PyTorch – How to compute the pseudoinverse of a matrix?

To compute the pseudoinverse of a square matrix, we could apply torch.linalg.pinv() method. It returns a new tensor with pseudoinverse of the given matrix. 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.pinv(M)

Where M is a matrix or batches of matrices.

Steps

We could use the following steps to compute the pseudoinverse of a 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 a matrix (2D tensor of size 3x4.

M = torch.randn(3,4)

• Compute the pseudoinverse matrix using torch.linalg.pinv(M). M is a matrix or batch/es of matrices. Optionally assign this value to a new variable.

Mpinv = torch.linalg.pinv(M)

• Print the above computed pseudoinverse matrix

print("Norm:", Mpinv)

Example 1

In this program, we compute the pseudoinverse matrix of a given input matrix.

# Python program to compute the pseudoinverse of a matrix # import required library import torch # define a matrix of size 3x4 M = torch.randn(3,4) print("Matrix M:
", M) print("Matrix size:", M.size()) # compute the inverse of above defined matrix Mpinv = torch.linalg.pinv(M) print("Pseudo inverse Matrix:
", Mpinv) print("Pseudo inverse Matrix size:", Mpinv.size())

Output

It will produce the following output −

Matrix M:    tensor([[ 1.1350, -1.0521, -0.6431, -0.1302],       [-0.5745, 1.2299, 0.9296, 1.6188],       [ 0.6129, -1.0834, -0.0711, 0.2382]]) Matrix size: torch.Size([3, 4]) Pseudo inverse Matrix:    tensor([[ 1.1440, 0.3123, -0.6687],       [ 0.7733, 0.2948, -1.3105],       [-0.8647, -0.0376, 0.9169],       [ 0.3150, 0.5262, 0.2319]]) Pseudo inverse Matrix size: torch.Size([4, 3])

Example 2

In this program, we compute the pseudoinverse matrix of a given input complex matrix.

# Python program to compute the # pseudo inverse of a complex matrix # import required library import torch # define a 3x2 matrix of random complex numbers M = torch.randn(3,2, dtype = torch.cfloat) print("Matrix M:
", M) print("Matrix size:", M.size()) # compute the inverse of above defined matrix Minv = torch.linalg.pinv(M) print("Pseudo inverse Matrix:
", Minv) print("Pseudo inverse Matrix size:", Minv.size())

Output

It will produce the following output −

Matrix M:    tensor([[ 0.5273-0.7986j, 0.7881+0.0765j],       [-0.6390-0.3126j, -0.1926+0.0727j],       [-0.7445-0.2163j, 0.0649+0.1611j]]) Matrix size: torch.Size([3, 2]) Pseudo inverse Matrix:    tensor([[ 0.0384+0.2124j, -0.3826+0.3125j, -0.5792+0.1700j],       [ 0.9675-0.1972j, -0.2763-0.5200j, 0.2895-0.6992j]]) Pseudo inverse Matrix size: torch.Size([2, 3])

Example 3

In this program, we compute the pseudoinverse of a batch of three matrices.

# Python program to compute the # pseudo inverse of batch of matrices # import the required library import torch # define a batch of three 3x2 matrices B = torch.randn(3,3,2) print("Batch of Matrices :
", B) print(B.size()) # compute the inverse of above defined batch of matrices Binv = torch.linalg.pinv(B) print("Pseudo inverse Matrices:
", Binv) print(Binv.size())

Output

It will produce the following output −

Batch of Matrices :    tensor([[[-0.1761, -1.4982],       [ 0.7792, -0.0071],       [-0.6187, -0.2396]],       [[-1.1825, 1.2347],       [ 0.0127, 1.0387],       [ 0.0319, 0.5046]],       [[-1.2648, -0.7298],       [-1.8663, -1.1158],       [-0.0148, 0.5049]]]) torch.Size([3, 3, 2]) Pseudo inverse Matrices:    tensor([[[ 0.0932, 0.8222, -0.6073],       [-0.6673, -0.1483, 0.0032]],       [[-0.8261, 0.7798, 0.4164],       [ 0.0185, 0.7538, 0.3850]],       [[-0.2850, -0.3336, -1.1492],       [ 0.0613, -0.0569, 1.9435]]]) torch.Size([3, 2, 3])