Eigenvalue solver using ARPACK, the routine dnaupd or znaupd. More...

#include <ARPACK.hh>

Inheritance diagram for eigensolver::ArPack< F, G, H >:

Public Types
enum	modus { NORMAL = 1, REGINV = 2, SHIFTINV = 3, SHIFTINVIMAG = 4 }
	Specify mode of ARPACK which should be used to compute the Ritz values $\nu$ of OP. More...

enum	which { LM, SM, LR, SR, LI, SI }
	Specify which of the Ritz values $\nu$ of OP (described in `modus`) to compute. More...

Public Member Functions
	ArPack (concepts::Operator< G > &OP, concepts::Operator< F > &A, concepts::Operator< H > &B, const int kmax=1, const Real tol=0.0, const int maxiter=300, enum which target=SM, enum modus mode=REGINV, const F sigma=0.0, const concepts::Vector< F > start=0, const concepts::Array< F > resid=0, const bool schur=false)
	Constructor. More...

virtual uint	converged () const
	Returns the number of converged eigenpairs. More...

virtual const concepts::Array< concepts::Vector< F > * > &	getEF ()
	Returns an array with the eigenfunctions. More...

virtual const concepts::Array< F > &	getEV ()
	Returns an array with the real parts of the eigenvalues in the first `kmax` entries and the imaginary parts of the eigenvalues in the second `kmax` entries. More...

concepts::Array< F >	getRESID ()
	Returns the RESID vector: More...

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

virtual	~ArPack ()

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

Private Member Functions
void	compute_ ()
	Compute eigenpairs. More...

void	computeCmplx_ ()

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

concepts::Operator< H > &	B_
	Operator B as described in `modus`. More...

bool	computed_
	Eigenpairs computed? More...

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

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

concepts::Array< concepts::Vector< F > * >	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 ARPACK should be used. More...

int	numop_

int	numopb_

int	numreo_

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

const concepts::Array< F > *	resid_in_
	Calculate vectors instead of eigenvectors Input of a residual vector (startvector) as array: More...

concepts::Array< F >	resid_out_
	The residual vector for output: More...

const bool	schur_

const F	sigma_
	Shift for the shift-invert modes: More...

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

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

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

Detailed Description

template<typename F, typename G = Real, typename H = Real>
class eigensolver::ArPack< F, G, H >

Eigenvalue solver using ARPACK, the routine dnaupd or znaupd.

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.

dnaupd uses implicitly restarted Arnoldi iteration to solve the generalized eigenvalue problem $A x = \lambda B x$ with A general non-symmetric and B symmetric and positive definite. For A symmetric, use ArPackSymm instead.

znaupd uses implicitly restarted Arnoldi iteration to solve the generalized eigenvalue problem $A x = \lambda B x$ with A general non-symmetric, complex and B symmetric and positive definite, real. For A symmetric and complex also use this routine.

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

Author: Christoph Winkelmann, 2004

Definition at line 70 of file ARPACK.hh.

Member Enumeration Documentation

◆ modus

template<typename F , typename G = Real, typename H = Real>

enum eigensolver::ArPack::modus

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

Enumerator
NORMAL
REGINV
SHIFTINV
SHIFTINVIMAG

Definition at line 92 of file ARPACK.hh.

◆ which

template<typename F , typename G = Real, typename H = Real>

enum eigensolver::ArPack::which

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

Enumerator
LM
SM
LR
SR
LI
SI

Definition at line 75 of file ARPACK.hh.

Constructor & Destructor Documentation

◆ ArPack()

template<typename F , typename G = Real, typename H = Real>

eigensolver::ArPack< F, G, H >::ArPack	(	concepts::Operator< G > &	OP,
		concepts::Operator< F > &	A,
		concepts::Operator< H > &	B,
		const int	kmax = `1`,
		const Real	tol = `0.0`,
		const int	maxiter = `300`,
		enum which	target = `SM`,
		enum modus	mode = `REGINV`,
		const F	sigma = `0.0`,
		const concepts::Vector< F > *	start = `0`,
		const concepts::Array< F > *	resid = `0`,
		const bool	schur = `false`
	)

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 ARPACK should be used
sigma	Shift for the shift-invert modes
start	Initial vector for iteration
schur	Calculate Schur vector basis instead of eigenvectors

◆ ~ArPack()

template<typename F , typename G = Real, typename H = Real>

virtual eigensolver::ArPack< F, G, H >::~ArPack ( )

virtual

Member Function Documentation

◆ compute_()

template<typename F , typename G = Real, typename H = Real>

void eigensolver::ArPack< F, G, H >::compute_ ( )

private

Compute eigenpairs.

◆ computeCmplx_()

template<typename F , typename G = Real, typename H = Real>

void eigensolver::ArPack< F, G, H >::computeCmplx_ ( )

private

◆ converged()

template<typename F , typename G = Real, typename H = Real>

virtual uint eigensolver::ArPack< F, G, H >::converged ( ) const

inlinevirtual

Returns the number of converged eigenpairs.

Implements eigensolver::EigenSolver< F >.

Definition at line 150 of file ARPACK.hh.

◆ getEF()

template<typename F , typename G = Real, typename H = Real>

virtual const concepts::Array<concepts::Vector<F>*>& eigensolver::ArPack< F, G, H >::getEF ( )

virtual

Returns an array with the eigenfunctions.

If eigenvalue k is real, entry k contains the (real) eigenfunction. If eigenvalues k and k+1 are complex conjugate, entry k contains the real part of and entry k+1 contains the imaginary part of eigenfunction k. Eigenfunction k+1 is the complex conjugate of eigenfunction k.

Implements eigensolver::EigenSolver< F >.

◆ getEV()

template<typename F , typename G = Real, typename H = Real>

virtual const concepts::Array<F>& eigensolver::ArPack< F, G, H >::getEV ( )

virtual

Returns an array with the real parts of the eigenvalues in the first kmax entries and the imaginary parts of the eigenvalues in the second kmax entries.

Implements eigensolver::EigenSolver< F >.

◆ getRESID()

template<typename F , typename G = Real, typename H = Real>

concepts::Array<F> eigensolver::ArPack< F, G, H >::getRESID ( )

inline

Returns the RESID vector:

Definition at line 152 of file ARPACK.hh.

◆ info()

template<typename F , typename G = Real, typename H = Real>

virtual std::ostream& eigensolver::ArPack< F, G, H >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< F >.

◆ iterations()

template<typename F , typename G = Real, typename H = Real>

virtual uint eigensolver::ArPack< F, G, H >::iterations ( ) const

inlinevirtual

Returns the number of iterations.

Implements eigensolver::EigenSolver< F >.

Definition at line 148 of file ARPACK.hh.

Member Data Documentation

◆ A_

template<typename F , typename G = Real, typename H = Real>

concepts::Operator<F>& eigensolver::ArPack< F, G, H >::A_

private

Stiffness matrix.

Definition at line 159 of file ARPACK.hh.

◆ B_

template<typename F , typename G = Real, typename H = Real>

concepts::Operator<H>& eigensolver::ArPack< F, G, H >::B_

private

Operator B as described in modus.

Definition at line 161 of file ARPACK.hh.

◆ computed_

template<typename F , typename G = Real, typename H = Real>

bool eigensolver::ArPack< F, G, H >::computed_

private

Eigenpairs computed?

Definition at line 188 of file ARPACK.hh.

◆ eigenvalues_

template<typename F , typename G = Real, typename H = Real>

concepts::Array<F> eigensolver::ArPack< F, G, H >::eigenvalues_

private

Storage space for eigenvalues.

Definition at line 170 of file ARPACK.hh.

◆ eigenvectors_

template<typename F , typename G = Real, typename H = Real>

concepts::Array<F> eigensolver::ArPack< F, G, H >::eigenvectors_

private

Storage space for eigenvectors.

Definition at line 172 of file ARPACK.hh.

◆ ev_

template<typename F , typename G = Real, typename H = Real>

concepts::Array<concepts::Vector<F>*> eigensolver::ArPack< F, G, H >::ev_

private

References into storage for eigenvectors.

Definition at line 174 of file ARPACK.hh.

◆ iter_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::iter_

private

Definition at line 168 of file ARPACK.hh.

◆ k_conv_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::k_conv_

private

Definition at line 168 of file ARPACK.hh.

◆ kmax_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::kmax_

private

Number of eigenpairs to be computed.

Definition at line 163 of file ARPACK.hh.

◆ maxiter_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::maxiter_

private

Maximum number of Arnoldi iterations allowed.

Definition at line 165 of file ARPACK.hh.

◆ mode_

template<typename F , typename G = Real, typename H = Real>

enum modus eigensolver::ArPack< F, G, H >::mode_

private

Mode in which ARPACK should be used.

Definition at line 174 of file ARPACK.hh.

◆ numop_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::numop_

private

Definition at line 168 of file ARPACK.hh.

◆ numopb_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::numopb_

private

Definition at line 168 of file ARPACK.hh.

◆ numreo_

template<typename F , typename G = Real, typename H = Real>

int eigensolver::ArPack< F, G, H >::numreo_

private

Definition at line 168 of file ARPACK.hh.

◆ OP_

template<typename F , typename G = Real, typename H = Real>

concepts::Operator<G>& eigensolver::ArPack< F, G, H >::OP_

private

Operator OP as described in modus.

Definition at line 157 of file ARPACK.hh.

◆ resid_in_

template<typename F , typename G = Real, typename H = Real>

const concepts::Array<F>* eigensolver::ArPack< F, G, H >::resid_in_

private

Calculate vectors instead of eigenvectors Input of a residual vector (startvector) as array:

Definition at line 185 of file ARPACK.hh.

◆ resid_out_

template<typename F , typename G = Real, typename H = Real>

concepts::Array<F> eigensolver::ArPack< F, G, H >::resid_out_

private

The residual vector for output:

Definition at line 190 of file ARPACK.hh.

◆ schur_

template<typename F , typename G = Real, typename H = Real>

const bool eigensolver::ArPack< F, G, H >::schur_

private

Definition at line 186 of file ARPACK.hh.

◆ sigma_

template<typename F , typename G = Real, typename H = Real>

const F eigensolver::ArPack< F, G, H >::sigma_

private

Shift for the shift-invert modes:

Definition at line 180 of file ARPACK.hh.

◆ start_

template<typename F , typename G = Real, typename H = Real>

const concepts::Vector<F>* eigensolver::ArPack< F, G, H >::start_

private

Starting vector, if not given ARPACK invents one.

Definition at line 182 of file ARPACK.hh.

◆ target_

template<typename F , typename G = Real, typename H = Real>

enum which eigensolver::ArPack< F, G, H >::target_

private

Sort of eigenvalues to compute.

Definition at line 174 of file ARPACK.hh.

◆ tol_

template<typename F , typename G = Real, typename H = Real>

Real eigensolver::ArPack< F, G, H >::tol_

private

Convergence tolerance for the eigenpairs.

Definition at line 167 of file ARPACK.hh.

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

eigensolver/ARPACK.hh

eigensolver::ArPack< F, G, H > Class Template Reference

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename F, typename G = Real, typename H = Real> class eigensolver::ArPack< F, G, H >

Member Enumeration Documentation

◆ modus

◆ which

Constructor & Destructor Documentation

◆ ArPack()

◆ ~ArPack()

Member Function Documentation

◆ compute_()

◆ computeCmplx_()

◆ converged()

◆ getEF()

◆ getEV()

◆ getRESID()

◆ info()

◆ iterations()

Member Data Documentation

◆ A_

◆ B_

◆ computed_

◆ eigenvalues_

◆ eigenvectors_

◆ ev_

◆ iter_

◆ k_conv_

◆ kmax_

◆ maxiter_

◆ mode_

◆ numop_

◆ numopb_

◆ numreo_

◆ OP_

◆ resid_in_

◆ resid_out_

◆ schur_

◆ sigma_

◆ start_

◆ target_

◆ tol_

template<typename F, typename G = Real, typename H = Real>
class eigensolver::ArPack< F, G, H >