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:
