public void SolverCoreTestSparseMatrixNd()
{
const int N = 50;
var a = new SparseMatrix(N, N);
// Make matrix diagonal
for (int i = 0; i < N; i++)
{
a[i, i] = 1;
}
// Apply random rotations around each pair of axes. This will keep det(A) ~ 1
var rand = new Random();
for (int i = 0; i < N; i++)
{
for (int j = i + 1; j < N; j++)
{
double angle = rand.NextDouble() * 2 * Math.PI;
var r = new SparseMatrix(N, N);
for (int k = 0; k < N; k++)
{
r[k, k] = 1;
}
r[i, i] = r[j, j] = Math.Cos(angle);
r[i, j] = Math.Sin(angle);
r[j, i] = -Math.Sin(angle);
a = a * r;
}
}
var ainit = a.Copy();
// Generate random vector
var b = Vector.Zeros(N);
for (int i = 0; i < N; i++)
{
b[i] = rand.NextDouble();
}
var binit = b.Clone();
// Solve system
var sw = new Stopwatch();
sw.Start();
var x = new Vector(Gauss.Solve(a, b));
sw.Stop();
Trace.WriteLine("Gaussian elimination took: " + sw.ElapsedTicks);
// Put solution into system
Vector b2 = ainit * x;
// Verify result is the same
Assert.IsTrue(Vector.GetLInfinityNorm(binit, b2) < 1e-6);
}
public void SolverCoreTest2d()
{
var a = new double[][] {
new double[] { 2, 1 },
new double[] { -1, 1 }
};
var b = new Vector(1, -2);
var x = Gauss.SolveCore(a, b);
var answer = new Vector(1, -1);
Assert.IsTrue(Vector.GetLInfinityNorm(x, answer) < 1e-10);
}
public void SolverCoreTest3d()
{
var a = new double[][] {
new double[] { 2, 1, -1 },
new double[] { -3, -1, 2 },
new double[] { -2, 1, 2 }
};
var b = new Vector(8, -11, -3);
var x = Gauss.SolveCore(a, b);
var answer = new Vector(2, 3, -1);
Assert.IsTrue(Vector.GetLInfinityNorm(x, answer) < 1e-10);
}
/// <summary>Solve A*x = b using Gaussian elimination with partial pivoting</summary>
/// <param name="b"> right hand side Vector</param>
/// <returns> The solution x = A^(-1) * b as a Vector</returns>
public Vector SolveGE(Vector b)
{
return(Gauss.Solve(this, b));
}
/// <summary>Gaussian elimination method for A*x=b with partial pivoting</summary>
/// <param name="b">The right hand side vector</param>
/// <returns>The solution x</returns>
public Vector SolveGE(Vector b)
{
return(Gauss.SolveCore(Copy(), b));
}
