# torch.norm¶

torch.norm(input, p='fro', dim=None, keepdim=False, out=None, dtype=None)[source]

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

Warning

torch.norm is deprecated and may be removed in a future PyTorch release. Use torch.linalg.norm() instead, but note that torch.linalg.norm() has a different signature and slightly different behavior that is more consistent with NumPy’s numpy.linalg.norm.

Parameters
• input (Tensor) – The input tensor. Its data type must be either a floating point or complex type. For complex inputs, the norm is calculated using the absolute value 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).

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

the order of norm. Default: 'fro' The following norms can be calculated:

ord

matrix norm

vector norm

’fro’

Frobenius norm

‘nuc’

nuclear norm

Number

sum(abs(x)**ord)**(1./ord)

The vector norm can be calculated across any number of dimensions. The corresponding dimensions of input are flattened into one dimension, and the norm is calculated on the flattened dimension.

Frobenius norm produces the same result as p=2 in all cases except when dim is a list of three or more dims, in which case Frobenius norm throws an error.

Nuclear norm can only be calculated across exactly two dimensions.

• dim (int, tuple of python:ints, list of python:ints, optional) – Specifies which dimension or dimensions of input to calculate the norm across. If dim is None, the norm will be calculated across all dimensions of input. If the norm type indicated by p does not support the specified number of dimensions, an error will occur.

• keepdim (bool, optional) – whether the output tensors have dim retained or not. Ignored if dim = None and out = None. Default: False

• out (Tensor, optional) – the output tensor. Ignored if dim = None and out = None.

• dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to :attr:’dtype’ while performing the operation. Default: None.

Note

Even though p='fro' supports any number of dimensions, the true mathematical definition of Frobenius norm only applies to tensors with exactly two dimensions. torch.linalg.norm() with ord='fro' aligns with the mathematical definition, since it can only be applied across exactly two dimensions.

Example:

>>> import torch
>>> a = torch.arange(9, dtype= torch.float) - 4
>>> b = a.reshape((3, 3))
>>> torch.norm(a)
tensor(7.7460)
>>> torch.norm(b)
tensor(7.7460)
>>> torch.norm(a, float('inf'))
tensor(4.)
>>> torch.norm(b, float('inf'))
tensor(4.)
>>> c = torch.tensor([[ 1, 2, 3],[-1, 1, 4]] , dtype= torch.float)
>>> torch.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000])
>>> torch.norm(c, dim=1)
tensor([3.7417, 4.2426])
>>> torch.norm(c, p=1, dim=1)
tensor([6., 6.])
>>> d = torch.arange(8, dtype= torch.float).reshape(2,2,2)
>>> torch.norm(d, dim=(1,2))
tensor([ 3.7417, 11.2250])
>>> torch.norm(d[0, :, :]), torch.norm(d[1, :, :])
(tensor(3.7417), tensor(11.2250))