package com.imsl.test.example.stat;

import com.imsl.stat.*;

/**
 * <p>
 * Fits a nonlinear regression on scaled data.
 * </p>
 * In this example some non default tolerances and scales are used to fit a
 * nonlinear model. The data is \(1.e-10\) times the data of example
 * {@link NonlinearRegressionEx1}. In order to fit this model without rescaling
 * the data we first set the absolute function tolerance to \(0.0\). The default
 * value would have caused the program to terminate after one iteration because
 * the residual sum of squares is roughly \(1.e-19\). We also set the relative
 * function tolerance to \(0.0\). The gradient tolerance is properly scaled for
 * this problem so we leave it at its default value. Finally, we set the
 * elements of scale to be the absolute value of the reciprocal of the starting
 * value. The derivatives are obtained by finite differences.
 *
 *
 * @see <a href="NonlinearRegressionEx3.java">Code</a>
 * @see <a href="doc-files/NonlinearRegressionEx3.out">Output</a>
 */
public class NonlinearRegressionEx3 {

    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.e-10, 50.e-10, 45.e-10, 37.e-10, 35.e-10,
                    25.e-10, 20.e-10, 16.e-10, 18.e-10, 13.e-10, 8.e-10, 11.e-10,
                    8.e-10, 4.e-10, 6.e-10};
                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[] = {6.e-9, -0.03};
        double scale[] = new double[nparm];
        NonlinearRegression regression = new NonlinearRegression(nparm);
        regression.setGuess(theta);
        regression.setAbsoluteTolerance(0.0);
        regression.setRelativeTolerance(0.0);
        scale[0] = 1.0 / Math.abs(theta[0]);
        scale[1] = 1.0 / Math.abs(theta[1]);
        regression.setScale(scale);
        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();
        System.out.println("R from the QR decomposition is "
                + r[0][0] + " " + r[0][1]);
        System.out.println("                               "
                + r[1][0] + " " + r[1][1]);
    }
}