Finding the matrix rank using QR decomposition

Here’s an example program in Java that uses QR decomposition to find the rank of a matrix:

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

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

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

public class MatrixRankQRDecomposition {

    public static void main(String[] args) {

        double[][] matrixData = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };  

        RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);

        QRDecomposition qrDecomposition = new QRDecomposition(matrix);

        RealMatrix rMatrix = qrDecomposition.getR();

        int rank = getMatrixRank(rMatrix);

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

    }

    private static int getMatrixRank(RealMatrix matrix) {

        double[] singularValues = matrix.getSingularValues();

        int rank = 0;
 
        for (double singularValue : singularValues) {

            if (Math.abs(singularValue) > 1e-10) {

                rank++;

            }

        }

        return rank;

    }

}

In this program, we are using the Apache Commons Math library, specifically the `QRDecomposition` class, to perform the QR decomposition of the matrix. The `QRDecomposition` class provides the upper triangular matrix `R` as a result. We then calculate the rank of the matrix by counting the number of non-zero singular values in the `R` matrix.

Make sure you have the Apache Commons Math library added to your project dependencies in order to run this program successfully.