Example 4: Solve a Small Linear System Stored in Sparse Form With Preconditioning

using System;
using Imsl.Math;
public class GenMinResEx4 : GenMinRes.IPreconditioner
{
    private static SparseMatrix A;
    private static double[] a = {6.0, 10.0, 15.0, -3.0, 10.0, -1.0, 
                                -1.0, -3.0, -5.0, 1.0, 10.0, -1.0, 
                                -2.0, -1.0, -2.0};
    private static double[] b = {10.0, 7.0, 45.0, 33.0, -34.0, 31.0};
    private static double[] xguess = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
    private static double[] diagin = {0.1, 0.1, 0.066666666666667, 0.1, 
                                      1.0, 0.1666666666666667};
    private static int[] irow = {5, 1, 2, 1, 3, 3, 4, 4, 4, 4, 0, 5, 5, 1, 3};
    private static int[] jcol = {5, 1, 2, 2, 3, 4, 0, 5, 3, 4, 0, 0, 1, 3, 0};
    
    public virtual void  Amultp(double[] p, double[] z)
    {
        double[] result;
        result = Imsl.Math.SparseMatrix.Multiply(A, p);
        Array.Copy(result, 0, z, 0, z.Length);
    }
    
    public void  Preconditioner(double[] r, double[] z)
    {
        int n = z.Length;
        for (int i = 0; i < n; i++)
        {
            z[i] = diagin[i] * r[i];
        }
    }
    
    public static void  Main(String[] args)
    {
        int n = 6;
        A = new SparseMatrix(n, n);
        for (int i = 0; i < a.Length; i++)
        {
            A.Set(irow[i], jcol[i], a[i]);
        }
        GenMinResEx4 atp = new GenMinResEx4();
        
        // Construct a GenMinRes object
        GenMinRes gnmnrs = new GenMinRes(n, atp);
        gnmnrs.SetGuess(xguess);
        // Solve Ax = b
        new PrintMatrix("x").Print(gnmnrs.Solve(b));
    }
}

Output

          x
          0          
0  1                 
1  2                 
2  3                 
3  4                 
4  5.00000000000001  
5  6