package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 *
 * <p>
 * Solves a nonlinear least squares problem
 * subject to bounds with a supplied Jacobian and initial guess.
 * </p>
 *
 * <p>
 * This examples solves the nonlinear least squares problem
 * </p>
 * $$\min \frac{1}{2}\sum\limits_{i = 0}^1 {f_i \left( x \right)^2 }$$
 *
 * <p>
 * subject to the bounds</p>
 * $$- 2 \le x_0 \le 0.5$$ $$-1 \le x_1 \le 2$$
 *
 * <p>
 * and where</p>
 * $$f_0 (x) = 10(x_1 - x_0^2 ) \,\, {\rm{and}} \,\, f_1 (x) = (1 - x_0 ).$$
 *
 * <p>
 * An initial guess \((-1.2, 1.0)\) is supplied, as well as the analytic
 * Jacobian. The residual at the approximate solution is returned.</p>
 *
 * @see <a href="BoundedLeastSquaresEx2.java">Code</a>
 * @see <a href="doc-files/BoundedLeastSquaresEx2.out">Output</a>
 *
 */
public class BoundedLeastSquaresEx2 {

    public static void main(String args[]) throws Exception {
        int m = 2;
        int n = 2;
        int ibtype = 0;
        double[] xlb = {-2.0, -1.0};
        double[] xub = {0.5, 2.0};
        double[] xguess = {-1.2, 1.0};

        BoundedLeastSquares.Function rosbck
                = new BoundedLeastSquares.Function() {
            public void compute(double[] x, double[] f) {
                f[0] = 10.0 * (x[1] - x[0] * x[0]);
                f[1] = 1.0 - x[0];
            }
        };

        BoundedLeastSquares.Jacobian jacob
                = new BoundedLeastSquares.Jacobian() {
            public void compute(double[] x, double[] fjac) {
                fjac[0] = -20.0 * x[0];
                fjac[1] = 10.0;
                fjac[2] = -1.0;
                fjac[3] = 0.0;
            }
        };

        BoundedLeastSquares zf
                = new BoundedLeastSquares(rosbck, m, n, ibtype, xlb, xub);

        zf.setJacobian(jacob);
        zf.setGuess(xguess);
        zf.solve();
        new PrintMatrix("Solution").print(zf.getSolution());
        new PrintMatrix("Residuals").print(zf.getResiduals());
    }
}