PyTorch – How to compute the norm of a vector or matrix?

To compute the norm of a vector or a matrix, we could apply torch.linalg.norm() method. It returns a new tensor with computed norm. It accepts a vector, matrix, a batch of matrices and also batches of matrices.

A vector is a 1D torch Tensor where a matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types. We can compute the norm of the matrix or batch/es of matrices along the different dimensions. For example, we could compute the norm of a matrix along dimension 0 or along dimension1.

Syntax

torch.linalg.norm(A)

A is a vector, matrix or batch/s of matrices. A vector is a 1D torch tensor and a matrix is a 2D torch tensor.

Steps

We could use the following steps to compute the norm of a vector or matrix −

• Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.

import torch

• Define a vector or matrix. Here, we define matrix (2D tensor of size 3×3) of random numbers.

A = torch.randn(3,3)

• Compute the norm of the vector or matrix using torch.linalg.norm(A). A is a vector or matrix or batch/s of matrices. Optionally assign this value to a new variable.

norm_A = torch.linalg.norm(A)

• Print the computed norm

print("Norm:", norm_A)

Example 1

In this program, we compute the norm of a vector.

# import required library
import torch

# create a vector/ 1D tensor
v = torch.randn(3)

# print the above created vector
print("Vector:
", v)

# computet the norm of the vector
n = torch.linalg.norm(v)
print("Norm:
", n)

Output

Vector:
   tensor([-0.3792, -1.1512, 0.2590])
Norm:
   tensor(1.2394)

Example 2

In this program, we compute the norm of a matrix.

# import required library
import torch

# create a 3x4 matrix
mat = torch.randn(3,3)

# print the above created matrix
print("Matrix:
", mat)

# compute the norm of the matrix
nor = torch.linalg.norm(mat)

# print the computed determinants
print("Norm:
", nor)

Output

Matrix:
   tensor([[ 0.2376, 0.5451, -0.2423],
      [-0.2320, -0.2493, 1.3164],
      [-0.0265, -0.9278, -0.8413]])
Norm:
   tensor(1.9572)

Example 3

In this program, we compute the norm of a matrix along different dimensions.

# Python program to compute the norm of a matrix
# import torch library
import torch

# create a 3x3 matrix
mat = torch.tensor([[1.,2.,3.],[4.,5.,6.]])

# print the above created matrix
print("Matrix:
", mat)

# compute the norm of the matrix in dim 0
nor0 = torch.linalg.norm(mat, dim = 0)

# print the computed norm
print("Norm in 0 dim:
", nor0)

# compute the norm of the matrix in dim 1
nor1 = torch.linalg.norm(mat, dim = 1)

# print the computed norm
print("Norm in 1 dim:
", nor1)

Output

Matrix:
   tensor([[1., 2., 3.],
   [4., 5., 6.]])
Norm in 0 dim:
   tensor([4.1231, 5.3852, 6.7082])
Norm in 1 dim:
   tensor([3.7417, 8.7750])

Example 4

In this program, we compute the norm of a complex matrix.

# import required library
import torch

# create a 3x4 matrix
mat = torch.randn(3,4, dtype = torch.cfloat)

# print the above created matrix
print("Matrix:
", mat)

# compute the norm of the matrix
nor = torch.linalg.norm(mat)

# print the computed norm
print("Norm:
", nor)

# compute the norm of the matrix in dim 0
nor0 = torch.linalg.norm(mat, dim = 0)

# print the computed norm
print("Norm in 0 dim:
", nor0)

# compute the norm of the matrix in dim 1
nor1 = torch.linalg.norm(mat, dim = 1)

# print the computed norm
print("Norm in 1 dim:
", nor1)

Output

Matrix:
   tensor([[-0.2689+0.1693j, -1.5259-0.5821j, -0.2348-0.0016j, -0.9439+0.0868j],
      [-1.1065-0.5374j, 0.4492-0.0664j, 0.1469+1.0838j, -0.1163+0.2847j],
      [ 0.7928-1.0270j, 0.9414+1.0902j, 0.5717+0.9329j, -0.1108+0.2115j]])
Norm:
   tensor(3.4270)
Norm in 0 dim:
   tensor([1.8159, 2.2244, 1.5648, 1.0247])
Norm in 1 dim:
   tensor([1.9292, 1.7350, 2.2388])