Finding the Moore-Penrose inverse of a matrix.

Here’s an example of a Java program that calculates the Moore-Penrose inverse of a matrix using the Singular Value Decomposition (SVD) method:

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

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

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

    public class MoorePenroseInverse {

    public static RealMatrix calculateMoorePenroseInverse(RealMatrix matrix) {

        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);

        RealMatrix u = svd.getU();

        RealMatrix s = svd.getS();

        RealMatrix v = svd.getVT();

        // Calculate the Moore-Penrose inverse of S

        RealMatrix sInverse = MatrixUtils.createRealMatrix(s.getColumnDimension(), s.getRowDimension());

        double epsilon = 1e-10; // A small threshold for considering singular values as zero

        for (int i = 0; i < s.getRowDimension(); i++) {

            double singularValue = s.getEntry(i, i);

            if (Math.abs(singularValue) > epsilon) {

                sInverse.setEntry(i, i, 1.0 / singularValue);

            }

        }

        // Calculate the Moore-Penrose inverse of the matrix

        RealMatrix matrixInverse = v.multiply(sInverse).multiply(u.transpose());

        return matrixInverse;

    }

    public static void main(String[] args) {

        // Example usage

        double[][] data = {

            {1, 2},

            {3, 4},

            {5, 6}

        };

        RealMatrix matrix = MatrixUtils.createRealMatrix(data);

        RealMatrix inverse = calculateMoorePenroseInverse(matrix);

        // Print the result

        for (int i = 0; i < inverse.getRowDimension(); i++) {

            for (int j = 0; j < inverse.getColumnDimension(); j++) {

                System.out.print(inverse.getEntry(i, j) + " ");

            }

            System.out.println();

        }
    }
}

This program uses the Apache Commons Math library to perform the matrix operations and calculate the Singular Value Decomposition (SVD). You can include the library in your project by adding the appropriate JAR file to your classpath. The example code calculates the Moore-Penrose inverse of a 3×2 matrix and prints the result to the console.