How to compute the eigenvalues and eigenvectors of a square matrix in PyTorch?
In this article, we are going to discuss how to compute the eigenvalues and eigenvectors of a square matrix in PyTorch.
Compute the eigenvalues and eigenvectors of a square matrix in PyTorch
torch.linalg.eig() method computes the eigenvalue decomposition of a square matrix or a batch of matrices. The decomposition exists if the input matrix is diagonalizable. This method also supports the input of float, double, cfloat, and cdouble data types. It will return a named tuple (eigenvalues, eigenvectors). The eigenvalues and eigenvectors are always complex-valued and the eigenvectors are given by columns of eigenvectors. Below is the syntax of torch.linalg.eig() method.
Syntax: torch.linalg.eig(mat)
Parameter:
- mat (Tensor): square matrix or a batch of matrices.
Return: It will return a named tuple (eigenvalues, eigenvectors).
Example 1:
In this example, we see how to compute the eigenvalues and eigenvectors of a square matrix.
Python3
# import the required library import torch # define a 3x3 square matrix mat = torch.tensor([[-0.3371, -0.2975, 1.8739], [1.4078, 1.6856, 0.3799], [1.9002, -0.4428, 1.5552]]) # print the above created matrix print("\n Matrix: \n", mat) # compute the eigenvalues and eigenvectors eigenvalues, eigenvectors = torch.linalg.eig(mat) # print output print("\n Eigenvalues: \n", eigenvalues) print("\n Eigenvectors: \n", eigenvectors) |
Output:
EigenValues and EigenVectors
Example 2:
In this example, we see how to compute the eigenvalues and eigenvectors of a batch of matrices.
Python3
# import the required library import torch # define a batch of matrices mat = 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]]]) # print the above batch of matrices print("\n Matrix: \n", mat) # compute the eigenvalues and eigenvectors eigenvalues, eigenvectors = torch.linalg.eig(mat) # print output print("\n Eigenvalues: \n", eigenvalues) print("\n Eigenvectors: \n", eigenvectors) |
Output:
EigenValues and EigenVectors
