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 NonlinearRegression.TooManyIterationsException, 
      NonlinearRegression.NegativeFreqException, 
      NonlinearRegression.NegativeWeightException,
      NonlinearRegression.NoProgressException {

      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 49.45929986247219
R from the QR decomposition 
     0        1      
0  1.874  1,139.928  
1  0      1,139.798