Example 2: Bounded Least Squares

where

is solved. An initial guess (-1.2, 1.0) is supplied, as well as the analytic Jacobian. The residual at the approximate solution is returned.

using System;
using Imsl.Math;

public class BoundedLeastSquaresEx2 : BoundedLeastSquares.IJacobian
{
    public void F(double[] x, double[] f)
    {
        f[0] = 10.0 * (x[1] - x[0] * x[0]);
        f[1] = 1.0 - x[0];
    }

    public void Jacobian(double[] x, double[] fjac)
    {
        fjac[0] = -20.0 * x[0];
        fjac[1] = 10.0;
        fjac[2] = -1.0;
        fjac[3] = 0.0;
    }


    public static void Main(String[] args)
    {
        int m = 2;
        int n = 2;
        int ibtype = 0;
        double[] xlb = { -2.0, -1.0 };
        double[] xub = { 0.5, 2.0 };

        BoundedLeastSquares.IJacobian rosbck =
            new BoundedLeastSquaresEx2();
        BoundedLeastSquares zf =
            new BoundedLeastSquares(rosbck, m, n, ibtype, xlb, xub);
        zf.SetGuess(new double[] { -1.2, 1.0 });
        zf.Solve();
        new PrintMatrix("Solution").Print(zf.GetSolution());
        new PrintMatrix("Residuals").Print(zf.GetResiduals());
    }
}

Output

Solution
    0    
0  0.5   
1  0.25  

Residuals
    0   
0  0    
1  0.5