public void SquareVandermondeMatrixEigenvalues()
{
for (int d = 1; d <= 8; d++)
{
SquareMatrix H = CreateVandermondeMatrix(d);
double tr = H.Trace();
ComplexEigensystem E = H.Eigensystem();
double sum = 0.0;
for (int i = 0; i < d; i++)
{
Console.WriteLine(E.Eigenvalue(i));
double e = E.Eigenvalue(i).Re;
sum += e;
Complex[] vc = E.Eigenvector(i);
ColumnVector v = new ColumnVector(d);
for (int j = 0; j < d; j++)
{
//Console.WriteLine(" {0}", vc[j]);
v[j] = vc[j].Re;
}
ColumnVector Hv = H * v;
ColumnVector ev = e * v;
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(H, v, e));
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(tr, sum));
}
}
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 Bug8021()
{
// User presented a matrix with a large number (138) of zero eigenvalues.
// QR algorithm got tripped up on high degeneracy, but eigenvalues could
// be revealed before QR by simple index permutation. Added code to isolate
// these "cheap" eigenvalues before starting QR algorithm.
int n = 276;
SquareMatrix A = new SquareMatrix(n);
using (System.IO.StreamReader reader = System.IO.File.OpenText(@"Bug8021.csv")) {
int r = 0;
while (!reader.EndOfStream)
{
string line = reader.ReadLine();
string[] cells = line.Split(',');
for (int c = 0; c < cells.Length; c++)
{
string cell = cells[c];
double value = Double.Parse(cell);
A[r, c] = value;
}
r++;
}
}
ComplexEigendecomposition S = A.Eigendecomposition();
foreach (ComplexEigenpair pair in S.Eigenpairs)
{
TestUtilities.IsNearlyEigenpair(A, pair.Eigenvector, pair.Eigenvalue);
}
Complex[] eigenvalues = A.Eigenvalues();
double trace = A.Trace();
Complex sum = 0.0;
for (int i = 0; i < eigenvalues.Length; i++)
{
sum += eigenvalues[i];
}
TestUtilities.IsNearlyEqual(trace, sum);
}
public void SquareRandomMatrixEigenvalues()
{
for (int d = 1; d <= 67; d = d + 11)
{
SquareMatrix M = CreateSquareRandomMatrix(d, d);
double tr = M.Trace();
DateTime start = DateTime.Now;
ComplexEigendecomposition E = M.Eigendecomposition();
DateTime finish = DateTime.Now;
Console.WriteLine("d={0} t={1} ms", d, (finish - start).Milliseconds);
Assert.IsTrue(E.Dimension == d);
Complex[] es = new Complex[d];
for (int i = 0; i < d; i++)
{
es[i] = E.Eigenpairs[i].Eigenvalue;
ComplexColumnVector v = E.Eigenpairs[i].Eigenvector;
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(M, v, es[i]));
}
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(es, tr));
}
}
public void SquareVandermondeMatrixEigenvalues()
{
for (int d = 1; d <= 8; d++)
{
SquareMatrix H = CreateVandermondeMatrix(d);
double tr = H.Trace();
ComplexEigendecomposition E = H.Eigendecomposition();
double sum = 0.0;
foreach (ComplexEigenpair pair in E.Eigenpairs)
{
double e = pair.Eigenvalue.Re;
sum += e;
ComplexColumnVector vc = pair.Eigenvector;
ColumnVector v = new ColumnVector(d);
for (int j = 0; j < d; j++)
{
v[j] = vc[j].Re;
}
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(H, v, e));
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(tr, sum));
}
}