package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves an optimization problem with supplied numerical gradients.</p>
 *
 * This example uses <code>MinUnconMultiVar</code> to minimize $$f(x_1,x_2) =
 * 100(x_2 - x_1^2)^2 + (1-x_1)^2$$ while using
 * <code>NumericalDerivatives</code> to compute the numerical gradients.
 *
 * @see <a href="NumericalDerivativesEx6.java">Code</a>
 * @see <a href="doc-files/NumericalDerivativesEx6.out">Output</a>
 */
public class NumericalDerivativesEx6 {

    static private int m = 1, n = 2;

    static double fcnEvaluation(double[] x) {
        return 100. * ((x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0]))
                + (1. - x[0]) * (1. - x[0]);
    }

    static class MyFunction implements MinUnconMultiVar.Gradient {

        @Override
        public double f(double[] x) {
            return fcnEvaluation(x);
        }

        @Override
        public void gradient(double[] x, double[] gp) {
            NumericalDerivatives.Function fcn
                    = new NumericalDerivatives.Function() {
                @Override
                public double[] f(int varIndex, double[] y) {
                    double[] tmp = new double[m];
                    tmp[0] = fcnEvaluation(y);
                    return tmp;
                }
            };

            NumericalDerivatives nderv = new NumericalDerivatives(fcn);
            double[][] jacobian = nderv.evaluateJ(x);

            gp[0] = jacobian[0][0];
            gp[1] = jacobian[0][1];
        }
    }

    public static void main(String args[]) throws Exception {
        MinUnconMultiVar solver = new MinUnconMultiVar(n);
        solver.setGuess(new double[]{-1.2, 1.0});
        double x[] = solver.computeMin(new MyFunction());
        System.out.println("Minimum point is (" + x[0] + ", " + x[1] + ")");
    }
}