package com.imsl.test.example.stat;

import com.imsl.stat.*;
import com.imsl.math.*;

/**
 * <p>
 * Fits a nonlinear regression using finite differences for the derivatives.</p>
 *
 * In this example the nonlinear model 
 * $$y = \theta_0 - \theta_0*\exp(\theta_1x) $$
 * is fit to data. The derivatives are obtained by
 * finite differences.
 *
 * @see <a href="NonlinearRegressionEx1.java">Code</a>
 * @see <a href="doc-files/NonlinearRegressionEx1.out">Output</a>
 */

public class NonlinearRegressionEx1 {

    public static void main(String args[]) throws Exception {
        NonlinearRegression.Function f = new NonlinearRegression.Function() {

            @Override
            public boolean f(double theta[], int iobs, double frq[],
                    double wt[], double e[]) {

                double ydata[] = {
                    54.0, 50.0, 45.0, 37.0, 35.0, 25.0, 20.0,
                    16.0, 18.0, 13.0, 8.0, 11.0, 8.0, 4.0, 6.0
                };
                double xdata[] = {
                    2.0, 5.0, 7.0, 10.0, 14.0, 19.0, 26.0, 31.0,
                    34.0, 38.0, 45.0, 52.0, 53.0, 60.0, 65.0
                };
                boolean iend;
                int nobs = 15;

                if (iobs < nobs) {
                    wt[0] = 1.0;
                    frq[0] = 1.0;
                    iend = true;
                    e[0] = ydata[iobs] - theta[0] * Math.exp(theta[1]
                            * xdata[iobs]);
                } else {
                    iend = false;
                }
                return iend;
            }
        };

        int nparm = 2;
        double theta[] = {60.0, -0.03};
        NonlinearRegression regression = new NonlinearRegression(nparm);
        regression.setGuess(theta);
        double coef[] = regression.solve(f);
        System.out.println("The computed regression coefficients are {"
                + coef[0] + ", " + coef[1] + "}");
        int rank = regression.getRank();
        System.out.println("The computed rank is " + rank);
        double dfe = regression.getDFError();
        System.out.println("The degrees of freedom for error are " + dfe);
        double sse = regression.getSSE();
        System.out.println("The sums of squares for error is " + sse);
        double r[][] = regression.getR();
        new PrintMatrix("R from the QR decomposition ").print(r);
    }
}