/// <summary>
/// Check residuals of generalized symmetric eigenvalue problem.
/// </summary>
/// <param name="A">The matrix A.</param>
/// <param name="B">The matrix B.</param>
/// <param name="result">The eigensolver result.</param>
/// <param name="symmetric">Indicates, whether the problem is symmetric.</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, IEigenSolverResult result, bool symmetric, bool print)
{
if (symmetric)
{
return(CheckResiduals(A, B, result.ConvergedEigenValues, result.EigenValuesReal(), result.EigenVectorsReal(), print));
}
return(CheckResiduals(A, B, result.ConvergedEigenValues, result.EigenValues, result.EigenVectors, print));
}
/// <summary>
/// Check residuals of eigenvalue problem.
/// </summary>
/// <param name="A">The matrix.</param>
/// <param name="result">The eigensolver result.</param>
/// <param name="print">If true, print residuals.</param>
/// <returns>True, if all residuals are below threshold.</returns>
public static bool CheckResiduals(SparseMatrix A, IEigenSolverResult result, bool print)
{
int N = A.RowCount;
var m = result.ConvergedEigenValues;
var v = result.EigenValues;
var X = result.EigenVectors;
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 < m; i++)
{
var lambda = v[i].Real;
X.Column(i, x);
Vector.Copy(x, y);
// y = A*x - lambda*x
A.Multiply(1.0, x, -lambda, y);
double r = Vector.Norm(y);
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>
/// Check residuals of symmetric eigenvalue problem.
/// </summary>
/// <param name="A">The matrix A.</param>
/// <param name="result">The eigensolver result.</param>
/// <param name="symmetric">Indicates, whether the problem is symmetric.</param>
/// <param name="print">If true, print residuals.</param>
/// <returns>True, if all residuals are below threshold.</returns>
public static bool CheckResiduals(SparseMatrix A, IEigenSolverResult result, bool symmetric, bool print)
{
return(CheckResiduals(A, null, result, symmetric, print));
}
