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PyTorch – How to compute the inverse of a square matrix?
To compute the inverse of a square matrix, we could apply torch.linalg.inv() method. It returns a new tensor with inverse of the given matrix. It accepts a square matrix, a batch of square matrices, and also batches of square matrices.
A matrix is a 2D torch Tensor. It supports input of float, double, cfloat, and cdouble data types. The inverse matrix exists if and only if the square matrix is invertible.
Syntax
torch.linalg.inv(M)
Where M is a square matrix or a batch of square matrices. It returns the inverse matrix.
Steps
We could use the following steps to compute the inverse of a square 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 square matrix. Here, we define a square matrix (2D tensor of size 3×3.
M = torch.tensor([[1.,2., 3.],[1.5, 2., 2.3],[.1, .2, .5]])
Compute the inverse of square matrix using torch.linalg.inv(M). M is the square matrix or batch/es of square matrices. Optionally assign this value to a new variable.
M_inv = torch.linalg.inv(M)
Print the above computed inverse matrix.
print("Norm:", M_inv)Let's take a couple of examples to demonstrate how to compute the inverse of a square matrix.
Example 1
# Python program to compute the inverse of a square matrix
# import required library
import torch
# define a 3x3 square matrix
M = torch.tensor([[1.,2., 3.],[1.5, 2., 2.3],[.1, .2, .5]])
print("Matrix M:
", M)
# compute the inverse of above defined matrix
Minv = torch.linalg.inv(M)
print("Inversr Matrix:
", Minv)Output
It will produce the following output −
Matrix M: tensor([[1.0000, 2.0000, 3.0000], [1.5000, 2.0000, 2.3000], [0.1000, 0.2000, 0.5000]]) Inversr Matrix: tensor([[ -2.7000, 2.0000, 7.0000], [ 2.6000, -1.0000, -11.0000], [ -0.5000, 0.0000, 5.0000]])
Example 2
# Python program to compute the inverse of a square matrix
# import required library
import torch
# define a 3x3 square matrix of random complex numbers
M = torch.randn(3,3, dtype = torch.complex128)
print("Matrix M:
", M)
# compute the inverse of above defined matrix
Minv = torch.linalg.inv(M)
print("Inverse Matrix:
", Minv)Output
It will produce the following output −
Matrix M: tensor([[ 0.4425-1.4046j, -0.2492+0.7280j, -0.4746-0.4261j], [-0.0246-0.4826j, -0.0250-0.3656j, 1.1983-0.4130j], [ 0.1904+0.7817j, 0.5823-0.2140j, 0.6129+0.0590j]], dtype=torch.complex128) Inversr Matrix: tensor([[ 0.3491+0.2565j, -0.2743+0.2843j, 0.4041-0.3382j], [ 0.4856-0.6789j, -0.2541+0.0598j, 1.2471-0.5962j], [ 0.0221+0.2874j, 0.6732+0.0512j, 0.1537+0.5768j]], dtype=torch.complex128)
Example 3
# Python program to compute the inverse of batch of matrices
# import required library
import torch
# define a batch of two 3x3 square matrices
B = torch.randn(2,3,3)
print("Batch of Matrices :
", B)
# compute the inverse of above defined batch matrices
Binv = torch.linalg.inv(B)
print("Inverse Matrices:
", Binv)Output
It will produce the following output −
Batch of Matrices : tensor([[[ 1.0002, 0.4318, -0.9800], [-1.7990, 0.0913, 0.9440], [-0.1339, 0.0824, -0.5501]], [[ 0.5289, -0.0909, 0.0354], [-0.2159, -0.5417, 0.3659], [-0.7216, -0.0669, -0.6662]]]) Inverse Matrices: tensor([[[ 0.2685, -0.3290, -1.0427], [ 2.3415, 1.4297, -1.7177], [ 0.2852, 0.2941, -1.8211]], [[ 1.6932, -0.2766, -0.0620], [-1.7919, -1.4360, -0.8838], [-1.6543, 0.4438, -1.3452]]])
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