Anasazi operator for computing generalized eigenvalues using Cayley transformations. More...

#include <LOCA_AnasaziOperator_Cayley.H>

Inheritance diagram for LOCA::AnasaziOperator::Cayley:

Collaboration diagram for LOCA::AnasaziOperator::Cayley:

Public Member Functions
	Cayley (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &eigenParams, const Teuchos::RCP< Teuchos::ParameterList > &solverParams, const Teuchos::RCP< LOCA::TimeDependent::AbstractGroup > &grp)
	Constructor. More...

virtual	~Cayley ()
	Destructor.

virtual const std::string &	label () const
	Return name of this operator.

virtual void	apply (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &output) const
	Apply the operator. More...

virtual void	preProcessSeedVector (NOX::Abstract::MultiVector &ivec)
	PreProcess the random seed vector. More...

virtual void	transformEigenvalue (double &ev_r, double &ev_i) const
	Transform eigenvalue. More...

virtual NOX::Abstract::Group::ReturnType	rayleighQuotient (NOX::Abstract::Vector &evec_r, NOX::Abstract::Vector &evec_i, double &rq_r, double &rq_i) const
	Compute Rayleigh quotient. More...

Public Member Functions inherited from LOCA::AnasaziOperator::AbstractStrategy
	AbstractStrategy ()
	Constructor.

virtual	~AbstractStrategy ()
	Destructor.

virtual void	beginPostProcessing ()
	Hook to precompute info for subsequent repeated calls to tranformEigenvalue and rayleighQuotient.

Protected Attributes
Teuchos::RCP< LOCA::GlobalData >	globalData
	Global data.

std::string	myLabel
	Name of this operator.

Teuchos::RCP < Teuchos::ParameterList >	eigenParams
	Stores parameters relating to the operator.

Teuchos::RCP < Teuchos::ParameterList >	solverParams
	Stores linear solver parameters.

Teuchos::RCP < LOCA::TimeDependent::AbstractGroup >	grp
	Stores group representing Jacobian and Mass matrix.

Teuchos::RCP < NOX::Abstract::MultiVector >	tmp_r
	Stores a temporary vector for computing Rayleigh quotients.

Teuchos::RCP < NOX::Abstract::MultiVector >	tmp_i
	Stores a temporary vector for computing Rayleigh quotients.

double	sigma
	Stores Cayley pole $\sigma$ .

double	mu
	Stores Cayley zero $\mu$ .

Detailed Description

Anasazi operator for computing generalized eigenvalues using Cayley transformations.

This class implements the LOCA::AnasaziOperator::AbstractStrategy interface for computing generalized eigenvalues $\lambda$ and eigenvectors $z$ of the system

$J z = \lambda M z *$

where $J$ is the Jacobian matrix and $M$ is the mass matrix. The eigenvalues are computed using a Cayley transformation, i.e. solving

$(J - \sigma M) z = (J - \mu M) r$

where $\sigma$ is the Cayley pole and $\mu$ is the Cayley zero.

The parameters used by this class supplied in the constructor are:

"Cayley Pole" - $\sigma$ as defined above (Default 0.0)
"Cayley Zero" - $\mu$ as defined above (Default 0.0)

Also the grp argument to the constructor must be a child of LOCA::TimeDependent::AbstractGroup for the shift-invert operations.

Constructor & Destructor Documentation

LOCA::AnasaziOperator::Cayley::Cayley	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		const Teuchos::RCP< LOCA::Parameter::SublistParser > &	topParams,
		const Teuchos::RCP< Teuchos::ParameterList > &	eigenParams,
		const Teuchos::RCP< Teuchos::ParameterList > &	solverParams,
		const Teuchos::RCP< LOCA::TimeDependent::AbstractGroup > &	grp
	)

Constructor.

Argument grp must be of type LOCA::TimeDependent::AbstractGroup. See class description for a list of eigenParams.

References eigenParams, Teuchos::ParameterList::get(), mu, and sigma.

Member Function Documentation

void LOCA::AnasaziOperator::Cayley::apply	(	const NOX::Abstract::MultiVector &	input,
		NOX::Abstract::MultiVector &	output
	)		const

virtual

Apply the operator.

Applies the inverse of the shifted operator, i.e., solves

$(J-\omega I)z = M r$

for $z$ , where $r = \mbox{input}$ and $z = \mbox{output}$ .

Implements LOCA::AnasaziOperator::AbstractStrategy.

References NOX::Abstract::MultiVector::clone(), NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::Group::Ok, and NOX::ShapeCopy.

void LOCA::AnasaziOperator::Cayley::preProcessSeedVector ( NOX::Abstract::MultiVector & ivec )

virtual

PreProcess the random seed vector.

Performs one backward Euler iteration on the random initial seed vector, to satisfy contraints

Reimplemented from LOCA::AnasaziOperator::AbstractStrategy.

References NOX::Abstract::MultiVector::clone(), NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::Group::Ok, and NOX::ShapeCopy.

NOX::Abstract::Group::ReturnType LOCA::AnasaziOperator::Cayley::rayleighQuotient	(	NOX::Abstract::Vector &	evec_r,
		NOX::Abstract::Vector &	evec_i,
		double &	rq_r,
		double &	rq_i
	)		const

virtual

Compute Rayleigh quotient.

Computes the Rayleigh quotient $z^T J z / z^T M z$ for the eigenvector $z$ .

Implements LOCA::AnasaziOperator::AbstractStrategy.

References NOX::Abstract::Vector::createMultiVector(), NOX::Abstract::Vector::innerProduct(), NOX::Abstract::Group::Ok, NOX::Abstract::Vector::scale(), and NOX::ShapeCopy.

void LOCA::AnasaziOperator::Cayley::transformEigenvalue	(	double &	ev_r,
		double &	ev_i
	)		const

virtual

Transform eigenvalue.

Transforms the given eigenvalue to the eigenvalue of the Jacobian-mass matrix system by shifting and inverting it.

Implements LOCA::AnasaziOperator::AbstractStrategy.

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

LOCA_AnasaziOperator_Cayley.H
LOCA_AnasaziOperator_Cayley.C

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation