public void SolveGETest()
{
const int N = 50;
var a = new SparseDoubleMatrix(N, N);
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 SparseDoubleMatrix(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.Clone();
// Generate random vector
var b = new DoubleVector(N);
for (int i = 0; i < N; i++)
{
b[i] = rand.NextDouble();
}
var binit = b.Clone();
// Solve system
var solver = new GaussianEliminationSolver();
var sw = new Stopwatch();
sw.Start();
var x = solver.SolveDestructive(a, b.GetInternalData());
sw.Stop();
Trace.WriteLine("Gaussian elimination took: " + sw.ElapsedTicks);
// Put solution into system
var b2 = ainit * x;
// Verify result is the same
Assert.IsTrue(VectorMath.LInfinityNorm(binit, b2) < 1e-6);
}
public void TextBanded01()
{
var rnd = new Random(642332);
for (int testRuns = 0; testRuns < 1000; ++testRuns)
{
for (int N = 11; N <= 13; ++N) // for even and odd matrix dimensions
{
for (int lowerBandwidth = 0; lowerBandwidth <= (N + 1) / 2; ++lowerBandwidth) // for all lower bandwidths
{
for (int upperBandwidth = 0; upperBandwidth <= (N + 1) / 2; ++upperBandwidth) // for all upper bandwidths
{
var A = new DoubleMatrix(N, N);
for (int i = 0; i < N; ++i)
{
int start = Math.Max(0, i - lowerBandwidth);
int end = Math.Min(N, i + upperBandwidth + 1);
for (int j = start; j < end; ++j)
{
A[i, j] = rnd.Next(1, 99);
}
}
var x = new DoubleVector(N);
for (int i = 0; i < N; ++i)
{
x[i] = rnd.Next(-99, 99);
}
var b = A * x;
// now do gaussian elimination
var solver = new GaussianEliminationSolver();
var xr = new double[N];
solver.SolveDestructiveBanded(A, lowerBandwidth, upperBandwidth, b.GetInternalData(), xr);
// compare result
for (int i = 0; i < N; ++i)
{
Assert.AreEqual(x[i], xr[i], 1E-6);
}
}
}
}
}
}