mindspore.ops.norm

mindspore.ops.norm(A, ord=None, dim=None, keepdim=False, *, dtype=None)

Compute the matrix norm or vector norm of the tensor along a specified dimension.

ord is the calculation mode of norm. The following norm modes are supported.

ord	norm for matrices	norm for vectors
None (default)	Frobenius norm	2-norm (see below)
'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	largest singular value	as below
-2	smallest singular value	as below
other int or float	– not supported –	$sum(abs(x{)}^{ord}{)}^{(1/ord)}$

Parameters

• A (Tensor) – The input tensor.

• ord (Union[int, float, inf, -inf, 'fro', 'nuc'], optional) – Specify the kind of norm to take. Default None .

• dim (Union[int, Tuple(int)], optional) –

  Specify the dimension for computation. Default None .

  • If dim is int, calculate the vector norm.

  • if dim is a 2-tuple, calculate the matrix norm.

  • If dim is None and ord is None , flattened A to 1D and calculate 2-norm of the vector.

  • If dim is None and ord is not None, A must be 1D or 2D.

• keepdim (bool) – Whether the output tensor has dim retained. Default False .

Keyword Arguments

dtype (mindspore.dtype, optional) – The data type returned. The data type returned. When set, A will be converted to the specified data type, before calculaing. Default None .

Returns

Tensor

Supported Platforms:

Ascend GPU CPU

Note

Currently, complex numbers are not supported.

Examples

>>> import mindspore
>>> # Vector norms:
>>> A = mindspore.tensor([3., 4., 12.])
>>> mindspore.ops.norm(A)
Tensor(shape=[], dtype=Float32, value= 13)
>>> mindspore.ops.norm(A, ord=1)
Tensor(shape=[], dtype=Float32, value= 19)
>>> mindspore.ops.norm(A, ord=0)
Tensor(shape=[], dtype=Float32, value= 3)
>>>
>>> # Matrix norms:
>>> A = mindspore.tensor([[1., 2., 3.],
...                       [4., 5., 7.]])
>>> mindspore.ops.norm(A)  # Frobenius norm
Tensor(shape=[], dtype=Float32, value= 10.198)
>>> mindspore.ops.norm(A, ord='nuc')  # nuclear norm
Tensor(shape=[], dtype=Float32, value= 10.7625)
>>> mindspore.ops.norm(A, ord=1)  # 1-norm
Tensor(shape=[], dtype=Float32, value= 10)
>>>
>>> # Batched vector norm:
>>> mindspore.ops.norm(A, dim=1)
Tensor(shape=[2], dtype=Float32, value= [ 3.74165726e+00,  9.48683262e+00])