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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])
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