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

#include <AnasaziSolverUtils.hpp>

Public Member Functions
Constructor/Destructor
	SolverUtils ()
	Constructor.
virtual	~SolverUtils ()
	Destructor.
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`.
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`.
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.
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)`
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 scaled by the maximum coefficient of `MX`.

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 61 of file AnasaziSolverUtils.hpp.

Constructor & Destructor Documentation

template<class ScalarType , class MV , class OP >

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

Constructor.

Definition at line 184 of file AnasaziSolverUtils.hpp.

template<class ScalarType, class MV, class OP>

virtual Anasazi::SolverUtils< ScalarType, MV, OP >::~SolverUtils ( ) [inline, virtual]

Destructor.

Definition at line 74 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 196 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 260 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 columns
H	[in] a $n \times k$ matrix containing the encoded Householder vectors, as returned from `GEQRF` (see below)
tau	[in] the 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 288 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)

Parameters:

size	[in] Dimension of the eigenproblem (KK, MM)
KK	[in] Hermitian "stiffness" matrix
MM	[in] Hermitian positive-definite "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 ( ) 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

Definition at line 357 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 636 of file AnasaziSolverUtils.hpp.

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

AnasaziSolverUtils.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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