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# 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.

Parameters
• input (Tensor) – the input tensor

• 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

None

Frobenius norm

2-norm

’fro’

Frobenius norm

‘nuc’

nuclear norm

Other

as vec norm when dim is None

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

• dim (int, 2-tuple of python:ints, 2-list of python:ints, optional) – If it is an int, vector norm will be calculated, if it is 2-tuple of ints, matrix norm will be calculated. If the value is None, matrix norm will be calculated when the input tensor only has two dimensions, vector norm will be calculated when the input tensor only has one dimension. If the input tensor has more than two dimensions, the vector norm will be applied to last dimension.

• 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.

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)) ## Docs

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