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.

Warning

Non-backward-compatible change after version 2.9.0: ord will be renamed to p, and the default value will change from None to 2.

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 , flatten 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. When set, A will be converted to the specified data type, before calculating. Default None .

Returns

Tensor

Supported Platforms:

Ascend GPU CPU

Note

• Currently, complex numbers are not supported.

• Depending on the input range of values, the Ascend backend calculation results may have precision errors.

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])