mindspore.ops.norm

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

Returns the matrix norm or vector norm of a given tensor.

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) – Tensor of shape \((*, n)\) or \((*, m, n)\) where * is zero or more batch dimensions.
ord (Union[int, float, inf, -inf, 'fro', 'nuc'], optional) – norm's mode. refer to the table above for behavior. Default: None .
dim (Union[int, Tuple(int)], optional) –
calculate the dimension of vector norm or matrix norm. Default: None .
- When dim is int, it will be calculated by vector norm.
- When dim is a 2-tuple, it will be calculated by matrix norm.
- If dim is None and ord is None, A will be flattened to 1D and the 2-norm of the vector will be calculated.
- If dim is None and ord is not None, A must be 1D or 2D.
keepdim (bool) – whether the output Tensor retains the original dimension. Default: False .

Keyword Arguments

dtype (mindspore.dtype, optional) – When set, A will be converted to the specified type, dtype, before execution, and dtype of returned Tensor will also be dtype. Default: None .

Returns

Tensor, the result of norm calculation on the specified dimension, dim, has the same dtype as A.

Raises

ValueError – If dim is out of range.
TypeError – If dim is neither an int nor a tuple of int.
TypeError – If A is a vector and ord is a str.
ValueError – If A is a matrices and ord is not in valid mode.
ValueError – If A is a matrices and ord is an integer but not in [1, -1, 2, -2].
ValueError – If two elements of dim is same after normalize.
ValueError – If any elements of dim is out of range.

Supported Platforms:: Ascend GPU CPU

Note

Currently, complex numbers are not supported.

Examples

>>> import mindspore as ms
>>> from mindspore import ops
>>> data_range = ops.arange(-13, 13, dtype=ms.float32)
>>> # Exclude 0 from original data for 0 is invalid input when `ord` is negative.
>>> x = data_range[data_range != 0]
>>> y = x.reshape(5, 5)
>>> print(ops.norm(x))
38.327538
>>> print(ops.norm(x, float('inf')))
13.0
>>> print(ops.norm(x, float('-inf')))
1.0
>>> print(ops.norm(x, 0))
25.0
>>> print(ops.norm(x, 1))
169.0
>>> print(ops.norm(x, -1))
0.15915091
>>> print(ops.norm(x, 2))
38.327538
>>> print(ops.norm(x, -2))
0.5647041
>>> print(ops.norm(x, 3))
24.309084
>>> print(ops.norm(x, -3))
0.74708974
>>> print(ops.norm(y))
38.327538
>>> print(ops.norm(y, 'fro'))
38.327538
>>> print(ops.norm(y, 'nuc'))
45.56681
>>> print(ops.norm(y, float('inf')))
55.0
>>> print(ops.norm(y, float('-inf')))
9.0
>>> print(ops.norm(y, 1))
35.0
>>> print(ops.norm(y, -1))
33.0
>>> print(ops.norm(y, 2))
37.57774
>>> print(ops.norm(y, -2))
1.590545e-07
>>> m = ms.Tensor([[1., -1., 2.], [-2., 3., -4.]])
>>> print(ops.norm(m, dim=0))
[2.236068  3.1622777 4.472136 ]
>>> print(ops.norm(m, dim=1))
[2.4494898 5.3851647]
>>> print(ops.norm(m, ord=1, dim=1))
[4. 9.]
>>> print(ops.norm(m, ord=-2, dim=0))
[0.8944272  0.94868326 1.7888544 ]
>>> print(ops.norm(m, ord=2, dim=1))
[2.4494898 5.3851647]
>>> n = ops.arange(27, dtype=ms.float32).reshape(3, 3, 3)
>>> print(ops.norm(n, dim=(1, 2)))
[14.282857 39.76179  66.45299 ]
>>> print(ops.norm(n[0, :, :]), ops.norm(n[1, :, :]), ops.norm(n[2, :, :]))
14.282857 39.76179 66.45299