oneflow.linalg¶

OneFlow linear algebra operations.¶

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)

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)

oneflow.linalg.vector_norm(input, ord=2, dim=None, keepdim=False, *, dtype=None, out=None) → Tensor¶

Computes a vector norm.

Supports input of float, double dtypes.

This function does not necessarily treat multidimensonal attr:input as a batch of vectors, instead:

If dim= None, input will be flattened before the norm is computed.
If dim is an int or a tuple, the norm will be computed over these dimensions and the other dimensions will be treated as batch dimensions.

This behavior is for consistency with flow.linalg.norm().

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

`ord`	vector norm
2 (default)	2-norm (see below)
inf	max(abs(x))
-inf	min(abs(x))
0	sum(x != 0)
other int or float	sum(abs(x)^{ord})^{(1 / ord)}

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

Parameters

input (Tensor) – tensor, flattened by default, but this behavior can be controlled using dim.
ord (int, float, inf, -inf, 'fro', 'nuc', optional) – order of norm. Default: 2
dim (int, Tuple[int], optional) – dimensions over which to compute the norm. See above for the behavior when dim= None. Default: None
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) - 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.vector_norm(a, ord=3.5)
tensor(5.4345, dtype=oneflow.float32)
>>> LA.vector_norm(b, ord=3.5)
tensor(5.4345, dtype=oneflow.float32)