package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a positive definite linear system using the conjugate gradient
 * method.</p>
 *
 * The solution to a positive definite linear system is found. The coefficient
 * matrix is stored as a full matrix. The system is \(Ax = b\) where 
 * $$
 * A=\begin{bmatrix}
 * 1.0 & -3.0 & 2.0 \\
 * -3.0 & 10.0 & -5.0 \\
 * 2.0 & -5.0 & 6.0
 * \end{bmatrix}
 * $$
 * <p>
 * and \( b = (27.0, -78.0, 64.0)^T\) </p>
 *
 * @see <a href="ConjugateGradientEx1.java">Code</a>
 * @see <a href="doc-files/ConjugateGradientEx1.out">Output</a>
 *
 */
public class ConjugateGradientEx1 implements ConjugateGradient.Function {

    static private double[][] a = {
        {1.0, -3.0, 2.0},
        {-3.0, 10.0, -5.0},
        {2.0, -5.0, 6.0}
    };
    static private double[] b = {27.0, -78.0, 64.0};

    @Override
    public void amultp(double[] p, double[] z) {
        double w[] = Matrix.multiply(a, p);
        System.arraycopy(w, 0, z, 0, z.length);
    }

    public static void main(String args[]) throws Exception {
        int n = 3;

        ConjugateGradientEx1 atp = new ConjugateGradientEx1();

        // Construct Cg object
        ConjugateGradient cg = new ConjugateGradient(n, atp);

        // Solve Ax=b
        new PrintMatrix("Solution").print(cg.solve(b));
    }
}