package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a nonlinear least squares problem using a finite difference Jacobian.</p>
 *
 * A nonlinear least squares problem is solved using a finite difference
 * Jacobian. 
 * The problem is to minimize the vector-function, $$ f(x_1,x_2) =
 * \begin{bmatrix}10.0(x_2-x_1^2)\\ 1.0-x_1 \end{bmatrix} $$ 
 * 
 * <p> The analytic Jacobian is
 * $$ J(x_1,x_2) = \begin{bmatrix}-20.0x_1 & 10.0\\ -1.0 & 0.0
 * \end{bmatrix}. $$
 * </p>
 * @see <a href="NonlinLeastSquaresEx1.java">Code</a>
 * @see <a href="doc-files/NonlinLeastSquaresEx1.out">Output</a>
 */
public class NonlinLeastSquaresEx1 {

    public static void main(String args[])
            throws NonlinLeastSquares.TooManyIterationsException {
        NonlinLeastSquares.Function zsf = new NonlinLeastSquares.Function() {

            @Override
            public void f(double x[], double f[]) {
                f[0] = 10. * (x[1] - x[0] * x[0]);
                f[1] = 1. - x[0];
            }
        };

        int m = 2;
        int n = 2;
        double xguess[] = {-1.2, 1.};
        double xscale[] = {1., 1.};
        double fscale[] = {1., 1.};

        NonlinLeastSquares zs = new NonlinLeastSquares(m, n);
        zs.setGuess(xguess);
        zs.setXscale(xscale);
        zs.setFscale(fscale);
        double[] x = zs.solve(zsf);

        for (int k = 0; k < n; k++) {
            System.out.println("x[" + k + "] = " + x[k]);
        }
    }
}