/// <summary>
/// Check residuals of generalized eigenvalue problem.
/// </summary>
/// <param name="A">Symmetric matrix.</param>
/// <param name="B">Symmetric matrix.</param>
/// <param name="k">The number of converged eigenvalues.</param>
/// <param name="v">The eigenvalues array.</param>
/// <param name="X">The eigenvectors matrix.</param>
/// <param name="print">If true, print residuals.</param>
/// <returns>True, if all residuals are below threshold.</returns>
public static bool CheckResiduals(SparseMatrix A, SparseMatrix B, int k, Complex[] v, Matrix <Complex> X, bool print)
{
int N = A.RowCount;
// If more eigenvalues converged than were requested (real, non-symmetric case only).
k = Math.Min(k, X.ColumnCount);
if (print)
{
Console.WriteLine();
Console.WriteLine(" Lambda Residual");
}
var x = new Complex[N];
var y = new Complex[N];
bool ok = true;
for (int i = 0; i < k; i++)
{
var lambda = v[i];
X.Column(i, x);
CVector.Copy(x, y);
if (B != null)
{
// y = B*x
B.Multiply(x, y);
}
// y = A*x - lambda*B*x
A.Multiply(1.0, x, -lambda, y);
double r = CVector.Norm(y) / Complex.Abs(lambda);
if (r > ERROR_THRESHOLD)
{
ok = false;
}
if (print)
{
Console.WriteLine("{0,3}: {1,10:0.00000000} {2,10:0.00e+00}", i, lambda, r);
}
}
return(ok);
}
/// <summary>
/// Prints eigenvalues and eigenvectors of nonsymmetric generalized eigen-problems.
/// </summary>
public static void General(SparseMatrix A, SparseMatrix B, SpectraResult result, bool shift, bool cshift = false)
{
if (!EnsureSuccess(result))
{
return;
}
int n = A.RowCount;
int nconv = result.ConvergedEigenValues;
Console.WriteLine();
Console.WriteLine("Testing ARPACK++ class ARluNonSymGenEig");
Console.WriteLine("Real nonsymmetric generalized eigenvalue problem: A*x - lambda*B*x");
Console.WriteLine(!shift ? "Regular mode" :
(cshift ? "Shift and invert mode (using the imaginary part of OP)" : "Shift and invert mode (using the real part of OP)"));
Console.WriteLine();
Console.WriteLine("Dimension of the system : " + n);
Console.WriteLine("Number of 'requested' eigenvalues : " + result.Count);
Console.WriteLine("Number of 'converged' eigenvalues : " + nconv);
Console.WriteLine("Number of Arnoldi vectors generated: " + result.ArnoldiCount);
Console.WriteLine("Number of iterations taken : " + result.IterationsTaken);
Console.WriteLine();
var evals = result.EigenValues;
var evecs = result.EigenVectors;
// Printing eigenvalues.
Console.WriteLine("Eigenvalues:");
for (int i = 0; i < nconv; i++)
{
Console.WriteLine(" lambda[" + (i + 1) + "]: " + evals[i]);
}
Console.WriteLine();
if (evecs != null)
{
// Printing the residual norm || A*x - lambda*B*x ||
// for the nconv accurately computed eigenvectors.
var x = new Complex[n];
var y = new Complex[n];
var r = new double[nconv]; // residuals
for (int i = 0; i < nconv; i++)
{
var lambda = evals[i];
evecs.Column(i, x);
CVector.Copy(x, y);
// y = B*x
B.Multiply(x, y);
// y = A*x - lambda*B*x
A.Multiply(1.0, x, -lambda, y);
r[i] = CVector.Norm(y) / Complex.Abs(lambda);
}
for (int i = 0; i < nconv; i++)
{
Console.WriteLine("||A*x(" + i + ") - lambda(" + i + ")*B*x(" + i + ")||: " + r[i]);
}
Console.WriteLine();
}
}
