public void SquareMatrixNotInvertable()
{
SquareMatrix A = new SquareMatrix(2);
A[1, 1] = 1.0;
// Inverting should throw
try {
A.Inverse();
Assert.IsTrue(false);
} catch (DivideByZeroException) {
}
// LU Decomposing should throw
try {
A.LUDecomposition();
Assert.IsTrue(false);
} catch (DivideByZeroException) {
}
// SVD should succeed, and give infinite condition number
SingularValueDecomposition SVD = A.SingularValueDecomposition();
Assert.IsTrue(Double.IsInfinity(SVD.ConditionNumber));
}
public void SquareRandomMatrixLUDecomposition()
{
for (int d = 1; d <= 256; d += 11)
{
SquareMatrix M = CreateSquareRandomMatrix(d);
// LU decompose the matrix
//Stopwatch sw = Stopwatch.StartNew();
LUDecomposition LU = M.LUDecomposition();
//sw.Stop();
//Console.WriteLine(sw.ElapsedMilliseconds);
Assert.IsTrue(LU.Dimension == d);
// test that the decomposition works
SquareMatrix P = LU.PMatrix();
SquareMatrix L = LU.LMatrix();
SquareMatrix U = LU.UMatrix();
Assert.IsTrue(TestUtilities.IsNearlyEqual(P * M, L * U));
// check that the inverse works
SquareMatrix MI = LU.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * MI, UnitMatrix.OfDimension(d)));
// test that a solution works
ColumnVector t = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
t[i] = i;
}
ColumnVector s = LU.Solve(t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * s, t));
}
}
public void SquareUnitMatrixLUDecomposition()
{
for (int d = 1; d <= 10; d++)
{
SquareMatrix I = UnitMatrix.OfDimension(d).ToSquareMatrix();
Assert.IsTrue(I.Trace() == d);
LUDecomposition LU = I.LUDecomposition();
Assert.IsTrue(LU.Determinant() == 1.0);
SquareMatrix II = LU.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(II, I));
}
}
public void SquareVandermondeMatrixLUDecomposition()
{
// fails now for d = 8 because determinant slightly off
for (int d = 1; d <= 7; d++)
{
Console.WriteLine("d={0}", d);
double[] x = new double[d];
for (int i = 0; i < d; i++)
{
x[i] = i;
}
double det = 1.0;
for (int i = 0; i < d; i++)
{
for (int j = 0; j < i; j++)
{
det = det * (x[i] - x[j]);
}
}
// LU decompose the matrix
SquareMatrix V = CreateVandermondeMatrix(d);
LUDecomposition LU = V.LUDecomposition();
// test that the decomposition works
SquareMatrix P = LU.PMatrix();
SquareMatrix L = LU.LMatrix();
SquareMatrix U = LU.UMatrix();
Assert.IsTrue(TestUtilities.IsNearlyEqual(P * V, L * U));
// check that the determinant agrees with the analytic expression
Console.WriteLine("det {0} {1}", LU.Determinant(), det);
Assert.IsTrue(TestUtilities.IsNearlyEqual(LU.Determinant(), det));
// check that the inverse works
SquareMatrix VI = LU.Inverse();
//PrintMatrix(VI);
//PrintMatrix(V * VI);
SquareMatrix I = TestUtilities.CreateSquareUnitMatrix(d);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V * VI, I));
// test that a solution works
ColumnVector t = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
t[i] = 1.0;
}
ColumnVector s = LU.Solve(t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(V * s, t));
}
}
public void SparseSquareMatrixSolutionAgreement()
{
Random rng = new Random(2);
int n = 16;
//for (int n = 8; n < 100; n+= 11) {
// create dense and sparse matrices with the same entries
SquareMatrix M = new SquareMatrix(n);
SparseSquareMatrix S = new SparseSquareMatrix(n);
for (int r = 0; r < n; r++)
{
for (int c = 0; c < n; c++)
{
if (rng.NextDouble() < 0.5)
{
M[r, c] = rng.NextDouble();
S[r, c] = M[r, c];
}
}
}
// pick a RHS
ColumnVector b = new ColumnVector(n);
for (int i = 0; i < n; i++)
{
b[i] = rng.NextDouble();
}
// solve each
ColumnVector Mx = M.LUDecomposition().Solve(b);
ColumnVector Sx = S.Solve(b);
// the solutions should be the same
Assert.IsTrue(TestUtilities.IsNearlyEqual(Mx, Sx, TestUtilities.TargetPrecision * 100.0));
//}
}