GenMinRes Simple Example with User Supplied Inner Product

Example 2: Solve a Small Linear System with User Supplied Inner Product

A solution to a small linear system is found. The coefficient matrix is stored as a full matrix and no preconditioning is used. Typically, preconditioning is required to achieve convergence in a reasonable number of iterations. The user supplies a function to compute the inner product and norm within the Gram-Schmidt implementation.

using System;
using Imsl.Math;
using IMSLException = Imsl.IMSLException;

public class GenMinResEx2 : GenMinRes.IFunction, GenMinRes.IVectorProducts
{
	private static double[,] a = {
					{33.0, 16.0, 72.0},
					{-24.0, -10.0, -57.0},
					{18.0, -11.0, 7.0}
								 };
	private static double[] b = {129.0, -96.0, 8.5};
	// If A were to be read in from some outside source the   //
	// code to read the matrix could reside in a constructor. //
	
	public void  Amultp(double[] p, double[] z)
	{
		double[] result;
		result = Matrix.Multiply(a, p);
		Array.Copy(result, 0, z, 0, z.Length);
	}
	
	public double Innerproduct(double[] x, double[] y)
	{
		int n = x.Length;
		double tmp = 0.0;
		for (int i = 0; i < n; i++)
		{
			tmp += x[i] * y[i];
		}
		return tmp;
	}
	
	public double Norm(double[] x)
	{
		int n = x.Length;
		double tmp = 0.0;
		for (int i = 0; i < n; i++)
		{
			tmp += x[i] * x[i];
		}
		return System.Math.Sqrt(tmp);
	}
	
	public static void  Main(String[] args)
	{
		int n = 3;
		
		GenMinResEx2 atp = new GenMinResEx2();
		
		// Construct a GenMinRes object
		GenMinRes gnmnrs = new GenMinRes(n, atp);
		gnmnrs.SetVectorProducts(atp);
		
		// Solve Ax = b
		new PrintMatrix("x").Print(gnmnrs.Solve(b));
	}
}

Output

          x
           0          
0  0.999999999999999  
1  1.5                
2  1

Link to C# source.