Example 2: Nonlinear Regression with User-supplied Derivatives

In this example a nonlinear model is fitted. The derivatives are supplied by the user.

using System;
using Imsl.Math;
using Imsl.Stat;
public class NonlinearRegressionEx2 : NonlinearRegression.IDerivative
{


        double[] ydata = new double[]{
            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 = new double[]{
            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};
        bool iend;
        int nobs = 15;
        
        public bool 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 bool 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;
        }
    public static void Main(String[] args)
    {                
        int nparm = 2;
        double[] theta = new double[]{60.0, - 0.03};
        NonlinearRegression regression = new NonlinearRegression(nparm);
        regression.Guess = theta;
        double[] coef = regression.Solve(new NonlinearRegressionEx2());

        Console.Out.WriteLine("The computed regression coefficients are {" +
            coef[0] + ", " + coef[1] + "}");
        Console.Out.WriteLine("The computed rank is " + regression.Rank);
        Console.Out.WriteLine("The degrees of freedom for error are " + 
            regression.DFError);
        Console.Out.WriteLine("The sums of squares for error is " + 
            regression.GetSSE());
        new PrintMatrix("R from the QR decomposition ").Print(regression.R);
    }
}

Output

The computed regression coefficients are {58.6065629254192, -0.0395864472775247}
The computed rank is 2
The degrees of freedom for error are 13
The sums of squares for error is 49.4592998624722
     R from the QR decomposition 
          0                 1          
0  1.87385998422826  1139.92837730064  
1  0                 1139.79757620697