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import sys
import torch
from torch._C import _add_docstr, _linalg # type: ignore
Tensor = torch.Tensor
# Note: This not only adds doc strings for functions in the linalg namespace, but
# also connects the torch.linalg Python namespace to the torch._C._linalg builtins.
det = _add_docstr(_linalg.linalg_det, r"""
linalg.det(input) -> Tensor
Alias of :func:`torch.det`.
""")
norm = _add_docstr(_linalg.linalg_norm, r"""
linalg.norm(input, ord=None, dim=None, keepdim=False, *, out=None, dtype=None) -> Tensor
Returns the matrix norm or vector norm of a given tensor.
This function can calculate one of eight different types of matrix norms, or one
of an infinite number of vector norms, depending on both the number of reduction
dimensions and the value of the `ord` parameter.
Args:
input (Tensor): The input tensor. If dim is None, x must be 1-D or 2-D, unless :attr:`ord`
is None. If both :attr:`dim` and :attr:`ord` are None, the 2-norm of the input flattened to 1-D
will be returned.
ord (int, float, inf, -inf, 'fro', 'nuc', optional): The order of norm.
inf refers to :attr:`float('inf')`, numpy's :attr:`inf` object, or any equivalent object.
The following norms can be calculated:
===== ============================ ==========================
ord norm for matrices norm for vectors
===== ============================ ==========================
None Frobenius norm 2-norm
'fro' Frobenius norm -- not supported --
'nuc' nuclear norm -- not supported --
inf max(sum(abs(x), dim=1)) max(abs(x))
-inf min(sum(abs(x), dim=1)) min(abs(x))
0 -- not supported -- sum(x != 0)
1 max(sum(abs(x), dim=0)) as below
-1 min(sum(abs(x), dim=0)) as below
2 2-norm (largest sing. value) as below
-2 smallest singular value as below
other -- not supported -- sum(abs(x)**ord)**(1./ord)
===== ============================ ==========================
Default: ``None``
dim (int, 2-tuple of ints, 2-list of ints, optional): If :attr:`dim` is an int,
vector norm will be calculated over the specified dimension. If :attr:`dim`
is a 2-tuple of ints, matrix norm will be calculated over the specified
dimensions. If :attr:`dim` is None, matrix norm will be calculated
when the input tensor has two dimensions, and vector norm will be
calculated when the input tensor has one dimension. Default: ``None``
keepdim (bool, optional): If set to True, the reduced dimensions are retained
in the result as dimensions with size one. Default: ``False``
Keyword args:
out (Tensor, optional): The output tensor. Ignored if ``None``. Default: ``None``
dtype (:class:`torch.dtype`, optional): If specified, the input tensor is cast to
:attr:`dtype` before performing the operation, and the returned tensor's type
will be :attr:`dtype`. If this argument is used in conjunction with the
:attr:`out` argument, the output tensor's type must match this argument or a
RuntimeError will be raised. This argument is not currently supported for
:attr:`ord='nuc'` or :attr:`ord='fro'`. Default: ``None``
Examples::
>>> import torch
>>> from torch import linalg as LA
>>> a = torch.arange(9, dtype=torch.float) - 4
>>> a
tensor([-4., -3., -2., -1., 0., 1., 2., 3., 4.])
>>> b = a.reshape((3, 3))
>>> b
tensor([[-4., -3., -2.],
[-1., 0., 1.],
[ 2., 3., 4.]])
>>> LA.norm(a)
tensor(7.7460)
>>> LA.norm(b)
tensor(7.7460)
>>> LA.norm(b, 'fro')
tensor(7.7460)
>>> LA.norm(a, float('inf'))
tensor(4.)
>>> LA.norm(b, float('inf'))
tensor(9.)
>>> LA.norm(a, -float('inf'))
tensor(0.)
>>> LA.norm(b, -float('inf'))
tensor(2.)
>>> LA.norm(a, 1)
tensor(20.)
>>> LA.norm(b, 1)
tensor(7.)
>>> LA.norm(a, -1)
tensor(0.)
>>> LA.norm(b, -1)
tensor(6.)
>>> LA.norm(a, 2)
tensor(7.7460)
>>> LA.norm(b, 2)
tensor(7.3485)
>>> LA.norm(a, -2)
tensor(0.)
>>> LA.norm(b.double(), -2)
tensor(1.8570e-16, dtype=torch.float64)
>>> LA.norm(a, 3)
tensor(5.8480)
>>> LA.norm(a, -3)
tensor(0.)
Using the :attr:`dim` argument to compute vector norms::
>>> c = torch.tensor([[1., 2., 3.],
... [-1, 1, 4]])
>>> LA.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000])
>>> LA.norm(c, dim=1)
tensor([3.7417, 4.2426])
>>> LA.norm(c, ord=1, dim=1)
tensor([6., 6.])
Using the :attr:`dim` argument to compute matrix norms::
>>> m = torch.arange(8, dtype=torch.float).reshape(2, 2, 2)
>>> LA.norm(m, dim=(1,2))
tensor([ 3.7417, 11.2250])
>>> LA.norm(m[0, :, :]), LA.norm(m[1, :, :])
(tensor(3.7417), tensor(11.2250))
""")
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