Anasazi::BlockKrylovSchur< ScalarType, MV, OP > Class Template Reference
[Anasazi Eigensolver Framework]

This class implements the block Krylov-Schur iteration, for solving linear eigenvalue problems. More...

#include <AnasaziBlockKrylovSchur.hpp>

Inheritance diagram for Anasazi::BlockKrylovSchur< ScalarType, MV, OP >:

List of all members.

Public Member Functions
Constructor/Destructor
	BlockKrylovSchur (const Teuchos::RCP< Eigenproblem< ScalarType, MV, OP > > &problem, const Teuchos::RCP< SortManager< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > > &sorter, const Teuchos::RCP< OutputManager< ScalarType > > &printer, const Teuchos::RCP< StatusTest< ScalarType, MV, OP > > &tester, const Teuchos::RCP< OrthoManager< ScalarType, MV > > &ortho, Teuchos::ParameterList &params)
	BlockKrylovSchur constructor with eigenproblem, solver utilities, and parameter list of solver options.
virtual	~BlockKrylovSchur ()
	BlockKrylovSchur destructor.
Solver methods
void	iterate ()
	This method performs Block Krylov-Schur iterations until the status test indicates the need to stop or an error occurs (in which case, an exception is thrown).
void	initialize (BlockKrylovSchurState< ScalarType, MV > state)
	Initialize the solver to an iterate, providing a Krylov basis and Hessenberg matrix.
void	initialize ()
	Initialize the solver with the initial vectors from the eigenproblem or random data.
bool	isInitialized () const
	Indicates whether the solver has been initialized or not.
BlockKrylovSchurState< ScalarType, MV >	getState () const
	Get the current state of the eigensolver.
Status methods
int	getNumIters () const
	Get the current iteration count.
void	resetNumIters ()
	Reset the iteration count.
Teuchos::RCP< const MV >	getRitzVectors ()
	Get the Ritz vectors.
std::vector< Value< ScalarType > >	getRitzValues ()
	Get the Ritz values.
std::vector< int >	getRitzIndex ()
	Get the Ritz index vector.
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType >	getResNorms ()
	Get the current residual norms.
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType >	getRes2Norms ()
	Get the current residual 2-norms.
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType >	getRitzRes2Norms ()
	Get the current Ritz residual 2-norms.
Accessor routines
void	setStatusTest (Teuchos::RCP< StatusTest< ScalarType, MV, OP > > test)
	Set a new StatusTest for the solver.
Teuchos::RCP< StatusTest< ScalarType, MV, OP > >	getStatusTest () const
	Get the current StatusTest used by the solver.
const Eigenproblem< ScalarType, MV, OP > &	getProblem () const
	Get a constant reference to the eigenvalue problem.
void	setSize (int blockSize, int numBlocks)
	Set the blocksize and number of blocks to be used by the iterative solver in solving this eigenproblem.
void	setBlockSize (int blockSize)
	Set the blocksize.
void	setStepSize (int stepSize)
	Set the step size.
void	setNumRitzVectors (int numRitzVecs)
	Set the number of Ritz vectors to compute.
int	getStepSize () const
	Get the step size.
int	getBlockSize () const
	Get the blocksize to be used by the iterative solver in solving this eigenproblem.
int	getNumRitzVectors () const
	Get the number of Ritz vectors to compute.
int	getCurSubspaceDim () const
	Get the dimension of the search subspace used to generate the current eigenvectors and eigenvalues.
int	getMaxSubspaceDim () const
	Get the maximum dimension allocated for the search subspace.
void	setAuxVecs (const Teuchos::Array< Teuchos::RCP< const MV > > &auxvecs)
	Set the auxiliary vectors for the solver.
Teuchos::Array< Teuchos::RCP< const MV > >	getAuxVecs () const
	Get the auxiliary vectors for the solver.
Output methods
void	currentStatus (std::ostream &os)
	This method requests that the solver print out its current status to screen.
Block-Krylov Schur status routines
bool	isRitzVecsCurrent () const
	Get the status of the Ritz vectors currently stored in the eigensolver.
bool	isRitzValsCurrent () const
	Get the status of the Ritz values currently stored in the eigensolver.
bool	isSchurCurrent () const
	Get the status of the Schur form currently stored in the eigensolver.
Block-Krylov Schur compute routines
void	computeRitzVectors ()
	Compute the Ritz vectors using the current Krylov factorization.
void	computeRitzValues ()
	Compute the Ritz values using the current Krylov factorization.
void	computeSchurForm (const bool sort=true)
	Compute the Schur form of the projected eigenproblem from the current Krylov factorization.

---

Detailed Description

template<class ScalarType, class MV, class OP>
class Anasazi::BlockKrylovSchur< ScalarType, MV, OP >

This class implements the block Krylov-Schur iteration, for solving linear eigenvalue problems.

This method is a block version of the iteration presented by G.W. Stewart in "A Krylov-Schur Algorithm for Large Eigenproblems", SIAM J. Matrix Anal. Appl., Vol 23(2001), No. 3, pp. 601-614.

Author:

Chris Baker, Ulrich Hetmaniuk, Rich Lehoucq, Heidi Thornquist

---

Constructor & Destructor Documentation

template<class ScalarType, class MV, class OP>

Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::BlockKrylovSchur	(	const Teuchos::RCP< Eigenproblem< ScalarType, MV, OP > > &	problem,
		const Teuchos::RCP< SortManager< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > > &	sorter,
		const Teuchos::RCP< OutputManager< ScalarType > > &	printer,
		const Teuchos::RCP< StatusTest< ScalarType, MV, OP > > &	tester,
		const Teuchos::RCP< OrthoManager< ScalarType, MV > > &	ortho,
		Teuchos::ParameterList &	params
	)

BlockKrylovSchur constructor with eigenproblem, solver utilities, and parameter list of solver options.

This constructor takes pointers required by the eigensolver, in addition to a parameter list of options for the eigensolver. These options include the following:

• "Block Size" - an int specifying the block size used by the algorithm. This can also be specified using the setBlockSize() method. Default: 1
• "Num Blocks" - an int specifying the maximum number of blocks allocated for the solver basis. Default: 3*problem->getNEV()
• "Step Size" - an int specifying how many iterations are performed between computations of eigenvalues and eigenvectors.
  Note: This parameter is mandatory.
• "Number of Ritz Vectors" - an int specifying how many Ritz vectors are computed on calls to getRitzVectors(). Default: 0
• "Print Number of Ritz Values" - an int specifying how many Ritz values are printed on calls to currentStatus(). Default: "Block Size"

template<class ScalarType, class MV, class OP>

virtual Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::~BlockKrylovSchur

(

)

[inline, virtual]

BlockKrylovSchur destructor.

---

Member Function Documentation

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::iterate

(

)

[virtual]

This method performs Block Krylov-Schur iterations until the status test indicates the need to stop or an error occurs (in which case, an exception is thrown).

iterate() will first determine whether the solver is inintialized; if not, it will call initialize() using default arguments. After initialization, the solver performs Block Krylov-Schur iterations until the status test evaluates as Passed, at which point the method returns to the caller.

The Block Krylov-Schur iteration proceeds as follows:

1. The operator problem->getOperator() is applied to the newest blockSize vectors in the Krylov basis.
2. The resulting vectors are orthogonalized against the auxiliary vectors and the previous basis vectors, and made orthonormal.
3. The Hessenberg matrix is updated.
4. If we have performed stepSize iterations since the last update, update the Ritz values and Ritz residuals.

The status test is queried at the beginning of the iteration.

Possible exceptions thrown include the BlockKrylovSchurOrthoFailure.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::initialize

(

BlockKrylovSchurState< ScalarType, MV >

state

)

Initialize the solver to an iterate, providing a Krylov basis and Hessenberg matrix.

The BlockKrylovSchur eigensolver contains a certain amount of state, consisting of the current Krylov basis and the associated Hessenberg matrix.

initialize() gives the user the opportunity to manually set these, although this must be done with caution, abiding by the rules given below. All notions of orthogonality and orthonormality are derived from the inner product specified by the orthogonalization manager.

Postcondition:

isInitialized() == true (see post-conditions of isInitialize())

The user has the option of specifying any component of the state using initialize(). However, these arguments are assumed to match the post-conditions specified under isInitialized(). Any necessary component of the state not given to initialize() will be generated.

Note, for any pointer in newstate which directly points to the multivectors in the solver, the data is not copied.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::initialize

(

)

[virtual]

Initialize the solver with the initial vectors from the eigenproblem or random data.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

bool Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::isInitialized

(

)

const [inline, virtual]

Indicates whether the solver has been initialized or not.

Returns:

bool indicating the state of the solver.

Postcondition:

If isInitialized() == true:

• the first getCurSubspaceDim() vectors of V are orthogonal to auxiliary vectors and have orthonormal columns
• the principal Hessenberg submatrix of of H contains the Hessenberg matrix associated with V

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

BlockKrylovSchurState<ScalarType,MV> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getState

(

)

const [inline]

Get the current state of the eigensolver.

The data is only valid if isInitialized() == true.

Returns:

A BlockKrylovSchurState object containing const pointers to the current solver state.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getNumIters

(

)

const [inline, virtual]

Get the current iteration count.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::resetNumIters

(

)

[inline, virtual]

Reset the iteration count.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

Teuchos::RCP<const MV> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getRitzVectors

(

)

[inline, virtual]

Get the Ritz vectors.

Returns:

A multivector of columns not exceeding the maximum dimension of the subspace containing the Ritz vectors from the most recent call to computeRitzVectors().

Note:

To see if the returned Ritz vectors are current, call isRitzVecsCurrent().

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

std::vector<Value<ScalarType> > Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getRitzValues

(

)

[inline, virtual]

Get the Ritz values.

Returns:

A vector of length not exceeding the maximum dimension of the subspace containing the Ritz values from the most recent Schur form update.

Note:

To see if the returned Ritz values are current, call isRitzValsCurrent().

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

std::vector<int> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getRitzIndex

(

)

[inline, virtual]

Get the Ritz index vector.

Returns:

A vector of length not exceeding the maximum dimension of the subspace containing the index vector for the Ritz values and Ritz vectors, if they are computed.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getResNorms

(

)

[inline, virtual]

Get the current residual norms.

Note:

Block Krylov-Schur cannot provide this so a zero length vector will be returned.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getRes2Norms

(

)

[inline, virtual]

Get the current residual 2-norms.

Note:

Block Krylov-Schur cannot provide this so a zero length vector will be returned.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getRitzRes2Norms

(

)

[inline, virtual]

Get the current Ritz residual 2-norms.

Returns:

A vector of length blockSize containing the 2-norms of the Ritz residuals.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setStatusTest

(

Teuchos::RCP< StatusTest< ScalarType, MV, OP > >

test

)

[virtual]

Set a new StatusTest for the solver.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

Teuchos::RCP< StatusTest< ScalarType, MV, OP > > Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getStatusTest

(

)

const [virtual]

Get the current StatusTest used by the solver.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

const Eigenproblem<ScalarType,MV,OP>& Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getProblem

(

)

const [inline, virtual]

Get a constant reference to the eigenvalue problem.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setSize	(	int	blockSize,
		int	numBlocks
	)

Set the blocksize and number of blocks to be used by the iterative solver in solving this eigenproblem.

Changing either the block size or the number of blocks will reset the solver to an uninitialized state.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setBlockSize

(

int

blockSize

)

[virtual]

Set the blocksize.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setStepSize

(

int

stepSize

)

Set the step size.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setNumRitzVectors

(

int

numRitzVecs

)

Set the number of Ritz vectors to compute.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getStepSize

(

)

const [inline]

Get the step size.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getBlockSize

(

)

const [inline, virtual]

Get the blocksize to be used by the iterative solver in solving this eigenproblem.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getNumRitzVectors

(

)

const [inline]

Get the number of Ritz vectors to compute.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getCurSubspaceDim

(

)

const [inline, virtual]

Get the dimension of the search subspace used to generate the current eigenvectors and eigenvalues.

Returns:

An integer specifying the rank of the Krylov subspace currently in use by the eigensolver. If isInitialized() == false, the return is 0.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

int Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getMaxSubspaceDim

(

)

const [inline, virtual]

Get the maximum dimension allocated for the search subspace.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::setAuxVecs

(

const Teuchos::Array< Teuchos::RCP< const MV > > &

auxvecs

)

[virtual]

Set the auxiliary vectors for the solver.

Because the current Krylov subspace cannot be assumed orthogonal to the new auxiliary vectors, a call to setAuxVecs() will reset the solver to the uninitialized state. This happens only in the case where the new auxiliary vectors have a combined dimension of greater than zero.

In order to preserve the current state, the user will need to extract it from the solver using getState(), orthogonalize it against the new auxiliary vectors, and reinitialize using initialize().

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

Teuchos::Array<Teuchos::RCP<const MV> > Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::getAuxVecs

(

)

const [inline, virtual]

Get the auxiliary vectors for the solver.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::currentStatus

(

std::ostream &

os

)

[virtual]

This method requests that the solver print out its current status to screen.

Implements Anasazi::Eigensolver< ScalarType, MV, OP >.

template<class ScalarType, class MV, class OP>

bool Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::isRitzVecsCurrent

(

)

const [inline]

Get the status of the Ritz vectors currently stored in the eigensolver.

template<class ScalarType, class MV, class OP>

bool Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::isRitzValsCurrent

(

)

const [inline]

Get the status of the Ritz values currently stored in the eigensolver.

template<class ScalarType, class MV, class OP>

bool Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::isSchurCurrent

(

)

const [inline]

Get the status of the Schur form currently stored in the eigensolver.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::computeRitzVectors

(

)

Compute the Ritz vectors using the current Krylov factorization.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::computeRitzValues

(

)

Compute the Ritz values using the current Krylov factorization.

template<class ScalarType, class MV, class OP>

void Anasazi::BlockKrylovSchur< ScalarType, MV, OP >::computeSchurForm

(

const bool

sort = true

)

Compute the Schur form of the projected eigenproblem from the current Krylov factorization.

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

• AnasaziBlockKrylovSchur.hpp

---