Find the eigenvalues of a sparse symmetric matrix. More...

#include <vnl_sparse_symmetric_eigensystem.h>

Public Member Functions
	vnl_sparse_symmetric_eigensystem ()

	~vnl_sparse_symmetric_eigensystem ()

int	CalculateNPairs (vnl_sparse_matrix< double > &M, int n, bool smallest=true, long nfigures=10)
	Here is where the fortran converted code gets called. More...

int	CalculateNPairs (vnl_sparse_matrix< double > &A, vnl_sparse_matrix< double > &B, int nEV, double tolerance=0, int numberLanczosVecs=0, bool smallest=false, bool magnitude=true, int maxIterations=0, double sigma=0.0)
	Here is where the fortran converted code gets called. More...

vnl_vector< double >	get_eigenvector (int i) const
	Return a calculated eigenvector. More...

double	get_eigenvalue (int i) const

int	CalculateProduct (int n, int m, const double p, double q)
	Callback from solver to calculate the product A p. More...

int	SaveVectors (int n, int m, const double *q, int base)
	Callback to store vectors for dnlaso. More...

int	RestoreVectors (int n, int m, double *q, int base)
	Callback to restore vectors for dnlaso. More...

Protected Attributes
int	nvalues

vnl_vector< double > *	vectors

double *	values

vnl_sparse_matrix< double > *	mat

vnl_sparse_matrix< double > *	Bmat

std::vector< double * >	temp_store

Detailed Description

Find the eigenvalues of a sparse symmetric matrix.

Solve the standard eigenproblem $A x = \lambda x$ , or the generalized eigenproblem of $A x = \lambda B x$ , where $A$ symmetric and sparse and, optionally, B sparse, symmetric, and positive definite. The block Lanczos algorithm is used to allow the recovery of a number of eigenvalue/eigenvector pairs from either end of the spectrum, to a required accuracy.

Uses the dnlaso routine from the LASO package of netlib for solving the standard case. Uses the dsaupd routine from the ARPACK package of netlib for solving the generalized case.

Definition at line 37 of file vnl_sparse_symmetric_eigensystem.h.

Constructor & Destructor Documentation

◆ vnl_sparse_symmetric_eigensystem()

vnl_sparse_symmetric_eigensystem::vnl_sparse_symmetric_eigensystem ( )

Definition at line 53 of file vnl_sparse_symmetric_eigensystem.cxx.

◆ ~vnl_sparse_symmetric_eigensystem()

vnl_sparse_symmetric_eigensystem::~vnl_sparse_symmetric_eigensystem ( )

Definition at line 58 of file vnl_sparse_symmetric_eigensystem.cxx.

Member Function Documentation

◆ CalculateNPairs() [1/2]

int vnl_sparse_symmetric_eigensystem::CalculateNPairs	(	vnl_sparse_matrix< double > &	M,
		int	n,
		bool	smallest = `true`,
		long	nfigures = `10`
	)

Here is where the fortran converted code gets called.

The sparse matrix M is assumed to be symmetric. The n smallest eigenvalues and their corresponding eigenvectors are calculated if smallest is true (the default). Otherwise the n largest eigenpairs are found. The accuracy of the eigenvalues is to nfigures decimal digits. Returns 0 if successful, non-zero otherwise.

Definition at line 74 of file vnl_sparse_symmetric_eigensystem.cxx.

◆ CalculateNPairs() [2/2]

int vnl_sparse_symmetric_eigensystem::CalculateNPairs	(	vnl_sparse_matrix< double > &	A,
		vnl_sparse_matrix< double > &	B,
		int	nEV,
		double	tolerance = `0`,
		int	numberLanczosVecs = `0`,
		bool	smallest = `false`,
		bool	magnitude = `true`,
		int	maxIterations = `0`,
		double	sigma = `0.0`
	)

Here is where the fortran converted code gets called.

The sparse matrix A is assumed to be symmetric. Find n eigenvalue/eigenvectors of the eigenproblem A * x = lambda * B * x. !smallest and !magnitude - compute the N largest (algebraic) eigenvalues smallest and !magnitude - compute the N smallest (algebraic) eigenvalues !smallest and magnitude - compute the N largest (magnitude) eigenvalues smallest and magnitude - compute the nev smallest (magnitude) eigenvalues set sigma for shift/invert mode

Definition at line 204 of file vnl_sparse_symmetric_eigensystem.cxx.