467 lines
18 KiB
Python
467 lines
18 KiB
Python
|
from __future__ import annotations
|
||
|
|
|
||
|
|
from ._dtypes import (
|
||
|
|
_floating_dtypes,
|
||
|
|
_numeric_dtypes,
|
||
|
|
float32,
|
||
|
|
float64,
|
||
|
|
complex64,
|
||
|
|
complex128
|
||
|
|
)
|
||
|
|
from ._manipulation_functions import reshape
|
||
|
|
from ._elementwise_functions import conj
|
||
|
|
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:
|
||
|
|
U = Array._new(L).mT
|
||
|
|
if U.dtype in [complex64, complex128]:
|
||
|
|
U = conj(U)
|
||
|
|
return U
|
||
|
|
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'
|
||
|
|
with np.errstate(call=_raise_linalgerror_singular, invalid='call',
|
||
|
|
over='ignore', divide='ignore', under='ignore'):
|
||
|
|
r = gufunc(a, b, signature=signature)
|
||
|
|
|
||
|
|
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']
|