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

This class implements the Locally-Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for solving Hermitian eigenvalue problems. More...

#include <AnasaziLOBPCG.hpp>

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

Anasazi::Eigensolver< ScalarType, MV, OP > List of all members.

Public Member Functions

Constructor/Destructor
 LOBPCG (const Teuchos::RefCountPtr< Eigenproblem< ScalarType, MV, OP > > &problem, const Teuchos::RefCountPtr< SortManager< ScalarType, MV, OP > > &sorter, const Teuchos::RefCountPtr< OutputManager< ScalarType > > &printer, const Teuchos::RefCountPtr< StatusTest< ScalarType, MV, OP > > &tester, const Teuchos::RefCountPtr< MatOrthoManager< ScalarType, MV, OP > > &ortho, Teuchos::ParameterList &params)
 LOBPCG constructor with eigenproblem, solver utilities, and parameter list of solver options.
virtual ~LOBPCG ()
 LOBPCG destructor
Solver methods
void iterate ()
 This method performs LOBPCG iterations until the status test indicates the need to stop or an error occurs (in which case, an exception is thrown).
void initialize (LOBPCGState< ScalarType, MV > newstate)
 Initialize the solver to an iterate, optionally providing the Ritz values, residual, and search direction.
void initialize ()
 Initialize the solver with the initial vectors from the eigenproblem or random data.
bool isInitialized ()
 Indicates whether the solver has been initialized or not.
LOBPCGState< 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::RefCountPtr< const
MV > 
getRitzVectors ()
 Get the Ritz vectors from the previous iteration.
std::vector< Value< ScalarType > > getRitzValues ()
 Get the Ritz values from the previous iteration.
std::vector< int > getRitzIndex ()
 Get the index used for extracting Ritz vectors from getRitzVectors().
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 2-norms of the Ritz residuals.
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. For LOBPCG, this always returns 3*getBlockSize(), the dimension of the subspace colspan([X H P]).
Accessor routines from Eigensolver
const Eigenproblem< ScalarType,
MV, OP > & 
getProblem () const
 Get a constant reference to the eigenvalue problem.
void setBlockSize (int blockSize)
 Set the blocksize to be used by the iterative solver in solving this eigenproblem.
int getBlockSize () const
 Get the blocksize to be used by the iterative solver in solving this eigenproblem.
void setAuxVecs (const Teuchos::Array< Teuchos::RefCountPtr< const MV > > &auxvecs)
 Set the auxiliary vectors for the solver.
Teuchos::Array< Teuchos::RefCountPtr<
const MV > > 
getAuxVecs () const
 Get the current auxiliary vectors.
LOBPCG-specific accessor routines
void setFullOrtho (bool fullOrtho)
 Instruct the LOBPCG iteration to use full orthogonality.
bool getFullOrtho () const
 Determine if the LOBPCG iteration is using full orthogonality.
bool hasP ()
 Indicates whether the search direction given by getState() is valid.
Output methods
void currentStatus (ostream &os)
 This method requests that the solver print out its current status to screen.

Detailed Description

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

This class implements the Locally-Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for solving Hermitian eigenvalue problems.

This implementation is a modification of the one found in A. Knyazev, "Toward the optimal preconditioned eigensolver: Locally optimal block preconditioner conjugate gradient method", SIAM J. Sci. Comput., vol 23, n 2, pp. 517-541.

The modification consists of the orthogonalization steps recommended in U. Hetmaniuk and R. Lehoucq, "Basis Selection in LOBPCG", Journal of Computational Physics.

These modifcation are referred to as full orthogonalization, and consist of also conducting the local optimization using an orthonormal basis.

Author:
Chris Baker, Ulrich Hetmaniuk, Rich Lehoucq, Heidi Thornquist

Definition at line 196 of file AnasaziLOBPCG.hpp.


Constructor & Destructor Documentation

template<class ScalarType, class MV, class OP>
Anasazi::LOBPCG< ScalarType, MV, OP >::LOBPCG const Teuchos::RefCountPtr< Eigenproblem< ScalarType, MV, OP > > &  problem,
const Teuchos::RefCountPtr< SortManager< ScalarType, MV, OP > > &  sorter,
const Teuchos::RefCountPtr< OutputManager< ScalarType > > &  printer,
const Teuchos::RefCountPtr< StatusTest< ScalarType, MV, OP > > &  tester,
const Teuchos::RefCountPtr< MatOrthoManager< ScalarType, MV, OP > > &  ortho,
Teuchos::ParameterList params
 

LOBPCG 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.
  • "Full Ortho" - a bool specifying whether the solver should employ a full orthogonalization technique. This can also be specified using the setFullOrtho() method.

Definition at line 616 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
virtual Anasazi::LOBPCG< ScalarType, MV, OP >::~LOBPCG  )  [inline, virtual]
 

LOBPCG destructor

Definition at line 218 of file AnasaziLOBPCG.hpp.


Member Function Documentation

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::iterate  )  [virtual]
 

This method performs LOBPCG 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 initialized; if not, it will call initialize() using default arguments. After initialization, the solver performs LOBPCG iterations until the status test evaluates as Passed, at which point the method returns to the caller.

The LOBPCG iteration proceeds as follows:

  1. The current residual (R) is preconditioned to form H
  2. H is orthogonalized against the auxiliary vectors and, if full orthogonalization
    is enabled, against X and P.
  3. The basis [X H P] is used to project the problem matrices.
  4. The projected eigenproblem is solved, and the desired eigenvectors and eigenvalues are selected.
  5. These are used to form the new eigenvector estimates (X) and the search directions (P).
    If full orthogonalization is enabled, these are generated to be mutually orthogonal and with orthonormal columns.
  6. The new residual (R) is formed.

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

Possible exceptions thrown include std::logic_error, std::invalid_argument or one of the LOBPCG-specific exceptions.

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

Definition at line 1154 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::initialize LOBPCGState< ScalarType, MV >  newstate  ) 
 

Initialize the solver to an iterate, optionally providing the Ritz values, residual, and search direction.

The LOBPCG eigensolver contains a certain amount of state relating to the current iterate, including the current residual, the current search direction, and the images of these spaces under the operators.

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())
  • If newstate.P != Teuchos::null, hasP() == true.
    Otherwise, hasP() == false
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 component of the state (i.e., KX) not given to initialize() will be generated.

Definition at line 873 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::initialize  )  [virtual]
 

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

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

Definition at line 1126 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
bool Anasazi::LOBPCG< ScalarType, MV, OP >::isInitialized  )  [inline, virtual]
 

Indicates whether the solver has been initialized or not.

Returns:
bool indicating the state of the solver.
Postcondition:
If isInitialized() == true:
  • X is orthogonal to auxiliary vectors and has orthonormal columns
  • KX == Op*X
  • MX == M*X if M != Teuchos::null
    Otherwise, MX == Teuchos::null
  • getRitzValues() returns the sorted Ritz values with respect to X
  • getResidualVecs() returns the residual vectors with respect to X
  • If hasP() == true,
    • P orthogonal to auxiliary vectors
    • If getFullOrtho() == true,
      • P is orthogonal to X and has orthonormal columns
    • KP == Op*P
    • MP == M*P if M != Teuchos::null
      Otherwise, MP == Teuchos::null

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

Definition at line 302 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
LOBPCGState<ScalarType,MV> Anasazi::LOBPCG< ScalarType, MV, OP >::getState  )  const [inline]
 

Get the current state of the eigensolver.

The data is only valid if isInitialized() == true. The data for the search directions P is only meaningful if hasP() == true. Finally, the data for the preconditioned residual (H) is only meaningful in the situation where the solver throws an ::LOBPCGRitzFailure exception during iterate().

Returns:
An LOBPCGState object containing const pointers to the current solver state.

Definition at line 314 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::LOBPCG< ScalarType, MV, OP >::getNumIters  )  const [inline, virtual]
 

Get the current iteration count.

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

Definition at line 343 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::resetNumIters  )  [inline, virtual]
 

Reset the iteration count.

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

Definition at line 346 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::RefCountPtr<const MV> Anasazi::LOBPCG< ScalarType, MV, OP >::getRitzVectors  )  [inline, virtual]
 

Get the Ritz vectors from the previous iteration.

Returns:
A multivector with getBlockSize() vectors containing the sorted Ritz vectors corresponding to the most significant Ritz values. The i-th vector of the return corresponds to the i-th Ritz vector; there is no need to use getRitzIndex().

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

Definition at line 355 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
std::vector<Value<ScalarType> > Anasazi::LOBPCG< ScalarType, MV, OP >::getRitzValues  )  [inline, virtual]
 

Get the Ritz values from the previous iteration.

Returns:
A vector of length getCurSubspaceDim() containing the Ritz values from the previous projected eigensolve.

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

Definition at line 362 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
std::vector<int> Anasazi::LOBPCG< ScalarType, MV, OP >::getRitzIndex  )  [inline, virtual]
 

Get the index used for extracting Ritz vectors from getRitzVectors().

Because BlockDavidson is a Hermitian solver, all Ritz values are real and all Ritz vectors can be represented in a single column of a multivector. Therefore, getRitzIndex() is not needed when using the output from getRitzVectors().

Returns:
An int vector of size getCurSubspaceDim() composed of zeros.

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

Definition at line 378 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > Anasazi::LOBPCG< ScalarType, MV, OP >::getResNorms  )  [virtual]
 

Get the current residual norms.

Returns:
A vector of length getCurSubspaceDim() containing the norms of the residuals, with respect to the orthogonalization manager norm() method.

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

Definition at line 1757 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > Anasazi::LOBPCG< ScalarType, MV, OP >::getRes2Norms  )  [virtual]
 

Get the current residual 2-norms.

Returns:
A vector of length getCurSubspaceDim() containing the 2-norms of the residuals.

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

Definition at line 1771 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> Anasazi::LOBPCG< ScalarType, MV, OP >::getRitzRes2Norms  )  [inline, virtual]
 

Get the 2-norms of the Ritz residuals.

Returns:
A vector of length getCurSubspaceDim() containing the 2-norms of the Ritz residuals.

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

Definition at line 406 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::LOBPCG< ScalarType, MV, OP >::getCurSubspaceDim  )  const [inline, virtual]
 

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

LOBPCG employs a sequential subspace iteration, maintaining a fixed-rank basis, as opposed to an expanding subspace mechanism employed by Krylov-subspace solvers like BlockKrylovSchur and BlockDavidson.

Returns:
An integer specifying the rank of the subspace generated by the eigensolver. If isInitialized() == false, the return is 0. Otherwise, the return will be 2*getBlockSize() or 3*getBlockSize().

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

Definition at line 421 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::LOBPCG< ScalarType, MV, OP >::getMaxSubspaceDim  )  const [inline, virtual]
 

Get the maximum dimension allocated for the search subspace. For LOBPCG, this always returns 3*getBlockSize(), the dimension of the subspace colspan([X H P]).

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

Definition at line 429 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
const Eigenproblem<ScalarType,MV,OP>& Anasazi::LOBPCG< ScalarType, MV, OP >::getProblem  )  const [inline, virtual]
 

Get a constant reference to the eigenvalue problem.

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

Definition at line 438 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::setBlockSize int  blockSize  )  [virtual]
 

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

If the block size is reduced, then the new iterate (and residual and search direction) are chosen as the subset of the current iterate preferred by the sort manager. Otherwise, the solver state is set to uninitialized.

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

Definition at line 692 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::LOBPCG< 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 >.

Definition at line 453 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::setAuxVecs const Teuchos::Array< Teuchos::RefCountPtr< const MV > > &  auxvecs  )  [virtual]
 

Set the auxiliary vectors for the solver.

Because the current iterate X and search direction P cannot be assumed orthogonal to the new auxiliary vectors, a call to setAuxVecs() with a non-empty argument will reset the solver to the uninitialized state.

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 manually reinitialize the solver using initialize().

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

Definition at line 828 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::Array<Teuchos::RefCountPtr<const MV> > Anasazi::LOBPCG< ScalarType, MV, OP >::getAuxVecs  )  const [inline, virtual]
 

Get the current auxiliary vectors.

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

Definition at line 470 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::setFullOrtho bool  fullOrtho  ) 
 

Instruct the LOBPCG iteration to use full orthogonality.

If the getFullOrtho() == false and isInitialized() == true and hasP() == true, then P will be invalidated by setting full orthogonalization to true.

Definition at line 1136 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
bool Anasazi::LOBPCG< ScalarType, MV, OP >::getFullOrtho  )  const [inline]
 

Determine if the LOBPCG iteration is using full orthogonality.

Definition at line 485 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
bool Anasazi::LOBPCG< ScalarType, MV, OP >::hasP  )  [inline]
 

Indicates whether the search direction given by getState() is valid.

Definition at line 488 of file AnasaziLOBPCG.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::LOBPCG< ScalarType, MV, OP >::currentStatus ostream &  os  )  [virtual]
 

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

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

Definition at line 1912 of file AnasaziLOBPCG.hpp.


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