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 SquareVandermondeMatrixInverse()
{
for (int d = 1; d < 8; d++)
{
SquareMatrix H = CreateVandermondeMatrix(d);
SquareMatrix HI = H.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(H * HI, UnitMatrix.OfDimension(d)));
}
}
public void SquareRandomMatrixInverse()
{
for (int d = 1; d <= 100; d = d + 11)
{
SquareMatrix M = CreateSquareRandomMatrix(d, 1);
SquareMatrix MI = M.Inverse();
Assert.IsTrue(TestUtilities.IsNearlyEqual(M * MI, UnitMatrix.OfDimension(d)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(MI * M, UnitMatrix.OfDimension(d)));
}
}
public void SquareVandermondeMatrixInverse()
{
for (int d = 1; d <= 8; d++)
{
SquareMatrix I = TestUtilities.CreateSquareUnitMatrix(d);
SquareMatrix H = CreateVandermondeMatrix(d);
DateTime start = DateTime.Now;
SquareMatrix HI = H.Inverse();
DateTime finish = DateTime.Now;
Console.WriteLine("d={0} t={1} ms", d, (finish - start).Milliseconds);
PrintMatrix(HI);
PrintMatrix(H * HI);
Assert.IsTrue(TestUtilities.IsNearlyEqual(H * HI, I));
}
}
public void Bug7208()
{
// this matrix has two eigenpairs with the same eigenvalue but distinct eigenvectors
// we would report the same eigenvector for both, making the matrix of eigenvectors
// non-invertible
int n = 4;
SquareMatrix matrix = new SquareMatrix(n + 1);
double d = (3 + 2 * Math.Cos(2 * Math.PI / n));
double w = (64 * n) / (40 - d * d) - n;
double w1 = w / (w + n);
double w2 = 1 / (w + n);
matrix[0, 0] = w1;
for (int i = 1; i < n; i++)
{
matrix[0, i + 1] = w2;
matrix[i + 1, 0] = 3.0 / 8;
matrix[i + 1, i + 1] = 3.0 / 8;
matrix[i, i + 1] = 1.0 / 8;
matrix[i + 1, i] = 1.0 / 8;
}
matrix[0, 1] = w2;
matrix[1, 0] = 3.0 / 8;
matrix[1, 1] = 3.0 / 8;
matrix[1, n] = 1.0 / 8;
matrix[n, 1] = 1.0 / 8;
ComplexEigensystem ces = matrix.Eigensystem();
Console.WriteLine("output");
SquareMatrix V = new SquareMatrix(n + 1);
for (int i = 0; i < n + 1; i++)
{
Console.WriteLine("#{0}: {1}", i, ces.Eigenvalue(i));
for (int j = 0; j < n + 1; j++)
{
V[i, j] = ces.Eigenvector(i)[j].Re;
Console.WriteLine(V[i, j]);
}
}
SquareMatrix inv = V.Inverse();
}
