torch.linalg.norm(input, ord=None, dim=None, keepdim=False, *, out=None, dtype=None) → Tensor  
Returns the matrix norm or vector norm of a given tensor. This function can calculate one of eight different types of matrix norms, or one of an infinite number of vector norms, depending on both the number of reduction dimensions and the value of the ord parameter.  Parameters 
 
input (Tensor) – The input tensor. If dim is None, x must be 1-D or 2-D, unless ord is None. If both dim and ord are None, the 2-norm of the input flattened to 1-D will be returned. Its data type must be either a floating point or complex type. For complex inputs, the norm is calculated on of the absolute values 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). 
ord (int, float, inf, -inf, 'fro', 'nuc', optional) – 
The order of norm. inf refers to float('inf'), numpy’s inf object, or any equivalent object. The following norms can be calculated:   
ord norm for matrices norm for vectors   
None Frobenius norm 2-norm  
’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 2-norm (largest sing. value) as below  
-2 smallest singular value as below  
other – not supported – sum(abs(x)**ord)**(1./ord)   Default: None  
dim (int, 2-tuple of python:ints, 2-list of python:ints, optional) – If dim is an int, vector norm will be calculated over the specified dimension. If dim is a 2-tuple of ints, matrix norm will be calculated over the specified dimensions. If dim is None, matrix norm will be calculated when the input tensor has two dimensions, and vector norm will be calculated when the input tensor has one dimension. Default: None
 
keepdim (bool, optional) – If set to True, the reduced dimensions are retained in the result as dimensions with size one. Default: False
   Keyword Arguments 
 
out (Tensor, optional) – The output tensor. Ignored if None. Default: None
 
dtype (torch.dtype, optional) – If specified, the input tensor is cast to dtype before performing the operation, and the returned tensor’s type will be dtype. If this argument is used in conjunction with the out argument, the output tensor’s type must match this argument or a RuntimeError will be raised. Default: None
    Examples: >>> import torch
>>> from torch import linalg as LA
>>> a = torch.arange(9, dtype=torch.float) - 4
>>> a
tensor([-4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])
>>> b = a.reshape((3, 3))
>>> b
tensor([[-4., -3., -2.],
        [-1.,  0.,  1.],
        [ 2.,  3.,  4.]])

>>> LA.norm(a)
tensor(7.7460)
>>> LA.norm(b)
tensor(7.7460)
>>> LA.norm(b, 'fro')
tensor(7.7460)
>>> LA.norm(a, float('inf'))
tensor(4.)
>>> LA.norm(b, float('inf'))
tensor(9.)
>>> LA.norm(a, -float('inf'))
tensor(0.)
>>> LA.norm(b, -float('inf'))
tensor(2.)

>>> LA.norm(a, 1)
tensor(20.)
>>> LA.norm(b, 1)
tensor(7.)
>>> LA.norm(a, -1)
tensor(0.)
>>> LA.norm(b, -1)
tensor(6.)
>>> LA.norm(a, 2)
tensor(7.7460)
>>> LA.norm(b, 2)
tensor(7.3485)

>>> LA.norm(a, -2)
tensor(0.)
>>> LA.norm(b.double(), -2)
tensor(1.8570e-16, dtype=torch.float64)
>>> LA.norm(a, 3)
tensor(5.8480)
>>> LA.norm(a, -3)
tensor(0.)
 Using the dim argument to compute vector norms: >>> c = torch.tensor([[1., 2., 3.],
...                   [-1, 1, 4]])
>>> LA.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000])
>>> LA.norm(c, dim=1)
tensor([3.7417, 4.2426])
>>> LA.norm(c, ord=1, dim=1)
tensor([6., 6.])
 Using the dim argument to compute matrix norms: >>> m = torch.arange(8, dtype=torch.float).reshape(2, 2, 2)
>>> LA.norm(m, dim=(1,2))
tensor([ 3.7417, 11.2250])
>>> LA.norm(m[0, :, :]), LA.norm(m[1, :, :])
(tensor(3.7417), tensor(11.2250))