Python PyTorch – torch.linalg.cond() Function

In this article, we are going to discuss how to compute the condition number of a matrix in PyTorch. we can get the condition number of a matrix by using torch.linalg.cond() method. 

torch.linalg.cond() method

This method is used to compute the condition number of a matrix with respect to a matrix norm. This method accepts a matrix and batch of matrices as input. It will return a tensor with a computed condition number. It supports input of double, float, cfloat, and cdouble data types. before moving further let’s see the syntax of this method.

Syntax: torch.linalg.cond(M, P=None)

Parameters:

• M (Tensor): It’s a matrix or a batch of matrices.
• P (int, inf, -inf, ‘fro’, ‘nuc’, optional): It’s defines the matrix norm that is computed. The default value of P 2-norm.

Returns: It will return a tensor with a computed condition number.

Example 1

In this example, we defined a tensor using torch.tensor, and we will compute the condition number of a matrix with the help of torch.linalg.cond method.

Python3

# import the required library
import torch

# define a tensor (matrix)
M = torch.tensor([[-0.1345, -0.7437, 1.2377],
                  [0.9337, 1.6473, 0.4346],
                  [-1.6345, 0.9344, -0.2456]])

# display input tensor
print("\n Input Matrix M: \n", M)

# compute the condition number
Output = torch.linalg.cond(M)

# Display result
print("\n Condition Number: ", Output)

Output:

Example 2

In this example, we will compute the condition number of a matrix for different values of P with the help of torch.linalg.cond method.

Python3

# import the required library
import torch

# define a tensor (matrix)
M = torch.tensor([[-0.1345, -0.7437, 1.2377],
                  [0.9337, 1.6473, 0.4346],
                  [-1.6345, 0.9344, -0.2456]])

# display input tensor
print("\n Input Matrix M: \n", M)

print("When P is fro = ", torch.linalg.cond(M, p='fro'))
print("When P is nuc =",  torch.linalg.cond(M, p='nuc'))
print("When P is inf =", torch.linalg.cond(M, p=float('inf')))
print("When P is -inf =", torch.linalg.cond(M, p=float('-inf')))
print("When P is 1 =", torch.linalg.cond(M, p=1))
print("When P is -1 =", torch.linalg.cond(M, p=-1))
print("When P is 2 =", torch.linalg.cond(M, p=2))
print("When P is -2 =", torch.linalg.cond(M, p=-2))

Output:

Example 3

In this example, we will compute the condition number of a batch of matrices with the help of torch.linalg.cond method.

Python3

# import the required library
import torch

# define a tensor (matrix)
M = torch.tensor([[[-0.1345, -0.7437, 1.2377],
                   [0.9337, 1.6473, 0.4346],
                   [-1.6345, 0.9344, -0.2456]],
                  [[1.3343, -1.3456, 0.7373],
                   [1.4334, 0.2473, 1.1333],
                   [-1.5341, 1.5348, -1.4567]]])

# display input tensor
print(" Input Matrix M: \n", M)

# compute the condition number
Output = torch.linalg.cond(M)

# Display result
print("\n Condition Number: ", Output)

Output: