Example 3: Solve a Small Linear System Stored in Sparse Form
A solution to a small linear system in which the coefficient matrix has been stored in SparseMatrix
form is found. An initial guess of ones is set before solving the system.
using System;
using Imsl.Math;
public class GenMinResEx3 : GenMinRes.IFunction
{
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 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};
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};
public void Amultp(double[] p, double[] z)
{
double[] result;
result = Imsl.Math.SparseMatrix.Multiply(A, p);
Array.Copy(result, 0, z, 0, z.Length);
}
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]);
}
GenMinResEx3 atp = new GenMinResEx3();
// 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
5 6
Link to C# source.