462 lines
18 KiB
Python
462 lines
18 KiB
Python
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from __future__ import annotations
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from ._dtypes import (
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_floating_dtypes,
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_numeric_dtypes,
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float32,
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float64,
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complex64,
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complex128
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)
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from ._manipulation_functions import reshape
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from ._array_object import Array
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from ..core.numeric import normalize_axis_tuple
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from typing import TYPE_CHECKING
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if TYPE_CHECKING:
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from ._typing import Literal, Optional, Sequence, Tuple, Union, Dtype
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from typing import NamedTuple
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import numpy.linalg
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import numpy as np
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class EighResult(NamedTuple):
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eigenvalues: Array
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eigenvectors: Array
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class QRResult(NamedTuple):
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Q: Array
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R: Array
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class SlogdetResult(NamedTuple):
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sign: Array
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logabsdet: Array
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class SVDResult(NamedTuple):
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U: Array
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S: Array
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Vh: Array
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# Note: the inclusion of the upper keyword is different from
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# np.linalg.cholesky, which does not have it.
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def cholesky(x: Array, /, *, upper: bool = False) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.cholesky.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in cholesky')
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L = np.linalg.cholesky(x._array)
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if upper:
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return Array._new(L).mT
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return Array._new(L)
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# Note: cross is the numpy top-level namespace, not np.linalg
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def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`.
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See its docstring for more information.
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"""
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if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
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raise TypeError('Only numeric dtypes are allowed in cross')
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# Note: this is different from np.cross(), which broadcasts
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if x1.shape != x2.shape:
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raise ValueError('x1 and x2 must have the same shape')
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if x1.ndim == 0:
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raise ValueError('cross() requires arrays of dimension at least 1')
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# Note: this is different from np.cross(), which allows dimension 2
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if x1.shape[axis] != 3:
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raise ValueError('cross() dimension must equal 3')
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return Array._new(np.cross(x1._array, x2._array, axis=axis))
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def det(x: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.det.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in det')
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return Array._new(np.linalg.det(x._array))
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# Note: diagonal is the numpy top-level namespace, not np.linalg
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def diagonal(x: Array, /, *, offset: int = 0) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`.
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See its docstring for more information.
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"""
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# Note: diagonal always operates on the last two axes, whereas np.diagonal
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# operates on the first two axes by default
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return Array._new(np.diagonal(x._array, offset=offset, axis1=-2, axis2=-1))
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def eigh(x: Array, /) -> EighResult:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.eigh.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in eigh')
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# Note: the return type here is a namedtuple, which is different from
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# np.eigh, which only returns a tuple.
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return EighResult(*map(Array._new, np.linalg.eigh(x._array)))
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def eigvalsh(x: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.eigvalsh.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in eigvalsh')
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return Array._new(np.linalg.eigvalsh(x._array))
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def inv(x: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.inv.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in inv')
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return Array._new(np.linalg.inv(x._array))
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# Note: matmul is the numpy top-level namespace but not in np.linalg
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def matmul(x1: Array, x2: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`.
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See its docstring for more information.
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"""
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# Note: the restriction to numeric dtypes only is different from
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# np.matmul.
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if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
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raise TypeError('Only numeric dtypes are allowed in matmul')
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return Array._new(np.matmul(x1._array, x2._array))
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# Note: the name here is different from norm(). The array API norm is split
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# into matrix_norm and vector_norm().
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# The type for ord should be Optional[Union[int, float, Literal[np.inf,
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# -np.inf, 'fro', 'nuc']]], but Literal does not support floating-point
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# literals.
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def matrix_norm(x: Array, /, *, keepdims: bool = False, ord: Optional[Union[int, float, Literal['fro', 'nuc']]] = 'fro') -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.norm.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in matrix_norm')
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return Array._new(np.linalg.norm(x._array, axis=(-2, -1), keepdims=keepdims, ord=ord))
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def matrix_power(x: Array, n: int, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.matrix_power.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed for the first argument of matrix_power')
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# np.matrix_power already checks if n is an integer
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return Array._new(np.linalg.matrix_power(x._array, n))
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# Note: the keyword argument name rtol is different from np.linalg.matrix_rank
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def matrix_rank(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`.
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See its docstring for more information.
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"""
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# Note: this is different from np.linalg.matrix_rank, which supports 1
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# dimensional arrays.
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if x.ndim < 2:
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raise np.linalg.LinAlgError("1-dimensional array given. Array must be at least two-dimensional")
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S = np.linalg.svd(x._array, compute_uv=False)
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if rtol is None:
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tol = S.max(axis=-1, keepdims=True) * max(x.shape[-2:]) * np.finfo(S.dtype).eps
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else:
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if isinstance(rtol, Array):
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rtol = rtol._array
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# Note: this is different from np.linalg.matrix_rank, which does not multiply
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# the tolerance by the largest singular value.
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tol = S.max(axis=-1, keepdims=True)*np.asarray(rtol)[..., np.newaxis]
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return Array._new(np.count_nonzero(S > tol, axis=-1))
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# Note: this function is new in the array API spec. Unlike transpose, it only
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# transposes the last two axes.
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def matrix_transpose(x: Array, /) -> Array:
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if x.ndim < 2:
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raise ValueError("x must be at least 2-dimensional for matrix_transpose")
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return Array._new(np.swapaxes(x._array, -1, -2))
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# Note: outer is the numpy top-level namespace, not np.linalg
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def outer(x1: Array, x2: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`.
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See its docstring for more information.
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"""
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# Note: the restriction to numeric dtypes only is different from
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# np.outer.
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if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
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raise TypeError('Only numeric dtypes are allowed in outer')
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# Note: the restriction to only 1-dim arrays is different from np.outer
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if x1.ndim != 1 or x2.ndim != 1:
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raise ValueError('The input arrays to outer must be 1-dimensional')
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return Array._new(np.outer(x1._array, x2._array))
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# Note: the keyword argument name rtol is different from np.linalg.pinv
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def pinv(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.pinv.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in pinv')
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# Note: this is different from np.linalg.pinv, which does not multiply the
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# default tolerance by max(M, N).
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if rtol is None:
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rtol = max(x.shape[-2:]) * np.finfo(x.dtype).eps
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return Array._new(np.linalg.pinv(x._array, rcond=rtol))
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def qr(x: Array, /, *, mode: Literal['reduced', 'complete'] = 'reduced') -> QRResult:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.qr.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in qr')
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# Note: the return type here is a namedtuple, which is different from
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# np.linalg.qr, which only returns a tuple.
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return QRResult(*map(Array._new, np.linalg.qr(x._array, mode=mode)))
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def slogdet(x: Array, /) -> SlogdetResult:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.slogdet.
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if x.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in slogdet')
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# Note: the return type here is a namedtuple, which is different from
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# np.linalg.slogdet, which only returns a tuple.
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return SlogdetResult(*map(Array._new, np.linalg.slogdet(x._array)))
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# Note: unlike np.linalg.solve, the array API solve() only accepts x2 as a
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# vector when it is exactly 1-dimensional. All other cases treat x2 as a stack
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# of matrices. The np.linalg.solve behavior of allowing stacks of both
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# matrices and vectors is ambiguous c.f.
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# https://github.com/numpy/numpy/issues/15349 and
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# https://github.com/data-apis/array-api/issues/285.
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# To workaround this, the below is the code from np.linalg.solve except
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# only calling solve1 in the exactly 1D case.
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def _solve(a, b):
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from ..linalg.linalg import (_makearray, _assert_stacked_2d,
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_assert_stacked_square, _commonType,
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isComplexType, get_linalg_error_extobj,
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_raise_linalgerror_singular)
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from ..linalg import _umath_linalg
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a, _ = _makearray(a)
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_assert_stacked_2d(a)
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_assert_stacked_square(a)
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b, wrap = _makearray(b)
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t, result_t = _commonType(a, b)
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# This part is different from np.linalg.solve
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if b.ndim == 1:
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gufunc = _umath_linalg.solve1
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else:
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gufunc = _umath_linalg.solve
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# This does nothing currently but is left in because it will be relevant
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# when complex dtype support is added to the spec in 2022.
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signature = 'DD->D' if isComplexType(t) else 'dd->d'
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extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
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r = gufunc(a, b, signature=signature, extobj=extobj)
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return wrap(r.astype(result_t, copy=False))
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def solve(x1: Array, x2: Array, /) -> Array:
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"""
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Array API compatible wrapper for :py:func:`np.linalg.solve <numpy.linalg.solve>`.
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See its docstring for more information.
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"""
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# Note: the restriction to floating-point dtypes only is different from
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# np.linalg.solve.
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if x1.dtype not in _floating_dtypes or x2.dtype not in _floating_dtypes:
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raise TypeError('Only floating-point dtypes are allowed in solve')
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return Array._new(_solve(x1._array, x2._array))
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def svd(x: Array, /, *, full_matrices: bool = True) -> SVDResult:
|
||
|
|
"""
|
||
|
|
Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`.
|
||
|
|
|
||
|
|
See its docstring for more information.
|
||
|
|
"""
|
||
|
|
# Note: the restriction to floating-point dtypes only is different from
|
||
|
|
# np.linalg.svd.
|
||
|
|
if x.dtype not in _floating_dtypes:
|
||
|
|
raise TypeError('Only floating-point dtypes are allowed in svd')
|
||
|
|
|
||
|
|
# Note: the return type here is a namedtuple, which is different from
|
||
|
|
# np.svd, which only returns a tuple.
|
||
|
|
return SVDResult(*map(Array._new, np.linalg.svd(x._array, full_matrices=full_matrices)))
|
||
|
|
|
||
|
|
# Note: svdvals is not in NumPy (but it is in SciPy). It is equivalent to
|
||
|
|
# np.linalg.svd(compute_uv=False).
|
||
|
|
def svdvals(x: Array, /) -> Union[Array, Tuple[Array, ...]]:
|
||
|
|
if x.dtype not in _floating_dtypes:
|
||
|
|
raise TypeError('Only floating-point dtypes are allowed in svdvals')
|
||
|
|
return Array._new(np.linalg.svd(x._array, compute_uv=False))
|
||
|
|
|
||
|
|
# Note: tensordot is the numpy top-level namespace but not in np.linalg
|
||
|
|
|
||
|
|
# Note: axes must be a tuple, unlike np.tensordot where it can be an array or array-like.
|
||
|
|
def tensordot(x1: Array, x2: Array, /, *, axes: Union[int, Tuple[Sequence[int], Sequence[int]]] = 2) -> Array:
|
||
|
|
# Note: the restriction to numeric dtypes only is different from
|
||
|
|
# np.tensordot.
|
||
|
|
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
|
||
|
|
raise TypeError('Only numeric dtypes are allowed in tensordot')
|
||
|
|
|
||
|
|
return Array._new(np.tensordot(x1._array, x2._array, axes=axes))
|
||
|
|
|
||
|
|
# Note: trace is the numpy top-level namespace, not np.linalg
|
||
|
|
def trace(x: Array, /, *, offset: int = 0, dtype: Optional[Dtype] = None) -> Array:
|
||
|
|
"""
|
||
|
|
Array API compatible wrapper for :py:func:`np.trace <numpy.trace>`.
|
||
|
|
|
||
|
|
See its docstring for more information.
|
||
|
|
"""
|
||
|
|
if x.dtype not in _numeric_dtypes:
|
||
|
|
raise TypeError('Only numeric dtypes are allowed in trace')
|
||
|
|
|
||
|
|
# Note: trace() works the same as sum() and prod() (see
|
||
|
|
# _statistical_functions.py)
|
||
|
|
if dtype is None:
|
||
|
|
if x.dtype == float32:
|
||
|
|
dtype = float64
|
||
|
|
elif x.dtype == complex64:
|
||
|
|
dtype = complex128
|
||
|
|
# Note: trace always operates on the last two axes, whereas np.trace
|
||
|
|
# operates on the first two axes by default
|
||
|
|
return Array._new(np.asarray(np.trace(x._array, offset=offset, axis1=-2, axis2=-1, dtype=dtype)))
|
||
|
|
|
||
|
|
# Note: vecdot is not in NumPy
|
||
|
|
def vecdot(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
|
||
|
|
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
|
||
|
|
raise TypeError('Only numeric dtypes are allowed in vecdot')
|
||
|
|
ndim = max(x1.ndim, x2.ndim)
|
||
|
|
x1_shape = (1,)*(ndim - x1.ndim) + tuple(x1.shape)
|
||
|
|
x2_shape = (1,)*(ndim - x2.ndim) + tuple(x2.shape)
|
||
|
|
if x1_shape[axis] != x2_shape[axis]:
|
||
|
|
raise ValueError("x1 and x2 must have the same size along the given axis")
|
||
|
|
|
||
|
|
x1_, x2_ = np.broadcast_arrays(x1._array, x2._array)
|
||
|
|
x1_ = np.moveaxis(x1_, axis, -1)
|
||
|
|
x2_ = np.moveaxis(x2_, axis, -1)
|
||
|
|
|
||
|
|
res = x1_[..., None, :] @ x2_[..., None]
|
||
|
|
return Array._new(res[..., 0, 0])
|
||
|
|
|
||
|
|
|
||
|
|
# Note: the name here is different from norm(). The array API norm is split
|
||
|
|
# into matrix_norm and vector_norm().
|
||
|
|
|
||
|
|
# The type for ord should be Optional[Union[int, float, Literal[np.inf,
|
||
|
|
# -np.inf]]] but Literal does not support floating-point literals.
|
||
|
|
def vector_norm(x: Array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = None, keepdims: bool = False, ord: Optional[Union[int, float]] = 2) -> Array:
|
||
|
|
"""
|
||
|
|
Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.
|
||
|
|
|
||
|
|
See its docstring for more information.
|
||
|
|
"""
|
||
|
|
# Note: the restriction to floating-point dtypes only is different from
|
||
|
|
# np.linalg.norm.
|
||
|
|
if x.dtype not in _floating_dtypes:
|
||
|
|
raise TypeError('Only floating-point dtypes are allowed in norm')
|
||
|
|
|
||
|
|
# np.linalg.norm tries to do a matrix norm whenever axis is a 2-tuple or
|
||
|
|
# when axis=None and the input is 2-D, so to force a vector norm, we make
|
||
|
|
# it so the input is 1-D (for axis=None), or reshape so that norm is done
|
||
|
|
# on a single dimension.
|
||
|
|
a = x._array
|
||
|
|
if axis is None:
|
||
|
|
# Note: np.linalg.norm() doesn't handle 0-D arrays
|
||
|
|
a = a.ravel()
|
||
|
|
_axis = 0
|
||
|
|
elif isinstance(axis, tuple):
|
||
|
|
# Note: The axis argument supports any number of axes, whereas
|
||
|
|
# np.linalg.norm() only supports a single axis for vector norm.
|
||
|
|
normalized_axis = normalize_axis_tuple(axis, x.ndim)
|
||
|
|
rest = tuple(i for i in range(a.ndim) if i not in normalized_axis)
|
||
|
|
newshape = axis + rest
|
||
|
|
a = np.transpose(a, newshape).reshape(
|
||
|
|
(np.prod([a.shape[i] for i in axis], dtype=int), *[a.shape[i] for i in rest]))
|
||
|
|
_axis = 0
|
||
|
|
else:
|
||
|
|
_axis = axis
|
||
|
|
|
||
|
|
res = Array._new(np.linalg.norm(a, axis=_axis, ord=ord))
|
||
|
|
|
||
|
|
if keepdims:
|
||
|
|
# We can't reuse np.linalg.norm(keepdims) because of the reshape hacks
|
||
|
|
# above to avoid matrix norm logic.
|
||
|
|
shape = list(x.shape)
|
||
|
|
_axis = normalize_axis_tuple(range(x.ndim) if axis is None else axis, x.ndim)
|
||
|
|
for i in _axis:
|
||
|
|
shape[i] = 1
|
||
|
|
res = reshape(res, tuple(shape))
|
||
|
|
|
||
|
|
return res
|
||
|
|
|
||
|
|
__all__ = ['cholesky', 'cross', 'det', 'diagonal', 'eigh', 'eigvalsh', 'inv', 'matmul', 'matrix_norm', 'matrix_power', 'matrix_rank', 'matrix_transpose', 'outer', 'pinv', 'qr', 'slogdet', 'solve', 'svd', 'svdvals', 'tensordot', 'trace', 'vecdot', 'vector_norm']
|