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