Finding the matrix condition number using QR decomposition

Here’s an example program in Java that calculates the condition number of a matrix using QR decomposition:

import Jama.Matrix;

import Jama.QRDecomposition;

public class MatrixConditionNumber {

    public static void main(String[] args) {

        double[][] data = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        Matrix matrix = new Matrix(data);

        QRDecomposition decomposition = new QRDecomposition(matrix);

        Matrix qMatrix = decomposition.getQ();

        Matrix rMatrix = decomposition.getR();

        Matrix inverseR = rMatrix.inverse();

        Matrix inverseQ = qMatrix.inverse();

        Matrix inverseMatrix = inverseR.times(inverseQ);

        double matrixConditionNumber = matrix.norm() * inverseMatrix.norm();

        System.out.println("Matrix Condition Number: " + matrixConditionNumber);

    }

}

In this program, we use the JAMA library (Java Matrix Package) to perform QR decomposition and matrix operations. First, we create a 2D array `data` to represent the matrix. Then, we create a `Matrix` object with the data.

Next, we create a `QRDecomposition` object with the matrix and obtain the Q and R matrices from the decomposition.

To calculate the condition number, we calculate the inverse of the Q and R matrices and multiply them to obtain the inverse of the original matrix. We then calculate the norms of the original matrix and the inverse matrix and multiply them together to get the condition number.

Finally, we print the calculated condition number.

Please note that you need to include the JAMA library in your project for this program to work. You can download the JAMA library from https://math.nist.gov/javanumerics/jama/