/// <summary>
/// Example program that illustrates how to solve a real symmetric generalized eigenvalue
/// problem in Cayley mode.
/// </summary>
/// <remarks>
/// MODULE LSymGCay.cc
///
/// In this example we try to solve A*x = B*x*lambda in Cayley mode, where A and B are obtained
/// from the finite element discretization of the 1-dimensional discrete Laplacian
/// d^2u / dx^2
/// on the interval [0,1] with zero Dirichlet boundary conditions using piecewise linear elements.
///
/// The SuperLU package is called to solve some linear systems involving (A-sigma*B).
/// </remarks>
static void LSymGCay()
{
int n = 100; // Dimension of the problem.
// Creating matrices A and B.
var A = Symmetrize(Generate.SymmetricMatrixC(n));
var B = Symmetrize(Generate.SymmetricMatrixD(n));
// Defining what we need: the four eigenvectors nearest to 150.0.
var prob = new Spectra(A, B, true)
{
ComputeEigenVectors = true
};
// Finding eigenvalues and eigenvectors.
var result = prob.SolveGeneralized(4, 150.0, ShiftMode.Cayley);
// Printing solution.
Solution.Symmetric(A, B, (SpectraResult)result, ShiftMode.Cayley);
}
/// <summary>
/// Example program that illustrates how to solve a real symmetric generalized eigenvalue
/// problem in regular mode.
/// </summary>
/// <remarks>
/// MODULE LSymGReg.cc
///
/// In this example we try to solve A*x = B*x*lambda in regular mode, where A and B are obtained
/// from the finite element discretization of the 1-dimensional discrete Laplacian
/// d^2u / dx^2
/// on the interval [0,1] with zero Dirichlet boundary conditions using piecewise linear elements.
///
/// The SuperLU package is called to solve some linear systems involving B.
/// </remarks>
static void LSymGReg()
{
int n = 100; // Dimension of the problem.
// Creating matrices A and B.
var A = Symmetrize(Generate.SymmetricMatrixC(n));
var B = Symmetrize(Generate.SymmetricMatrixD(n));
// Defining what we need: the four eigenvectors with largest magnitude.
var prob = new Spectra(A, B, true)
{
ComputeEigenVectors = true
};
// Finding eigenvalues and eigenvectors.
var result = prob.SolveGeneralized(4, Spectrum.LargestMagnitude);
// Printing solution.
Solution.Symmetric(A, B, (SpectraResult)result, ShiftMode.None);
}
/// <summary>
/// Example program that illustrates how to solve a real nonsymmetric generalized eigenvalue
/// problem in real shift and invert mode.
/// </summary>
/// <remarks>
/// MODULE LNSymGSh.cc
///
/// In this example we try to solve A*x = B*x*lambda in shift and inverse mode, where A and B
/// are derived from the finite element discretization of the 1-dimensional convection-diffusion
/// operator
/// (d^2u / dx^2) + rho*(du/dx)
/// on the interval [0,1] with zero Dirichlet boundary conditions using linear elements.
/// The shift sigma is a real number.
///
/// The SuperLU package is called to solve some linear systems involving (A-sigma*B).
/// </remarks>
static void LNSymGSh()
{
int n = 100; // Dimension of the problem.
double rho = 10.0; // A parameter used in StiffnessMatrix.
// Creating matrices A and B.
var A = Generate.StiffnessMatrix(n, rho);
var B = Generate.MassMatrix(n);
// Defining what we need: the four eigenvectors nearest to 1.0.
var prob = new Spectra(A, B)
{
ComputeEigenVectors = true
};
// Finding eigenvalues and eigenvectors.
var result = prob.SolveGeneralized(4, 1.0);
// Printing solution.
Solution.General(A, B, (SpectraResult)result, true);
}
