Finding the matrix rank using SVD.

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

import Jama.Matrix;

import Jama.SingularValueDecomposition;

public class MatrixRankFinder {

    public static int findMatrixRank(double[][] matrixData) {

        Matrix matrix = new Matrix(matrixData);

        SingularValueDecomposition svd = matrix.svd();

        double[] singularValues = svd.getSingularValues();

        int rank = 0;

        double threshold = Math.max(matrix.getRowDimension(), matrix.getColumnDimension()) * singularValues[0] * Math.ulp(1.0);

        for (double singularValue : singularValues) {

            if (singularValue > threshold) {

                rank++;

            }

        }

        return rank;

    }

    public static void main(String[] args) {

        double[][] matrixData = {

            {1.0, 2.0, 3.0},

            {4.0, 5.0, 6.0},

            {7.0, 8.0, 9.0}

        };

        int rank = findMatrixRank(matrixData);

        System.out.println("Matrix Rank: " + rank);

    }

}

In this program, we use the Jama library, which provides classes for performing matrix operations. We create a `Matrix` object from the input matrix data and then compute the Singular Value Decomposition (SVD) using the `svd()` method.

The `getSingularValues()` method returns an array of singular values. We iterate over these singular values and count the number of values that are greater than a threshold. The threshold is calculated based on the maximum dimension of the matrix and the largest singular value.

Finally, we return the rank of the matrix. In the example `main` method, we create a 3×3 matrix and find its rank using the `findMatrixRank` method. The result is then printed to the console.

Make sure to include the Jama library in your project dependencies for this code to compile and run successfully.