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# torch.linalg.matrix_norm¶

torch.linalg.matrix_norm(A, ord='fro', dim=(- 2, - 1), keepdim=False, *, dtype=None, out=None)

Computes a matrix norm.

If A is complex valued, it computes the norm of A.abs()

Support input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices: the norm will be computed over the dimensions specified by the 2-tuple dim and the other dimensions will be treated as batch dimensions. The output will have the same batch dimensions.

ord defines the matrix norm that is computed. The following norms are supported:

ord

matrix norm

‘fro’ (default)

Frobenius norm

‘nuc’

nuclear norm

inf

max(sum(abs(x), dim=1))

-inf

min(sum(abs(x), dim=1))

1

max(sum(abs(x), dim=0))

-1

min(sum(abs(x), dim=0))

2

largest singular value

-2

smallest singular value

where inf refers to float(‘inf’), NumPy’s inf object, or any equivalent object.

Parameters:
• A (Tensor) – tensor with two or more dimensions. By default its shape is interpreted as (*, m, n) where * is zero or more batch dimensions, but this behavior can be controlled using dim.

• ord (int, inf, -inf, 'fro', 'nuc', optional) – order of norm. Default: ‘fro’

• dim (Tuple[int, int], optional) – dimensions over which to compute the norm. Default: (-2, -1)

• keepdim (bool, optional) – If set to True, the reduced dimensions are retained in the result as dimensions with size one. Default: False

Keyword Arguments:
• out (Tensor, optional) – output tensor. Ignored if None. Default: None.

• dtype (torch.dtype, optional) – If specified, the input tensor is cast to dtype before performing the operation, and the returned tensor’s type will be dtype. Default: None

Returns:

A real-valued tensor, even when A is complex.

Examples:

>>> from torch import linalg as LA
>>> A = torch.arange(9, dtype=torch.float).reshape(3, 3)
>>> A
tensor([[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]])
>>> LA.matrix_norm(A)
tensor(14.2829)
>>> LA.matrix_norm(A, ord=-1)
tensor(9.)
>>> B = A.expand(2, -1, -1)
>>> B
tensor([[[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]],

[[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]]])
>>> LA.matrix_norm(B)
tensor([14.2829, 14.2829])
>>> LA.matrix_norm(B, dim=(0, 2))
tensor([ 3.1623, 10.0000, 17.2627])


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