oneflow.linalg.matrix_norm

oneflow.linalg.matrix_norm(input, ord='fro', dim=(- 2, - 1), keepdim=False, *, dtype=None, out=None) → Tensor

Computes a matrix norm.

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’

– not supported yet –

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

– not supported yet –

-2

– not supported yet –

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

Parameters

  • input (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

Returns

A real-valued tensor.

Examples:

>>> import oneflow as flow
>>> from oneflow import linalg as LA
>>> import numpy as np
>>> a = flow.tensor(np.arange(9, dtype=np.float32)).reshape(3,3)
>>> a
tensor([[0., 1., 2.],
        [3., 4., 5.],
        [6., 7., 8.]], dtype=oneflow.float32)
>>> LA.matrix_norm(a)
tensor(14.2829, dtype=oneflow.float32)
>>> LA.matrix_norm(a, ord=-1)
tensor(9., dtype=oneflow.float32)
>>> 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.]]], dtype=oneflow.float32)
>>> LA.matrix_norm(b, dim=(0, 2))
tensor([ 3.1623, 10.0000, 17.2627], dtype=oneflow.float32)