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

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

#include <AnasaziSolverUtils.hpp>

Public Member Functions

Constructor/Destructor
 SolverUtils ()
 Constructor. More...
 
virtual ~SolverUtils ()
 Destructor. More...
 

Static Public Member Functions

Sorting Methods
static void permuteVectors (const int n, const std::vector< int > &perm, MV &Q, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > *resids=0)
 Permute the vectors in a multivector according to the permutation vector perm, and optionally the residual vector resids. More...
 
static void permuteVectors (const std::vector< int > &perm, Teuchos::SerialDenseMatrix< int, ScalarType > &Q)
 Permute the columns of a Teuchos::SerialDenseMatrix according to the permutation vector perm. More...
 
Basis update methods
static void applyHouse (int k, MV &V, const Teuchos::SerialDenseMatrix< int, ScalarType > &H, const std::vector< ScalarType > &tau, Teuchos::RCP< MV > workMV=Teuchos::null)
 Apply a sequence of Householder reflectors (from GEQRF) to a multivector, using minimal workspace. More...
 
Eigensolver Projection Methods
static int directSolver (int size, const Teuchos::SerialDenseMatrix< int, ScalarType > &KK, Teuchos::RCP< const Teuchos::SerialDenseMatrix< int, ScalarType > > MM, Teuchos::SerialDenseMatrix< int, ScalarType > &EV, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &theta, int &nev, int esType=0)
 Routine for computing the first NEV generalized eigenpairs of the Hermitian pencil (KK, MM) More...
 
Sanity Checking Methods
static Teuchos::ScalarTraits
< ScalarType >::magnitudeType 		errorEquality (const MV &X, const MV &MX, Teuchos::RCP< const OP > M=Teuchos::null)
 Return the maximum coefficient of the matrix $M * X - MX$ scaled by the maximum coefficient of MX. More...
 

Detailed Description

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

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

This class provides concrete, templated implementations of utilities necessary for the solvers. 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

Definition at line 42 of file AnasaziSolverUtils.hpp.

Constructor & Destructor Documentation

template<class ScalarType , class MV , class OP >
Anasazi::SolverUtils< ScalarType, MV, OP >::SolverUtils ( )

Constructor.

Definition at line 164 of file AnasaziSolverUtils.hpp.

template<class ScalarType, class MV, class OP>
virtual Anasazi::SolverUtils< ScalarType, MV, OP >::~SolverUtils ( )
inlinevirtual

Destructor.

Definition at line 55 of file AnasaziSolverUtils.hpp.

Member Function Documentation

template<class ScalarType , class MV , class OP >
void Anasazi::SolverUtils< ScalarType, MV, OP >::permuteVectors ( const int  n,
const std::vector< int > &  perm,
MV &  Q,
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > *  resids = 0 
)
static

Permute the vectors in a multivector according to the permutation vector perm, and optionally the residual vector resids.

Definition at line 176 of file AnasaziSolverUtils.hpp.

template<class ScalarType , class MV , class OP >
void Anasazi::SolverUtils< ScalarType, MV, OP >::permuteVectors ( const std::vector< int > &  perm,
Teuchos::SerialDenseMatrix< int, ScalarType > &  Q 
)
static

Permute the columns of a Teuchos::SerialDenseMatrix according to the permutation vector perm.

Definition at line 240 of file AnasaziSolverUtils.hpp.

template<class ScalarType , class MV , class OP >
void Anasazi::SolverUtils< ScalarType, MV, OP >::applyHouse ( int  k,
MV &  V,
const Teuchos::SerialDenseMatrix< int, ScalarType > &  H,
const std::vector< ScalarType > &  tau,
Teuchos::RCP< MV >  workMV = Teuchos::null 
)
static

Apply a sequence of Householder reflectors (from GEQRF) to a multivector, using minimal workspace.

Parameters
k[in] the number of Householder reflectors composing the product
V[in/out] the multivector to be modified, with $n$ columns
H[in] a $n \times k$ matrix containing the encoded Householder vectors, as returned from GEQRF (see below)
tau[in] the $n$ coefficients for the Householder reflects, as returned from GEQRF
workMV[work] (optional) a multivector used for workspace. it need contain only a single vector; it if contains more, only the first vector will be modified.

This routine applies a sequence of Householder reflectors, $H_1 H_2 \cdots H_k$, to a multivector $V$. The reflectors are applied individually, as rank-one updates to the multivector. The benefit of this is that the only required workspace is a one-column multivector. This workspace can be provided by the user. If it is not, it will be allocated locally on each call to applyHouse.

Each $H_i$ ( $i=1,\ldots,k \leq n$) has the form
$ H_i = I - \tau_i v_i v_i^T $
where $\tau_i$ is a scalar and $v_i$ is a vector with $v_i(1:i-1) = 0$ and $e_i^T v_i = 1$; $v(i+1:n)$ is stored below H(i,i) and $\tau_i$ in tau[i-1]. (Note: zero-based indexing used for data structures H and tau, while one-based indexing used for mathematic object $v_i$).

If the multivector is $m \times n$ and we apply $k$ Householder reflectors, the total cost of the method is $4mnk - 2m(k^2-k)$ flops. For $k=n$, this becomes $2mn^2$, the same as for a matrix-matrix multiplication by the accumulated Householder reflectors.

Definition at line 268 of file AnasaziSolverUtils.hpp.

template<class ScalarType , class MV , class OP >
int Anasazi::SolverUtils< ScalarType, MV, OP >::directSolver ( int  size,
const Teuchos::SerialDenseMatrix< int, ScalarType > &  KK,
Teuchos::RCP< const Teuchos::SerialDenseMatrix< int, ScalarType > >  MM,
Teuchos::SerialDenseMatrix< int, ScalarType > &  EV,
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &  theta,
int &  nev,
int  esType = 0 
)
static

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

  @param size [in] Dimension of the eigenproblem (KK, MM)
  @param KK [in] Hermitian "stiffness" matrix
  @param MM [in] Hermitian positive-definite "mass" matrix
  @param EV [in] Dense matrix to store the nev eigenvectors
  @param theta [in] Array to store the eigenvalues (Size = nev )
  @param nev [in/out] Number of the smallest eigenvalues requested (in) / computed (out)
  @param esType [in] Flag to select the algorithm
  <ul>
  <li> esType =  0  (default) Uses LAPACK routine (Cholesky factorization of MM)
                    with deflation of MM to get orthonormality of
                    eigenvectors ( \form#90)
  <li> esType =  1  Uses LAPACK routine (Cholesky factorization of MM)
                    (no check of orthonormality)
  <li> esType = 10  Uses LAPACK routine for simple eigenproblem on KK
                    (MM is not referenced in this case)
  </ul>

  \note The code accesses only the upper triangular part of KK and MM.
  \return Integer \c 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

Definition at line 337 of file AnasaziSolverUtils.hpp.

template<class ScalarType , class MV , class OP >
Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::SolverUtils< ScalarType, MV, OP >::errorEquality ( const MV &  X,
const MV &  MX,
Teuchos::RCP< const OP >  M = Teuchos::null 
)
static

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.

Definition at line 616 of file AnasaziSolverUtils.hpp.

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