Eigenvalue solver using ArPack, the routine dsaupd. More...

#include <ARPACKsymm.hh>

Inheritance diagram for eigensolver::ArPackSymm:

Collaboration diagram for eigensolver::ArPackSymm:

Public Types
enum	modus { NORMAL = 1, REGINV = 2, SHIFTINV = 3, BUCKLING = 4, CAYLEY = 5 }
	Specify mode of ArPackSymm which should be used to compute the Ritz values $\nu$ of OP. More...
enum	which { LA, SA, LM, SM, BE }
	Specify which of the Ritz values $\nu$ of OP (described in `modus`) to compute. More...
Public Member Functions
	ArPackSymm (concepts::Operator< Real > &OP, concepts::Operator< Real > &A, concepts::Operator< Real > &B, const int kmax=1, const Real tol=0.0, const int maxiter=300, enum which target=SM, enum modus mode=REGINV, const Real sigma=0.0, const concepts::Vector< Real > *start=0)
	Constructor.
virtual uint	converged () const
	Returns the number of converged eigen pairs.
virtual const concepts::Array < concepts::Vector< Real > * > &	getEF ()
virtual const concepts::Array < Real > &	getEV ()
	Returns an array with the eigen values.
virtual uint	iterations () const
	Returns the number of iterations.
virtual	~ArPackSymm ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Member Functions
void	compute_ ()
Private Attributes
concepts::Operator< Real > &	A_
	Stiffness matrix.
concepts::Operator< Real > &	B_
	Operator B as descirbed in `modus`.
bool	computed_
concepts::Array< Real >	eigenvalues_
	Storage space for eigenvalues.
concepts::Array< Real >	eigenvectors_
	Storage space for eigenvectors.
concepts::Array < concepts::Vector< Real > * >	ev_
	References into storage for eigenvectors.
int	iter_
int	k_conv_
int	kmax_
	Number of eigenpairs to be computed.
int	maxiter_
	Maximum number of Arnoldi iterations allowed.
enum modus	mode_
	Mode in which ArPackSymm should be used.
int	numop_
int	numopb_
int	numreo_
concepts::Operator< Real > &	OP_
	Operator OP as described in `modus`.
const Real	sigma_
	Shift for the shift-invert, Buckling or Cayley mode.
const concepts::Vector< Real > *	start_
	Starting vector, if not given ArPackSymm invents one.
enum which	target_
	Sort of eigenvalues to compute.
Real	tol_
	Convergence tolerance for the eigenpairs.

Detailed Description

Eigenvalue solver using ArPack, the routine dsaupd.

ArPack is designed to solve large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A. This software is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems.

ArPack software is capable of solving large scale symmetric, nonsymmetric, and generalized eigenproblems from significant application areas. The software is designed to compute a few (k) eigenvalues with user specified features such as those of largest real part or largest magnitude. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigen-space is computed which is numerically orthogonal to working precision. Numerically accurate eigenvectors are available on request.

dsaupd uses implicitly restarted Arnoldi iteration to solve the generalized eigenvalue problem $A x = \lambda B x$ with B symmetric and positive definite. For symmetric problems this reduces to a variant of the Lanczos method.

See also:: Richard B. Lehoucq, Kristyn J. Maschhoff, Danny C. Sorensen, and Chao Yang, ArPackSymm Homepage.; Richard B. Lehoucq, Danny C. Sorensen, and Chao Yang. ArPackSymm users' guide. Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1998.

Test:

test::GolubExample

test::GolubExampleSum

test::MaxwellTransmissionEVP

Author:: Philipp Frauenfelder, 2002

Definition at line 62 of file ARPACKsymm.hh.

Member Enumeration Documentation

enum eigensolver::ArPackSymm::modus

Specify mode of ArPackSymm which should be used to compute the Ritz values $\nu$ of OP.

Enumerator:

NORMAL
REGINV
SHIFTINV
BUCKLING
CAYLEY

Definition at line 84 of file ARPACKsymm.hh.

enum eigensolver::ArPackSymm::which

Specify which of the Ritz values $\nu$ of OP (described in modus) to compute.

Enumerator:

LA
SA
LM
SM
BE

Definition at line 67 of file ARPACKsymm.hh.

Constructor & Destructor Documentation

eigensolver::ArPackSymm::ArPackSymm	(	concepts::Operator< Real > &	OP,
		concepts::Operator< Real > &	A,
		concepts::Operator< Real > &	B,
		const int	kmax = `1`,
		const Real	tol = `0.0`,
		const int	maxiter = `300`,
		enum which	target = `SM`,
		enum modus	mode = `REGINV`,
		const Real	sigma = `0.0`,
		const concepts::Vector< Real > *	start = `0`
	)

Constructor.

Parameters:

OP	Operator OP as described in `modus`
A	Stiffness matrix
B	Operator B as descirbed in `modus`
kmax	Number of eigenpairs to be computed
tol	Convergence tolerance for the eigenpairs. The default value 0.0 is replaced by `DLAMCH`('EPS') from LAPACK.
maxiter	Maximum number of Arnoldi iterations allowed
target	What sort of eigenvalues to compute
mode	Mode in which ArPackSymm should be used
sigma	Shift for the shift-invert, Buckling or Cayley mode