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LOCA::AnasaziOperator::Cayley Class Reference

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

#include <LOCA_AnasaziOperator_Cayley.H>

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List of all members.

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.
virtual ~Cayley ()
 Destructor.
virtual const string & label () const
 Return name of this operator.
virtual void apply (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &output) const
 Apply the operator.
virtual void preProcessSeedVector (NOX::Abstract::MultiVector &ivec)
 PreProcess the random seed vector.
virtual void transformEigenvalue (double &ev_r, double &ev_i) const
 Transform eigenvalue.
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.

Protected Attributes

Teuchos::RCP< LOCA::GlobalDataglobalData
 Global data.
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:

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::RCP< T >::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]
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:
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