Example 1: Nonlinear Regression using Finite Differences

In this example a nonlinear model is fitted. The derivatives are obtained by finite differences.

using System;
using Imsl.Math;
using Imsl.Stat;
public class NonlinearRegressionEx1 : NonlinearRegression.IFunction
{
	public bool f(double[] theta, int iobs, double[] frq, double[] wt, double[] e)
	{
			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;
			
			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 static void Main(String[] args)
	{		
		int nparm = 2;
		double[] theta = new double[]{60.0, - 0.03};
		NonlinearRegression regression = new NonlinearRegression(nparm);
		regression.Guess = theta;
		NonlinearRegression.IFunction fcn = new NonlinearRegressionEx1();
		double[] coef = regression.Solve(fcn);

		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 {58.6065629385189, -0.0395864472964795}
The computed rank is 2
The degrees of freedom for error are 13
The sums of squares for error is 49.4592998624719
     R from the QR decomposition 
          0                 1          
0  1.87385998095046  1139.92835934133  
1  0                 1139.79755002385