Main Page | Class Hierarchy | Alphabetical List | Class List | File List | Class Members | Search for 

Anasazi::ModalSolverUtils< ScalarType, MV, OP > Class Template Reference

Anasazi's templated, static class providing utilities for the modal solvers. More...

#include <AnasaziModalSolverUtils.hpp>

List of all members.

Public Member Functions

Constructor/Destructor
 ModalSolverUtils (const Teuchos::RefCountPtr< OutputManager< ScalarType > > &om)
 Basic constructor.
virtual ~ModalSolverUtils ()
 Destructor.
Sorting Methods
int sortScalars (int n, ScalarType *y, int *perm=0) const
 Sort the vector of eigenvalues y, optionally returning the permutation vector perm.
int sortScalars_Vectors (int n, ScalarType *lambda, MV *Q, std::vector< ScalarType > *resids=0) const
 Sort the vector of eigenvalues lambda, and optionally the corresponding multi-vector Q and residual vector resids.
Eigensolver Projection Methods
int massOrthonormalize (MV &X, MV &MX, const OP *M, const MV &Q, int howMany, int orthoType=0, ScalarType kappa=1.5625) const
 Mass orthogonalize X with-respect-to the orthogonalization parameter orthoType.
int directSolver (int size, const Teuchos::SerialDenseMatrix< int, ScalarType > &KK, const Teuchos::SerialDenseMatrix< int, ScalarType > *MM, Teuchos::SerialDenseMatrix< int, ScalarType > *EV, std::vector< ScalarType > *theta, int nev, int esType=0) const
 Routine for computing the first NEV generalized eigenpairs of the symmetric pencil (KK, MM).
Sanity Checking Methods
ScalarType errorOrthogonality (const MV *X, const MV *R, const OP *M=0) const
 Return the maximum value of $R_i^T M X_j / || MR_i || || X_j ||$.
ScalarType errorOrthonormality (const MV *X, const OP *M=0) const
 Return the maximum coefficient of the matrix $X^T M X - I$.
ScalarType errorEquality (const MV *X, const MV *MX, const OP *M=0) const
 Return the maximum coefficient of the matrix $M * X - MX$ scaled by the maximum coefficient of MX.

Detailed Description

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

Anasazi's templated, static class providing utilities for the modal solvers.

This class provides concrete, templated implementations of utilities necessary for the modal solvers (Davidson, LOBPCG, ...). These utilities include sorting, orthogonalization, projecting/solving local eigensystems, and sanity checking. These are internal utilties, so the user should not alter this class.

Author:
Ulrich Hetmaniuk, Rich Lehoucq, and Heidi Thornquist

Constructor & Destructor Documentation

template<class ScalarType, class MV, class OP>
Anasazi::ModalSolverUtils< ScalarType, MV, OP >::ModalSolverUtils (  const Teuchos::RefCountPtr< OutputManager< ScalarType > > &  om  ) 
 

Basic constructor.

Parameters:
om [in] OutputManager to handle output from the utilities.

Member Function Documentation

template<class ScalarType, class MV, class OP>
int Anasazi::ModalSolverUtils< ScalarType, MV, OP >::directSolver (  int  size,
const Teuchos::SerialDenseMatrix< int, ScalarType > &  KK,
const Teuchos::SerialDenseMatrix< int, ScalarType > *  MM,
Teuchos::SerialDenseMatrix< int, ScalarType > *  EV,
std::vector< ScalarType > *  theta,
int  nev,
int  esType = 0
)  const
 

Routine for computing the first NEV generalized eigenpairs of the symmetric pencil (KK, MM).

Parameters:
size [in] Dimension of the eigenproblem (KK, MM)
KK [in] Symmetric "stiffness" matrix
MM [in] Symmetric Positive "mass" matrix
EV [in] Dense matrix to store the nev eigenvectors
theta [in] Array to store the eigenvalues (Size = nev )
nev [in/out] Number of the smallest eigenvalues requested (in) / computed (out)
esType [in] Flag to select the algorithm
  • esType = 0 (default) Uses LAPACK routine (Cholesky factorization of MM) with deflation of MM to get orthonormality of eigenvectors ($S^TMMS = I$)
  • esType = 1 Uses LAPACK routine (Cholesky factorization of MM) (no check of orthonormality)
  • esType = 10 Uses LAPACK routine for simple eigenproblem on KK (MM is not referenced in this case)
Note:
The code accesses only the upper triangular part of KK and MM.
Returns:
Integer info on the status of the computation Return the integer info on the status of the computation
  • info = 0 >> Success
  • info = - 20 >> Failure in LAPACK routine

template<class ScalarType, class MV, class OP>
ScalarType Anasazi::ModalSolverUtils< ScalarType, MV, OP >::errorEquality (  const MV *  X,
const MV *  MX,
const OP *  M = 0
)  const
 

Return the maximum coefficient of the matrix $M * X - MX$ scaled by the maximum coefficient of MX.

Note:
When M is not specified, the identity is used.

template<class ScalarType, class MV, class OP>
ScalarType Anasazi::ModalSolverUtils< ScalarType, MV, OP >::errorOrthogonality (  const MV *  X,
const MV *  R,
const OP *  M = 0
)  const
 

Return the maximum value of $R_i^T M X_j / || MR_i || || X_j ||$.

Note:
When M is not specified, the identity is used.

template<class ScalarType, class MV, class OP>
ScalarType Anasazi::ModalSolverUtils< ScalarType, MV, OP >::errorOrthonormality (  const MV *  X,
const OP *  M = 0
)  const
 

Return the maximum coefficient of the matrix $X^T M X - I$.

Note:
When M is not specified, the identity is used.

template<class ScalarType, class MV, class OP>
int Anasazi::ModalSolverUtils< ScalarType, MV, OP >::massOrthonormalize (  MV &  X,
MV &  MX,
const OP *  M,
const MV &  Q,
int  howMany,
int  orthoType = 0,
ScalarType  kappa = 1.5625
)  const
 

Mass orthogonalize X with-respect-to the orthogonalization parameter orthoType.

Parameters:
X [in/out] Multi-vector being orthogonalized/orthonormalized.
MX [in/out] Image of the multi-vector X by the mass matrix M, not referenced if MX=0.
M [in] Pointer to the mass matrix, not referenced if 0.
Q [in] Vectors to orthogonalize against.
howMany [in] Number of vectors X to orthogonalize.
orthoType [in] Orthogonalization type
  • orthoType = 0 (default) > Performs both operations
  • orthoType = 1 > Performs $Q^TMX = 0$
  • orthoType = 2 > Performs $X^TMX = I$
kappa [in] Coefficient determining when to perform a second Gram-Schmidt step Default value = 1.5625 = (1.25)^2 (as suggested in Parlett's book)
Returns:
Integer info on the status of the computation
  • info = 0 >> Success
  • info > 0 >> Indicate how many vectors have been tried to avoid rank deficiency for X
  • info =-1 >> Failure: X has zero columns, #col of X > #rows of X, #col of [Q X] > #rows of X, or no good random vectors could be found

The documentation for this class was generated from the following file:
Generated on Thu Sep 18 12:41:36 2008 for Anasazi by doxygen 1.3.9.1