oneflow.linalg.norm

oneflow.linalg.norm(input, ord=None, dim=None, keepdim=False, *, dtype=None, out=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.

Parameters

  • input (Tensor) – The input tensor. If dim is None, input must be 1-D or 2-D, unless ord is None. If both dim and ord are None, the 2-norm of the input flattened to 1-D will be returned. Its data type must be either a floating point or complex type. For complex inputs, the norm is calculated on of the absolute values of each element. If the input is complex and neither dtype nor out is specified, the result’s data type will be the corresponding floating point type (e.g. float if input is complexfloat).

  • ord (int, inf, -inf, 'fro', 'nuc', optional) –

    order of norm. Default: ‘None’ The following norms can be calculated:

    ord

    norm for matrices

    norm for vectors

    None

    Frobenius norm

    2-norm

    ’fro’

    Frobenius norm

    – not supported –

    ‘nuc’

    – not supported yet –

    – 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

    – not supported yet –

    as below

    -2

    – not supported yet –

    as below

    other

    – not supported –

    sum(abs(x)^{ord})^{(1 / ord)}

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

  • dim (int, 2-tuple of ints, 2-list of ints, optional) – If dim is an int, vector norm will be calculated over the specified dimension. If dim is a 2-tuple of ints, matrix norm will be calculated over the specified dimensions. If 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

  • out (Tensor, optional) – The output tensor.

For example:

>>> import oneflow as flow
>>> from oneflow import linalg as LA
>>> import numpy as np
>>> a = flow.tensor(np.arange(9, dtype=np.float32) - 4)
>>> a
tensor([-4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.], dtype=oneflow.float32)
>>> b = a.reshape(3, 3)
>>> b
tensor([[-4., -3., -2.],
        [-1.,  0.,  1.],
        [ 2.,  3.,  4.]], dtype=oneflow.float32)
>>> LA.norm(a)
tensor(7.7460, dtype=oneflow.float32)
>>> LA.norm(b)
tensor(7.7460, dtype=oneflow.float32)
>>> LA.norm(b, 'fro')
tensor(7.7460, dtype=oneflow.float32)
>>> LA.norm(a, float('inf'))
tensor(4., dtype=oneflow.float32)
>>> LA.norm(b, float('inf'))
tensor(9., dtype=oneflow.float32)
>>> LA.norm(a, -float('inf'))
tensor(0., dtype=oneflow.float32)
>>> LA.norm(b, -float('inf'))
tensor(2., dtype=oneflow.float32)
>>> LA.norm(a, 1)
tensor(20., dtype=oneflow.float32)
>>> LA.norm(b, 1)
tensor(7., dtype=oneflow.float32)
>>> LA.norm(a, -1)
tensor(0., dtype=oneflow.float32)
>>> LA.norm(b, -1)
tensor(6., dtype=oneflow.float32)
>>> LA.norm(a, 2)
tensor(7.7460, dtype=oneflow.float32)
>>> LA.norm(a, -2)
tensor(0., dtype=oneflow.float32)
>>> LA.norm(a, 3)
tensor(5.8480, dtype=oneflow.float32)
>>> LA.norm(a, -3)
tensor(0., dtype=oneflow.float32)
>>> c = flow.tensor([[1., 2., 3.],
...                   [-1, 1, 4]])
>>> LA.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000], dtype=oneflow.float32)
>>> LA.norm(c, dim=1, keepdim = True)
tensor([[3.7417],
        [4.2426]], dtype=oneflow.float32)
>>> LA.norm(c, ord=1, dim=1)
tensor([6., 6.], dtype=oneflow.float32)