package com.imsl.test.example.math;

import com.imsl.math.*;
import java.util.logging.*;

/**
 * <p>
 * ZeroSystem Example 2: Solves a system of nonlinear equations with logging
 * enabled.</p>
 *
 *
 * The following system is solved with a higher relative error tolerance and
 * logging enabled.
 * 
 * $$
 * \begin{align}
 * y_0 &= 0.5 * x_0 + x_1 + 0.5 * x_2 - x_5 / x_6 \\
 * y_1 &= x_2 + x_3 + 2 * x_4 - 2.0 / x_6 \\
 * y_2 &= x_0 + x_1 + x_4 - 1 / x_6 \\
 * y_3 &= -28837 * x_0 - 139009 * x_1 - 78213 * x_2 + 18927 x_3 + 8427 * x_4 + 13492 / x_6 - 10690 * x_5 / x_6 \\
 * y_4 &= x_0 + x_1 + x_2 + x_3 + x_4 - 1 \\
 * y_5 &= 400 * x_0 * x_3 * x_3 * x_3 - 178370.0 * x_2 * x_4 \\
 * y_6 &= x_0 * x_2 - 2.6058 * x_1 * x_3
 * \end{align}
 * $$
 *
 * @see <a href="ZeroSystemEx2.java">Code</a>
 * @see <a href ="doc-files/ZeroSystemEx2.out">Output</a>
 */

public class ZeroSystemEx2 {

    public static void main(String args[]) throws com.imsl.IMSLException {

        ZeroSystem.Function fcn = new ZeroSystem.Function() {

            @Override
            public void f(double x[], double f[]) {
                f[0] = 0.5 * x[0] + x[1] + 0.5 * x[2] - x[5] / x[6];
                f[1] = x[2] + x[3] + 2 * x[4] - 2.0 / x[6];
                f[2] = x[0] + x[1] + x[4] - 1 / x[6];
                f[3] = -28837 * x[0] - 139009 * x[1] - 78213 * x[2] + 18927
                        * x[3] + 8427 * x[4] + 13492 / x[6]
                        - 10690 * x[5] / x[6];
                f[4] = x[0] + x[1] + x[2] + x[3] + x[4] - 1;
                f[5] = 400 * x[0] * x[3] * x[3] * x[3] - 178370.0 * x[2] * x[4];
                f[6] = x[0] * x[2] - 2.6058 * x[1] * x[3];
            }
        };

        ZeroSystem zf = new ZeroSystem(7);
        zf.setRelativeError(1e-2);      // reduced accuracy
        double guess[] = {0.5, 0.0, 0.0, 0.5, 0.0, 0.5, 2.0};
        zf.setGuess(guess);

        Logger logger = zf.getLogger();
        ConsoleHandler ch = new ConsoleHandler();
        ch.setLevel(Level.ALL);       // default ConsoleHandler Level is INFO
        logger.setLevel(Level.FINER);
        logger.addHandler(ch);
        ch.setFormatter(new com.imsl.IMSLFormatter());

        new PrintMatrix("zeros").print(zf.solve(fcn));
    }
}