PyTorch – torch.linalg.cond()

To compute the condition number of a matrix with respect to a matrix norm, we could apply torch.linalg.cond() method. It returns a new tensor with computed condition number. It accepts a matrix, a batch of matrices and also batches of matrices. A matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types

Syntax

torch.linalg.cond(M, p=None)

Parameters

• M – A matrix or batch of matrices.

• p – A type of matrix norm to be used in computation of condition number. Default matrix norm is 2-norm.

It returns a real-valued tensor of condition number.

Steps

We could use the following steps to compute the condition number of the 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 matrix. Here, we define matrix (2D tensor of size 3×4) of random numbers

M = torch.randn(3,4)

• Compute the condition number of a matrix using torch.linalg.cond(A, p = None). A is a matrix or batch/es of matrices. p is a type of matrix norm. Optionally assign this value to a new variable.

Mcond = torch.linalg.cond(M)

• Print the computed tensor with condition number.

print("Norm:", Mcond)

Example 1

The following program demonstrates how to compute the condition number of a matrix with respect to the default matrix norm. The default matrix norm is 2-norm.

# Python program to compute the condition number of a matrix
# import required library
import torch

# define a matrix of size 3x4
M = torch.randn(3,4)
print("Matrix M:
", M)

# compute the condition number of above defined matrix
Mcond = torch.linalg.cond(M)

# print condition number of the matrix
print("Condition Number:
", Mcond)

Output

It will produce the following output −

Matrix M:
   tensor([[-0.3241, 1.6410, 1.5067, -1.4944],
      [-0.5977, -0.4599, 0.6367, 0.1683],
      [ 1.4590, 0.9267, -0.2186, -0.5963]])
Condition Number:
tensor(7.4035)

Example 2

In this program, we compute the condition number with respect to different matrix norms.

import torch

# define a matrix of size 3x3
M = torch.randn(3,3)
print("Matrix:
", M)
print("
Condition Number with different Norms:")
print(torch.linalg.cond(M))
print(torch.linalg.cond(M, p = 'fro'))
print(torch.linalg.cond(M, p = 'nuc'))
print(torch.linalg.cond(M, p = 1))
print(torch.linalg.cond(M, p = -1))
print(torch.linalg.cond(M, p = 2))
print(torch.linalg.cond(M, p = -2))
print(torch.linalg.cond(M, p = float('inf')))
print(torch.linalg.cond(M, p = float('-inf')))

Output

It will produce the following output −

Matrix:
   tensor([[-0.0328, 0.1970, -0.1466],
      [ 0.1721, 0.0765, 1.1714],
      [ 1.1040, 1.7493, 0.8331]])

Condition Number with different Norms:
tensor(21.0871)
tensor(23.1940)
tensor(36.1807)
tensor(27.7410)
tensor(1.4686)
tensor(21.0871)
tensor(0.0474)
tensor(37.5561)
tensor(0.7646)

Shahid Akhtar Khan

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Updated on: 07-Jan-2022

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