fail. Instead, we'll use `np.empty` to explicitly create the
# array with shape `(len(ar),)`. Because `dtype` in this case has
# itemsize 0, the total size of the result is still 0 bytes.
consolidated = np.empty(len(ar), dtype=dtype)
except TypeError as e:
# There's no good way to do this for object arrays, etc...
msg = 'The axis argument to unique is not supported for dtype {dt}'
raise TypeError(msg.format(dt=ar.dtype)) from e
def reshape_uniq(uniq):
n = len(uniq)
uniq = uniq.view(orig_dtype)
uniq = uniq.reshape(n, *orig_shape[1:])
uniq = np.moveaxis(uniq, 0, axis)
return uniq
output = _unique1d(consolidated, return_index,
return_inverse, return_counts, equal_nan=equal_nan)
output = (reshape_uniq(output[0]),) + output[1:]
return _unpack_tuple(output)
The provided code snippet includes necessary dependencies for implementing the `union1d` function. Write a Python function `def union1d(ar1, ar2)` to solve the following problem:
Find the union of two arrays. Return the unique, sorted array of values that are in either of the two input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. They are flattened if they are not already 1D. Returns ------- union1d : ndarray Unique, sorted union of the input arrays. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.union1d([-1, 0, 1], [-2, 0, 2]) array([-2, -1, 0, 1, 2]) To find the union of more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([1, 2, 3, 4, 6])
Here is the function:
def union1d(ar1, ar2):
"""
Find the union of two arrays.
Return the unique, sorted array of values that are in either of the two
input arrays.
Parameters
----------
ar1, ar2 : array_like
Input arrays. They are flattened if they are not already 1D.
Returns
-------
union1d : ndarray
Unique, sorted union of the input arrays.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
>>> np.union1d([-1, 0, 1], [-2, 0, 2])
array([-2, -1, 0, 1, 2])
To find the union of more than two arrays, use functools.reduce:
>>> from functools import reduce
>>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
array([1, 2, 3, 4, 6])
"""
return unique(np.concatenate((ar1, ar2), axis=None)) | Find the union of two arrays. Return the unique, sorted array of values that are in either of the two input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. They are flattened if they are not already 1D. Returns ------- union1d : ndarray Unique, sorted union of the input arrays. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.union1d([-1, 0, 1], [-2, 0, 2]) array([-2, -1, 0, 1, 2]) To find the union of more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([1, 2, 3, 4, 6]) |
168,713 | import functools
import numpy as np
from numpy.core import overrides
def _setdiff1d_dispatcher(ar1, ar2, assume_unique=None):
return (ar1, ar2) | null |
168,714 | import functools
import numpy as np
from numpy.core import overrides
def unique(ar, return_index=False, return_inverse=False,
return_counts=False, axis=None, *, equal_nan=True):
"""
Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional
outputs in addition to the unique elements:
* the indices of the input array that give the unique values
* the indices of the unique array that reconstruct the input array
* the number of times each unique value comes up in the input array
Parameters
----------
ar : array_like
Input array. Unless `axis` is specified, this will be flattened if it
is not already 1-D.
return_index : bool, optional
If True, also return the indices of `ar` (along the specified axis,
if provided, or in the flattened array) that result in the unique array.
return_inverse : bool, optional
If True, also return the indices of the unique array (for the specified
axis, if provided) that can be used to reconstruct `ar`.
return_counts : bool, optional
If True, also return the number of times each unique item appears
in `ar`.
axis : int or None, optional
The axis to operate on. If None, `ar` will be flattened. If an integer,
the subarrays indexed by the given axis will be flattened and treated
as the elements of a 1-D array with the dimension of the given axis,
see the notes for more details. Object arrays or structured arrays
that contain objects are not supported if the `axis` kwarg is used. The
default is None.
.. versionadded:: 1.13.0
equal_nan : bool, optional
If True, collapses multiple NaN values in the return array into one.
.. versionadded:: 1.24
Returns
-------
unique : ndarray
The sorted unique values.
unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the
original array. Only provided if `return_index` is True.
unique_inverse : ndarray, optional
The indices to reconstruct the original array from the
unique array. Only provided if `return_inverse` is True.
unique_counts : ndarray, optional
The number of times each of the unique values comes up in the
original array. Only provided if `return_counts` is True.
.. versionadded:: 1.9.0
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
repeat : Repeat elements of an array.
Notes
-----
When an axis is specified the subarrays indexed by the axis are sorted.
This is done by making the specified axis the first dimension of the array
(move the axis to the first dimension to keep the order of the other axes)
and then flattening the subarrays in C order. The flattened subarrays are
then viewed as a structured type with each element given a label, with the
effect that we end up with a 1-D array of structured types that can be
treated in the same way as any other 1-D array. The result is that the
flattened subarrays are sorted in lexicographic order starting with the
first element.
.. versionchanged: NumPy 1.21
If nan values are in the input array, a single nan is put
to the end of the sorted unique values.
Also for complex arrays all NaN values are considered equivalent
(no matter whether the NaN is in the real or imaginary part).
As the representant for the returned array the smallest one in the
lexicographical order is chosen - see np.sort for how the lexicographical
order is defined for complex arrays.
Examples
--------
>>> np.unique([1, 1, 2, 2, 3, 3])
array([1, 2, 3])
>>> a = np.array([[1, 1], [2, 3]])
>>> np.unique(a)
array([1, 2, 3])
Return the unique rows of a 2D array
>>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
>>> np.unique(a, axis=0)
array([[1, 0, 0], [2, 3, 4]])
Return the indices of the original array that give the unique values:
>>> a = np.array(['a', 'b', 'b', 'c', 'a'])
>>> u, indices = np.unique(a, return_index=True)
>>> u
array(['a', 'b', 'c'], dtype='<U1')
>>> indices
array([0, 1, 3])
>>> a[indices]
array(['a', 'b', 'c'], dtype='<U1')
Reconstruct the input array from the unique values and inverse:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> u, indices = np.unique(a, return_inverse=True)
>>> u
array([1, 2, 3, 4, 6])
>>> indices
array([0, 1, 4, 3, 1, 2, 1])
>>> u[indices]
array([1, 2, 6, 4, 2, 3, 2])
Reconstruct the input values from the unique values and counts:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2])
>>> values, counts = np.unique(a, return_counts=True)
>>> values
array([1, 2, 3, 4, 6])
>>> counts
array([1, 3, 1, 1, 1])
>>> np.repeat(values, counts)
array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved
"""
ar = np.asanyarray(ar)
if axis is None:
ret = _unique1d(ar, return_index, return_inverse, return_counts,
equal_nan=equal_nan)
return _unpack_tuple(ret)
# axis was specified and not None
try:
ar = np.moveaxis(ar, axis, 0)
except np.AxisError:
# this removes the "axis1" or "axis2" prefix from the error message
raise np.AxisError(axis, ar.ndim) from None
# Must reshape to a contiguous 2D array for this to work...
orig_shape, orig_dtype = ar.shape, ar.dtype
ar = ar.reshape(orig_shape[0], np.prod(orig_shape[1:], dtype=np.intp))
ar = np.ascontiguousarray(ar)
dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
# At this point, `ar` has shape `(n, m)`, and `dtype` is a structured
# data type with `m` fields where each field has the data type of `ar`.
# In the following, we create the array `consolidated`, which has
# shape `(n,)` with data type `dtype`.
try:
if ar.shape[1] > 0:
consolidated = ar.view(dtype)
else:
# If ar.shape[1] == 0, then dtype will be `np.dtype([])`, which is
# a data type with itemsize 0, and the call `ar.view(dtype)` will
# fail. Instead, we'll use `np.empty` to explicitly create the
# array with shape `(len(ar),)`. Because `dtype` in this case has
# itemsize 0, the total size of the result is still 0 bytes.
consolidated = np.empty(len(ar), dtype=dtype)
except TypeError as e:
# There's no good way to do this for object arrays, etc...
msg = 'The axis argument to unique is not supported for dtype {dt}'
raise TypeError(msg.format(dt=ar.dtype)) from e
def reshape_uniq(uniq):
n = len(uniq)
uniq = uniq.view(orig_dtype)
uniq = uniq.reshape(n, *orig_shape[1:])
uniq = np.moveaxis(uniq, 0, axis)
return uniq
output = _unique1d(consolidated, return_index,
return_inverse, return_counts, equal_nan=equal_nan)
output = (reshape_uniq(output[0]),) + output[1:]
return _unpack_tuple(output)
def in1d(ar1, ar2, assume_unique=False, invert=False, *, kind=None):
"""
Test whether each element of a 1-D array is also present in a second array.
Returns a boolean array the same length as `ar1` that is True
where an element of `ar1` is in `ar2` and False otherwise.
We recommend using :func:`isin` instead of `in1d` for new code.
Parameters
----------
ar1 : (M,) array_like
Input array.
ar2 : array_like
The values against which to test each value of `ar1`.
assume_unique : bool, optional
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
invert : bool, optional
If True, the values in the returned array are inverted (that is,
False where an element of `ar1` is in `ar2` and True otherwise).
Default is False. ``np.in1d(a, b, invert=True)`` is equivalent
to (but is faster than) ``np.invert(in1d(a, b))``.
kind : {None, 'sort', 'table'}, optional
The algorithm to use. This will not affect the final result,
but will affect the speed and memory use. The default, None,
will select automatically based on memory considerations.
* If 'sort', will use a mergesort-based approach. This will have
a memory usage of roughly 6 times the sum of the sizes of
`ar1` and `ar2`, not accounting for size of dtypes.
* If 'table', will use a lookup table approach similar
to a counting sort. This is only available for boolean and
integer arrays. This will have a memory usage of the
size of `ar1` plus the max-min value of `ar2`. `assume_unique`
has no effect when the 'table' option is used.
* If None, will automatically choose 'table' if
the required memory allocation is less than or equal to
6 times the sum of the sizes of `ar1` and `ar2`,
otherwise will use 'sort'. This is done to not use
a large amount of memory by default, even though
'table' may be faster in most cases. If 'table' is chosen,
`assume_unique` will have no effect.
.. versionadded:: 1.8.0
Returns
-------
in1d : (M,) ndarray, bool
The values `ar1[in1d]` are in `ar2`.
See Also
--------
isin : Version of this function that preserves the
shape of ar1.
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Notes
-----
`in1d` can be considered as an element-wise function version of the
python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly
equivalent to ``np.array([item in b for item in a])``.
However, this idea fails if `ar2` is a set, or similar (non-sequence)
container: As ``ar2`` is converted to an array, in those cases
``asarray(ar2)`` is an object array rather than the expected array of
contained values.
Using ``kind='table'`` tends to be faster than `kind='sort'` if the
following relationship is true:
``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
but may use greater memory. The default value for `kind` will
be automatically selected based only on memory usage, so one may
manually set ``kind='table'`` if memory constraints can be relaxed.
.. versionadded:: 1.4.0
Examples
--------
>>> test = np.array([0, 1, 2, 5, 0])
>>> states = [0, 2]
>>> mask = np.in1d(test, states)
>>> mask
array([ True, False, True, False, True])
>>> test[mask]
array([0, 2, 0])
>>> mask = np.in1d(test, states, invert=True)
>>> mask
array([False, True, False, True, False])
>>> test[mask]
array([1, 5])
"""
# Ravel both arrays, behavior for the first array could be different
ar1 = np.asarray(ar1).ravel()
ar2 = np.asarray(ar2).ravel()
# Ensure that iteration through object arrays yields size-1 arrays
if ar2.dtype == object:
ar2 = ar2.reshape(-1, 1)
if kind not in {None, 'sort', 'table'}:
raise ValueError(
f"Invalid kind: '{kind}'. Please use None, 'sort' or 'table'.")
# Can use the table method if all arrays are integers or boolean:
is_int_arrays = all(ar.dtype.kind in ("u", "i", "b") for ar in (ar1, ar2))
use_table_method = is_int_arrays and kind in {None, 'table'}
if use_table_method:
if ar2.size == 0:
if invert:
return np.ones_like(ar1, dtype=bool)
else:
return np.zeros_like(ar1, dtype=bool)
# Convert booleans to uint8 so we can use the fast integer algorithm
if ar1.dtype == bool:
ar1 = ar1.astype(np.uint8)
if ar2.dtype == bool:
ar2 = ar2.astype(np.uint8)
ar2_min = np.min(ar2)
ar2_max = np.max(ar2)
ar2_range = int(ar2_max) - int(ar2_min)
# Constraints on whether we can actually use the table method:
# 1. Assert memory usage is not too large
below_memory_constraint = ar2_range <= 6 * (ar1.size + ar2.size)
# 2. Check overflows for (ar2 - ar2_min); dtype=ar2.dtype
range_safe_from_overflow = ar2_range <= np.iinfo(ar2.dtype).max
# 3. Check overflows for (ar1 - ar2_min); dtype=ar1.dtype
if ar1.size > 0:
ar1_min = np.min(ar1)
ar1_max = np.max(ar1)
# After masking, the range of ar1 is guaranteed to be
# within the range of ar2:
ar1_upper = min(int(ar1_max), int(ar2_max))
ar1_lower = max(int(ar1_min), int(ar2_min))
range_safe_from_overflow &= all((
ar1_upper - int(ar2_min) <= np.iinfo(ar1.dtype).max,
ar1_lower - int(ar2_min) >= np.iinfo(ar1.dtype).min
))
# Optimal performance is for approximately
# log10(size) > (log10(range) - 2.27) / 0.927.
# However, here we set the requirement that by default
# the intermediate array can only be 6x
# the combined memory allocation of the original
# arrays. See discussion on
# https://github.com/numpy/numpy/pull/12065.
if (
range_safe_from_overflow and
(below_memory_constraint or kind == 'table')
):
if invert:
outgoing_array = np.ones_like(ar1, dtype=bool)
else:
outgoing_array = np.zeros_like(ar1, dtype=bool)
# Make elements 1 where the integer exists in ar2
if invert:
isin_helper_ar = np.ones(ar2_range + 1, dtype=bool)
isin_helper_ar[ar2 - ar2_min] = 0
else:
isin_helper_ar = np.zeros(ar2_range + 1, dtype=bool)
isin_helper_ar[ar2 - ar2_min] = 1
# Mask out elements we know won't work
basic_mask = (ar1 <= ar2_max) & (ar1 >= ar2_min)
outgoing_array[basic_mask] = isin_helper_ar[ar1[basic_mask] -
ar2_min]
return outgoing_array
elif kind == 'table': # not range_safe_from_overflow
raise RuntimeError(
"You have specified kind='table', "
"but the range of values in `ar2` or `ar1` exceed the "
"maximum integer of the datatype. "
"Please set `kind` to None or 'sort'."
)
elif kind == 'table':
raise ValueError(
"The 'table' method is only "
"supported for boolean or integer arrays. "
"Please select 'sort' or None for kind."
)
# Check if one of the arrays may contain arbitrary objects
contains_object = ar1.dtype.hasobject or ar2.dtype.hasobject
# This code is run when
# a) the first condition is true, making the code significantly faster
# b) the second condition is true (i.e. `ar1` or `ar2` may contain
# arbitrary objects), since then sorting is not guaranteed to work
if len(ar2) < 10 * len(ar1) ** 0.145 or contains_object:
if invert:
mask = np.ones(len(ar1), dtype=bool)
for a in ar2:
mask &= (ar1 != a)
else:
mask = np.zeros(len(ar1), dtype=bool)
for a in ar2:
mask |= (ar1 == a)
return mask
# Otherwise use sorting
if not assume_unique:
ar1, rev_idx = np.unique(ar1, return_inverse=True)
ar2 = np.unique(ar2)
ar = np.concatenate((ar1, ar2))
# We need this to be a stable sort, so always use 'mergesort'
# here. The values from the first array should always come before
# the values from the second array.
order = ar.argsort(kind='mergesort')
sar = ar[order]
if invert:
bool_ar = (sar[1:] != sar[:-1])
else:
bool_ar = (sar[1:] == sar[:-1])
flag = np.concatenate((bool_ar, [invert]))
ret = np.empty(ar.shape, dtype=bool)
ret[order] = flag
if assume_unique:
return ret[:len(ar1)]
else:
return ret[rev_idx]
The provided code snippet includes necessary dependencies for implementing the `setdiff1d` function. Write a Python function `def setdiff1d(ar1, ar2, assume_unique=False)` to solve the following problem:
Find the set difference of two arrays. Return the unique values in `ar1` that are not in `ar2`. Parameters ---------- ar1 : array_like Input array. ar2 : array_like Input comparison array. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setdiff1d : ndarray 1D array of values in `ar1` that are not in `ar2`. The result is sorted when `assume_unique=False`, but otherwise only sorted if the input is sorted. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4, 1]) >>> b = np.array([3, 4, 5, 6]) >>> np.setdiff1d(a, b) array([1, 2])
Here is the function:
def setdiff1d(ar1, ar2, assume_unique=False):
"""
Find the set difference of two arrays.
Return the unique values in `ar1` that are not in `ar2`.
Parameters
----------
ar1 : array_like
Input array.
ar2 : array_like
Input comparison array.
assume_unique : bool
If True, the input arrays are both assumed to be unique, which
can speed up the calculation. Default is False.
Returns
-------
setdiff1d : ndarray
1D array of values in `ar1` that are not in `ar2`. The result
is sorted when `assume_unique=False`, but otherwise only sorted
if the input is sorted.
See Also
--------
numpy.lib.arraysetops : Module with a number of other functions for
performing set operations on arrays.
Examples
--------
>>> a = np.array([1, 2, 3, 2, 4, 1])
>>> b = np.array([3, 4, 5, 6])
>>> np.setdiff1d(a, b)
array([1, 2])
"""
if assume_unique:
ar1 = np.asarray(ar1).ravel()
else:
ar1 = unique(ar1)
ar2 = unique(ar2)
return ar1[in1d(ar1, ar2, assume_unique=True, invert=True)] | Find the set difference of two arrays. Return the unique values in `ar1` that are not in `ar2`. Parameters ---------- ar1 : array_like Input array. ar2 : array_like Input comparison array. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setdiff1d : ndarray 1D array of values in `ar1` that are not in `ar2`. The result is sorted when `assume_unique=False`, but otherwise only sorted if the input is sorted. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4, 1]) >>> b = np.array([3, 4, 5, 6]) >>> np.setdiff1d(a, b) array([1, 2]) |
168,715 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
class NpzFile(Mapping):
"""
NpzFile(fid)
A dictionary-like object with lazy-loading of files in the zipped
archive provided on construction.
`NpzFile` is used to load files in the NumPy ``.npz`` data archive
format. It assumes that files in the archive have a ``.npy`` extension,
other files are ignored.
The arrays and file strings are lazily loaded on either
getitem access using ``obj['key']`` or attribute lookup using
``obj.f.key``. A list of all files (without ``.npy`` extensions) can
be obtained with ``obj.files`` and the ZipFile object itself using
``obj.zip``.
Attributes
----------
files : list of str
List of all files in the archive with a ``.npy`` extension.
zip : ZipFile instance
The ZipFile object initialized with the zipped archive.
f : BagObj instance
An object on which attribute can be performed as an alternative
to getitem access on the `NpzFile` instance itself.
allow_pickle : bool, optional
Allow loading pickled data. Default: False
.. versionchanged:: 1.16.3
Made default False in response to CVE-2019-6446.
pickle_kwargs : dict, optional
Additional keyword arguments to pass on to pickle.load.
These are only useful when loading object arrays saved on
Python 2 when using Python 3.
max_header_size : int, optional
Maximum allowed size of the header. Large headers may not be safe
to load securely and thus require explicitly passing a larger value.
See :py:meth:`ast.literal_eval()` for details.
This option is ignored when `allow_pickle` is passed. In that case
the file is by definition trusted and the limit is unnecessary.
Parameters
----------
fid : file or str
The zipped archive to open. This is either a file-like object
or a string containing the path to the archive.
own_fid : bool, optional
Whether NpzFile should close the file handle.
Requires that `fid` is a file-like object.
Examples
--------
>>> from tempfile import TemporaryFile
>>> outfile = TemporaryFile()
>>> x = np.arange(10)
>>> y = np.sin(x)
>>> np.savez(outfile, x=x, y=y)
>>> _ = outfile.seek(0)
>>> npz = np.load(outfile)
>>> isinstance(npz, np.lib.npyio.NpzFile)
True
>>> sorted(npz.files)
['x', 'y']
>>> npz['x'] # getitem access
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> npz.f.x # attribute lookup
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
"""
# Make __exit__ safe if zipfile_factory raises an exception
zip = None
fid = None
def __init__(self, fid, own_fid=False, allow_pickle=False,
pickle_kwargs=None, *,
max_header_size=format._MAX_HEADER_SIZE):
# Import is postponed to here since zipfile depends on gzip, an
# optional component of the so-called standard library.
_zip = zipfile_factory(fid)
self._files = _zip.namelist()
self.files = []
self.allow_pickle = allow_pickle
self.max_header_size = max_header_size
self.pickle_kwargs = pickle_kwargs
for x in self._files:
if x.endswith('.npy'):
self.files.append(x[:-4])
else:
self.files.append(x)
self.zip = _zip
self.f = BagObj(self)
if own_fid:
self.fid = fid
def __enter__(self):
return self
def __exit__(self, exc_type, exc_value, traceback):
self.close()
def close(self):
"""
Close the file.
"""
if self.zip is not None:
self.zip.close()
self.zip = None
if self.fid is not None:
self.fid.close()
self.fid = None
self.f = None # break reference cycle
def __del__(self):
self.close()
# Implement the Mapping ABC
def __iter__(self):
return iter(self.files)
def __len__(self):
return len(self.files)
def __getitem__(self, key):
# FIXME: This seems like it will copy strings around
# more than is strictly necessary. The zipfile
# will read the string and then
# the format.read_array will copy the string
# to another place in memory.
# It would be better if the zipfile could read
# (or at least uncompress) the data
# directly into the array memory.
member = False
if key in self._files:
member = True
elif key in self.files:
member = True
key += '.npy'
if member:
bytes = self.zip.open(key)
magic = bytes.read(len(format.MAGIC_PREFIX))
bytes.close()
if magic == format.MAGIC_PREFIX:
bytes = self.zip.open(key)
return format.read_array(bytes,
allow_pickle=self.allow_pickle,
pickle_kwargs=self.pickle_kwargs,
max_header_size=self.max_header_size)
else:
return self.zip.read(key)
else:
raise KeyError("%s is not a file in the archive" % key)
The provided code snippet includes necessary dependencies for implementing the `load` function. Write a Python function `def load(file, mmap_mode=None, allow_pickle=False, fix_imports=True, encoding='ASCII', *, max_header_size=format._MAX_HEADER_SIZE)` to solve the following problem:
Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files. .. warning:: Loading files that contain object arrays uses the ``pickle`` module, which is not secure against erroneous or maliciously constructed data. Consider passing ``allow_pickle=False`` to load data that is known not to contain object arrays for the safer handling of untrusted sources. Parameters ---------- file : file-like object, string, or pathlib.Path The file to read. File-like objects must support the ``seek()`` and ``read()`` methods and must always be opened in binary mode. Pickled files require that the file-like object support the ``readline()`` method as well. mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional If not None, then memory-map the file, using the given mode (see `numpy.memmap` for a detailed description of the modes). A memory-mapped array is kept on disk. However, it can be accessed and sliced like any ndarray. Memory mapping is especially useful for accessing small fragments of large files without reading the entire file into memory. allow_pickle : bool, optional Allow loading pickled object arrays stored in npy files. Reasons for disallowing pickles include security, as loading pickled data can execute arbitrary code. If pickles are disallowed, loading object arrays will fail. Default: False .. versionchanged:: 1.16.3 Made default False in response to CVE-2019-6446. fix_imports : bool, optional Only useful when loading Python 2 generated pickled files on Python 3, which includes npy/npz files containing object arrays. If `fix_imports` is True, pickle will try to map the old Python 2 names to the new names used in Python 3. encoding : str, optional What encoding to use when reading Python 2 strings. Only useful when loading Python 2 generated pickled files in Python 3, which includes npy/npz files containing object arrays. Values other than 'latin1', 'ASCII', and 'bytes' are not allowed, as they can corrupt numerical data. Default: 'ASCII' max_header_size : int, optional Maximum allowed size of the header. Large headers may not be safe to load securely and thus require explicitly passing a larger value. See :py:meth:`ast.literal_eval()` for details. This option is ignored when `allow_pickle` is passed. In that case the file is by definition trusted and the limit is unnecessary. Returns ------- result : array, tuple, dict, etc. Data stored in the file. For ``.npz`` files, the returned instance of NpzFile class must be closed to avoid leaking file descriptors. Raises ------ OSError If the input file does not exist or cannot be read. UnpicklingError If ``allow_pickle=True``, but the file cannot be loaded as a pickle. ValueError The file contains an object array, but ``allow_pickle=False`` given. See Also -------- save, savez, savez_compressed, loadtxt memmap : Create a memory-map to an array stored in a file on disk. lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file. Notes ----- - If the file contains pickle data, then whatever object is stored in the pickle is returned. - If the file is a ``.npy`` file, then a single array is returned. - If the file is a ``.npz`` file, then a dictionary-like object is returned, containing ``{filename: array}`` key-value pairs, one for each file in the archive. - If the file is a ``.npz`` file, the returned value supports the context manager protocol in a similar fashion to the open function:: with load('foo.npz') as data: a = data['a'] The underlying file descriptor is closed when exiting the 'with' block. Examples -------- Store data to disk, and load it again: >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]])) >>> np.load('/tmp/123.npy') array([[1, 2, 3], [4, 5, 6]]) Store compressed data to disk, and load it again: >>> a=np.array([[1, 2, 3], [4, 5, 6]]) >>> b=np.array([1, 2]) >>> np.savez('/tmp/123.npz', a=a, b=b) >>> data = np.load('/tmp/123.npz') >>> data['a'] array([[1, 2, 3], [4, 5, 6]]) >>> data['b'] array([1, 2]) >>> data.close() Mem-map the stored array, and then access the second row directly from disk: >>> X = np.load('/tmp/123.npy', mmap_mode='r') >>> X[1, :] memmap([4, 5, 6])
Here is the function:
def load(file, mmap_mode=None, allow_pickle=False, fix_imports=True,
encoding='ASCII', *, max_header_size=format._MAX_HEADER_SIZE):
"""
Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files.
.. warning:: Loading files that contain object arrays uses the ``pickle``
module, which is not secure against erroneous or maliciously
constructed data. Consider passing ``allow_pickle=False`` to
load data that is known not to contain object arrays for the
safer handling of untrusted sources.
Parameters
----------
file : file-like object, string, or pathlib.Path
The file to read. File-like objects must support the
``seek()`` and ``read()`` methods and must always
be opened in binary mode. Pickled files require that the
file-like object support the ``readline()`` method as well.
mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional
If not None, then memory-map the file, using the given mode (see
`numpy.memmap` for a detailed description of the modes). A
memory-mapped array is kept on disk. However, it can be accessed
and sliced like any ndarray. Memory mapping is especially useful
for accessing small fragments of large files without reading the
entire file into memory.
allow_pickle : bool, optional
Allow loading pickled object arrays stored in npy files. Reasons for
disallowing pickles include security, as loading pickled data can
execute arbitrary code. If pickles are disallowed, loading object
arrays will fail. Default: False
.. versionchanged:: 1.16.3
Made default False in response to CVE-2019-6446.
fix_imports : bool, optional
Only useful when loading Python 2 generated pickled files on Python 3,
which includes npy/npz files containing object arrays. If `fix_imports`
is True, pickle will try to map the old Python 2 names to the new names
used in Python 3.
encoding : str, optional
What encoding to use when reading Python 2 strings. Only useful when
loading Python 2 generated pickled files in Python 3, which includes
npy/npz files containing object arrays. Values other than 'latin1',
'ASCII', and 'bytes' are not allowed, as they can corrupt numerical
data. Default: 'ASCII'
max_header_size : int, optional
Maximum allowed size of the header. Large headers may not be safe
to load securely and thus require explicitly passing a larger value.
See :py:meth:`ast.literal_eval()` for details.
This option is ignored when `allow_pickle` is passed. In that case
the file is by definition trusted and the limit is unnecessary.
Returns
-------
result : array, tuple, dict, etc.
Data stored in the file. For ``.npz`` files, the returned instance
of NpzFile class must be closed to avoid leaking file descriptors.
Raises
------
OSError
If the input file does not exist or cannot be read.
UnpicklingError
If ``allow_pickle=True``, but the file cannot be loaded as a pickle.
ValueError
The file contains an object array, but ``allow_pickle=False`` given.
See Also
--------
save, savez, savez_compressed, loadtxt
memmap : Create a memory-map to an array stored in a file on disk.
lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.
Notes
-----
- If the file contains pickle data, then whatever object is stored
in the pickle is returned.
- If the file is a ``.npy`` file, then a single array is returned.
- If the file is a ``.npz`` file, then a dictionary-like object is
returned, containing ``{filename: array}`` key-value pairs, one for
each file in the archive.
- If the file is a ``.npz`` file, the returned value supports the
context manager protocol in a similar fashion to the open function::
with load('foo.npz') as data:
a = data['a']
The underlying file descriptor is closed when exiting the 'with'
block.
Examples
--------
Store data to disk, and load it again:
>>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]]))
>>> np.load('/tmp/123.npy')
array([[1, 2, 3],
[4, 5, 6]])
Store compressed data to disk, and load it again:
>>> a=np.array([[1, 2, 3], [4, 5, 6]])
>>> b=np.array([1, 2])
>>> np.savez('/tmp/123.npz', a=a, b=b)
>>> data = np.load('/tmp/123.npz')
>>> data['a']
array([[1, 2, 3],
[4, 5, 6]])
>>> data['b']
array([1, 2])
>>> data.close()
Mem-map the stored array, and then access the second row
directly from disk:
>>> X = np.load('/tmp/123.npy', mmap_mode='r')
>>> X[1, :]
memmap([4, 5, 6])
"""
if encoding not in ('ASCII', 'latin1', 'bytes'):
# The 'encoding' value for pickle also affects what encoding
# the serialized binary data of NumPy arrays is loaded
# in. Pickle does not pass on the encoding information to
# NumPy. The unpickling code in numpy.core.multiarray is
# written to assume that unicode data appearing where binary
# should be is in 'latin1'. 'bytes' is also safe, as is 'ASCII'.
#
# Other encoding values can corrupt binary data, and we
# purposefully disallow them. For the same reason, the errors=
# argument is not exposed, as values other than 'strict'
# result can similarly silently corrupt numerical data.
raise ValueError("encoding must be 'ASCII', 'latin1', or 'bytes'")
pickle_kwargs = dict(encoding=encoding, fix_imports=fix_imports)
with contextlib.ExitStack() as stack:
if hasattr(file, 'read'):
fid = file
own_fid = False
else:
fid = stack.enter_context(open(os_fspath(file), "rb"))
own_fid = True
# Code to distinguish from NumPy binary files and pickles.
_ZIP_PREFIX = b'PK\x03\x04'
_ZIP_SUFFIX = b'PK\x05\x06' # empty zip files start with this
N = len(format.MAGIC_PREFIX)
magic = fid.read(N)
# If the file size is less than N, we need to make sure not
# to seek past the beginning of the file
fid.seek(-min(N, len(magic)), 1) # back-up
if magic.startswith(_ZIP_PREFIX) or magic.startswith(_ZIP_SUFFIX):
# zip-file (assume .npz)
# Potentially transfer file ownership to NpzFile
stack.pop_all()
ret = NpzFile(fid, own_fid=own_fid, allow_pickle=allow_pickle,
pickle_kwargs=pickle_kwargs,
max_header_size=max_header_size)
return ret
elif magic == format.MAGIC_PREFIX:
# .npy file
if mmap_mode:
if allow_pickle:
max_header_size = 2**64
return format.open_memmap(file, mode=mmap_mode,
max_header_size=max_header_size)
else:
return format.read_array(fid, allow_pickle=allow_pickle,
pickle_kwargs=pickle_kwargs,
max_header_size=max_header_size)
else:
# Try a pickle
if not allow_pickle:
raise ValueError("Cannot load file containing pickled data "
"when allow_pickle=False")
try:
return pickle.load(fid, **pickle_kwargs)
except Exception as e:
raise pickle.UnpicklingError(
f"Failed to interpret file {file!r} as a pickle") from e | Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files. .. warning:: Loading files that contain object arrays uses the ``pickle`` module, which is not secure against erroneous or maliciously constructed data. Consider passing ``allow_pickle=False`` to load data that is known not to contain object arrays for the safer handling of untrusted sources. Parameters ---------- file : file-like object, string, or pathlib.Path The file to read. File-like objects must support the ``seek()`` and ``read()`` methods and must always be opened in binary mode. Pickled files require that the file-like object support the ``readline()`` method as well. mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional If not None, then memory-map the file, using the given mode (see `numpy.memmap` for a detailed description of the modes). A memory-mapped array is kept on disk. However, it can be accessed and sliced like any ndarray. Memory mapping is especially useful for accessing small fragments of large files without reading the entire file into memory. allow_pickle : bool, optional Allow loading pickled object arrays stored in npy files. Reasons for disallowing pickles include security, as loading pickled data can execute arbitrary code. If pickles are disallowed, loading object arrays will fail. Default: False .. versionchanged:: 1.16.3 Made default False in response to CVE-2019-6446. fix_imports : bool, optional Only useful when loading Python 2 generated pickled files on Python 3, which includes npy/npz files containing object arrays. If `fix_imports` is True, pickle will try to map the old Python 2 names to the new names used in Python 3. encoding : str, optional What encoding to use when reading Python 2 strings. Only useful when loading Python 2 generated pickled files in Python 3, which includes npy/npz files containing object arrays. Values other than 'latin1', 'ASCII', and 'bytes' are not allowed, as they can corrupt numerical data. Default: 'ASCII' max_header_size : int, optional Maximum allowed size of the header. Large headers may not be safe to load securely and thus require explicitly passing a larger value. See :py:meth:`ast.literal_eval()` for details. This option is ignored when `allow_pickle` is passed. In that case the file is by definition trusted and the limit is unnecessary. Returns ------- result : array, tuple, dict, etc. Data stored in the file. For ``.npz`` files, the returned instance of NpzFile class must be closed to avoid leaking file descriptors. Raises ------ OSError If the input file does not exist or cannot be read. UnpicklingError If ``allow_pickle=True``, but the file cannot be loaded as a pickle. ValueError The file contains an object array, but ``allow_pickle=False`` given. See Also -------- save, savez, savez_compressed, loadtxt memmap : Create a memory-map to an array stored in a file on disk. lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file. Notes ----- - If the file contains pickle data, then whatever object is stored in the pickle is returned. - If the file is a ``.npy`` file, then a single array is returned. - If the file is a ``.npz`` file, then a dictionary-like object is returned, containing ``{filename: array}`` key-value pairs, one for each file in the archive. - If the file is a ``.npz`` file, the returned value supports the context manager protocol in a similar fashion to the open function:: with load('foo.npz') as data: a = data['a'] The underlying file descriptor is closed when exiting the 'with' block. Examples -------- Store data to disk, and load it again: >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]])) >>> np.load('/tmp/123.npy') array([[1, 2, 3], [4, 5, 6]]) Store compressed data to disk, and load it again: >>> a=np.array([[1, 2, 3], [4, 5, 6]]) >>> b=np.array([1, 2]) >>> np.savez('/tmp/123.npz', a=a, b=b) >>> data = np.load('/tmp/123.npz') >>> data['a'] array([[1, 2, 3], [4, 5, 6]]) >>> data['b'] array([1, 2]) >>> data.close() Mem-map the stored array, and then access the second row directly from disk: >>> X = np.load('/tmp/123.npy', mmap_mode='r') >>> X[1, :] memmap([4, 5, 6]) |
168,716 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _save_dispatcher(file, arr, allow_pickle=None, fix_imports=None):
return (arr,) | null |
168,717 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
The provided code snippet includes necessary dependencies for implementing the `save` function. Write a Python function `def save(file, arr, allow_pickle=True, fix_imports=True)` to solve the following problem:
Save an array to a binary file in NumPy ``.npy`` format. Parameters ---------- file : file, str, or pathlib.Path File or filename to which the data is saved. If file is a file-object, then the filename is unchanged. If file is a string or Path, a ``.npy`` extension will be appended to the filename if it does not already have one. arr : array_like Array data to be saved. allow_pickle : bool, optional Allow saving object arrays using Python pickles. Reasons for disallowing pickles include security (loading pickled data can execute arbitrary code) and portability (pickled objects may not be loadable on different Python installations, for example if the stored objects require libraries that are not available, and not all pickled data is compatible between Python 2 and Python 3). Default: True fix_imports : bool, optional Only useful in forcing objects in object arrays on Python 3 to be pickled in a Python 2 compatible way. If `fix_imports` is True, pickle will try to map the new Python 3 names to the old module names used in Python 2, so that the pickle data stream is readable with Python 2. See Also -------- savez : Save several arrays into a ``.npz`` archive savetxt, load Notes ----- For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. Any data saved to the file is appended to the end of the file. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> np.save(outfile, x) >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file >>> np.load(outfile) array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> with open('test.npy', 'wb') as f: ... np.save(f, np.array([1, 2])) ... np.save(f, np.array([1, 3])) >>> with open('test.npy', 'rb') as f: ... a = np.load(f) ... b = np.load(f) >>> print(a, b) # [1 2] [1 3]
Here is the function:
def save(file, arr, allow_pickle=True, fix_imports=True):
"""
Save an array to a binary file in NumPy ``.npy`` format.
Parameters
----------
file : file, str, or pathlib.Path
File or filename to which the data is saved. If file is a file-object,
then the filename is unchanged. If file is a string or Path, a ``.npy``
extension will be appended to the filename if it does not already
have one.
arr : array_like
Array data to be saved.
allow_pickle : bool, optional
Allow saving object arrays using Python pickles. Reasons for disallowing
pickles include security (loading pickled data can execute arbitrary
code) and portability (pickled objects may not be loadable on different
Python installations, for example if the stored objects require libraries
that are not available, and not all pickled data is compatible between
Python 2 and Python 3).
Default: True
fix_imports : bool, optional
Only useful in forcing objects in object arrays on Python 3 to be
pickled in a Python 2 compatible way. If `fix_imports` is True, pickle
will try to map the new Python 3 names to the old module names used in
Python 2, so that the pickle data stream is readable with Python 2.
See Also
--------
savez : Save several arrays into a ``.npz`` archive
savetxt, load
Notes
-----
For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.
Any data saved to the file is appended to the end of the file.
Examples
--------
>>> from tempfile import TemporaryFile
>>> outfile = TemporaryFile()
>>> x = np.arange(10)
>>> np.save(outfile, x)
>>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file
>>> np.load(outfile)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> with open('test.npy', 'wb') as f:
... np.save(f, np.array([1, 2]))
... np.save(f, np.array([1, 3]))
>>> with open('test.npy', 'rb') as f:
... a = np.load(f)
... b = np.load(f)
>>> print(a, b)
# [1 2] [1 3]
"""
if hasattr(file, 'write'):
file_ctx = contextlib.nullcontext(file)
else:
file = os_fspath(file)
if not file.endswith('.npy'):
file = file + '.npy'
file_ctx = open(file, "wb")
with file_ctx as fid:
arr = np.asanyarray(arr)
format.write_array(fid, arr, allow_pickle=allow_pickle,
pickle_kwargs=dict(fix_imports=fix_imports)) | Save an array to a binary file in NumPy ``.npy`` format. Parameters ---------- file : file, str, or pathlib.Path File or filename to which the data is saved. If file is a file-object, then the filename is unchanged. If file is a string or Path, a ``.npy`` extension will be appended to the filename if it does not already have one. arr : array_like Array data to be saved. allow_pickle : bool, optional Allow saving object arrays using Python pickles. Reasons for disallowing pickles include security (loading pickled data can execute arbitrary code) and portability (pickled objects may not be loadable on different Python installations, for example if the stored objects require libraries that are not available, and not all pickled data is compatible between Python 2 and Python 3). Default: True fix_imports : bool, optional Only useful in forcing objects in object arrays on Python 3 to be pickled in a Python 2 compatible way. If `fix_imports` is True, pickle will try to map the new Python 3 names to the old module names used in Python 2, so that the pickle data stream is readable with Python 2. See Also -------- savez : Save several arrays into a ``.npz`` archive savetxt, load Notes ----- For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. Any data saved to the file is appended to the end of the file. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> np.save(outfile, x) >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file >>> np.load(outfile) array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> with open('test.npy', 'wb') as f: ... np.save(f, np.array([1, 2])) ... np.save(f, np.array([1, 3])) >>> with open('test.npy', 'rb') as f: ... a = np.load(f) ... b = np.load(f) >>> print(a, b) # [1 2] [1 3] |
168,718 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _savez_dispatcher(file, *args, **kwds):
yield from args
yield from kwds.values() | null |
168,719 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _savez(file, args, kwds, compress, allow_pickle=True, pickle_kwargs=None):
# Import is postponed to here since zipfile depends on gzip, an optional
# component of the so-called standard library.
import zipfile
if not hasattr(file, 'write'):
file = os_fspath(file)
if not file.endswith('.npz'):
file = file + '.npz'
namedict = kwds
for i, val in enumerate(args):
key = 'arr_%d' % i
if key in namedict.keys():
raise ValueError(
"Cannot use un-named variables and keyword %s" % key)
namedict[key] = val
if compress:
compression = zipfile.ZIP_DEFLATED
else:
compression = zipfile.ZIP_STORED
zipf = zipfile_factory(file, mode="w", compression=compression)
for key, val in namedict.items():
fname = key + '.npy'
val = np.asanyarray(val)
# always force zip64, gh-10776
with zipf.open(fname, 'w', force_zip64=True) as fid:
format.write_array(fid, val,
allow_pickle=allow_pickle,
pickle_kwargs=pickle_kwargs)
zipf.close()
The provided code snippet includes necessary dependencies for implementing the `savez` function. Write a Python function `def savez(file, *args, **kwds)` to solve the following problem:
Save several arrays into a single file in uncompressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- save : Save a single array to a binary file in NumPy format. savetxt : Save an array to a file as plain text. savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is not compressed and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Keys passed in `kwds` are used as filenames inside the ZIP archive. Therefore, keys should be valid filenames; e.g., avoid keys that begin with ``/`` or contain ``.``. When naming variables with keyword arguments, it is not possible to name a variable ``file``, as this would cause the ``file`` argument to be defined twice in the call to ``savez``. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> y = np.sin(x) Using `savez` with \\*args, the arrays are saved with default names. >>> np.savez(outfile, x, y) >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file >>> npzfile = np.load(outfile) >>> npzfile.files ['arr_0', 'arr_1'] >>> npzfile['arr_0'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) Using `savez` with \\**kwds, the arrays are saved with the keyword names. >>> outfile = TemporaryFile() >>> np.savez(outfile, x=x, y=y) >>> _ = outfile.seek(0) >>> npzfile = np.load(outfile) >>> sorted(npzfile.files) ['x', 'y'] >>> npzfile['x'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Here is the function:
def savez(file, *args, **kwds):
"""Save several arrays into a single file in uncompressed ``.npz`` format.
Provide arrays as keyword arguments to store them under the
corresponding name in the output file: ``savez(fn, x=x, y=y)``.
If arrays are specified as positional arguments, i.e., ``savez(fn,
x, y)``, their names will be `arr_0`, `arr_1`, etc.
Parameters
----------
file : str or file
Either the filename (string) or an open file (file-like object)
where the data will be saved. If file is a string or a Path, the
``.npz`` extension will be appended to the filename if it is not
already there.
args : Arguments, optional
Arrays to save to the file. Please use keyword arguments (see
`kwds` below) to assign names to arrays. Arrays specified as
args will be named "arr_0", "arr_1", and so on.
kwds : Keyword arguments, optional
Arrays to save to the file. Each array will be saved to the
output file with its corresponding keyword name.
Returns
-------
None
See Also
--------
save : Save a single array to a binary file in NumPy format.
savetxt : Save an array to a file as plain text.
savez_compressed : Save several arrays into a compressed ``.npz`` archive
Notes
-----
The ``.npz`` file format is a zipped archive of files named after the
variables they contain. The archive is not compressed and each file
in the archive contains one variable in ``.npy`` format. For a
description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.
When opening the saved ``.npz`` file with `load` a `NpzFile` object is
returned. This is a dictionary-like object which can be queried for
its list of arrays (with the ``.files`` attribute), and for the arrays
themselves.
Keys passed in `kwds` are used as filenames inside the ZIP archive.
Therefore, keys should be valid filenames; e.g., avoid keys that begin with
``/`` or contain ``.``.
When naming variables with keyword arguments, it is not possible to name a
variable ``file``, as this would cause the ``file`` argument to be defined
twice in the call to ``savez``.
Examples
--------
>>> from tempfile import TemporaryFile
>>> outfile = TemporaryFile()
>>> x = np.arange(10)
>>> y = np.sin(x)
Using `savez` with \\*args, the arrays are saved with default names.
>>> np.savez(outfile, x, y)
>>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file
>>> npzfile = np.load(outfile)
>>> npzfile.files
['arr_0', 'arr_1']
>>> npzfile['arr_0']
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
Using `savez` with \\**kwds, the arrays are saved with the keyword names.
>>> outfile = TemporaryFile()
>>> np.savez(outfile, x=x, y=y)
>>> _ = outfile.seek(0)
>>> npzfile = np.load(outfile)
>>> sorted(npzfile.files)
['x', 'y']
>>> npzfile['x']
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
"""
_savez(file, args, kwds, False) | Save several arrays into a single file in uncompressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- save : Save a single array to a binary file in NumPy format. savetxt : Save an array to a file as plain text. savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is not compressed and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Keys passed in `kwds` are used as filenames inside the ZIP archive. Therefore, keys should be valid filenames; e.g., avoid keys that begin with ``/`` or contain ``.``. When naming variables with keyword arguments, it is not possible to name a variable ``file``, as this would cause the ``file`` argument to be defined twice in the call to ``savez``. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> y = np.sin(x) Using `savez` with \\*args, the arrays are saved with default names. >>> np.savez(outfile, x, y) >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file >>> npzfile = np.load(outfile) >>> npzfile.files ['arr_0', 'arr_1'] >>> npzfile['arr_0'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) Using `savez` with \\**kwds, the arrays are saved with the keyword names. >>> outfile = TemporaryFile() >>> np.savez(outfile, x=x, y=y) >>> _ = outfile.seek(0) >>> npzfile = np.load(outfile) >>> sorted(npzfile.files) ['x', 'y'] >>> npzfile['x'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) |
168,720 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _savez_compressed_dispatcher(file, *args, **kwds):
yield from args
yield from kwds.values() | null |
168,721 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _savez(file, args, kwds, compress, allow_pickle=True, pickle_kwargs=None):
# Import is postponed to here since zipfile depends on gzip, an optional
# component of the so-called standard library.
import zipfile
if not hasattr(file, 'write'):
file = os_fspath(file)
if not file.endswith('.npz'):
file = file + '.npz'
namedict = kwds
for i, val in enumerate(args):
key = 'arr_%d' % i
if key in namedict.keys():
raise ValueError(
"Cannot use un-named variables and keyword %s" % key)
namedict[key] = val
if compress:
compression = zipfile.ZIP_DEFLATED
else:
compression = zipfile.ZIP_STORED
zipf = zipfile_factory(file, mode="w", compression=compression)
for key, val in namedict.items():
fname = key + '.npy'
val = np.asanyarray(val)
# always force zip64, gh-10776
with zipf.open(fname, 'w', force_zip64=True) as fid:
format.write_array(fid, val,
allow_pickle=allow_pickle,
pickle_kwargs=pickle_kwargs)
zipf.close()
The provided code snippet includes necessary dependencies for implementing the `savez_compressed` function. Write a Python function `def savez_compressed(file, *args, **kwds)` to solve the following problem:
Save several arrays into a single file in compressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- numpy.save : Save a single array to a binary file in NumPy format. numpy.savetxt : Save an array to a file as plain text. numpy.savez : Save several arrays into an uncompressed ``.npz`` file format numpy.load : Load the files created by savez_compressed. Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is compressed with ``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Examples -------- >>> test_array = np.random.rand(3, 2) >>> test_vector = np.random.rand(4) >>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector) >>> loaded = np.load('/tmp/123.npz') >>> print(np.array_equal(test_array, loaded['a'])) True >>> print(np.array_equal(test_vector, loaded['b'])) True
Here is the function:
def savez_compressed(file, *args, **kwds):
"""
Save several arrays into a single file in compressed ``.npz`` format.
Provide arrays as keyword arguments to store them under the
corresponding name in the output file: ``savez(fn, x=x, y=y)``.
If arrays are specified as positional arguments, i.e., ``savez(fn,
x, y)``, their names will be `arr_0`, `arr_1`, etc.
Parameters
----------
file : str or file
Either the filename (string) or an open file (file-like object)
where the data will be saved. If file is a string or a Path, the
``.npz`` extension will be appended to the filename if it is not
already there.
args : Arguments, optional
Arrays to save to the file. Please use keyword arguments (see
`kwds` below) to assign names to arrays. Arrays specified as
args will be named "arr_0", "arr_1", and so on.
kwds : Keyword arguments, optional
Arrays to save to the file. Each array will be saved to the
output file with its corresponding keyword name.
Returns
-------
None
See Also
--------
numpy.save : Save a single array to a binary file in NumPy format.
numpy.savetxt : Save an array to a file as plain text.
numpy.savez : Save several arrays into an uncompressed ``.npz`` file format
numpy.load : Load the files created by savez_compressed.
Notes
-----
The ``.npz`` file format is a zipped archive of files named after the
variables they contain. The archive is compressed with
``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable
in ``.npy`` format. For a description of the ``.npy`` format, see
:py:mod:`numpy.lib.format`.
When opening the saved ``.npz`` file with `load` a `NpzFile` object is
returned. This is a dictionary-like object which can be queried for
its list of arrays (with the ``.files`` attribute), and for the arrays
themselves.
Examples
--------
>>> test_array = np.random.rand(3, 2)
>>> test_vector = np.random.rand(4)
>>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector)
>>> loaded = np.load('/tmp/123.npz')
>>> print(np.array_equal(test_array, loaded['a']))
True
>>> print(np.array_equal(test_vector, loaded['b']))
True
"""
_savez(file, args, kwds, True) | Save several arrays into a single file in compressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- numpy.save : Save a single array to a binary file in NumPy format. numpy.savetxt : Save an array to a file as plain text. numpy.savez : Save several arrays into an uncompressed ``.npz`` file format numpy.load : Load the files created by savez_compressed. Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is compressed with ``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Examples -------- >>> test_array = np.random.rand(3, 2) >>> test_vector = np.random.rand(4) >>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector) >>> loaded = np.load('/tmp/123.npz') >>> print(np.array_equal(test_array, loaded['a'])) True >>> print(np.array_equal(test_vector, loaded['b'])) True |
168,722 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _loadtxt_dispatcher(
fname, dtype=None, comments=None, delimiter=None,
converters=None, skiprows=None, usecols=None, unpack=None,
ndmin=None, encoding=None, max_rows=None, *, like=None):
return (like,) | null |
168,723 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _read(fname, *, delimiter=',', comment='#', quote='"',
imaginary_unit='j', usecols=None, skiplines=0,
max_rows=None, converters=None, ndmin=None, unpack=False,
dtype=np.float64, encoding="bytes"):
r"""
Read a NumPy array from a text file.
Parameters
----------
fname : str or file object
The filename or the file to be read.
delimiter : str, optional
Field delimiter of the fields in line of the file.
Default is a comma, ','. If None any sequence of whitespace is
considered a delimiter.
comment : str or sequence of str or None, optional
Character that begins a comment. All text from the comment
character to the end of the line is ignored.
Multiple comments or multiple-character comment strings are supported,
but may be slower and `quote` must be empty if used.
Use None to disable all use of comments.
quote : str or None, optional
Character that is used to quote string fields. Default is '"'
(a double quote). Use None to disable quote support.
imaginary_unit : str, optional
Character that represent the imaginay unit `sqrt(-1)`.
Default is 'j'.
usecols : array_like, optional
A one-dimensional array of integer column numbers. These are the
columns from the file to be included in the array. If this value
is not given, all the columns are used.
skiplines : int, optional
Number of lines to skip before interpreting the data in the file.
max_rows : int, optional
Maximum number of rows of data to read. Default is to read the
entire file.
converters : dict or callable, optional
A function to parse all columns strings into the desired value, or
a dictionary mapping column number to a parser function.
E.g. if column 0 is a date string: ``converters = {0: datestr2num}``.
Converters can also be used to provide a default value for missing
data, e.g. ``converters = lambda s: float(s.strip() or 0)`` will
convert empty fields to 0.
Default: None
ndmin : int, optional
Minimum dimension of the array returned.
Allowed values are 0, 1 or 2. Default is 0.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = read(...)``. When used with a structured
data-type, arrays are returned for each field. Default is False.
dtype : numpy data type
A NumPy dtype instance, can be a structured dtype to map to the
columns of the file.
encoding : str, optional
Encoding used to decode the inputfile. The special value 'bytes'
(the default) enables backwards-compatible behavior for `converters`,
ensuring that inputs to the converter functions are encoded
bytes objects. The special value 'bytes' has no additional effect if
``converters=None``. If encoding is ``'bytes'`` or ``None``, the
default system encoding is used.
Returns
-------
ndarray
NumPy array.
Examples
--------
First we create a file for the example.
>>> s1 = '1.0,2.0,3.0\n4.0,5.0,6.0\n'
>>> with open('example1.csv', 'w') as f:
... f.write(s1)
>>> a1 = read_from_filename('example1.csv')
>>> a1
array([[1., 2., 3.],
[4., 5., 6.]])
The second example has columns with different data types, so a
one-dimensional array with a structured data type is returned.
The tab character is used as the field delimiter.
>>> s2 = '1.0\t10\talpha\n2.3\t25\tbeta\n4.5\t16\tgamma\n'
>>> with open('example2.tsv', 'w') as f:
... f.write(s2)
>>> a2 = read_from_filename('example2.tsv', delimiter='\t')
>>> a2
array([(1. , 10, b'alpha'), (2.3, 25, b'beta'), (4.5, 16, b'gamma')],
dtype=[('f0', '<f8'), ('f1', 'u1'), ('f2', 'S5')])
"""
# Handle special 'bytes' keyword for encoding
byte_converters = False
if encoding == 'bytes':
encoding = None
byte_converters = True
if dtype is None:
raise TypeError("a dtype must be provided.")
dtype = np.dtype(dtype)
read_dtype_via_object_chunks = None
if dtype.kind in 'SUM' and (
dtype == "S0" or dtype == "U0" or dtype == "M8" or dtype == 'm8'):
# This is a legacy "flexible" dtype. We do not truly support
# parametric dtypes currently (no dtype discovery step in the core),
# but have to support these for backward compatibility.
read_dtype_via_object_chunks = dtype
dtype = np.dtype(object)
if usecols is not None:
# Allow usecols to be a single int or a sequence of ints, the C-code
# handles the rest
try:
usecols = list(usecols)
except TypeError:
usecols = [usecols]
_ensure_ndmin_ndarray_check_param(ndmin)
if comment is None:
comments = None
else:
# assume comments are a sequence of strings
if "" in comment:
raise ValueError(
"comments cannot be an empty string. Use comments=None to "
"disable comments."
)
comments = tuple(comment)
comment = None
if len(comments) == 0:
comments = None # No comments at all
elif len(comments) == 1:
# If there is only one comment, and that comment has one character,
# the normal parsing can deal with it just fine.
if isinstance(comments[0], str) and len(comments[0]) == 1:
comment = comments[0]
comments = None
else:
# Input validation if there are multiple comment characters
if delimiter in comments:
raise TypeError(
f"Comment characters '{comments}' cannot include the "
f"delimiter '{delimiter}'"
)
# comment is now either a 1 or 0 character string or a tuple:
if comments is not None:
# Note: An earlier version support two character comments (and could
# have been extended to multiple characters, we assume this is
# rare enough to not optimize for.
if quote is not None:
raise ValueError(
"when multiple comments or a multi-character comment is "
"given, quotes are not supported. In this case quotechar "
"must be set to None.")
if len(imaginary_unit) != 1:
raise ValueError('len(imaginary_unit) must be 1.')
_check_nonneg_int(skiplines)
if max_rows is not None:
_check_nonneg_int(max_rows)
else:
# Passing -1 to the C code means "read the entire file".
max_rows = -1
fh_closing_ctx = contextlib.nullcontext()
filelike = False
try:
if isinstance(fname, os.PathLike):
fname = os.fspath(fname)
if isinstance(fname, str):
fh = np.lib._datasource.open(fname, 'rt', encoding=encoding)
if encoding is None:
encoding = getattr(fh, 'encoding', 'latin1')
fh_closing_ctx = contextlib.closing(fh)
data = fh
filelike = True
else:
if encoding is None:
encoding = getattr(fname, 'encoding', 'latin1')
data = iter(fname)
except TypeError as e:
raise ValueError(
f"fname must be a string, filehandle, list of strings,\n"
f"or generator. Got {type(fname)} instead.") from e
with fh_closing_ctx:
if comments is not None:
if filelike:
data = iter(data)
filelike = False
data = _preprocess_comments(data, comments, encoding)
if read_dtype_via_object_chunks is None:
arr = _load_from_filelike(
data, delimiter=delimiter, comment=comment, quote=quote,
imaginary_unit=imaginary_unit,
usecols=usecols, skiplines=skiplines, max_rows=max_rows,
converters=converters, dtype=dtype,
encoding=encoding, filelike=filelike,
byte_converters=byte_converters)
else:
# This branch reads the file into chunks of object arrays and then
# casts them to the desired actual dtype. This ensures correct
# string-length and datetime-unit discovery (like `arr.astype()`).
# Due to chunking, certain error reports are less clear, currently.
if filelike:
data = iter(data) # cannot chunk when reading from file
c_byte_converters = False
if read_dtype_via_object_chunks == "S":
c_byte_converters = True # Use latin1 rather than ascii
chunks = []
while max_rows != 0:
if max_rows < 0:
chunk_size = _loadtxt_chunksize
else:
chunk_size = min(_loadtxt_chunksize, max_rows)
next_arr = _load_from_filelike(
data, delimiter=delimiter, comment=comment, quote=quote,
imaginary_unit=imaginary_unit,
usecols=usecols, skiplines=skiplines, max_rows=max_rows,
converters=converters, dtype=dtype,
encoding=encoding, filelike=filelike,
byte_converters=byte_converters,
c_byte_converters=c_byte_converters)
# Cast here already. We hope that this is better even for
# large files because the storage is more compact. It could
# be adapted (in principle the concatenate could cast).
chunks.append(next_arr.astype(read_dtype_via_object_chunks))
skiprows = 0 # Only have to skip for first chunk
if max_rows >= 0:
max_rows -= chunk_size
if len(next_arr) < chunk_size:
# There was less data than requested, so we are done.
break
# Need at least one chunk, but if empty, the last one may have
# the wrong shape.
if len(chunks) > 1 and len(chunks[-1]) == 0:
del chunks[-1]
if len(chunks) == 1:
arr = chunks[0]
else:
arr = np.concatenate(chunks, axis=0)
# NOTE: ndmin works as advertised for structured dtypes, but normally
# these would return a 1D result plus the structured dimension,
# so ndmin=2 adds a third dimension even when no squeezing occurs.
# A `squeeze=False` could be a better solution (pandas uses squeeze).
arr = _ensure_ndmin_ndarray(arr, ndmin=ndmin)
if arr.shape:
if arr.shape[0] == 0:
warnings.warn(
f'loadtxt: input contained no data: "{fname}"',
category=UserWarning,
stacklevel=3
)
if unpack:
# Unpack structured dtypes if requested:
dt = arr.dtype
if dt.names is not None:
# For structured arrays, return an array for each field.
return [arr[field] for field in dt.names]
else:
return arr.T
else:
return arr
_loadtxt_with_like = array_function_dispatch(
_loadtxt_dispatcher
)(loadtxt)
The provided code snippet includes necessary dependencies for implementing the `loadtxt` function. Write a Python function `def loadtxt(fname, dtype=float, comments='#', delimiter=None, converters=None, skiprows=0, usecols=None, unpack=False, ndmin=0, encoding='bytes', max_rows=None, *, quotechar=None, like=None)` to solve the following problem:
r""" Load data from a text file. Parameters ---------- fname : file, str, pathlib.Path, list of str, generator File, filename, list, or generator to read. If the filename extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note that generators must return bytes or strings. The strings in a list or produced by a generator are treated as lines. dtype : data-type, optional Data-type of the resulting array; default: float. If this is a structured data-type, the resulting array will be 1-dimensional, and each row will be interpreted as an element of the array. In this case, the number of columns used must match the number of fields in the data-type. comments : str or sequence of str or None, optional The characters or list of characters used to indicate the start of a comment. None implies no comments. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is '#'. delimiter : str, optional The character used to separate the values. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is whitespace. .. versionchanged:: 1.23.0 Only single character delimiters are supported. Newline characters cannot be used as the delimiter. converters : dict or callable, optional Converter functions to customize value parsing. If `converters` is callable, the function is applied to all columns, else it must be a dict that maps column number to a parser function. See examples for further details. Default: None. .. versionchanged:: 1.23.0 The ability to pass a single callable to be applied to all columns was added. skiprows : int, optional Skip the first `skiprows` lines, including comments; default: 0. usecols : int or sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns. The default, None, results in all columns being read. .. versionchanged:: 1.11.0 When a single column has to be read it is possible to use an integer instead of a tuple. E.g ``usecols = 3`` reads the fourth column the same way as ``usecols = (3,)`` would. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = loadtxt(...)``. When used with a structured data-type, arrays are returned for each field. Default is False. ndmin : int, optional The returned array will have at least `ndmin` dimensions. Otherwise mono-dimensional axes will be squeezed. Legal values: 0 (default), 1 or 2. .. versionadded:: 1.6.0 encoding : str, optional Encoding used to decode the inputfile. Does not apply to input streams. The special value 'bytes' enables backward compatibility workarounds that ensures you receive byte arrays as results if possible and passes 'latin1' encoded strings to converters. Override this value to receive unicode arrays and pass strings as input to converters. If set to None the system default is used. The default value is 'bytes'. .. versionadded:: 1.14.0 max_rows : int, optional Read `max_rows` rows of content after `skiprows` lines. The default is to read all the rows. Note that empty rows containing no data such as empty lines and comment lines are not counted towards `max_rows`, while such lines are counted in `skiprows`. .. versionadded:: 1.16.0 .. versionchanged:: 1.23.0 Lines containing no data, including comment lines (e.g., lines starting with '#' or as specified via `comments`) are not counted towards `max_rows`. quotechar : unicode character or None, optional The character used to denote the start and end of a quoted item. Occurrences of the delimiter or comment characters are ignored within a quoted item. The default value is ``quotechar=None``, which means quoting support is disabled. If two consecutive instances of `quotechar` are found within a quoted field, the first is treated as an escape character. See examples. .. versionadded:: 1.23.0 ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- out : ndarray Data read from the text file. See Also -------- load, fromstring, fromregex genfromtxt : Load data with missing values handled as specified. scipy.io.loadmat : reads MATLAB data files Notes ----- This function aims to be a fast reader for simply formatted files. The `genfromtxt` function provides more sophisticated handling of, e.g., lines with missing values. Each row in the input text file must have the same number of values to be able to read all values. If all rows do not have same number of values, a subset of up to n columns (where n is the least number of values present in all rows) can be read by specifying the columns via `usecols`. .. versionadded:: 1.10.0 The strings produced by the Python float.hex method can be used as input for floats. Examples -------- >>> from io import StringIO # StringIO behaves like a file object >>> c = StringIO("0 1\n2 3") >>> np.loadtxt(c) array([[0., 1.], [2., 3.]]) >>> d = StringIO("M 21 72\nF 35 58") >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'), ... 'formats': ('S1', 'i4', 'f4')}) array([(b'M', 21, 72.), (b'F', 35, 58.)], dtype=[('gender', 'S1'), ('age', '<i4'), ('weight', '<f4')]) >>> c = StringIO("1,0,2\n3,0,4") >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True) >>> x array([1., 3.]) >>> y array([2., 4.]) The `converters` argument is used to specify functions to preprocess the text prior to parsing. `converters` can be a dictionary that maps preprocessing functions to each column: >>> s = StringIO("1.618, 2.296\n3.141, 4.669\n") >>> conv = { ... 0: lambda x: np.floor(float(x)), # conversion fn for column 0 ... 1: lambda x: np.ceil(float(x)), # conversion fn for column 1 ... } >>> np.loadtxt(s, delimiter=",", converters=conv) array([[1., 3.], [3., 5.]]) `converters` can be a callable instead of a dictionary, in which case it is applied to all columns: >>> s = StringIO("0xDE 0xAD\n0xC0 0xDE") >>> import functools >>> conv = functools.partial(int, base=16) >>> np.loadtxt(s, converters=conv) array([[222., 173.], [192., 222.]]) This example shows how `converters` can be used to convert a field with a trailing minus sign into a negative number. >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94') >>> def conv(fld): ... return -float(fld[:-1]) if fld.endswith(b'-') else float(fld) ... >>> np.loadtxt(s, converters=conv) array([[ 10.01, -31.25], [ 19.22, 64.31], [-17.57, 63.94]]) Using a callable as the converter can be particularly useful for handling values with different formatting, e.g. floats with underscores: >>> s = StringIO("1 2.7 100_000") >>> np.loadtxt(s, converters=float) array([1.e+00, 2.7e+00, 1.e+05]) This idea can be extended to automatically handle values specified in many different formats: >>> def conv(val): ... try: ... return float(val) ... except ValueError: ... return float.fromhex(val) >>> s = StringIO("1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2") >>> np.loadtxt(s, delimiter=",", converters=conv, encoding=None) array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00]) Note that with the default ``encoding="bytes"``, the inputs to the converter function are latin-1 encoded byte strings. To deactivate the implicit encoding prior to conversion, use ``encoding=None`` >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94') >>> conv = lambda x: -float(x[:-1]) if x.endswith('-') else float(x) >>> np.loadtxt(s, converters=conv, encoding=None) array([[ 10.01, -31.25], [ 19.22, 64.31], [-17.57, 63.94]]) Support for quoted fields is enabled with the `quotechar` parameter. Comment and delimiter characters are ignored when they appear within a quoted item delineated by `quotechar`: >>> s = StringIO('"alpha, #42", 10.0\n"beta, #64", 2.0\n') >>> dtype = np.dtype([("label", "U12"), ("value", float)]) >>> np.loadtxt(s, dtype=dtype, delimiter=",", quotechar='"') array([('alpha, #42', 10.), ('beta, #64', 2.)], dtype=[('label', '<U12'), ('value', '<f8')]) Quoted fields can be separated by multiple whitespace characters: >>> s = StringIO('"alpha, #42" 10.0\n"beta, #64" 2.0\n') >>> dtype = np.dtype([("label", "U12"), ("value", float)]) >>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='"') array([('alpha, #42', 10.), ('beta, #64', 2.)], dtype=[('label', '<U12'), ('value', '<f8')]) Two consecutive quote characters within a quoted field are treated as a single escaped character: >>> s = StringIO('"Hello, my name is ""Monty""!"') >>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"') array('Hello, my name is "Monty"!', dtype='<U26') Read subset of columns when all rows do not contain equal number of values: >>> d = StringIO("1 2\n2 4\n3 9 12\n4 16 20") >>> np.loadtxt(d, usecols=(0, 1)) array([[ 1., 2.], [ 2., 4.], [ 3., 9.], [ 4., 16.]])
Here is the function:
def loadtxt(fname, dtype=float, comments='#', delimiter=None,
converters=None, skiprows=0, usecols=None, unpack=False,
ndmin=0, encoding='bytes', max_rows=None, *, quotechar=None,
like=None):
r"""
Load data from a text file.
Parameters
----------
fname : file, str, pathlib.Path, list of str, generator
File, filename, list, or generator to read. If the filename
extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note
that generators must return bytes or strings. The strings
in a list or produced by a generator are treated as lines.
dtype : data-type, optional
Data-type of the resulting array; default: float. If this is a
structured data-type, the resulting array will be 1-dimensional, and
each row will be interpreted as an element of the array. In this
case, the number of columns used must match the number of fields in
the data-type.
comments : str or sequence of str or None, optional
The characters or list of characters used to indicate the start of a
comment. None implies no comments. For backwards compatibility, byte
strings will be decoded as 'latin1'. The default is '#'.
delimiter : str, optional
The character used to separate the values. For backwards compatibility,
byte strings will be decoded as 'latin1'. The default is whitespace.
.. versionchanged:: 1.23.0
Only single character delimiters are supported. Newline characters
cannot be used as the delimiter.
converters : dict or callable, optional
Converter functions to customize value parsing. If `converters` is
callable, the function is applied to all columns, else it must be a
dict that maps column number to a parser function.
See examples for further details.
Default: None.
.. versionchanged:: 1.23.0
The ability to pass a single callable to be applied to all columns
was added.
skiprows : int, optional
Skip the first `skiprows` lines, including comments; default: 0.
usecols : int or sequence, optional
Which columns to read, with 0 being the first. For example,
``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns.
The default, None, results in all columns being read.
.. versionchanged:: 1.11.0
When a single column has to be read it is possible to use
an integer instead of a tuple. E.g ``usecols = 3`` reads the
fourth column the same way as ``usecols = (3,)`` would.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = loadtxt(...)``. When used with a
structured data-type, arrays are returned for each field.
Default is False.
ndmin : int, optional
The returned array will have at least `ndmin` dimensions.
Otherwise mono-dimensional axes will be squeezed.
Legal values: 0 (default), 1 or 2.
.. versionadded:: 1.6.0
encoding : str, optional
Encoding used to decode the inputfile. Does not apply to input streams.
The special value 'bytes' enables backward compatibility workarounds
that ensures you receive byte arrays as results if possible and passes
'latin1' encoded strings to converters. Override this value to receive
unicode arrays and pass strings as input to converters. If set to None
the system default is used. The default value is 'bytes'.
.. versionadded:: 1.14.0
max_rows : int, optional
Read `max_rows` rows of content after `skiprows` lines. The default is
to read all the rows. Note that empty rows containing no data such as
empty lines and comment lines are not counted towards `max_rows`,
while such lines are counted in `skiprows`.
.. versionadded:: 1.16.0
.. versionchanged:: 1.23.0
Lines containing no data, including comment lines (e.g., lines
starting with '#' or as specified via `comments`) are not counted
towards `max_rows`.
quotechar : unicode character or None, optional
The character used to denote the start and end of a quoted item.
Occurrences of the delimiter or comment characters are ignored within
a quoted item. The default value is ``quotechar=None``, which means
quoting support is disabled.
If two consecutive instances of `quotechar` are found within a quoted
field, the first is treated as an escape character. See examples.
.. versionadded:: 1.23.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Data read from the text file.
See Also
--------
load, fromstring, fromregex
genfromtxt : Load data with missing values handled as specified.
scipy.io.loadmat : reads MATLAB data files
Notes
-----
This function aims to be a fast reader for simply formatted files. The
`genfromtxt` function provides more sophisticated handling of, e.g.,
lines with missing values.
Each row in the input text file must have the same number of values to be
able to read all values. If all rows do not have same number of values, a
subset of up to n columns (where n is the least number of values present
in all rows) can be read by specifying the columns via `usecols`.
.. versionadded:: 1.10.0
The strings produced by the Python float.hex method can be used as
input for floats.
Examples
--------
>>> from io import StringIO # StringIO behaves like a file object
>>> c = StringIO("0 1\n2 3")
>>> np.loadtxt(c)
array([[0., 1.],
[2., 3.]])
>>> d = StringIO("M 21 72\nF 35 58")
>>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'),
... 'formats': ('S1', 'i4', 'f4')})
array([(b'M', 21, 72.), (b'F', 35, 58.)],
dtype=[('gender', 'S1'), ('age', '<i4'), ('weight', '<f4')])
>>> c = StringIO("1,0,2\n3,0,4")
>>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True)
>>> x
array([1., 3.])
>>> y
array([2., 4.])
The `converters` argument is used to specify functions to preprocess the
text prior to parsing. `converters` can be a dictionary that maps
preprocessing functions to each column:
>>> s = StringIO("1.618, 2.296\n3.141, 4.669\n")
>>> conv = {
... 0: lambda x: np.floor(float(x)), # conversion fn for column 0
... 1: lambda x: np.ceil(float(x)), # conversion fn for column 1
... }
>>> np.loadtxt(s, delimiter=",", converters=conv)
array([[1., 3.],
[3., 5.]])
`converters` can be a callable instead of a dictionary, in which case it
is applied to all columns:
>>> s = StringIO("0xDE 0xAD\n0xC0 0xDE")
>>> import functools
>>> conv = functools.partial(int, base=16)
>>> np.loadtxt(s, converters=conv)
array([[222., 173.],
[192., 222.]])
This example shows how `converters` can be used to convert a field
with a trailing minus sign into a negative number.
>>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94')
>>> def conv(fld):
... return -float(fld[:-1]) if fld.endswith(b'-') else float(fld)
...
>>> np.loadtxt(s, converters=conv)
array([[ 10.01, -31.25],
[ 19.22, 64.31],
[-17.57, 63.94]])
Using a callable as the converter can be particularly useful for handling
values with different formatting, e.g. floats with underscores:
>>> s = StringIO("1 2.7 100_000")
>>> np.loadtxt(s, converters=float)
array([1.e+00, 2.7e+00, 1.e+05])
This idea can be extended to automatically handle values specified in
many different formats:
>>> def conv(val):
... try:
... return float(val)
... except ValueError:
... return float.fromhex(val)
>>> s = StringIO("1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2")
>>> np.loadtxt(s, delimiter=",", converters=conv, encoding=None)
array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00])
Note that with the default ``encoding="bytes"``, the inputs to the
converter function are latin-1 encoded byte strings. To deactivate the
implicit encoding prior to conversion, use ``encoding=None``
>>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94')
>>> conv = lambda x: -float(x[:-1]) if x.endswith('-') else float(x)
>>> np.loadtxt(s, converters=conv, encoding=None)
array([[ 10.01, -31.25],
[ 19.22, 64.31],
[-17.57, 63.94]])
Support for quoted fields is enabled with the `quotechar` parameter.
Comment and delimiter characters are ignored when they appear within a
quoted item delineated by `quotechar`:
>>> s = StringIO('"alpha, #42", 10.0\n"beta, #64", 2.0\n')
>>> dtype = np.dtype([("label", "U12"), ("value", float)])
>>> np.loadtxt(s, dtype=dtype, delimiter=",", quotechar='"')
array([('alpha, #42', 10.), ('beta, #64', 2.)],
dtype=[('label', '<U12'), ('value', '<f8')])
Quoted fields can be separated by multiple whitespace characters:
>>> s = StringIO('"alpha, #42" 10.0\n"beta, #64" 2.0\n')
>>> dtype = np.dtype([("label", "U12"), ("value", float)])
>>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='"')
array([('alpha, #42', 10.), ('beta, #64', 2.)],
dtype=[('label', '<U12'), ('value', '<f8')])
Two consecutive quote characters within a quoted field are treated as a
single escaped character:
>>> s = StringIO('"Hello, my name is ""Monty""!"')
>>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"')
array('Hello, my name is "Monty"!', dtype='<U26')
Read subset of columns when all rows do not contain equal number of values:
>>> d = StringIO("1 2\n2 4\n3 9 12\n4 16 20")
>>> np.loadtxt(d, usecols=(0, 1))
array([[ 1., 2.],
[ 2., 4.],
[ 3., 9.],
[ 4., 16.]])
"""
if like is not None:
return _loadtxt_with_like(
fname, dtype=dtype, comments=comments, delimiter=delimiter,
converters=converters, skiprows=skiprows, usecols=usecols,
unpack=unpack, ndmin=ndmin, encoding=encoding,
max_rows=max_rows, like=like
)
if isinstance(delimiter, bytes):
delimiter.decode("latin1")
if dtype is None:
dtype = np.float64
comment = comments
# Control character type conversions for Py3 convenience
if comment is not None:
if isinstance(comment, (str, bytes)):
comment = [comment]
comment = [
x.decode('latin1') if isinstance(x, bytes) else x for x in comment]
if isinstance(delimiter, bytes):
delimiter = delimiter.decode('latin1')
arr = _read(fname, dtype=dtype, comment=comment, delimiter=delimiter,
converters=converters, skiplines=skiprows, usecols=usecols,
unpack=unpack, ndmin=ndmin, encoding=encoding,
max_rows=max_rows, quote=quotechar)
return arr | r""" Load data from a text file. Parameters ---------- fname : file, str, pathlib.Path, list of str, generator File, filename, list, or generator to read. If the filename extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note that generators must return bytes or strings. The strings in a list or produced by a generator are treated as lines. dtype : data-type, optional Data-type of the resulting array; default: float. If this is a structured data-type, the resulting array will be 1-dimensional, and each row will be interpreted as an element of the array. In this case, the number of columns used must match the number of fields in the data-type. comments : str or sequence of str or None, optional The characters or list of characters used to indicate the start of a comment. None implies no comments. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is '#'. delimiter : str, optional The character used to separate the values. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is whitespace. .. versionchanged:: 1.23.0 Only single character delimiters are supported. Newline characters cannot be used as the delimiter. converters : dict or callable, optional Converter functions to customize value parsing. If `converters` is callable, the function is applied to all columns, else it must be a dict that maps column number to a parser function. See examples for further details. Default: None. .. versionchanged:: 1.23.0 The ability to pass a single callable to be applied to all columns was added. skiprows : int, optional Skip the first `skiprows` lines, including comments; default: 0. usecols : int or sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns. The default, None, results in all columns being read. .. versionchanged:: 1.11.0 When a single column has to be read it is possible to use an integer instead of a tuple. E.g ``usecols = 3`` reads the fourth column the same way as ``usecols = (3,)`` would. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = loadtxt(...)``. When used with a structured data-type, arrays are returned for each field. Default is False. ndmin : int, optional The returned array will have at least `ndmin` dimensions. Otherwise mono-dimensional axes will be squeezed. Legal values: 0 (default), 1 or 2. .. versionadded:: 1.6.0 encoding : str, optional Encoding used to decode the inputfile. Does not apply to input streams. The special value 'bytes' enables backward compatibility workarounds that ensures you receive byte arrays as results if possible and passes 'latin1' encoded strings to converters. Override this value to receive unicode arrays and pass strings as input to converters. If set to None the system default is used. The default value is 'bytes'. .. versionadded:: 1.14.0 max_rows : int, optional Read `max_rows` rows of content after `skiprows` lines. The default is to read all the rows. Note that empty rows containing no data such as empty lines and comment lines are not counted towards `max_rows`, while such lines are counted in `skiprows`. .. versionadded:: 1.16.0 .. versionchanged:: 1.23.0 Lines containing no data, including comment lines (e.g., lines starting with '#' or as specified via `comments`) are not counted towards `max_rows`. quotechar : unicode character or None, optional The character used to denote the start and end of a quoted item. Occurrences of the delimiter or comment characters are ignored within a quoted item. The default value is ``quotechar=None``, which means quoting support is disabled. If two consecutive instances of `quotechar` are found within a quoted field, the first is treated as an escape character. See examples. .. versionadded:: 1.23.0 ${ARRAY_FUNCTION_LIKE} .. versionadded:: 1.20.0 Returns ------- out : ndarray Data read from the text file. See Also -------- load, fromstring, fromregex genfromtxt : Load data with missing values handled as specified. scipy.io.loadmat : reads MATLAB data files Notes ----- This function aims to be a fast reader for simply formatted files. The `genfromtxt` function provides more sophisticated handling of, e.g., lines with missing values. Each row in the input text file must have the same number of values to be able to read all values. If all rows do not have same number of values, a subset of up to n columns (where n is the least number of values present in all rows) can be read by specifying the columns via `usecols`. .. versionadded:: 1.10.0 The strings produced by the Python float.hex method can be used as input for floats. Examples -------- >>> from io import StringIO # StringIO behaves like a file object >>> c = StringIO("0 1\n2 3") >>> np.loadtxt(c) array([[0., 1.], [2., 3.]]) >>> d = StringIO("M 21 72\nF 35 58") >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'), ... 'formats': ('S1', 'i4', 'f4')}) array([(b'M', 21, 72.), (b'F', 35, 58.)], dtype=[('gender', 'S1'), ('age', '<i4'), ('weight', '<f4')]) >>> c = StringIO("1,0,2\n3,0,4") >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True) >>> x array([1., 3.]) >>> y array([2., 4.]) The `converters` argument is used to specify functions to preprocess the text prior to parsing. `converters` can be a dictionary that maps preprocessing functions to each column: >>> s = StringIO("1.618, 2.296\n3.141, 4.669\n") >>> conv = { ... 0: lambda x: np.floor(float(x)), # conversion fn for column 0 ... 1: lambda x: np.ceil(float(x)), # conversion fn for column 1 ... } >>> np.loadtxt(s, delimiter=",", converters=conv) array([[1., 3.], [3., 5.]]) `converters` can be a callable instead of a dictionary, in which case it is applied to all columns: >>> s = StringIO("0xDE 0xAD\n0xC0 0xDE") >>> import functools >>> conv = functools.partial(int, base=16) >>> np.loadtxt(s, converters=conv) array([[222., 173.], [192., 222.]]) This example shows how `converters` can be used to convert a field with a trailing minus sign into a negative number. >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94') >>> def conv(fld): ... return -float(fld[:-1]) if fld.endswith(b'-') else float(fld) ... >>> np.loadtxt(s, converters=conv) array([[ 10.01, -31.25], [ 19.22, 64.31], [-17.57, 63.94]]) Using a callable as the converter can be particularly useful for handling values with different formatting, e.g. floats with underscores: >>> s = StringIO("1 2.7 100_000") >>> np.loadtxt(s, converters=float) array([1.e+00, 2.7e+00, 1.e+05]) This idea can be extended to automatically handle values specified in many different formats: >>> def conv(val): ... try: ... return float(val) ... except ValueError: ... return float.fromhex(val) >>> s = StringIO("1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2") >>> np.loadtxt(s, delimiter=",", converters=conv, encoding=None) array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00]) Note that with the default ``encoding="bytes"``, the inputs to the converter function are latin-1 encoded byte strings. To deactivate the implicit encoding prior to conversion, use ``encoding=None`` >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94') >>> conv = lambda x: -float(x[:-1]) if x.endswith('-') else float(x) >>> np.loadtxt(s, converters=conv, encoding=None) array([[ 10.01, -31.25], [ 19.22, 64.31], [-17.57, 63.94]]) Support for quoted fields is enabled with the `quotechar` parameter. Comment and delimiter characters are ignored when they appear within a quoted item delineated by `quotechar`: >>> s = StringIO('"alpha, #42", 10.0\n"beta, #64", 2.0\n') >>> dtype = np.dtype([("label", "U12"), ("value", float)]) >>> np.loadtxt(s, dtype=dtype, delimiter=",", quotechar='"') array([('alpha, #42', 10.), ('beta, #64', 2.)], dtype=[('label', '<U12'), ('value', '<f8')]) Quoted fields can be separated by multiple whitespace characters: >>> s = StringIO('"alpha, #42" 10.0\n"beta, #64" 2.0\n') >>> dtype = np.dtype([("label", "U12"), ("value", float)]) >>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='"') array([('alpha, #42', 10.), ('beta, #64', 2.)], dtype=[('label', '<U12'), ('value', '<f8')]) Two consecutive quote characters within a quoted field are treated as a single escaped character: >>> s = StringIO('"Hello, my name is ""Monty""!"') >>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"') array('Hello, my name is "Monty"!', dtype='<U26') Read subset of columns when all rows do not contain equal number of values: >>> d = StringIO("1 2\n2 4\n3 9 12\n4 16 20") >>> np.loadtxt(d, usecols=(0, 1)) array([[ 1., 2.], [ 2., 4.], [ 3., 9.], [ 4., 16.]]) |
168,724 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _savetxt_dispatcher(fname, X, fmt=None, delimiter=None, newline=None,
header=None, footer=None, comments=None,
encoding=None):
return (X,) | null |
168,725 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _is_string_like(obj):
"""
Check whether obj behaves like a string.
"""
try:
obj + ''
except (TypeError, ValueError):
return False
return True
The provided code snippet includes necessary dependencies for implementing the `savetxt` function. Write a Python function `def savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='', footer='', comments='# ', encoding=None)` to solve the following problem:
Save an array to a text file. Parameters ---------- fname : filename or file handle If the filename ends in ``.gz``, the file is automatically saved in compressed gzip format. `loadtxt` understands gzipped files transparently. X : 1D or 2D array_like Data to be saved to a text file. fmt : str or sequence of strs, optional A single format (%10.5f), a sequence of formats, or a multi-format string, e.g. 'Iteration %d -- %10.5f', in which case `delimiter` is ignored. For complex `X`, the legal options for `fmt` are: * a single specifier, `fmt='%.4e'`, resulting in numbers formatted like `' (%s+%sj)' % (fmt, fmt)` * a full string specifying every real and imaginary part, e.g. `' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'` for 3 columns * a list of specifiers, one per column - in this case, the real and imaginary part must have separate specifiers, e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns delimiter : str, optional String or character separating columns. newline : str, optional String or character separating lines. .. versionadded:: 1.5.0 header : str, optional String that will be written at the beginning of the file. .. versionadded:: 1.7.0 footer : str, optional String that will be written at the end of the file. .. versionadded:: 1.7.0 comments : str, optional String that will be prepended to the ``header`` and ``footer`` strings, to mark them as comments. Default: '# ', as expected by e.g. ``numpy.loadtxt``. .. versionadded:: 1.7.0 encoding : {None, str}, optional Encoding used to encode the outputfile. Does not apply to output streams. If the encoding is something other than 'bytes' or 'latin1' you will not be able to load the file in NumPy versions < 1.14. Default is 'latin1'. .. versionadded:: 1.14.0 See Also -------- save : Save an array to a binary file in NumPy ``.npy`` format savez : Save several arrays into an uncompressed ``.npz`` archive savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- Further explanation of the `fmt` parameter (``%[flag]width[.precision]specifier``): flags: ``-`` : left justify ``+`` : Forces to precede result with + or -. ``0`` : Left pad the number with zeros instead of space (see width). width: Minimum number of characters to be printed. The value is not truncated if it has more characters. precision: - For integer specifiers (eg. ``d,i,o,x``), the minimum number of digits. - For ``e, E`` and ``f`` specifiers, the number of digits to print after the decimal point. - For ``g`` and ``G``, the maximum number of significant digits. - For ``s``, the maximum number of characters. specifiers: ``c`` : character ``d`` or ``i`` : signed decimal integer ``e`` or ``E`` : scientific notation with ``e`` or ``E``. ``f`` : decimal floating point ``g,G`` : use the shorter of ``e,E`` or ``f`` ``o`` : signed octal ``s`` : string of characters ``u`` : unsigned decimal integer ``x,X`` : unsigned hexadecimal integer This explanation of ``fmt`` is not complete, for an exhaustive specification see [1]_. References ---------- .. [1] `Format Specification Mini-Language <https://docs.python.org/library/string.html#format-specification-mini-language>`_, Python Documentation. Examples -------- >>> x = y = z = np.arange(0.0,5.0,1.0) >>> np.savetxt('test.out', x, delimiter=',') # X is an array >>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays >>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation
Here is the function:
def savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='',
footer='', comments='# ', encoding=None):
"""
Save an array to a text file.
Parameters
----------
fname : filename or file handle
If the filename ends in ``.gz``, the file is automatically saved in
compressed gzip format. `loadtxt` understands gzipped files
transparently.
X : 1D or 2D array_like
Data to be saved to a text file.
fmt : str or sequence of strs, optional
A single format (%10.5f), a sequence of formats, or a
multi-format string, e.g. 'Iteration %d -- %10.5f', in which
case `delimiter` is ignored. For complex `X`, the legal options
for `fmt` are:
* a single specifier, `fmt='%.4e'`, resulting in numbers formatted
like `' (%s+%sj)' % (fmt, fmt)`
* a full string specifying every real and imaginary part, e.g.
`' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'` for 3 columns
* a list of specifiers, one per column - in this case, the real
and imaginary part must have separate specifiers,
e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns
delimiter : str, optional
String or character separating columns.
newline : str, optional
String or character separating lines.
.. versionadded:: 1.5.0
header : str, optional
String that will be written at the beginning of the file.
.. versionadded:: 1.7.0
footer : str, optional
String that will be written at the end of the file.
.. versionadded:: 1.7.0
comments : str, optional
String that will be prepended to the ``header`` and ``footer`` strings,
to mark them as comments. Default: '# ', as expected by e.g.
``numpy.loadtxt``.
.. versionadded:: 1.7.0
encoding : {None, str}, optional
Encoding used to encode the outputfile. Does not apply to output
streams. If the encoding is something other than 'bytes' or 'latin1'
you will not be able to load the file in NumPy versions < 1.14. Default
is 'latin1'.
.. versionadded:: 1.14.0
See Also
--------
save : Save an array to a binary file in NumPy ``.npy`` format
savez : Save several arrays into an uncompressed ``.npz`` archive
savez_compressed : Save several arrays into a compressed ``.npz`` archive
Notes
-----
Further explanation of the `fmt` parameter
(``%[flag]width[.precision]specifier``):
flags:
``-`` : left justify
``+`` : Forces to precede result with + or -.
``0`` : Left pad the number with zeros instead of space (see width).
width:
Minimum number of characters to be printed. The value is not truncated
if it has more characters.
precision:
- For integer specifiers (eg. ``d,i,o,x``), the minimum number of
digits.
- For ``e, E`` and ``f`` specifiers, the number of digits to print
after the decimal point.
- For ``g`` and ``G``, the maximum number of significant digits.
- For ``s``, the maximum number of characters.
specifiers:
``c`` : character
``d`` or ``i`` : signed decimal integer
``e`` or ``E`` : scientific notation with ``e`` or ``E``.
``f`` : decimal floating point
``g,G`` : use the shorter of ``e,E`` or ``f``
``o`` : signed octal
``s`` : string of characters
``u`` : unsigned decimal integer
``x,X`` : unsigned hexadecimal integer
This explanation of ``fmt`` is not complete, for an exhaustive
specification see [1]_.
References
----------
.. [1] `Format Specification Mini-Language
<https://docs.python.org/library/string.html#format-specification-mini-language>`_,
Python Documentation.
Examples
--------
>>> x = y = z = np.arange(0.0,5.0,1.0)
>>> np.savetxt('test.out', x, delimiter=',') # X is an array
>>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays
>>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation
"""
# Py3 conversions first
if isinstance(fmt, bytes):
fmt = asstr(fmt)
delimiter = asstr(delimiter)
class WriteWrap:
"""Convert to bytes on bytestream inputs.
"""
def __init__(self, fh, encoding):
self.fh = fh
self.encoding = encoding
self.do_write = self.first_write
def close(self):
self.fh.close()
def write(self, v):
self.do_write(v)
def write_bytes(self, v):
if isinstance(v, bytes):
self.fh.write(v)
else:
self.fh.write(v.encode(self.encoding))
def write_normal(self, v):
self.fh.write(asunicode(v))
def first_write(self, v):
try:
self.write_normal(v)
self.write = self.write_normal
except TypeError:
# input is probably a bytestream
self.write_bytes(v)
self.write = self.write_bytes
own_fh = False
if isinstance(fname, os_PathLike):
fname = os_fspath(fname)
if _is_string_like(fname):
# datasource doesn't support creating a new file ...
open(fname, 'wt').close()
fh = np.lib._datasource.open(fname, 'wt', encoding=encoding)
own_fh = True
elif hasattr(fname, 'write'):
# wrap to handle byte output streams
fh = WriteWrap(fname, encoding or 'latin1')
else:
raise ValueError('fname must be a string or file handle')
try:
X = np.asarray(X)
# Handle 1-dimensional arrays
if X.ndim == 0 or X.ndim > 2:
raise ValueError(
"Expected 1D or 2D array, got %dD array instead" % X.ndim)
elif X.ndim == 1:
# Common case -- 1d array of numbers
if X.dtype.names is None:
X = np.atleast_2d(X).T
ncol = 1
# Complex dtype -- each field indicates a separate column
else:
ncol = len(X.dtype.names)
else:
ncol = X.shape[1]
iscomplex_X = np.iscomplexobj(X)
# `fmt` can be a string with multiple insertion points or a
# list of formats. E.g. '%10.5f\t%10d' or ('%10.5f', '$10d')
if type(fmt) in (list, tuple):
if len(fmt) != ncol:
raise AttributeError('fmt has wrong shape. %s' % str(fmt))
format = asstr(delimiter).join(map(asstr, fmt))
elif isinstance(fmt, str):
n_fmt_chars = fmt.count('%')
error = ValueError('fmt has wrong number of %% formats: %s' % fmt)
if n_fmt_chars == 1:
if iscomplex_X:
fmt = [' (%s+%sj)' % (fmt, fmt), ] * ncol
else:
fmt = [fmt, ] * ncol
format = delimiter.join(fmt)
elif iscomplex_X and n_fmt_chars != (2 * ncol):
raise error
elif ((not iscomplex_X) and n_fmt_chars != ncol):
raise error
else:
format = fmt
else:
raise ValueError('invalid fmt: %r' % (fmt,))
if len(header) > 0:
header = header.replace('\n', '\n' + comments)
fh.write(comments + header + newline)
if iscomplex_X:
for row in X:
row2 = []
for number in row:
row2.append(number.real)
row2.append(number.imag)
s = format % tuple(row2) + newline
fh.write(s.replace('+-', '-'))
else:
for row in X:
try:
v = format % tuple(row) + newline
except TypeError as e:
raise TypeError("Mismatch between array dtype ('%s') and "
"format specifier ('%s')"
% (str(X.dtype), format)) from e
fh.write(v)
if len(footer) > 0:
footer = footer.replace('\n', '\n' + comments)
fh.write(comments + footer + newline)
finally:
if own_fh:
fh.close() | Save an array to a text file. Parameters ---------- fname : filename or file handle If the filename ends in ``.gz``, the file is automatically saved in compressed gzip format. `loadtxt` understands gzipped files transparently. X : 1D or 2D array_like Data to be saved to a text file. fmt : str or sequence of strs, optional A single format (%10.5f), a sequence of formats, or a multi-format string, e.g. 'Iteration %d -- %10.5f', in which case `delimiter` is ignored. For complex `X`, the legal options for `fmt` are: * a single specifier, `fmt='%.4e'`, resulting in numbers formatted like `' (%s+%sj)' % (fmt, fmt)` * a full string specifying every real and imaginary part, e.g. `' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'` for 3 columns * a list of specifiers, one per column - in this case, the real and imaginary part must have separate specifiers, e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns delimiter : str, optional String or character separating columns. newline : str, optional String or character separating lines. .. versionadded:: 1.5.0 header : str, optional String that will be written at the beginning of the file. .. versionadded:: 1.7.0 footer : str, optional String that will be written at the end of the file. .. versionadded:: 1.7.0 comments : str, optional String that will be prepended to the ``header`` and ``footer`` strings, to mark them as comments. Default: '# ', as expected by e.g. ``numpy.loadtxt``. .. versionadded:: 1.7.0 encoding : {None, str}, optional Encoding used to encode the outputfile. Does not apply to output streams. If the encoding is something other than 'bytes' or 'latin1' you will not be able to load the file in NumPy versions < 1.14. Default is 'latin1'. .. versionadded:: 1.14.0 See Also -------- save : Save an array to a binary file in NumPy ``.npy`` format savez : Save several arrays into an uncompressed ``.npz`` archive savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- Further explanation of the `fmt` parameter (``%[flag]width[.precision]specifier``): flags: ``-`` : left justify ``+`` : Forces to precede result with + or -. ``0`` : Left pad the number with zeros instead of space (see width). width: Minimum number of characters to be printed. The value is not truncated if it has more characters. precision: - For integer specifiers (eg. ``d,i,o,x``), the minimum number of digits. - For ``e, E`` and ``f`` specifiers, the number of digits to print after the decimal point. - For ``g`` and ``G``, the maximum number of significant digits. - For ``s``, the maximum number of characters. specifiers: ``c`` : character ``d`` or ``i`` : signed decimal integer ``e`` or ``E`` : scientific notation with ``e`` or ``E``. ``f`` : decimal floating point ``g,G`` : use the shorter of ``e,E`` or ``f`` ``o`` : signed octal ``s`` : string of characters ``u`` : unsigned decimal integer ``x,X`` : unsigned hexadecimal integer This explanation of ``fmt`` is not complete, for an exhaustive specification see [1]_. References ---------- .. [1] `Format Specification Mini-Language <https://docs.python.org/library/string.html#format-specification-mini-language>`_, Python Documentation. Examples -------- >>> x = y = z = np.arange(0.0,5.0,1.0) >>> np.savetxt('test.out', x, delimiter=',') # X is an array >>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays >>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation |
168,726 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
The provided code snippet includes necessary dependencies for implementing the `fromregex` function. Write a Python function `def fromregex(file, regexp, dtype, encoding=None)` to solve the following problem:
r""" Construct an array from a text file, using regular expression parsing. The returned array is always a structured array, and is constructed from all matches of the regular expression in the file. Groups in the regular expression are converted to fields of the structured array. Parameters ---------- file : path or file Filename or file object to read. .. versionchanged:: 1.22.0 Now accepts `os.PathLike` implementations. regexp : str or regexp Regular expression used to parse the file. Groups in the regular expression correspond to fields in the dtype. dtype : dtype or list of dtypes Dtype for the structured array; must be a structured datatype. encoding : str, optional Encoding used to decode the inputfile. Does not apply to input streams. .. versionadded:: 1.14.0 Returns ------- output : ndarray The output array, containing the part of the content of `file` that was matched by `regexp`. `output` is always a structured array. Raises ------ TypeError When `dtype` is not a valid dtype for a structured array. See Also -------- fromstring, loadtxt Notes ----- Dtypes for structured arrays can be specified in several forms, but all forms specify at least the data type and field name. For details see `basics.rec`. Examples -------- >>> from io import StringIO >>> text = StringIO("1312 foo\n1534 bar\n444 qux") >>> regexp = r"(\d+)\s+(...)" # match [digits, whitespace, anything] >>> output = np.fromregex(text, regexp, ... [('num', np.int64), ('key', 'S3')]) >>> output array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')], dtype=[('num', '<i8'), ('key', 'S3')]) >>> output['num'] array([1312, 1534, 444])
Here is the function:
def fromregex(file, regexp, dtype, encoding=None):
r"""
Construct an array from a text file, using regular expression parsing.
The returned array is always a structured array, and is constructed from
all matches of the regular expression in the file. Groups in the regular
expression are converted to fields of the structured array.
Parameters
----------
file : path or file
Filename or file object to read.
.. versionchanged:: 1.22.0
Now accepts `os.PathLike` implementations.
regexp : str or regexp
Regular expression used to parse the file.
Groups in the regular expression correspond to fields in the dtype.
dtype : dtype or list of dtypes
Dtype for the structured array; must be a structured datatype.
encoding : str, optional
Encoding used to decode the inputfile. Does not apply to input streams.
.. versionadded:: 1.14.0
Returns
-------
output : ndarray
The output array, containing the part of the content of `file` that
was matched by `regexp`. `output` is always a structured array.
Raises
------
TypeError
When `dtype` is not a valid dtype for a structured array.
See Also
--------
fromstring, loadtxt
Notes
-----
Dtypes for structured arrays can be specified in several forms, but all
forms specify at least the data type and field name. For details see
`basics.rec`.
Examples
--------
>>> from io import StringIO
>>> text = StringIO("1312 foo\n1534 bar\n444 qux")
>>> regexp = r"(\d+)\s+(...)" # match [digits, whitespace, anything]
>>> output = np.fromregex(text, regexp,
... [('num', np.int64), ('key', 'S3')])
>>> output
array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')],
dtype=[('num', '<i8'), ('key', 'S3')])
>>> output['num']
array([1312, 1534, 444])
"""
own_fh = False
if not hasattr(file, "read"):
file = os.fspath(file)
file = np.lib._datasource.open(file, 'rt', encoding=encoding)
own_fh = True
try:
if not isinstance(dtype, np.dtype):
dtype = np.dtype(dtype)
if dtype.names is None:
raise TypeError('dtype must be a structured datatype.')
content = file.read()
if isinstance(content, bytes) and isinstance(regexp, str):
regexp = asbytes(regexp)
elif isinstance(content, str) and isinstance(regexp, bytes):
regexp = asstr(regexp)
if not hasattr(regexp, 'match'):
regexp = re.compile(regexp)
seq = regexp.findall(content)
if seq and not isinstance(seq[0], tuple):
# Only one group is in the regexp.
# Create the new array as a single data-type and then
# re-interpret as a single-field structured array.
newdtype = np.dtype(dtype[dtype.names[0]])
output = np.array(seq, dtype=newdtype)
output.dtype = dtype
else:
output = np.array(seq, dtype=dtype)
return output
finally:
if own_fh:
file.close() | r""" Construct an array from a text file, using regular expression parsing. The returned array is always a structured array, and is constructed from all matches of the regular expression in the file. Groups in the regular expression are converted to fields of the structured array. Parameters ---------- file : path or file Filename or file object to read. .. versionchanged:: 1.22.0 Now accepts `os.PathLike` implementations. regexp : str or regexp Regular expression used to parse the file. Groups in the regular expression correspond to fields in the dtype. dtype : dtype or list of dtypes Dtype for the structured array; must be a structured datatype. encoding : str, optional Encoding used to decode the inputfile. Does not apply to input streams. .. versionadded:: 1.14.0 Returns ------- output : ndarray The output array, containing the part of the content of `file` that was matched by `regexp`. `output` is always a structured array. Raises ------ TypeError When `dtype` is not a valid dtype for a structured array. See Also -------- fromstring, loadtxt Notes ----- Dtypes for structured arrays can be specified in several forms, but all forms specify at least the data type and field name. For details see `basics.rec`. Examples -------- >>> from io import StringIO >>> text = StringIO("1312 foo\n1534 bar\n444 qux") >>> regexp = r"(\d+)\s+(...)" # match [digits, whitespace, anything] >>> output = np.fromregex(text, regexp, ... [('num', np.int64), ('key', 'S3')]) >>> output array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')], dtype=[('num', '<i8'), ('key', 'S3')]) >>> output['num'] array([1312, 1534, 444]) |
168,727 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def _genfromtxt_dispatcher(fname, dtype=None, comments=None, delimiter=None,
skip_header=None, skip_footer=None, converters=None,
missing_values=None, filling_values=None, usecols=None,
names=None, excludelist=None, deletechars=None,
replace_space=None, autostrip=None, case_sensitive=None,
defaultfmt=None, unpack=None, usemask=None, loose=None,
invalid_raise=None, max_rows=None, encoding=None,
*, ndmin=None, like=None):
return (like,) | null |
168,728 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def genfromtxt(fname, dtype=float, comments='#', delimiter=None,
skip_header=0, skip_footer=0, converters=None,
missing_values=None, filling_values=None, usecols=None,
names=None, excludelist=None,
deletechars=''.join(sorted(NameValidator.defaultdeletechars)),
replace_space='_', autostrip=False, case_sensitive=True,
defaultfmt="f%i", unpack=None, usemask=False, loose=True,
invalid_raise=True, max_rows=None, encoding='bytes',
*, ndmin=0, like=None):
"""
Load data from a text file, with missing values handled as specified.
Each line past the first `skip_header` lines is split at the `delimiter`
character, and characters following the `comments` character are discarded.
Parameters
----------
fname : file, str, pathlib.Path, list of str, generator
File, filename, list, or generator to read. If the filename
extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note
that generators must return bytes or strings. The strings
in a list or produced by a generator are treated as lines.
dtype : dtype, optional
Data type of the resulting array.
If None, the dtypes will be determined by the contents of each
column, individually.
comments : str, optional
The character used to indicate the start of a comment.
All the characters occurring on a line after a comment are discarded.
delimiter : str, int, or sequence, optional
The string used to separate values. By default, any consecutive
whitespaces act as delimiter. An integer or sequence of integers
can also be provided as width(s) of each field.
skiprows : int, optional
`skiprows` was removed in numpy 1.10. Please use `skip_header` instead.
skip_header : int, optional
The number of lines to skip at the beginning of the file.
skip_footer : int, optional
The number of lines to skip at the end of the file.
converters : variable, optional
The set of functions that convert the data of a column to a value.
The converters can also be used to provide a default value
for missing data: ``converters = {3: lambda s: float(s or 0)}``.
missing : variable, optional
`missing` was removed in numpy 1.10. Please use `missing_values`
instead.
missing_values : variable, optional
The set of strings corresponding to missing data.
filling_values : variable, optional
The set of values to be used as default when the data are missing.
usecols : sequence, optional
Which columns to read, with 0 being the first. For example,
``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns.
names : {None, True, str, sequence}, optional
If `names` is True, the field names are read from the first line after
the first `skip_header` lines. This line can optionally be preceded
by a comment delimiter. If `names` is a sequence or a single-string of
comma-separated names, the names will be used to define the field names
in a structured dtype. If `names` is None, the names of the dtype
fields will be used, if any.
excludelist : sequence, optional
A list of names to exclude. This list is appended to the default list
['return','file','print']. Excluded names are appended with an
underscore: for example, `file` would become `file_`.
deletechars : str, optional
A string combining invalid characters that must be deleted from the
names.
defaultfmt : str, optional
A format used to define default field names, such as "f%i" or "f_%02i".
autostrip : bool, optional
Whether to automatically strip white spaces from the variables.
replace_space : char, optional
Character(s) used in replacement of white spaces in the variable
names. By default, use a '_'.
case_sensitive : {True, False, 'upper', 'lower'}, optional
If True, field names are case sensitive.
If False or 'upper', field names are converted to upper case.
If 'lower', field names are converted to lower case.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = genfromtxt(...)``. When used with a
structured data-type, arrays are returned for each field.
Default is False.
usemask : bool, optional
If True, return a masked array.
If False, return a regular array.
loose : bool, optional
If True, do not raise errors for invalid values.
invalid_raise : bool, optional
If True, an exception is raised if an inconsistency is detected in the
number of columns.
If False, a warning is emitted and the offending lines are skipped.
max_rows : int, optional
The maximum number of rows to read. Must not be used with skip_footer
at the same time. If given, the value must be at least 1. Default is
to read the entire file.
.. versionadded:: 1.10.0
encoding : str, optional
Encoding used to decode the inputfile. Does not apply when `fname` is
a file object. The special value 'bytes' enables backward compatibility
workarounds that ensure that you receive byte arrays when possible
and passes latin1 encoded strings to converters. Override this value to
receive unicode arrays and pass strings as input to converters. If set
to None the system default is used. The default value is 'bytes'.
.. versionadded:: 1.14.0
ndmin : int, optional
Same parameter as `loadtxt`
.. versionadded:: 1.23.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Data read from the text file. If `usemask` is True, this is a
masked array.
See Also
--------
numpy.loadtxt : equivalent function when no data is missing.
Notes
-----
* When spaces are used as delimiters, or when no delimiter has been given
as input, there should not be any missing data between two fields.
* When the variables are named (either by a flexible dtype or with `names`),
there must not be any header in the file (else a ValueError
exception is raised).
* Individual values are not stripped of spaces by default.
When using a custom converter, make sure the function does remove spaces.
References
----------
.. [1] NumPy User Guide, section `I/O with NumPy
<https://docs.scipy.org/doc/numpy/user/basics.io.genfromtxt.html>`_.
Examples
--------
>>> from io import StringIO
>>> import numpy as np
Comma delimited file with mixed dtype
>>> s = StringIO(u"1,1.3,abcde")
>>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'),
... ('mystring','S5')], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
Using dtype = None
>>> _ = s.seek(0) # needed for StringIO example only
>>> data = np.genfromtxt(s, dtype=None,
... names = ['myint','myfloat','mystring'], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
Specifying dtype and names
>>> _ = s.seek(0)
>>> data = np.genfromtxt(s, dtype="i8,f8,S5",
... names=['myint','myfloat','mystring'], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
An example with fixed-width columns
>>> s = StringIO(u"11.3abcde")
>>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'],
... delimiter=[1,3,5])
>>> data
array((1, 1.3, b'abcde'),
dtype=[('intvar', '<i8'), ('fltvar', '<f8'), ('strvar', 'S5')])
An example to show comments
>>> f = StringIO('''
... text,# of chars
... hello world,11
... numpy,5''')
>>> np.genfromtxt(f, dtype='S12,S12', delimiter=',')
array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')],
dtype=[('f0', 'S12'), ('f1', 'S12')])
"""
if like is not None:
return _genfromtxt_with_like(
fname, dtype=dtype, comments=comments, delimiter=delimiter,
skip_header=skip_header, skip_footer=skip_footer,
converters=converters, missing_values=missing_values,
filling_values=filling_values, usecols=usecols, names=names,
excludelist=excludelist, deletechars=deletechars,
replace_space=replace_space, autostrip=autostrip,
case_sensitive=case_sensitive, defaultfmt=defaultfmt,
unpack=unpack, usemask=usemask, loose=loose,
invalid_raise=invalid_raise, max_rows=max_rows, encoding=encoding,
ndmin=ndmin,
like=like
)
_ensure_ndmin_ndarray_check_param(ndmin)
if max_rows is not None:
if skip_footer:
raise ValueError(
"The keywords 'skip_footer' and 'max_rows' can not be "
"specified at the same time.")
if max_rows < 1:
raise ValueError("'max_rows' must be at least 1.")
if usemask:
from numpy.ma import MaskedArray, make_mask_descr
# Check the input dictionary of converters
user_converters = converters or {}
if not isinstance(user_converters, dict):
raise TypeError(
"The input argument 'converter' should be a valid dictionary "
"(got '%s' instead)" % type(user_converters))
if encoding == 'bytes':
encoding = None
byte_converters = True
else:
byte_converters = False
# Initialize the filehandle, the LineSplitter and the NameValidator
if isinstance(fname, os_PathLike):
fname = os_fspath(fname)
if isinstance(fname, str):
fid = np.lib._datasource.open(fname, 'rt', encoding=encoding)
fid_ctx = contextlib.closing(fid)
else:
fid = fname
fid_ctx = contextlib.nullcontext(fid)
try:
fhd = iter(fid)
except TypeError as e:
raise TypeError(
"fname must be a string, a filehandle, a sequence of strings,\n"
f"or an iterator of strings. Got {type(fname)} instead."
) from e
with fid_ctx:
split_line = LineSplitter(delimiter=delimiter, comments=comments,
autostrip=autostrip, encoding=encoding)
validate_names = NameValidator(excludelist=excludelist,
deletechars=deletechars,
case_sensitive=case_sensitive,
replace_space=replace_space)
# Skip the first `skip_header` rows
try:
for i in range(skip_header):
next(fhd)
# Keep on until we find the first valid values
first_values = None
while not first_values:
first_line = _decode_line(next(fhd), encoding)
if (names is True) and (comments is not None):
if comments in first_line:
first_line = (
''.join(first_line.split(comments)[1:]))
first_values = split_line(first_line)
except StopIteration:
# return an empty array if the datafile is empty
first_line = ''
first_values = []
warnings.warn('genfromtxt: Empty input file: "%s"' % fname, stacklevel=2)
# Should we take the first values as names ?
if names is True:
fval = first_values[0].strip()
if comments is not None:
if fval in comments:
del first_values[0]
# Check the columns to use: make sure `usecols` is a list
if usecols is not None:
try:
usecols = [_.strip() for _ in usecols.split(",")]
except AttributeError:
try:
usecols = list(usecols)
except TypeError:
usecols = [usecols, ]
nbcols = len(usecols or first_values)
# Check the names and overwrite the dtype.names if needed
if names is True:
names = validate_names([str(_.strip()) for _ in first_values])
first_line = ''
elif _is_string_like(names):
names = validate_names([_.strip() for _ in names.split(',')])
elif names:
names = validate_names(names)
# Get the dtype
if dtype is not None:
dtype = easy_dtype(dtype, defaultfmt=defaultfmt, names=names,
excludelist=excludelist,
deletechars=deletechars,
case_sensitive=case_sensitive,
replace_space=replace_space)
# Make sure the names is a list (for 2.5)
if names is not None:
names = list(names)
if usecols:
for (i, current) in enumerate(usecols):
# if usecols is a list of names, convert to a list of indices
if _is_string_like(current):
usecols[i] = names.index(current)
elif current < 0:
usecols[i] = current + len(first_values)
# If the dtype is not None, make sure we update it
if (dtype is not None) and (len(dtype) > nbcols):
descr = dtype.descr
dtype = np.dtype([descr[_] for _ in usecols])
names = list(dtype.names)
# If `names` is not None, update the names
elif (names is not None) and (len(names) > nbcols):
names = [names[_] for _ in usecols]
elif (names is not None) and (dtype is not None):
names = list(dtype.names)
# Process the missing values ...............................
# Rename missing_values for convenience
user_missing_values = missing_values or ()
if isinstance(user_missing_values, bytes):
user_missing_values = user_missing_values.decode('latin1')
# Define the list of missing_values (one column: one list)
missing_values = [list(['']) for _ in range(nbcols)]
# We have a dictionary: process it field by field
if isinstance(user_missing_values, dict):
# Loop on the items
for (key, val) in user_missing_values.items():
# Is the key a string ?
if _is_string_like(key):
try:
# Transform it into an integer
key = names.index(key)
except ValueError:
# We couldn't find it: the name must have been dropped
continue
# Redefine the key as needed if it's a column number
if usecols:
try:
key = usecols.index(key)
except ValueError:
pass
# Transform the value as a list of string
if isinstance(val, (list, tuple)):
val = [str(_) for _ in val]
else:
val = [str(val), ]
# Add the value(s) to the current list of missing
if key is None:
# None acts as default
for miss in missing_values:
miss.extend(val)
else:
missing_values[key].extend(val)
# We have a sequence : each item matches a column
elif isinstance(user_missing_values, (list, tuple)):
for (value, entry) in zip(user_missing_values, missing_values):
value = str(value)
if value not in entry:
entry.append(value)
# We have a string : apply it to all entries
elif isinstance(user_missing_values, str):
user_value = user_missing_values.split(",")
for entry in missing_values:
entry.extend(user_value)
# We have something else: apply it to all entries
else:
for entry in missing_values:
entry.extend([str(user_missing_values)])
# Process the filling_values ...............................
# Rename the input for convenience
user_filling_values = filling_values
if user_filling_values is None:
user_filling_values = []
# Define the default
filling_values = [None] * nbcols
# We have a dictionary : update each entry individually
if isinstance(user_filling_values, dict):
for (key, val) in user_filling_values.items():
if _is_string_like(key):
try:
# Transform it into an integer
key = names.index(key)
except ValueError:
# We couldn't find it: the name must have been dropped,
continue
# Redefine the key if it's a column number and usecols is defined
if usecols:
try:
key = usecols.index(key)
except ValueError:
pass
# Add the value to the list
filling_values[key] = val
# We have a sequence : update on a one-to-one basis
elif isinstance(user_filling_values, (list, tuple)):
n = len(user_filling_values)
if (n <= nbcols):
filling_values[:n] = user_filling_values
else:
filling_values = user_filling_values[:nbcols]
# We have something else : use it for all entries
else:
filling_values = [user_filling_values] * nbcols
# Initialize the converters ................................
if dtype is None:
# Note: we can't use a [...]*nbcols, as we would have 3 times the same
# ... converter, instead of 3 different converters.
converters = [StringConverter(None, missing_values=miss, default=fill)
for (miss, fill) in zip(missing_values, filling_values)]
else:
dtype_flat = flatten_dtype(dtype, flatten_base=True)
# Initialize the converters
if len(dtype_flat) > 1:
# Flexible type : get a converter from each dtype
zipit = zip(dtype_flat, missing_values, filling_values)
converters = [StringConverter(dt, locked=True,
missing_values=miss, default=fill)
for (dt, miss, fill) in zipit]
else:
# Set to a default converter (but w/ different missing values)
zipit = zip(missing_values, filling_values)
converters = [StringConverter(dtype, locked=True,
missing_values=miss, default=fill)
for (miss, fill) in zipit]
# Update the converters to use the user-defined ones
uc_update = []
for (j, conv) in user_converters.items():
# If the converter is specified by column names, use the index instead
if _is_string_like(j):
try:
j = names.index(j)
i = j
except ValueError:
continue
elif usecols:
try:
i = usecols.index(j)
except ValueError:
# Unused converter specified
continue
else:
i = j
# Find the value to test - first_line is not filtered by usecols:
if len(first_line):
testing_value = first_values[j]
else:
testing_value = None
if conv is bytes:
user_conv = asbytes
elif byte_converters:
# converters may use decode to workaround numpy's old behaviour,
# so encode the string again before passing to the user converter
def tobytes_first(x, conv):
if type(x) is bytes:
return conv(x)
return conv(x.encode("latin1"))
user_conv = functools.partial(tobytes_first, conv=conv)
else:
user_conv = conv
converters[i].update(user_conv, locked=True,
testing_value=testing_value,
default=filling_values[i],
missing_values=missing_values[i],)
uc_update.append((i, user_conv))
# Make sure we have the corrected keys in user_converters...
user_converters.update(uc_update)
# Fixme: possible error as following variable never used.
# miss_chars = [_.missing_values for _ in converters]
# Initialize the output lists ...
# ... rows
rows = []
append_to_rows = rows.append
# ... masks
if usemask:
masks = []
append_to_masks = masks.append
# ... invalid
invalid = []
append_to_invalid = invalid.append
# Parse each line
for (i, line) in enumerate(itertools.chain([first_line, ], fhd)):
values = split_line(line)
nbvalues = len(values)
# Skip an empty line
if nbvalues == 0:
continue
if usecols:
# Select only the columns we need
try:
values = [values[_] for _ in usecols]
except IndexError:
append_to_invalid((i + skip_header + 1, nbvalues))
continue
elif nbvalues != nbcols:
append_to_invalid((i + skip_header + 1, nbvalues))
continue
# Store the values
append_to_rows(tuple(values))
if usemask:
append_to_masks(tuple([v.strip() in m
for (v, m) in zip(values,
missing_values)]))
if len(rows) == max_rows:
break
# Upgrade the converters (if needed)
if dtype is None:
for (i, converter) in enumerate(converters):
current_column = [itemgetter(i)(_m) for _m in rows]
try:
converter.iterupgrade(current_column)
except ConverterLockError:
errmsg = "Converter #%i is locked and cannot be upgraded: " % i
current_column = map(itemgetter(i), rows)
for (j, value) in enumerate(current_column):
try:
converter.upgrade(value)
except (ConverterError, ValueError):
errmsg += "(occurred line #%i for value '%s')"
errmsg %= (j + 1 + skip_header, value)
raise ConverterError(errmsg)
# Check that we don't have invalid values
nbinvalid = len(invalid)
if nbinvalid > 0:
nbrows = len(rows) + nbinvalid - skip_footer
# Construct the error message
template = " Line #%%i (got %%i columns instead of %i)" % nbcols
if skip_footer > 0:
nbinvalid_skipped = len([_ for _ in invalid
if _[0] > nbrows + skip_header])
invalid = invalid[:nbinvalid - nbinvalid_skipped]
skip_footer -= nbinvalid_skipped
#
# nbrows -= skip_footer
# errmsg = [template % (i, nb)
# for (i, nb) in invalid if i < nbrows]
# else:
errmsg = [template % (i, nb)
for (i, nb) in invalid]
if len(errmsg):
errmsg.insert(0, "Some errors were detected !")
errmsg = "\n".join(errmsg)
# Raise an exception ?
if invalid_raise:
raise ValueError(errmsg)
# Issue a warning ?
else:
warnings.warn(errmsg, ConversionWarning, stacklevel=2)
# Strip the last skip_footer data
if skip_footer > 0:
rows = rows[:-skip_footer]
if usemask:
masks = masks[:-skip_footer]
# Convert each value according to the converter:
# We want to modify the list in place to avoid creating a new one...
if loose:
rows = list(
zip(*[[conv._loose_call(_r) for _r in map(itemgetter(i), rows)]
for (i, conv) in enumerate(converters)]))
else:
rows = list(
zip(*[[conv._strict_call(_r) for _r in map(itemgetter(i), rows)]
for (i, conv) in enumerate(converters)]))
# Reset the dtype
data = rows
if dtype is None:
# Get the dtypes from the types of the converters
column_types = [conv.type for conv in converters]
# Find the columns with strings...
strcolidx = [i for (i, v) in enumerate(column_types)
if v == np.unicode_]
if byte_converters and strcolidx:
# convert strings back to bytes for backward compatibility
warnings.warn(
"Reading unicode strings without specifying the encoding "
"argument is deprecated. Set the encoding, use None for the "
"system default.",
np.VisibleDeprecationWarning, stacklevel=2)
def encode_unicode_cols(row_tup):
row = list(row_tup)
for i in strcolidx:
row[i] = row[i].encode('latin1')
return tuple(row)
try:
data = [encode_unicode_cols(r) for r in data]
except UnicodeEncodeError:
pass
else:
for i in strcolidx:
column_types[i] = np.bytes_
# Update string types to be the right length
sized_column_types = column_types[:]
for i, col_type in enumerate(column_types):
if np.issubdtype(col_type, np.character):
n_chars = max(len(row[i]) for row in data)
sized_column_types[i] = (col_type, n_chars)
if names is None:
# If the dtype is uniform (before sizing strings)
base = {
c_type
for c, c_type in zip(converters, column_types)
if c._checked}
if len(base) == 1:
uniform_type, = base
(ddtype, mdtype) = (uniform_type, bool)
else:
ddtype = [(defaultfmt % i, dt)
for (i, dt) in enumerate(sized_column_types)]
if usemask:
mdtype = [(defaultfmt % i, bool)
for (i, dt) in enumerate(sized_column_types)]
else:
ddtype = list(zip(names, sized_column_types))
mdtype = list(zip(names, [bool] * len(sized_column_types)))
output = np.array(data, dtype=ddtype)
if usemask:
outputmask = np.array(masks, dtype=mdtype)
else:
# Overwrite the initial dtype names if needed
if names and dtype.names is not None:
dtype.names = names
# Case 1. We have a structured type
if len(dtype_flat) > 1:
# Nested dtype, eg [('a', int), ('b', [('b0', int), ('b1', 'f4')])]
# First, create the array using a flattened dtype:
# [('a', int), ('b1', int), ('b2', float)]
# Then, view the array using the specified dtype.
if 'O' in (_.char for _ in dtype_flat):
if has_nested_fields(dtype):
raise NotImplementedError(
"Nested fields involving objects are not supported...")
else:
output = np.array(data, dtype=dtype)
else:
rows = np.array(data, dtype=[('', _) for _ in dtype_flat])
output = rows.view(dtype)
# Now, process the rowmasks the same way
if usemask:
rowmasks = np.array(
masks, dtype=np.dtype([('', bool) for t in dtype_flat]))
# Construct the new dtype
mdtype = make_mask_descr(dtype)
outputmask = rowmasks.view(mdtype)
# Case #2. We have a basic dtype
else:
# We used some user-defined converters
if user_converters:
ishomogeneous = True
descr = []
for i, ttype in enumerate([conv.type for conv in converters]):
# Keep the dtype of the current converter
if i in user_converters:
ishomogeneous &= (ttype == dtype.type)
if np.issubdtype(ttype, np.character):
ttype = (ttype, max(len(row[i]) for row in data))
descr.append(('', ttype))
else:
descr.append(('', dtype))
# So we changed the dtype ?
if not ishomogeneous:
# We have more than one field
if len(descr) > 1:
dtype = np.dtype(descr)
# We have only one field: drop the name if not needed.
else:
dtype = np.dtype(ttype)
#
output = np.array(data, dtype)
if usemask:
if dtype.names is not None:
mdtype = [(_, bool) for _ in dtype.names]
else:
mdtype = bool
outputmask = np.array(masks, dtype=mdtype)
# Try to take care of the missing data we missed
names = output.dtype.names
if usemask and names:
for (name, conv) in zip(names, converters):
missing_values = [conv(_) for _ in conv.missing_values
if _ != '']
for mval in missing_values:
outputmask[name] |= (output[name] == mval)
# Construct the final array
if usemask:
output = output.view(MaskedArray)
output._mask = outputmask
output = _ensure_ndmin_ndarray(output, ndmin=ndmin)
if unpack:
if names is None:
return output.T
elif len(names) == 1:
# squeeze single-name dtypes too
return output[names[0]]
else:
# For structured arrays with multiple fields,
# return an array for each field.
return [output[field] for field in names]
return output
class MaskedRecords(MaskedArray):
"""
Attributes
----------
_data : recarray
Underlying data, as a record array.
_mask : boolean array
Mask of the records. A record is masked when all its fields are
masked.
_fieldmask : boolean recarray
Record array of booleans, setting the mask of each individual field
of each record.
_fill_value : record
Filling values for each field.
"""
def __new__(cls, shape, dtype=None, buf=None, offset=0, strides=None,
formats=None, names=None, titles=None,
byteorder=None, aligned=False,
mask=nomask, hard_mask=False, fill_value=None, keep_mask=True,
copy=False,
**options):
self = recarray.__new__(cls, shape, dtype=dtype, buf=buf, offset=offset,
strides=strides, formats=formats, names=names,
titles=titles, byteorder=byteorder,
aligned=aligned,)
mdtype = ma.make_mask_descr(self.dtype)
if mask is nomask or not np.size(mask):
if not keep_mask:
self._mask = tuple([False] * len(mdtype))
else:
mask = np.array(mask, copy=copy)
if mask.shape != self.shape:
(nd, nm) = (self.size, mask.size)
if nm == 1:
mask = np.resize(mask, self.shape)
elif nm == nd:
mask = np.reshape(mask, self.shape)
else:
msg = "Mask and data not compatible: data size is %i, " + \
"mask size is %i."
raise MAError(msg % (nd, nm))
if not keep_mask:
self.__setmask__(mask)
self._sharedmask = True
else:
if mask.dtype == mdtype:
_mask = mask
else:
_mask = np.array([tuple([m] * len(mdtype)) for m in mask],
dtype=mdtype)
self._mask = _mask
return self
def __array_finalize__(self, obj):
# Make sure we have a _fieldmask by default
_mask = getattr(obj, '_mask', None)
if _mask is None:
objmask = getattr(obj, '_mask', nomask)
_dtype = ndarray.__getattribute__(self, 'dtype')
if objmask is nomask:
_mask = ma.make_mask_none(self.shape, dtype=_dtype)
else:
mdescr = ma.make_mask_descr(_dtype)
_mask = narray([tuple([m] * len(mdescr)) for m in objmask],
dtype=mdescr).view(recarray)
# Update some of the attributes
_dict = self.__dict__
_dict.update(_mask=_mask)
self._update_from(obj)
if _dict['_baseclass'] == ndarray:
_dict['_baseclass'] = recarray
return
def _data(self):
"""
Returns the data as a recarray.
"""
return ndarray.view(self, recarray)
def _fieldmask(self):
"""
Alias to mask.
"""
return self._mask
def __len__(self):
"""
Returns the length
"""
# We have more than one record
if self.ndim:
return len(self._data)
# We have only one record: return the nb of fields
return len(self.dtype)
def __getattribute__(self, attr):
try:
return object.__getattribute__(self, attr)
except AttributeError:
# attr must be a fieldname
pass
fielddict = ndarray.__getattribute__(self, 'dtype').fields
try:
res = fielddict[attr][:2]
except (TypeError, KeyError) as e:
raise AttributeError(
f'record array has no attribute {attr}') from e
# So far, so good
_localdict = ndarray.__getattribute__(self, '__dict__')
_data = ndarray.view(self, _localdict['_baseclass'])
obj = _data.getfield(*res)
if obj.dtype.names is not None:
raise NotImplementedError("MaskedRecords is currently limited to"
"simple records.")
# Get some special attributes
# Reset the object's mask
hasmasked = False
_mask = _localdict.get('_mask', None)
if _mask is not None:
try:
_mask = _mask[attr]
except IndexError:
# Couldn't find a mask: use the default (nomask)
pass
tp_len = len(_mask.dtype)
hasmasked = _mask.view((bool, ((tp_len,) if tp_len else ()))).any()
if (obj.shape or hasmasked):
obj = obj.view(MaskedArray)
obj._baseclass = ndarray
obj._isfield = True
obj._mask = _mask
# Reset the field values
_fill_value = _localdict.get('_fill_value', None)
if _fill_value is not None:
try:
obj._fill_value = _fill_value[attr]
except ValueError:
obj._fill_value = None
else:
obj = obj.item()
return obj
def __setattr__(self, attr, val):
"""
Sets the attribute attr to the value val.
"""
# Should we call __setmask__ first ?
if attr in ['mask', 'fieldmask']:
self.__setmask__(val)
return
# Create a shortcut (so that we don't have to call getattr all the time)
_localdict = object.__getattribute__(self, '__dict__')
# Check whether we're creating a new field
newattr = attr not in _localdict
try:
# Is attr a generic attribute ?
ret = object.__setattr__(self, attr, val)
except Exception:
# Not a generic attribute: exit if it's not a valid field
fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
optinfo = ndarray.__getattribute__(self, '_optinfo') or {}
if not (attr in fielddict or attr in optinfo):
raise
else:
# Get the list of names
fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
# Check the attribute
if attr not in fielddict:
return ret
if newattr:
# We just added this one or this setattr worked on an
# internal attribute.
try:
object.__delattr__(self, attr)
except Exception:
return ret
# Let's try to set the field
try:
res = fielddict[attr][:2]
except (TypeError, KeyError) as e:
raise AttributeError(
f'record array has no attribute {attr}') from e
if val is masked:
_fill_value = _localdict['_fill_value']
if _fill_value is not None:
dval = _localdict['_fill_value'][attr]
else:
dval = val
mval = True
else:
dval = filled(val)
mval = getmaskarray(val)
obj = ndarray.__getattribute__(self, '_data').setfield(dval, *res)
_localdict['_mask'].__setitem__(attr, mval)
return obj
def __getitem__(self, indx):
"""
Returns all the fields sharing the same fieldname base.
The fieldname base is either `_data` or `_mask`.
"""
_localdict = self.__dict__
_mask = ndarray.__getattribute__(self, '_mask')
_data = ndarray.view(self, _localdict['_baseclass'])
# We want a field
if isinstance(indx, str):
# Make sure _sharedmask is True to propagate back to _fieldmask
# Don't use _set_mask, there are some copies being made that
# break propagation Don't force the mask to nomask, that wreaks
# easy masking
obj = _data[indx].view(MaskedArray)
obj._mask = _mask[indx]
obj._sharedmask = True
fval = _localdict['_fill_value']
if fval is not None:
obj._fill_value = fval[indx]
# Force to masked if the mask is True
if not obj.ndim and obj._mask:
return masked
return obj
# We want some elements.
# First, the data.
obj = np.array(_data[indx], copy=False).view(mrecarray)
obj._mask = np.array(_mask[indx], copy=False).view(recarray)
return obj
def __setitem__(self, indx, value):
"""
Sets the given record to value.
"""
MaskedArray.__setitem__(self, indx, value)
if isinstance(indx, str):
self._mask[indx] = ma.getmaskarray(value)
def __str__(self):
"""
Calculates the string representation.
"""
if self.size > 1:
mstr = [f"({','.join([str(i) for i in s])})"
for s in zip(*[getattr(self, f) for f in self.dtype.names])]
return f"[{', '.join(mstr)}]"
else:
mstr = [f"{','.join([str(i) for i in s])}"
for s in zip([getattr(self, f) for f in self.dtype.names])]
return f"({', '.join(mstr)})"
def __repr__(self):
"""
Calculates the repr representation.
"""
_names = self.dtype.names
fmt = "%%%is : %%s" % (max([len(n) for n in _names]) + 4,)
reprstr = [fmt % (f, getattr(self, f)) for f in self.dtype.names]
reprstr.insert(0, 'masked_records(')
reprstr.extend([fmt % (' fill_value', self.fill_value),
' )'])
return str("\n".join(reprstr))
def view(self, dtype=None, type=None):
"""
Returns a view of the mrecarray.
"""
# OK, basic copy-paste from MaskedArray.view.
if dtype is None:
if type is None:
output = ndarray.view(self)
else:
output = ndarray.view(self, type)
# Here again.
elif type is None:
try:
if issubclass(dtype, ndarray):
output = ndarray.view(self, dtype)
else:
output = ndarray.view(self, dtype)
# OK, there's the change
except TypeError:
dtype = np.dtype(dtype)
# we need to revert to MaskedArray, but keeping the possibility
# of subclasses (eg, TimeSeriesRecords), so we'll force a type
# set to the first parent
if dtype.fields is None:
basetype = self.__class__.__bases__[0]
output = self.__array__().view(dtype, basetype)
output._update_from(self)
else:
output = ndarray.view(self, dtype)
output._fill_value = None
else:
output = ndarray.view(self, dtype, type)
# Update the mask, just like in MaskedArray.view
if (getattr(output, '_mask', nomask) is not nomask):
mdtype = ma.make_mask_descr(output.dtype)
output._mask = self._mask.view(mdtype, ndarray)
output._mask.shape = output.shape
return output
def harden_mask(self):
"""
Forces the mask to hard.
"""
self._hardmask = True
def soften_mask(self):
"""
Forces the mask to soft
"""
self._hardmask = False
def copy(self):
"""
Returns a copy of the masked record.
"""
copied = self._data.copy().view(type(self))
copied._mask = self._mask.copy()
return copied
def tolist(self, fill_value=None):
"""
Return the data portion of the array as a list.
Data items are converted to the nearest compatible Python type.
Masked values are converted to fill_value. If fill_value is None,
the corresponding entries in the output list will be ``None``.
"""
if fill_value is not None:
return self.filled(fill_value).tolist()
result = narray(self.filled().tolist(), dtype=object)
mask = narray(self._mask.tolist())
result[mask] = None
return result.tolist()
def __getstate__(self):
"""Return the internal state of the masked array.
This is for pickling.
"""
state = (1,
self.shape,
self.dtype,
self.flags.fnc,
self._data.tobytes(),
self._mask.tobytes(),
self._fill_value,
)
return state
def __setstate__(self, state):
"""
Restore the internal state of the masked array.
This is for pickling. ``state`` is typically the output of the
``__getstate__`` output, and is a 5-tuple:
- class name
- a tuple giving the shape of the data
- a typecode for the data
- a binary string for the data
- a binary string for the mask.
"""
(ver, shp, typ, isf, raw, msk, flv) = state
ndarray.__setstate__(self, (shp, typ, isf, raw))
mdtype = dtype([(k, bool_) for (k, _) in self.dtype.descr])
self.__dict__['_mask'].__setstate__((shp, mdtype, isf, msk))
self.fill_value = flv
def __reduce__(self):
"""
Return a 3-tuple for pickling a MaskedArray.
"""
return (_mrreconstruct,
(self.__class__, self._baseclass, (0,), 'b',),
self.__getstate__())
The provided code snippet includes necessary dependencies for implementing the `recfromtxt` function. Write a Python function `def recfromtxt(fname, **kwargs)` to solve the following problem:
Load ASCII data from a file and return it in a record array. If ``usemask=False`` a standard `recarray` is returned, if ``usemask=True`` a MaskedRecords array is returned. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data.
Here is the function:
def recfromtxt(fname, **kwargs):
"""
Load ASCII data from a file and return it in a record array.
If ``usemask=False`` a standard `recarray` is returned,
if ``usemask=True`` a MaskedRecords array is returned.
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function
Notes
-----
By default, `dtype` is None, which means that the data-type of the output
array will be determined from the data.
"""
kwargs.setdefault("dtype", None)
usemask = kwargs.get('usemask', False)
output = genfromtxt(fname, **kwargs)
if usemask:
from numpy.ma.mrecords import MaskedRecords
output = output.view(MaskedRecords)
else:
output = output.view(np.recarray)
return output | Load ASCII data from a file and return it in a record array. If ``usemask=False`` a standard `recarray` is returned, if ``usemask=True`` a MaskedRecords array is returned. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data. |
168,729 | import os
import re
import functools
import itertools
import warnings
import weakref
import contextlib
import operator
from operator import itemgetter, index as opindex, methodcaller
from collections.abc import Mapping
import numpy as np
from . import format
from ._datasource import DataSource
from numpy.core import overrides
from numpy.core.multiarray import packbits, unpackbits
from numpy.core._multiarray_umath import _load_from_filelike
from numpy.core.overrides import set_array_function_like_doc, set_module
from ._iotools import (
LineSplitter, NameValidator, StringConverter, ConverterError,
ConverterLockError, ConversionWarning, _is_string_like,
has_nested_fields, flatten_dtype, easy_dtype, _decode_line
)
from numpy.compat import (
asbytes, asstr, asunicode, os_fspath, os_PathLike,
pickle
)
def genfromtxt(fname, dtype=float, comments='#', delimiter=None,
skip_header=0, skip_footer=0, converters=None,
missing_values=None, filling_values=None, usecols=None,
names=None, excludelist=None,
deletechars=''.join(sorted(NameValidator.defaultdeletechars)),
replace_space='_', autostrip=False, case_sensitive=True,
defaultfmt="f%i", unpack=None, usemask=False, loose=True,
invalid_raise=True, max_rows=None, encoding='bytes',
*, ndmin=0, like=None):
"""
Load data from a text file, with missing values handled as specified.
Each line past the first `skip_header` lines is split at the `delimiter`
character, and characters following the `comments` character are discarded.
Parameters
----------
fname : file, str, pathlib.Path, list of str, generator
File, filename, list, or generator to read. If the filename
extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note
that generators must return bytes or strings. The strings
in a list or produced by a generator are treated as lines.
dtype : dtype, optional
Data type of the resulting array.
If None, the dtypes will be determined by the contents of each
column, individually.
comments : str, optional
The character used to indicate the start of a comment.
All the characters occurring on a line after a comment are discarded.
delimiter : str, int, or sequence, optional
The string used to separate values. By default, any consecutive
whitespaces act as delimiter. An integer or sequence of integers
can also be provided as width(s) of each field.
skiprows : int, optional
`skiprows` was removed in numpy 1.10. Please use `skip_header` instead.
skip_header : int, optional
The number of lines to skip at the beginning of the file.
skip_footer : int, optional
The number of lines to skip at the end of the file.
converters : variable, optional
The set of functions that convert the data of a column to a value.
The converters can also be used to provide a default value
for missing data: ``converters = {3: lambda s: float(s or 0)}``.
missing : variable, optional
`missing` was removed in numpy 1.10. Please use `missing_values`
instead.
missing_values : variable, optional
The set of strings corresponding to missing data.
filling_values : variable, optional
The set of values to be used as default when the data are missing.
usecols : sequence, optional
Which columns to read, with 0 being the first. For example,
``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns.
names : {None, True, str, sequence}, optional
If `names` is True, the field names are read from the first line after
the first `skip_header` lines. This line can optionally be preceded
by a comment delimiter. If `names` is a sequence or a single-string of
comma-separated names, the names will be used to define the field names
in a structured dtype. If `names` is None, the names of the dtype
fields will be used, if any.
excludelist : sequence, optional
A list of names to exclude. This list is appended to the default list
['return','file','print']. Excluded names are appended with an
underscore: for example, `file` would become `file_`.
deletechars : str, optional
A string combining invalid characters that must be deleted from the
names.
defaultfmt : str, optional
A format used to define default field names, such as "f%i" or "f_%02i".
autostrip : bool, optional
Whether to automatically strip white spaces from the variables.
replace_space : char, optional
Character(s) used in replacement of white spaces in the variable
names. By default, use a '_'.
case_sensitive : {True, False, 'upper', 'lower'}, optional
If True, field names are case sensitive.
If False or 'upper', field names are converted to upper case.
If 'lower', field names are converted to lower case.
unpack : bool, optional
If True, the returned array is transposed, so that arguments may be
unpacked using ``x, y, z = genfromtxt(...)``. When used with a
structured data-type, arrays are returned for each field.
Default is False.
usemask : bool, optional
If True, return a masked array.
If False, return a regular array.
loose : bool, optional
If True, do not raise errors for invalid values.
invalid_raise : bool, optional
If True, an exception is raised if an inconsistency is detected in the
number of columns.
If False, a warning is emitted and the offending lines are skipped.
max_rows : int, optional
The maximum number of rows to read. Must not be used with skip_footer
at the same time. If given, the value must be at least 1. Default is
to read the entire file.
.. versionadded:: 1.10.0
encoding : str, optional
Encoding used to decode the inputfile. Does not apply when `fname` is
a file object. The special value 'bytes' enables backward compatibility
workarounds that ensure that you receive byte arrays when possible
and passes latin1 encoded strings to converters. Override this value to
receive unicode arrays and pass strings as input to converters. If set
to None the system default is used. The default value is 'bytes'.
.. versionadded:: 1.14.0
ndmin : int, optional
Same parameter as `loadtxt`
.. versionadded:: 1.23.0
${ARRAY_FUNCTION_LIKE}
.. versionadded:: 1.20.0
Returns
-------
out : ndarray
Data read from the text file. If `usemask` is True, this is a
masked array.
See Also
--------
numpy.loadtxt : equivalent function when no data is missing.
Notes
-----
* When spaces are used as delimiters, or when no delimiter has been given
as input, there should not be any missing data between two fields.
* When the variables are named (either by a flexible dtype or with `names`),
there must not be any header in the file (else a ValueError
exception is raised).
* Individual values are not stripped of spaces by default.
When using a custom converter, make sure the function does remove spaces.
References
----------
.. [1] NumPy User Guide, section `I/O with NumPy
<https://docs.scipy.org/doc/numpy/user/basics.io.genfromtxt.html>`_.
Examples
--------
>>> from io import StringIO
>>> import numpy as np
Comma delimited file with mixed dtype
>>> s = StringIO(u"1,1.3,abcde")
>>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'),
... ('mystring','S5')], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
Using dtype = None
>>> _ = s.seek(0) # needed for StringIO example only
>>> data = np.genfromtxt(s, dtype=None,
... names = ['myint','myfloat','mystring'], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
Specifying dtype and names
>>> _ = s.seek(0)
>>> data = np.genfromtxt(s, dtype="i8,f8,S5",
... names=['myint','myfloat','mystring'], delimiter=",")
>>> data
array((1, 1.3, b'abcde'),
dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
An example with fixed-width columns
>>> s = StringIO(u"11.3abcde")
>>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'],
... delimiter=[1,3,5])
>>> data
array((1, 1.3, b'abcde'),
dtype=[('intvar', '<i8'), ('fltvar', '<f8'), ('strvar', 'S5')])
An example to show comments
>>> f = StringIO('''
... text,# of chars
... hello world,11
... numpy,5''')
>>> np.genfromtxt(f, dtype='S12,S12', delimiter=',')
array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')],
dtype=[('f0', 'S12'), ('f1', 'S12')])
"""
if like is not None:
return _genfromtxt_with_like(
fname, dtype=dtype, comments=comments, delimiter=delimiter,
skip_header=skip_header, skip_footer=skip_footer,
converters=converters, missing_values=missing_values,
filling_values=filling_values, usecols=usecols, names=names,
excludelist=excludelist, deletechars=deletechars,
replace_space=replace_space, autostrip=autostrip,
case_sensitive=case_sensitive, defaultfmt=defaultfmt,
unpack=unpack, usemask=usemask, loose=loose,
invalid_raise=invalid_raise, max_rows=max_rows, encoding=encoding,
ndmin=ndmin,
like=like
)
_ensure_ndmin_ndarray_check_param(ndmin)
if max_rows is not None:
if skip_footer:
raise ValueError(
"The keywords 'skip_footer' and 'max_rows' can not be "
"specified at the same time.")
if max_rows < 1:
raise ValueError("'max_rows' must be at least 1.")
if usemask:
from numpy.ma import MaskedArray, make_mask_descr
# Check the input dictionary of converters
user_converters = converters or {}
if not isinstance(user_converters, dict):
raise TypeError(
"The input argument 'converter' should be a valid dictionary "
"(got '%s' instead)" % type(user_converters))
if encoding == 'bytes':
encoding = None
byte_converters = True
else:
byte_converters = False
# Initialize the filehandle, the LineSplitter and the NameValidator
if isinstance(fname, os_PathLike):
fname = os_fspath(fname)
if isinstance(fname, str):
fid = np.lib._datasource.open(fname, 'rt', encoding=encoding)
fid_ctx = contextlib.closing(fid)
else:
fid = fname
fid_ctx = contextlib.nullcontext(fid)
try:
fhd = iter(fid)
except TypeError as e:
raise TypeError(
"fname must be a string, a filehandle, a sequence of strings,\n"
f"or an iterator of strings. Got {type(fname)} instead."
) from e
with fid_ctx:
split_line = LineSplitter(delimiter=delimiter, comments=comments,
autostrip=autostrip, encoding=encoding)
validate_names = NameValidator(excludelist=excludelist,
deletechars=deletechars,
case_sensitive=case_sensitive,
replace_space=replace_space)
# Skip the first `skip_header` rows
try:
for i in range(skip_header):
next(fhd)
# Keep on until we find the first valid values
first_values = None
while not first_values:
first_line = _decode_line(next(fhd), encoding)
if (names is True) and (comments is not None):
if comments in first_line:
first_line = (
''.join(first_line.split(comments)[1:]))
first_values = split_line(first_line)
except StopIteration:
# return an empty array if the datafile is empty
first_line = ''
first_values = []
warnings.warn('genfromtxt: Empty input file: "%s"' % fname, stacklevel=2)
# Should we take the first values as names ?
if names is True:
fval = first_values[0].strip()
if comments is not None:
if fval in comments:
del first_values[0]
# Check the columns to use: make sure `usecols` is a list
if usecols is not None:
try:
usecols = [_.strip() for _ in usecols.split(",")]
except AttributeError:
try:
usecols = list(usecols)
except TypeError:
usecols = [usecols, ]
nbcols = len(usecols or first_values)
# Check the names and overwrite the dtype.names if needed
if names is True:
names = validate_names([str(_.strip()) for _ in first_values])
first_line = ''
elif _is_string_like(names):
names = validate_names([_.strip() for _ in names.split(',')])
elif names:
names = validate_names(names)
# Get the dtype
if dtype is not None:
dtype = easy_dtype(dtype, defaultfmt=defaultfmt, names=names,
excludelist=excludelist,
deletechars=deletechars,
case_sensitive=case_sensitive,
replace_space=replace_space)
# Make sure the names is a list (for 2.5)
if names is not None:
names = list(names)
if usecols:
for (i, current) in enumerate(usecols):
# if usecols is a list of names, convert to a list of indices
if _is_string_like(current):
usecols[i] = names.index(current)
elif current < 0:
usecols[i] = current + len(first_values)
# If the dtype is not None, make sure we update it
if (dtype is not None) and (len(dtype) > nbcols):
descr = dtype.descr
dtype = np.dtype([descr[_] for _ in usecols])
names = list(dtype.names)
# If `names` is not None, update the names
elif (names is not None) and (len(names) > nbcols):
names = [names[_] for _ in usecols]
elif (names is not None) and (dtype is not None):
names = list(dtype.names)
# Process the missing values ...............................
# Rename missing_values for convenience
user_missing_values = missing_values or ()
if isinstance(user_missing_values, bytes):
user_missing_values = user_missing_values.decode('latin1')
# Define the list of missing_values (one column: one list)
missing_values = [list(['']) for _ in range(nbcols)]
# We have a dictionary: process it field by field
if isinstance(user_missing_values, dict):
# Loop on the items
for (key, val) in user_missing_values.items():
# Is the key a string ?
if _is_string_like(key):
try:
# Transform it into an integer
key = names.index(key)
except ValueError:
# We couldn't find it: the name must have been dropped
continue
# Redefine the key as needed if it's a column number
if usecols:
try:
key = usecols.index(key)
except ValueError:
pass
# Transform the value as a list of string
if isinstance(val, (list, tuple)):
val = [str(_) for _ in val]
else:
val = [str(val), ]
# Add the value(s) to the current list of missing
if key is None:
# None acts as default
for miss in missing_values:
miss.extend(val)
else:
missing_values[key].extend(val)
# We have a sequence : each item matches a column
elif isinstance(user_missing_values, (list, tuple)):
for (value, entry) in zip(user_missing_values, missing_values):
value = str(value)
if value not in entry:
entry.append(value)
# We have a string : apply it to all entries
elif isinstance(user_missing_values, str):
user_value = user_missing_values.split(",")
for entry in missing_values:
entry.extend(user_value)
# We have something else: apply it to all entries
else:
for entry in missing_values:
entry.extend([str(user_missing_values)])
# Process the filling_values ...............................
# Rename the input for convenience
user_filling_values = filling_values
if user_filling_values is None:
user_filling_values = []
# Define the default
filling_values = [None] * nbcols
# We have a dictionary : update each entry individually
if isinstance(user_filling_values, dict):
for (key, val) in user_filling_values.items():
if _is_string_like(key):
try:
# Transform it into an integer
key = names.index(key)
except ValueError:
# We couldn't find it: the name must have been dropped,
continue
# Redefine the key if it's a column number and usecols is defined
if usecols:
try:
key = usecols.index(key)
except ValueError:
pass
# Add the value to the list
filling_values[key] = val
# We have a sequence : update on a one-to-one basis
elif isinstance(user_filling_values, (list, tuple)):
n = len(user_filling_values)
if (n <= nbcols):
filling_values[:n] = user_filling_values
else:
filling_values = user_filling_values[:nbcols]
# We have something else : use it for all entries
else:
filling_values = [user_filling_values] * nbcols
# Initialize the converters ................................
if dtype is None:
# Note: we can't use a [...]*nbcols, as we would have 3 times the same
# ... converter, instead of 3 different converters.
converters = [StringConverter(None, missing_values=miss, default=fill)
for (miss, fill) in zip(missing_values, filling_values)]
else:
dtype_flat = flatten_dtype(dtype, flatten_base=True)
# Initialize the converters
if len(dtype_flat) > 1:
# Flexible type : get a converter from each dtype
zipit = zip(dtype_flat, missing_values, filling_values)
converters = [StringConverter(dt, locked=True,
missing_values=miss, default=fill)
for (dt, miss, fill) in zipit]
else:
# Set to a default converter (but w/ different missing values)
zipit = zip(missing_values, filling_values)
converters = [StringConverter(dtype, locked=True,
missing_values=miss, default=fill)
for (miss, fill) in zipit]
# Update the converters to use the user-defined ones
uc_update = []
for (j, conv) in user_converters.items():
# If the converter is specified by column names, use the index instead
if _is_string_like(j):
try:
j = names.index(j)
i = j
except ValueError:
continue
elif usecols:
try:
i = usecols.index(j)
except ValueError:
# Unused converter specified
continue
else:
i = j
# Find the value to test - first_line is not filtered by usecols:
if len(first_line):
testing_value = first_values[j]
else:
testing_value = None
if conv is bytes:
user_conv = asbytes
elif byte_converters:
# converters may use decode to workaround numpy's old behaviour,
# so encode the string again before passing to the user converter
def tobytes_first(x, conv):
if type(x) is bytes:
return conv(x)
return conv(x.encode("latin1"))
user_conv = functools.partial(tobytes_first, conv=conv)
else:
user_conv = conv
converters[i].update(user_conv, locked=True,
testing_value=testing_value,
default=filling_values[i],
missing_values=missing_values[i],)
uc_update.append((i, user_conv))
# Make sure we have the corrected keys in user_converters...
user_converters.update(uc_update)
# Fixme: possible error as following variable never used.
# miss_chars = [_.missing_values for _ in converters]
# Initialize the output lists ...
# ... rows
rows = []
append_to_rows = rows.append
# ... masks
if usemask:
masks = []
append_to_masks = masks.append
# ... invalid
invalid = []
append_to_invalid = invalid.append
# Parse each line
for (i, line) in enumerate(itertools.chain([first_line, ], fhd)):
values = split_line(line)
nbvalues = len(values)
# Skip an empty line
if nbvalues == 0:
continue
if usecols:
# Select only the columns we need
try:
values = [values[_] for _ in usecols]
except IndexError:
append_to_invalid((i + skip_header + 1, nbvalues))
continue
elif nbvalues != nbcols:
append_to_invalid((i + skip_header + 1, nbvalues))
continue
# Store the values
append_to_rows(tuple(values))
if usemask:
append_to_masks(tuple([v.strip() in m
for (v, m) in zip(values,
missing_values)]))
if len(rows) == max_rows:
break
# Upgrade the converters (if needed)
if dtype is None:
for (i, converter) in enumerate(converters):
current_column = [itemgetter(i)(_m) for _m in rows]
try:
converter.iterupgrade(current_column)
except ConverterLockError:
errmsg = "Converter #%i is locked and cannot be upgraded: " % i
current_column = map(itemgetter(i), rows)
for (j, value) in enumerate(current_column):
try:
converter.upgrade(value)
except (ConverterError, ValueError):
errmsg += "(occurred line #%i for value '%s')"
errmsg %= (j + 1 + skip_header, value)
raise ConverterError(errmsg)
# Check that we don't have invalid values
nbinvalid = len(invalid)
if nbinvalid > 0:
nbrows = len(rows) + nbinvalid - skip_footer
# Construct the error message
template = " Line #%%i (got %%i columns instead of %i)" % nbcols
if skip_footer > 0:
nbinvalid_skipped = len([_ for _ in invalid
if _[0] > nbrows + skip_header])
invalid = invalid[:nbinvalid - nbinvalid_skipped]
skip_footer -= nbinvalid_skipped
#
# nbrows -= skip_footer
# errmsg = [template % (i, nb)
# for (i, nb) in invalid if i < nbrows]
# else:
errmsg = [template % (i, nb)
for (i, nb) in invalid]
if len(errmsg):
errmsg.insert(0, "Some errors were detected !")
errmsg = "\n".join(errmsg)
# Raise an exception ?
if invalid_raise:
raise ValueError(errmsg)
# Issue a warning ?
else:
warnings.warn(errmsg, ConversionWarning, stacklevel=2)
# Strip the last skip_footer data
if skip_footer > 0:
rows = rows[:-skip_footer]
if usemask:
masks = masks[:-skip_footer]
# Convert each value according to the converter:
# We want to modify the list in place to avoid creating a new one...
if loose:
rows = list(
zip(*[[conv._loose_call(_r) for _r in map(itemgetter(i), rows)]
for (i, conv) in enumerate(converters)]))
else:
rows = list(
zip(*[[conv._strict_call(_r) for _r in map(itemgetter(i), rows)]
for (i, conv) in enumerate(converters)]))
# Reset the dtype
data = rows
if dtype is None:
# Get the dtypes from the types of the converters
column_types = [conv.type for conv in converters]
# Find the columns with strings...
strcolidx = [i for (i, v) in enumerate(column_types)
if v == np.unicode_]
if byte_converters and strcolidx:
# convert strings back to bytes for backward compatibility
warnings.warn(
"Reading unicode strings without specifying the encoding "
"argument is deprecated. Set the encoding, use None for the "
"system default.",
np.VisibleDeprecationWarning, stacklevel=2)
def encode_unicode_cols(row_tup):
row = list(row_tup)
for i in strcolidx:
row[i] = row[i].encode('latin1')
return tuple(row)
try:
data = [encode_unicode_cols(r) for r in data]
except UnicodeEncodeError:
pass
else:
for i in strcolidx:
column_types[i] = np.bytes_
# Update string types to be the right length
sized_column_types = column_types[:]
for i, col_type in enumerate(column_types):
if np.issubdtype(col_type, np.character):
n_chars = max(len(row[i]) for row in data)
sized_column_types[i] = (col_type, n_chars)
if names is None:
# If the dtype is uniform (before sizing strings)
base = {
c_type
for c, c_type in zip(converters, column_types)
if c._checked}
if len(base) == 1:
uniform_type, = base
(ddtype, mdtype) = (uniform_type, bool)
else:
ddtype = [(defaultfmt % i, dt)
for (i, dt) in enumerate(sized_column_types)]
if usemask:
mdtype = [(defaultfmt % i, bool)
for (i, dt) in enumerate(sized_column_types)]
else:
ddtype = list(zip(names, sized_column_types))
mdtype = list(zip(names, [bool] * len(sized_column_types)))
output = np.array(data, dtype=ddtype)
if usemask:
outputmask = np.array(masks, dtype=mdtype)
else:
# Overwrite the initial dtype names if needed
if names and dtype.names is not None:
dtype.names = names
# Case 1. We have a structured type
if len(dtype_flat) > 1:
# Nested dtype, eg [('a', int), ('b', [('b0', int), ('b1', 'f4')])]
# First, create the array using a flattened dtype:
# [('a', int), ('b1', int), ('b2', float)]
# Then, view the array using the specified dtype.
if 'O' in (_.char for _ in dtype_flat):
if has_nested_fields(dtype):
raise NotImplementedError(
"Nested fields involving objects are not supported...")
else:
output = np.array(data, dtype=dtype)
else:
rows = np.array(data, dtype=[('', _) for _ in dtype_flat])
output = rows.view(dtype)
# Now, process the rowmasks the same way
if usemask:
rowmasks = np.array(
masks, dtype=np.dtype([('', bool) for t in dtype_flat]))
# Construct the new dtype
mdtype = make_mask_descr(dtype)
outputmask = rowmasks.view(mdtype)
# Case #2. We have a basic dtype
else:
# We used some user-defined converters
if user_converters:
ishomogeneous = True
descr = []
for i, ttype in enumerate([conv.type for conv in converters]):
# Keep the dtype of the current converter
if i in user_converters:
ishomogeneous &= (ttype == dtype.type)
if np.issubdtype(ttype, np.character):
ttype = (ttype, max(len(row[i]) for row in data))
descr.append(('', ttype))
else:
descr.append(('', dtype))
# So we changed the dtype ?
if not ishomogeneous:
# We have more than one field
if len(descr) > 1:
dtype = np.dtype(descr)
# We have only one field: drop the name if not needed.
else:
dtype = np.dtype(ttype)
#
output = np.array(data, dtype)
if usemask:
if dtype.names is not None:
mdtype = [(_, bool) for _ in dtype.names]
else:
mdtype = bool
outputmask = np.array(masks, dtype=mdtype)
# Try to take care of the missing data we missed
names = output.dtype.names
if usemask and names:
for (name, conv) in zip(names, converters):
missing_values = [conv(_) for _ in conv.missing_values
if _ != '']
for mval in missing_values:
outputmask[name] |= (output[name] == mval)
# Construct the final array
if usemask:
output = output.view(MaskedArray)
output._mask = outputmask
output = _ensure_ndmin_ndarray(output, ndmin=ndmin)
if unpack:
if names is None:
return output.T
elif len(names) == 1:
# squeeze single-name dtypes too
return output[names[0]]
else:
# For structured arrays with multiple fields,
# return an array for each field.
return [output[field] for field in names]
return output
class MaskedRecords(MaskedArray):
"""
Attributes
----------
_data : recarray
Underlying data, as a record array.
_mask : boolean array
Mask of the records. A record is masked when all its fields are
masked.
_fieldmask : boolean recarray
Record array of booleans, setting the mask of each individual field
of each record.
_fill_value : record
Filling values for each field.
"""
def __new__(cls, shape, dtype=None, buf=None, offset=0, strides=None,
formats=None, names=None, titles=None,
byteorder=None, aligned=False,
mask=nomask, hard_mask=False, fill_value=None, keep_mask=True,
copy=False,
**options):
self = recarray.__new__(cls, shape, dtype=dtype, buf=buf, offset=offset,
strides=strides, formats=formats, names=names,
titles=titles, byteorder=byteorder,
aligned=aligned,)
mdtype = ma.make_mask_descr(self.dtype)
if mask is nomask or not np.size(mask):
if not keep_mask:
self._mask = tuple([False] * len(mdtype))
else:
mask = np.array(mask, copy=copy)
if mask.shape != self.shape:
(nd, nm) = (self.size, mask.size)
if nm == 1:
mask = np.resize(mask, self.shape)
elif nm == nd:
mask = np.reshape(mask, self.shape)
else:
msg = "Mask and data not compatible: data size is %i, " + \
"mask size is %i."
raise MAError(msg % (nd, nm))
if not keep_mask:
self.__setmask__(mask)
self._sharedmask = True
else:
if mask.dtype == mdtype:
_mask = mask
else:
_mask = np.array([tuple([m] * len(mdtype)) for m in mask],
dtype=mdtype)
self._mask = _mask
return self
def __array_finalize__(self, obj):
# Make sure we have a _fieldmask by default
_mask = getattr(obj, '_mask', None)
if _mask is None:
objmask = getattr(obj, '_mask', nomask)
_dtype = ndarray.__getattribute__(self, 'dtype')
if objmask is nomask:
_mask = ma.make_mask_none(self.shape, dtype=_dtype)
else:
mdescr = ma.make_mask_descr(_dtype)
_mask = narray([tuple([m] * len(mdescr)) for m in objmask],
dtype=mdescr).view(recarray)
# Update some of the attributes
_dict = self.__dict__
_dict.update(_mask=_mask)
self._update_from(obj)
if _dict['_baseclass'] == ndarray:
_dict['_baseclass'] = recarray
return
def _data(self):
"""
Returns the data as a recarray.
"""
return ndarray.view(self, recarray)
def _fieldmask(self):
"""
Alias to mask.
"""
return self._mask
def __len__(self):
"""
Returns the length
"""
# We have more than one record
if self.ndim:
return len(self._data)
# We have only one record: return the nb of fields
return len(self.dtype)
def __getattribute__(self, attr):
try:
return object.__getattribute__(self, attr)
except AttributeError:
# attr must be a fieldname
pass
fielddict = ndarray.__getattribute__(self, 'dtype').fields
try:
res = fielddict[attr][:2]
except (TypeError, KeyError) as e:
raise AttributeError(
f'record array has no attribute {attr}') from e
# So far, so good
_localdict = ndarray.__getattribute__(self, '__dict__')
_data = ndarray.view(self, _localdict['_baseclass'])
obj = _data.getfield(*res)
if obj.dtype.names is not None:
raise NotImplementedError("MaskedRecords is currently limited to"
"simple records.")
# Get some special attributes
# Reset the object's mask
hasmasked = False
_mask = _localdict.get('_mask', None)
if _mask is not None:
try:
_mask = _mask[attr]
except IndexError:
# Couldn't find a mask: use the default (nomask)
pass
tp_len = len(_mask.dtype)
hasmasked = _mask.view((bool, ((tp_len,) if tp_len else ()))).any()
if (obj.shape or hasmasked):
obj = obj.view(MaskedArray)
obj._baseclass = ndarray
obj._isfield = True
obj._mask = _mask
# Reset the field values
_fill_value = _localdict.get('_fill_value', None)
if _fill_value is not None:
try:
obj._fill_value = _fill_value[attr]
except ValueError:
obj._fill_value = None
else:
obj = obj.item()
return obj
def __setattr__(self, attr, val):
"""
Sets the attribute attr to the value val.
"""
# Should we call __setmask__ first ?
if attr in ['mask', 'fieldmask']:
self.__setmask__(val)
return
# Create a shortcut (so that we don't have to call getattr all the time)
_localdict = object.__getattribute__(self, '__dict__')
# Check whether we're creating a new field
newattr = attr not in _localdict
try:
# Is attr a generic attribute ?
ret = object.__setattr__(self, attr, val)
except Exception:
# Not a generic attribute: exit if it's not a valid field
fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
optinfo = ndarray.__getattribute__(self, '_optinfo') or {}
if not (attr in fielddict or attr in optinfo):
raise
else:
# Get the list of names
fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
# Check the attribute
if attr not in fielddict:
return ret
if newattr:
# We just added this one or this setattr worked on an
# internal attribute.
try:
object.__delattr__(self, attr)
except Exception:
return ret
# Let's try to set the field
try:
res = fielddict[attr][:2]
except (TypeError, KeyError) as e:
raise AttributeError(
f'record array has no attribute {attr}') from e
if val is masked:
_fill_value = _localdict['_fill_value']
if _fill_value is not None:
dval = _localdict['_fill_value'][attr]
else:
dval = val
mval = True
else:
dval = filled(val)
mval = getmaskarray(val)
obj = ndarray.__getattribute__(self, '_data').setfield(dval, *res)
_localdict['_mask'].__setitem__(attr, mval)
return obj
def __getitem__(self, indx):
"""
Returns all the fields sharing the same fieldname base.
The fieldname base is either `_data` or `_mask`.
"""
_localdict = self.__dict__
_mask = ndarray.__getattribute__(self, '_mask')
_data = ndarray.view(self, _localdict['_baseclass'])
# We want a field
if isinstance(indx, str):
# Make sure _sharedmask is True to propagate back to _fieldmask
# Don't use _set_mask, there are some copies being made that
# break propagation Don't force the mask to nomask, that wreaks
# easy masking
obj = _data[indx].view(MaskedArray)
obj._mask = _mask[indx]
obj._sharedmask = True
fval = _localdict['_fill_value']
if fval is not None:
obj._fill_value = fval[indx]
# Force to masked if the mask is True
if not obj.ndim and obj._mask:
return masked
return obj
# We want some elements.
# First, the data.
obj = np.array(_data[indx], copy=False).view(mrecarray)
obj._mask = np.array(_mask[indx], copy=False).view(recarray)
return obj
def __setitem__(self, indx, value):
"""
Sets the given record to value.
"""
MaskedArray.__setitem__(self, indx, value)
if isinstance(indx, str):
self._mask[indx] = ma.getmaskarray(value)
def __str__(self):
"""
Calculates the string representation.
"""
if self.size > 1:
mstr = [f"({','.join([str(i) for i in s])})"
for s in zip(*[getattr(self, f) for f in self.dtype.names])]
return f"[{', '.join(mstr)}]"
else:
mstr = [f"{','.join([str(i) for i in s])}"
for s in zip([getattr(self, f) for f in self.dtype.names])]
return f"({', '.join(mstr)})"
def __repr__(self):
"""
Calculates the repr representation.
"""
_names = self.dtype.names
fmt = "%%%is : %%s" % (max([len(n) for n in _names]) + 4,)
reprstr = [fmt % (f, getattr(self, f)) for f in self.dtype.names]
reprstr.insert(0, 'masked_records(')
reprstr.extend([fmt % (' fill_value', self.fill_value),
' )'])
return str("\n".join(reprstr))
def view(self, dtype=None, type=None):
"""
Returns a view of the mrecarray.
"""
# OK, basic copy-paste from MaskedArray.view.
if dtype is None:
if type is None:
output = ndarray.view(self)
else:
output = ndarray.view(self, type)
# Here again.
elif type is None:
try:
if issubclass(dtype, ndarray):
output = ndarray.view(self, dtype)
else:
output = ndarray.view(self, dtype)
# OK, there's the change
except TypeError:
dtype = np.dtype(dtype)
# we need to revert to MaskedArray, but keeping the possibility
# of subclasses (eg, TimeSeriesRecords), so we'll force a type
# set to the first parent
if dtype.fields is None:
basetype = self.__class__.__bases__[0]
output = self.__array__().view(dtype, basetype)
output._update_from(self)
else:
output = ndarray.view(self, dtype)
output._fill_value = None
else:
output = ndarray.view(self, dtype, type)
# Update the mask, just like in MaskedArray.view
if (getattr(output, '_mask', nomask) is not nomask):
mdtype = ma.make_mask_descr(output.dtype)
output._mask = self._mask.view(mdtype, ndarray)
output._mask.shape = output.shape
return output
def harden_mask(self):
"""
Forces the mask to hard.
"""
self._hardmask = True
def soften_mask(self):
"""
Forces the mask to soft
"""
self._hardmask = False
def copy(self):
"""
Returns a copy of the masked record.
"""
copied = self._data.copy().view(type(self))
copied._mask = self._mask.copy()
return copied
def tolist(self, fill_value=None):
"""
Return the data portion of the array as a list.
Data items are converted to the nearest compatible Python type.
Masked values are converted to fill_value. If fill_value is None,
the corresponding entries in the output list will be ``None``.
"""
if fill_value is not None:
return self.filled(fill_value).tolist()
result = narray(self.filled().tolist(), dtype=object)
mask = narray(self._mask.tolist())
result[mask] = None
return result.tolist()
def __getstate__(self):
"""Return the internal state of the masked array.
This is for pickling.
"""
state = (1,
self.shape,
self.dtype,
self.flags.fnc,
self._data.tobytes(),
self._mask.tobytes(),
self._fill_value,
)
return state
def __setstate__(self, state):
"""
Restore the internal state of the masked array.
This is for pickling. ``state`` is typically the output of the
``__getstate__`` output, and is a 5-tuple:
- class name
- a tuple giving the shape of the data
- a typecode for the data
- a binary string for the data
- a binary string for the mask.
"""
(ver, shp, typ, isf, raw, msk, flv) = state
ndarray.__setstate__(self, (shp, typ, isf, raw))
mdtype = dtype([(k, bool_) for (k, _) in self.dtype.descr])
self.__dict__['_mask'].__setstate__((shp, mdtype, isf, msk))
self.fill_value = flv
def __reduce__(self):
"""
Return a 3-tuple for pickling a MaskedArray.
"""
return (_mrreconstruct,
(self.__class__, self._baseclass, (0,), 'b',),
self.__getstate__())
The provided code snippet includes necessary dependencies for implementing the `recfromcsv` function. Write a Python function `def recfromcsv(fname, **kwargs)` to solve the following problem:
Load ASCII data stored in a comma-separated file. The returned array is a record array (if ``usemask=False``, see `recarray`) or a masked record array (if ``usemask=True``, see `ma.mrecords.MaskedRecords`). Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data.
Here is the function:
def recfromcsv(fname, **kwargs):
"""
Load ASCII data stored in a comma-separated file.
The returned array is a record array (if ``usemask=False``, see
`recarray`) or a masked record array (if ``usemask=True``,
see `ma.mrecords.MaskedRecords`).
Parameters
----------
fname, kwargs : For a description of input parameters, see `genfromtxt`.
See Also
--------
numpy.genfromtxt : generic function to load ASCII data.
Notes
-----
By default, `dtype` is None, which means that the data-type of the output
array will be determined from the data.
"""
# Set default kwargs for genfromtxt as relevant to csv import.
kwargs.setdefault("case_sensitive", "lower")
kwargs.setdefault("names", True)
kwargs.setdefault("delimiter", ",")
kwargs.setdefault("dtype", None)
output = genfromtxt(fname, **kwargs)
usemask = kwargs.get("usemask", False)
if usemask:
from numpy.ma.mrecords import MaskedRecords
output = output.view(MaskedRecords)
else:
output = output.view(np.recarray)
return output | Load ASCII data stored in a comma-separated file. The returned array is a record array (if ``usemask=False``, see `recarray`) or a masked record array (if ``usemask=True``, see `ma.mrecords.MaskedRecords`). Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data. |
168,730 | import collections.abc
import functools
import re
import sys
import warnings
import numpy as np
import numpy.core.numeric as _nx
from numpy.core import transpose
from numpy.core.numeric import (
ones, zeros_like, arange, concatenate, array, asarray, asanyarray, empty,
ndarray, take, dot, where, intp, integer, isscalar, absolute
)
from numpy.core.umath import (
pi, add, arctan2, frompyfunc, cos, less_equal, sqrt, sin,
mod, exp, not_equal, subtract
)
from numpy.core.fromnumeric import (
ravel, nonzero, partition, mean, any, sum
)
from numpy.core.numerictypes import typecodes
from numpy.core.overrides import set_module
from numpy.core import overrides
from numpy.core.function_base import add_newdoc
from numpy.lib.twodim_base import diag
from numpy.core.multiarray import (
_insert, add_docstring, bincount, normalize_axis_index, _monotonicity,
interp as compiled_interp, interp_complex as compiled_interp_complex
)
from numpy.core.umath import _add_newdoc_ufunc as add_newdoc_ufunc
import builtins
from numpy.lib.histograms import histogram, histogramdd
def _rot90_dispatcher(m, k=None, axes=None):
return (m,) | null |
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