Finding the matrix Moore-Penrose inverse using SVD.

Here’s a Java code snippet that demonstrates how to find the Moore-Penrose inverse of a matrix using Singular Value Decomposition (SVD):

import Jama.Matrix;

import Jama.SingularValueDecomposition;

public class MoorePenroseInverseExample {

    public static void main(String[] args) {

        // Example matrix

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

        // Create the matrix object

        Matrix matrix = new Matrix(data);

        // Compute SVD

        SingularValueDecomposition svd = matrix.svd();

        // Get the singular values

        Matrix s = svd.getS();

        // Compute the threshold value for pseudo-inverse

        double threshold = 1e-10 * Math.max(matrix.getRowDimension(), matrix.getColumnDimension()) * s.get(0, 0);

        // Compute the Moore-Penrose inverse

        Matrix inverse = computeMoorePenroseInverse(svd, threshold);

        // Print the inverse matrix

        inverse.print(5, 4);

    }

    private static Matrix computeMoorePenroseInverse(SingularValueDecomposition svd, double threshold) {

        Matrix s = svd.getS();

        Matrix u = svd.getU();

        Matrix v = svd.getV();

        int rank = 0;

        double[] singularValues = s.getColumnPackedCopy();

        for (double singularValue : singularValues) {

            if (singularValue > threshold) {

                rank++;

            }

        }

        Matrix sPlus = new Matrix(s.getRowDimension(), s.getColumnDimension());

        for (int i = 0; i < rank; i++) {

            double singularValue = singularValues[i];

            sPlus.set(i, i, 1.0 / singularValue);

        }

        Matrix uSub = u.getMatrix(0, u.getRowDimension() - 1, 0, rank - 1);

        Matrix vSub = v.getMatrix(0, v.getRowDimension() - 1, 0, rank - 1);

        return vSub.times(sPlus).times(uSub.transpose());

    }

}

In this code, we use the Jama library to perform the SVD and compute the Moore-Penrose inverse. The `computeMoorePenroseInverse` method takes the SVD decomposition, the threshold value, and returns the Moore-Penrose inverse matrix.

Note: Make sure you have the Jama library added to your project’s dependencies in order to run this code successfully.