Example 2: Nonlinear Regression with User-supplied Derivatives

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

public class NonlinearRegressionEx2 {

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

                    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;

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

                    public boolean derivative(double theta[], int iobs,
                            double frq[], double wt[], double de[]) {
                        if (iobs < nobs) {
                            wt[0] = 1.0;
                            frq[0] = 1.0;
                            iend = true;
                            de[0] = -Math.exp(theta[1] * xdata[iobs]);
                            de[1] = -theta[0] * xdata[iobs] * 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(deriv);
        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);
    }
}

Output

The computed regression coefficients are {58.60656292541919, -0.039586447277524736}
The computed rank is 2
The degrees of freedom for error are 13.0
The sums of squares for error is 49.459299862472186
R from the QR decomposition 
     0        1      
0  1.874  1,139.928  
1  0      1,139.798