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

#include <ARPACKsymm.hh>

Inheritance 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. More...

virtual uint	converged () const

virtual uint	converged () const=0
	Returns the number of converged eigen pairs. More...

virtual const concepts::Array< concepts::Vector< Real > * > &	getEF ()

virtual const concepts::Array< Real > &	getEV ()
	Returns an array with the eigen values. More...

virtual uint	iterations () const

virtual uint	iterations () const=0
	Returns the number of iterations. More...

virtual	~ArPackSymm ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Private Member Functions
void	compute_ ()

Private Attributes
concepts::Operator< Real > &	A_
	Stiffness matrix. More...

concepts::Operator< Real > &	B_
	Operator B as descirbed in `modus`. More...

bool	computed_

concepts::Array< Real >	eigenvalues_
	Storage space for eigenvalues. More...

concepts::Array< Real >	eigenvectors_
	Storage space for eigenvectors. More...

concepts::Array< concepts::Vector< Real > * >	ev_
	References into storage for eigenvectors. More...

int	iter_

int	k_conv_

int	kmax_
	Number of eigenpairs to be computed. More...

int	maxiter_
	Maximum number of Arnoldi iterations allowed. More...

enum modus	mode_
	Mode in which ArPackSymm should be used. More...

int	numop_

int	numopb_

int	numreo_

concepts::Operator< Real > &	OP_
	Operator OP as described in `modus`. More...

const Real	sigma_
	Shift for the shift-invert, Buckling or Cayley mode. More...

const concepts::Vector< Real > *	start_
	Starting vector, if not given ArPackSymm invents one. More...

enum which	target_
	Sort of eigenvalues to compute. More...

Real	tol_
	Convergence tolerance for the eigenpairs. More...

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 65 of file ARPACKsymm.hh.

Member Enumeration Documentation

◆ modus

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 87 of file ARPACKsymm.hh.

◆ which

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 70 of file ARPACKsymm.hh.

Constructor & Destructor Documentation

◆ ArPackSymm()

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

◆ ~ArPackSymm()

virtual eigensolver::ArPackSymm::~ArPackSymm ( )

virtual

Member Function Documentation

◆ compute_()

void eigensolver::ArPackSymm::compute_ ( )

private

◆ converged() [1/2]

virtual uint eigensolver::ArPackSymm::converged ( ) const

inlinevirtual

Definition at line 133 of file ARPACKsymm.hh.

◆ converged() [2/2]

virtual uint eigensolver::EigenSolver< Real >::converged ( ) const

pure virtualinherited

Returns the number of converged eigen pairs.

Implemented in eigensolver::ArPack< Real >.

◆ getEF()

virtual const concepts::Array<concepts::Vector<Real>*>& eigensolver::ArPackSymm::getEF ( )

virtual

Implements eigensolver::EigenSolver< Real >.

◆ getEV()

virtual const concepts::Array<Real>& eigensolver::ArPackSymm::getEV ( )

virtual

Returns an array with the eigen values.

Deprecated:: : this interface requires that the returned array must be hold as a member variable of the class.

(use std::auto_pointer or similar)

Implements eigensolver::EigenSolver< Real >.

◆ info()

virtual std::ostream& eigensolver::ArPackSymm::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< Real >.

◆ iterations() [1/2]

virtual uint eigensolver::ArPackSymm::iterations ( ) const

inlinevirtual

Definition at line 132 of file ARPACKsymm.hh.

◆ iterations() [2/2]

virtual uint eigensolver::EigenSolver< Real >::iterations ( ) const

pure virtualinherited

Returns the number of iterations.

Implemented in eigensolver::ArPack< Real >.

Member Data Documentation

◆ A_

concepts::Operator<Real>& eigensolver::ArPackSymm::A_

private

Stiffness matrix.

Definition at line 140 of file ARPACKsymm.hh.

◆ B_

concepts::Operator<Real>& eigensolver::ArPackSymm::B_

private

Operator B as descirbed in modus.

Definition at line 142 of file ARPACKsymm.hh.

◆ computed_

bool eigensolver::ArPackSymm::computed_

private

Definition at line 164 of file ARPACKsymm.hh.

◆ eigenvalues_

concepts::Array<Real> eigensolver::ArPackSymm::eigenvalues_

private

Storage space for eigenvalues.

Definition at line 151 of file ARPACKsymm.hh.

◆ eigenvectors_

concepts::Array<Real> eigensolver::ArPackSymm::eigenvectors_

private

Storage space for eigenvectors.

Definition at line 153 of file ARPACKsymm.hh.

◆ ev_

concepts::Array<concepts::Vector<Real>*> eigensolver::ArPackSymm::ev_

private

References into storage for eigenvectors.

Definition at line 155 of file ARPACKsymm.hh.

◆ iter_

int eigensolver::ArPackSymm::iter_

private

Definition at line 149 of file ARPACKsymm.hh.

◆ k_conv_

int eigensolver::ArPackSymm::k_conv_

private

Definition at line 149 of file ARPACKsymm.hh.

◆ kmax_

int eigensolver::ArPackSymm::kmax_

private

Number of eigenpairs to be computed.

Definition at line 144 of file ARPACKsymm.hh.

◆ maxiter_

int eigensolver::ArPackSymm::maxiter_

private

Maximum number of Arnoldi iterations allowed.

Definition at line 146 of file ARPACKsymm.hh.

◆ mode_

enum modus eigensolver::ArPackSymm::mode_

private

Mode in which ArPackSymm should be used.

Definition at line 155 of file ARPACKsymm.hh.

◆ numop_

int eigensolver::ArPackSymm::numop_

private

Definition at line 149 of file ARPACKsymm.hh.

◆ numopb_

int eigensolver::ArPackSymm::numopb_

private

Definition at line 149 of file ARPACKsymm.hh.

◆ numreo_

int eigensolver::ArPackSymm::numreo_

private

Definition at line 149 of file ARPACKsymm.hh.

◆ OP_

concepts::Operator<Real>& eigensolver::ArPackSymm::OP_

private

Operator OP as described in modus.

Definition at line 138 of file ARPACKsymm.hh.

◆ sigma_

const Real eigensolver::ArPackSymm::sigma_

private

Shift for the shift-invert, Buckling or Cayley mode.

Definition at line 161 of file ARPACKsymm.hh.

◆ start_

const concepts::Vector<Real>* eigensolver::ArPackSymm::start_

private

Starting vector, if not given ArPackSymm invents one.

Definition at line 163 of file ARPACKsymm.hh.

◆ target_

enum which eigensolver::ArPackSymm::target_

private

Sort of eigenvalues to compute.

Definition at line 155 of file ARPACKsymm.hh.

◆ tol_

Real eigensolver::ArPackSymm::tol_

private

Convergence tolerance for the eigenpairs.

Definition at line 148 of file ARPACKsymm.hh.

The documentation for this class was generated from the following file:

eigensolver/ARPACKsymm.hh

eigensolver::ArPackSymm Class Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

◆ modus

◆ which

Constructor & Destructor Documentation

◆ ArPackSymm()

◆ ~ArPackSymm()

Member Function Documentation

◆ compute_()

◆ converged() [1/2]

◆ converged() [2/2]

◆ getEF()

◆ getEV()

◆ info()

◆ iterations() [1/2]

◆ iterations() [2/2]

Member Data Documentation

◆ A_

◆ B_

◆ computed_

◆ eigenvalues_

◆ eigenvectors_

◆ ev_

◆ iter_

◆ k_conv_

◆ kmax_

◆ maxiter_

◆ mode_

◆ numop_

◆ numopb_

◆ numreo_

◆ OP_

◆ sigma_

◆ start_

◆ target_

◆ tol_