package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Performs the QR factorization of a matrix.</p>
 *
 * The QR factorization of a matrix is performed. A linear system is then solved
 * using the factorization. The rank of the input matrix is also computed.
 *
 * @see <a href="QREx1.java"> Code</a>
 * @see <a href ="doc-files/QREx1.out">Output</a>
 *
 */
public class QREx1 {

    public static void main(String args[]) throws SingularMatrixException {
        double a[][] = {
            {1, 2, 4},
            {1, 4, 16},
            {1, 6, 36},
            {1, 8, 64}
        };
        double b[] = {4.999, 9.001, 12.999, 17.001};

        // Compute the QR factorization of A
        QR qr = new QR(a);

        // Solve Ax = b
        double x[] = qr.solve(b);
        new PrintMatrix("x").print(x);

        // Print Q and R.
        new PrintMatrix("Q").print(qr.getQ());
        new PrintMatrix("R").print(qr.getR());

        // Find the rank of A.
        int rank = qr.getRank();
        System.out.println("rank = " + rank);
    }
}