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