package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * MinUnconMultiVar Example 1: Minimizes a multivariate function.
 * </p>
 * 
 * The minimum of \(100(x_2 - x_1^2)^2 + (1-x_1)^2\) is found using function
 * evaluations only.
 *
 * @see <a href="MinUnconMultiVarEx1.java">Code</a>
 * @see <a href="doc-files/MinUnconMultiVarEx1.out">Output</a>
 */
public class MinUnconMultiVarEx1 {

    public static void main(String args[]) throws Exception {
        MinUnconMultiVar solver = new MinUnconMultiVar(2);
        solver.setGuess(new double[]{-1.2, 1.0});
        double x[] = solver.computeMin(new MinUnconMultiVar.Function() {
            public double f(double[] x) {
                return 100. * ((x[1] - x[0] * x[0]) * (x[1] - x[0] * x[0]))
                        + (1. - x[0]) * (1. - x[0]);
            }
        });
        System.out.println("Minimum point is (" + x[0] + ", " + x[1] + ")");
    }
}