Solves a generalized eigenvalue problem subject to linear, homogeneous constraints. More...

#include <constrained.hh>

Inheritance diagram for eigensolver::Constrained:

Public Member Functions
	Constrained (concepts::Operator< Real > &A, concepts::Operator< Real > &M, const concepts::SparseMatrix< Real > &C, SolverFabric< Real > &solver)
	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	~Constrained ()

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

Private Member Functions
void	compute_ ()
	The real compute routine. More...

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

const concepts::SparseMatrix< Real > &	C_
	Matrix of constraints. $C^\top \vec x = g = 0$ is enforced. More...

bool	computed_
	If false, the code will have to compute, otherwise not. More...

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

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

concepts::TrivExtendRestrict< Real > *	ext

uint	it_
	Statistics. More...

uint	k_conv_

uint	kmax_
	Maximal number of eigenvalues which can be computed. More...

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

concepts::Operator< Real > &	M_
	Mass matrix. More...

concepts::Permutation< Real > *	Pr

std::unique_ptr< concepts::Compose< Real > >	PrQgt

std::unique_ptr< concepts::Permutation< Real > >	Prt

sparseqr::GivensRotations< Real > *	Qg

std::unique_ptr< concepts::Compose< Real > >	QgPrt

std::unique_ptr< concepts::Compose< Real > >	QgPrtext

sparseqr::GivensRotations< Real > *	Qgt

concepts::TrivExtendRestrict< Real > *	restr

std::unique_ptr< concepts::Compose< Real > >	restrPrQgt

std::unique_ptr< concepts::Compose< Real > >	restrPrQgtA

std::unique_ptr< concepts::Compose< Real > >	restrPrQgtAQgPrtext

std::unique_ptr< concepts::Compose< Real > >	restrPrQgtM

std::unique_ptr< concepts::Compose< Real > >	restrPrQgtMQgPrtext

SolverFabric< Real > &	solver_
	Fabric for the eigenvalue solver. More...

Detailed Description

Solves a generalized eigenvalue problem subject to linear, homogeneous constraints.

This class solve a generalized eigenvalue problem of the form

$A \vec x = \lambda M \vec x$

subject to the constraints $C^\top \vec x = g = 0$ where $C \in R^{n \times m}$ and $A, M \in R^{n \times n}$ . This is important for solving eigenvalue problems with essential boundary conditions like $\vec u \times \vec n = 0$ .

For the case , this is described in [1 section 12.6, 2]. For the much more complicated case of $g \neq 0$ , see [3, 4]. The first case should be sufficient for most applications.

See also: [1] Gene H. Golub and Charles F. van Loan, Matrix Computations, The Johns Hopkins University Press, 1983.
[2] Gene H. Golub, Some Modified Matrix Eigenvalue Problems, SIAM Review, 15 (1973), No. 2, 318–334.
[3] Walter Gander, Gene H. Golub and Urs von Matt, A Constrained Eigenvalue Problem, in Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Gene H. Golub and P. Van Dooren (eds.), NATO ASI Series, Vol. F70, 1991, 677–686.
[4] Walter Gander, Gene H. Golub and Urs von Matt, A Constrained Eigenvalue Problem, Linear Algebra and Its Applications, 114/115 (1989), 815–839.

Test:: test::ConstrainedEVP

Author: Philipp Frauenfelder, 2002

Definition at line 54 of file constrained.hh.

Constructor & Destructor Documentation

◆ Constrained()

eigensolver::Constrained::Constrained	(	concepts::Operator< Real > &	A,
		concepts::Operator< Real > &	M,
		const concepts::SparseMatrix< Real > &	C,
		SolverFabric< Real > &	solver
	)

inline

Constructor.

Parameters

A	Matrix
M	Matrix
C	Matrix of constraints
solver	Fabric for the eigenvalue solver

Definition at line 62 of file constrained.hh.

◆ ~Constrained()

virtual eigensolver::Constrained::~Constrained ( )

virtual

Member Function Documentation

◆ compute_()

void eigensolver::Constrained::compute_ ( )

private

The real compute routine.

Fills lambda_ and ev_

See also: computed_

◆ converged() [1/2]

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

inlinevirtual

Definition at line 74 of file constrained.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::Constrained::getEF ( )

virtual

Implements eigensolver::EigenSolver< Real >.

◆ getEV()

virtual const concepts::Array<Real>& eigensolver::Constrained::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::Constrained::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< Real >.

◆ iterations() [1/2]

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

inlinevirtual

Definition at line 73 of file constrained.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::Constrained::A_

private

Stiffness matrix.

Definition at line 89 of file constrained.hh.

◆ C_

const concepts::SparseMatrix<Real>& eigensolver::Constrained::C_

private

Matrix of constraints. $C^\top \vec x = g = 0$ is enforced.

Definition at line 93 of file constrained.hh.

◆ computed_

bool eigensolver::Constrained::computed_

private

If false, the code will have to compute, otherwise not.

Definition at line 86 of file constrained.hh.

◆ eigenvectors_

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

private

Storage space for eigenvectors.

Definition at line 98 of file constrained.hh.

◆ ev_

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

private

References into storage for eigenvectors.

Definition at line 100 of file constrained.hh.

◆ ext

concepts::TrivExtendRestrict<Real>* eigensolver::Constrained::ext

private

Definition at line 108 of file constrained.hh.

◆ it_

uint eigensolver::Constrained::it_

private

Statistics.

Definition at line 114 of file constrained.hh.

◆ k_conv_

uint eigensolver::Constrained::k_conv_

private

Definition at line 114 of file constrained.hh.

◆ kmax_

uint eigensolver::Constrained::kmax_

private

Maximal number of eigenvalues which can be computed.

Definition at line 103 of file constrained.hh.

◆ lambda_

concepts::Array<Real> eigensolver::Constrained::lambda_

private

Storage space for eigenvalues.

Definition at line 96 of file constrained.hh.

◆ M_

concepts::Operator<Real>& eigensolver::Constrained::M_

private

Mass matrix.

Definition at line 91 of file constrained.hh.

◆ Pr

concepts::Permutation<Real>* eigensolver::Constrained::Pr

private

Definition at line 105 of file constrained.hh.

◆ PrQgt

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::PrQgt

private

Definition at line 109 of file constrained.hh.

◆ Prt

std::unique_ptr<concepts::Permutation<Real> > eigensolver::Constrained::Prt

private

Definition at line 106 of file constrained.hh.

◆ Qg

sparseqr::GivensRotations<Real> * eigensolver::Constrained::Qg

private

Definition at line 107 of file constrained.hh.

◆ QgPrt

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::QgPrt

private

Definition at line 109 of file constrained.hh.

◆ QgPrtext

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::QgPrtext

private

Definition at line 110 of file constrained.hh.

◆ Qgt

sparseqr::GivensRotations<Real>* eigensolver::Constrained::Qgt

private

Definition at line 107 of file constrained.hh.

◆ restr

concepts::TrivExtendRestrict<Real> * eigensolver::Constrained::restr

private

Definition at line 108 of file constrained.hh.

◆ restrPrQgt

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::restrPrQgt

private

Definition at line 109 of file constrained.hh.

◆ restrPrQgtA

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::restrPrQgtA

private

Definition at line 110 of file constrained.hh.

◆ restrPrQgtAQgPrtext

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::restrPrQgtAQgPrtext

private

Definition at line 110 of file constrained.hh.

◆ restrPrQgtM

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::restrPrQgtM

private

Definition at line 110 of file constrained.hh.

◆ restrPrQgtMQgPrtext

std::unique_ptr<concepts::Compose<Real> > eigensolver::Constrained::restrPrQgtMQgPrtext

private

Definition at line 111 of file constrained.hh.

◆ solver_

SolverFabric<Real>& eigensolver::Constrained::solver_

private

Fabric for the eigenvalue solver.

Definition at line 79 of file constrained.hh.

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

eigensolver/constrained.hh

eigensolver::Constrained Class Referenceabstract

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Constrained()

◆ ~Constrained()

Member Function Documentation

◆ compute_()

◆ converged() [1/2]

◆ converged() [2/2]

◆ getEF()

◆ getEV()

◆ info()

◆ iterations() [1/2]

◆ iterations() [2/2]

Member Data Documentation

◆ A_

◆ C_

◆ computed_

◆ eigenvectors_

◆ ev_

◆ ext

◆ it_

◆ k_conv_

◆ kmax_

◆ lambda_

◆ M_

◆ Pr

◆ PrQgt

◆ Prt

◆ Qg

◆ QgPrt

◆ QgPrtext

◆ Qgt

◆ restr

◆ restrPrQgt

◆ restrPrQgtA

◆ restrPrQgtAQgPrtext

◆ restrPrQgtM

◆ restrPrQgtMQgPrtext

◆ solver_