public void RealEigenvalueOrdering()
{
int d = 10;
Random rng = new Random(d + 1);
SymmetricMatrix A = new SymmetricMatrix(d);
A.Fill((int r, int c) => -1.0 + 2.0 * rng.NextDouble());
RealEigensystem E = A.Eigensystem();
for (int i = 0; i < E.Dimension; i++) Console.WriteLine(E.Eigenvalue(i));
E.Sort(OrderBy.ValueAscending);
for (int i = 1; i < E.Dimension; i++) {
Assert.IsTrue(E.Eigenvalue(i - 1) <= E.Eigenvalue(i));
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(A, E.Eigenvector(i), E.Eigenvalue(i)));
}
E.Sort(OrderBy.ValueDescending);
for (int i = 1; i < E.Dimension; i++) {
Assert.IsTrue(E.Eigenvalue(i - 1) >= E.Eigenvalue(i));
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(A, E.Eigenvector(i), E.Eigenvalue(i)));
}
E.Sort(OrderBy.MagnitudeAscending);
for (int i = 1; i < E.Dimension; i++) {
Assert.IsTrue(Math.Abs(E.Eigenvalue(i - 1)) <= Math.Abs(E.Eigenvalue(i)));
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(A, E.Eigenvector(i), E.Eigenvalue(i)));
}
E.Sort(OrderBy.MagnitudeDescending);
for (int i = 1; i < E.Dimension; i++) {
Assert.IsTrue(Math.Abs(E.Eigenvalue(i - 1)) >= Math.Abs(E.Eigenvalue(i)));
Assert.IsTrue(TestUtilities.IsNearlyEigenpair(A, E.Eigenvector(i), E.Eigenvalue(i)));
}
}
public static SymmetricMatrix CreateSymmetricHilbertMatrix(int n)
{
SymmetricMatrix H = new SymmetricMatrix(n);
H.Fill((r, c) => 1.0 / (r + c + 1));
return (H);
}