Finding the matrix pseudo-inverse using SVD

Here’s an example of a Java program that finds the pseudo-inverse of a matrix using Singular Value Decomposition (SVD):

import org.apache.commons.math3.linear.*;

public class MatrixPseudoInverse {

    public static void main(String[] args) {

        double[][] matrixData = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

        RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);

        // Compute the SVD

        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);

        // Compute the pseudo-inverse

        RealMatrix pseudoInverse = svd.getSolver().getInverse();

        // Print the pseudo-inverse matrix

        double[][] pseudoInverseData = pseudoInverse.getData();

        System.out.println("Pseudo-Inverse Matrix:");

        for (double[] row : pseudoInverseData) {

            for (double value : row) {

                System.out.print(value + " ");

            }

            System.out.println();

        }

    }

}

In this example, we’re using the `RealMatrix` and `SingularValueDecomposition` classes from the Apache Commons Math library. You need to make sure you have the library added to your project’s dependencies.

The program creates a 3×3 matrix with some arbitrary values. It then computes the SVD of the matrix and obtains the pseudo-inverse using the `getInverse()` method of the `SingularValueDecomposition.Solver` class. Finally, it prints the pseudo-inverse matrix.

Make sure to include the Apache Commons Math library in your project for this code to work. You can download the library from the Apache Commons Math website or use a dependency management tool like Maven or Gradle to include it in your project.