An implementation of the Belos::MatOrthoManager that performs orthogonalization using (potentially) multiple steps of classical Gram-Schmidt. More...

#include <BelosDGKSOrthoManager.hpp>

Inheritance diagram for Belos::DGKSOrthoManager< ScalarType, MV, OP >:

[legend]

Private Types
typedef Teuchos::ScalarTraits < ScalarType >::magnitudeType	MagnitudeType

typedef Teuchos::ScalarTraits < MagnitudeType >	MGT

typedef Teuchos::ScalarTraits < ScalarType >	SCT

typedef MultiVecTraits < ScalarType, MV >	MVT

typedef OperatorTraits < ScalarType, MV, OP >	OPT

Private Member Functions
int	findBasis (MV &X, Teuchos::RCP< MV > MX, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > C, bool completeBasis, int howMany=-1) const
	Routine to find an orthonormal basis for X. More...

bool	blkOrtho1 (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Routine to compute the block orthogonalization. More...

bool	blkOrtho (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Routine to compute the block orthogonalization. More...

int	blkOrthoSing (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > QQ) const
	Project X against QQ and normalize X, one vector at a time. More...

Private Attributes
int	max_blk_ortho_
	Max number of (re)orthogonalization steps, including the first. More...

MagnitudeType	blk_tol_
	Block reorthogonalization threshold. More...

MagnitudeType	dep_tol_
	(Non-block) reorthogonalization threshold. More...

MagnitudeType	sing_tol_
	Singular block detection threshold. More...

std::string	label_
	Label for timer(s). More...

Teuchos::RCP < Teuchos::ParameterList >	defaultParams_
	Default parameter list. More...

Constructor/Destructor
	DGKSOrthoManager (const std::string &label="Belos", Teuchos::RCP< const OP > Op=Teuchos::null, const int max_blk_ortho=max_blk_ortho_default_, const MagnitudeType blk_tol=blk_tol_default_, const MagnitudeType dep_tol=dep_tol_default_, const MagnitudeType sing_tol=sing_tol_default_)
	Constructor specifying re-orthogonalization tolerance. More...

	DGKSOrthoManager (const Teuchos::RCP< Teuchos::ParameterList > &plist, const std::string &label="Belos", Teuchos::RCP< const OP > Op=Teuchos::null)
	Constructor that takes a list of parameters. More...

	~DGKSOrthoManager ()
	Destructor. More...

Implementation of Teuchos::ParameterListAcceptorDefaultBase interface
void	setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &plist)

Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

Accessor routines
void	setBlkTol (const MagnitudeType blk_tol)
	Set parameter for block re-orthogonalization threshhold. More...

void	setDepTol (const MagnitudeType dep_tol)
	Set parameter for re-orthogonalization threshhold. More...

void	setSingTol (const MagnitudeType sing_tol)
	Set parameter for singular block detection. More...

MagnitudeType	getBlkTol () const
	Return parameter for block re-orthogonalization threshhold. More...

MagnitudeType	getDepTol () const
	Return parameter for re-orthogonalization threshhold. More...

MagnitudeType	getSingTol () const
	Return parameter for singular block detection. More...

Orthogonalization methods
void	project (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Given a list of (mutually and internally) orthonormal bases `Q`, this method takes a multivector `X` and projects it onto the space orthogonal to the individual `Q[i]`, optionally returning the coefficients of `X` for the individual `Q[i]`. All of this is done with respect to the inner product innerProd(). More...

void	project (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	This method calls project(X,Teuchos::null,C,Q); see documentation for that function. More...

int	normalize (MV &X, Teuchos::RCP< MV > MX, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method takes a multivector `X` and attempts to compute an orthonormal basis for , with respect to innerProd(). More...

int	normalize (MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method calls normalize(X,Teuchos::null,B); see documentation for that function. More...

virtual int	projectAndNormalizeWithMxImpl (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Given a set of bases `Q[i]` and a multivector `X`, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ . More...

Error methods
Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormError (const MV &X) const
	This method computes the error in orthonormality of a multivector. More...

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormError (const MV &X, Teuchos::RCP< const MV > MX) const
	This method computes the error in orthonormality of a multivector. The method has the option of exploiting a caller-provided `MX`. More...

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogError (const MV &X1, const MV &X2) const
	This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of `innerProd(X,Y)`. More...

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogError (const MV &X1, Teuchos::RCP< const MV > MX1, const MV &X2) const
	This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of `innerProd(X,Y)`. The method has the option of exploiting a caller-provided `MX`. More...

Label methods
void	setLabel (const std::string &label)
	This method sets the label used by the timers in the orthogonalization manager. More...

const std::string &	getLabel () const
	This method returns the label being used by the timers in the orthogonalization manager. More...

Default orthogonalization constants
static const int	max_blk_ortho_default_ = 2
	Max number of (re)orthogonalization steps, including the first (default). More...

static const MagnitudeType	blk_tol_default_
	Block reorthogonalization threshold (default). More...

static const MagnitudeType	dep_tol_default_
	(Non-block) reorthogonalization threshold (default). More...

static const MagnitudeType	sing_tol_default_ = 10*Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::eps()
	Singular block detection threshold (default). More...

static const int	max_blk_ortho_fast_ = 1
	Max number of (re)orthogonalization steps, including the first (fast). More...

static const MagnitudeType	blk_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()
	Block reorthogonalization threshold (fast). More...

static const MagnitudeType	dep_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()
	(Non-block) reorthogonalization threshold (fast). More...

static const MagnitudeType	sing_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()
	Singular block detection threshold (fast). More...

Additional Inherited Members
Public Member Functions inherited from Belos::MatOrthoManager< ScalarType, MV, OP >
	MatOrthoManager (Teuchos::RCP< const OP > Op=Teuchos::null)
	Default constructor. More...

virtual	~MatOrthoManager ()
	Destructor. More...

void	setOp (Teuchos::RCP< const OP > Op)
	Set operator. More...

Teuchos::RCP< const OP >	getOp () const
	Get operator. More...

void	innerProd (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const
	Provides the inner product defining the orthogonality concepts, using the provided operator. More...

void	innerProd (const MV &X, const MV &Y, Teuchos::RCP< const MV > MY, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const
	Provides the inner product defining the orthogonality concepts, using the provided operator. The method has the options of exploiting a caller-provided `MX`. More...

void	norm (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const
	Provides the norm induced by innerProd(). More...

void	norm (const MV &X, Teuchos::RCP< const MV > MX, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const
	Compute norm of each column of X. More...

int	projectAndNormalize (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Given a set of bases `Q[i]` and a multivector `X`, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ . More...

Public Member Functions inherited from Belos::OrthoManager< ScalarType, MV >
	OrthoManager ()
	Default constructor. More...

virtual	~OrthoManager ()
	Destructor. More...

int	projectAndNormalize (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Project X against the Q[i] and normalize X. More...

Public Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase
RCP< ParameterList >	getNonconstParameterList ()

RCP< ParameterList >	unsetParameterList ()

RCP< const ParameterList >	getParameterList () const

Protected Member Functions inherited from Belos::MatOrthoManager< ScalarType, MV, OP >
virtual int	projectAndNormalizeImpl (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const

Protected Member Functions inherited from Belos::OrthoManager< ScalarType, MV >
Protected Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase
void	setMyParamList (const RCP< ParameterList > &paramList)

RCP< ParameterList >	getMyNonconstParamList ()

RCP< const ParameterList >	getMyParamList () const

Protected Attributes inherited from Belos::MatOrthoManager< ScalarType, MV, OP >
Teuchos::RCP< const OP >	_Op

bool	_hasOp

Detailed Description

template<class ScalarType, class MV, class OP>
class Belos::DGKSOrthoManager< ScalarType, MV, OP >

An implementation of the Belos::MatOrthoManager that performs orthogonalization using (potentially) multiple steps of classical Gram-Schmidt.

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

Definition at line 80 of file BelosDGKSOrthoManager.hpp.

Member Typedef Documentation

template<class ScalarType , class MV , class OP >

typedef Teuchos::ScalarTraits<ScalarType>::magnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType

private

Definition at line 84 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

typedef Teuchos::ScalarTraits<MagnitudeType> Belos::DGKSOrthoManager< ScalarType, MV, OP >::MGT

private

Definition at line 85 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

typedef Teuchos::ScalarTraits<ScalarType> Belos::DGKSOrthoManager< ScalarType, MV, OP >::SCT

private

Definition at line 86 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

typedef MultiVecTraits<ScalarType,MV> Belos::DGKSOrthoManager< ScalarType, MV, OP >::MVT

private

Definition at line 87 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

typedef OperatorTraits<ScalarType,MV,OP> Belos::DGKSOrthoManager< ScalarType, MV, OP >::OPT

private

Definition at line 88 of file BelosDGKSOrthoManager.hpp.

Constructor & Destructor Documentation

template<class ScalarType , class MV , class OP >

Belos::DGKSOrthoManager< ScalarType, MV, OP >::DGKSOrthoManager	(	const std::string &	label = `"Belos"`,
		Teuchos::RCP< const OP >	Op = `Teuchos::null`,
		const int	max_blk_ortho = `max_blk_ortho_default_`,
		const MagnitudeType	blk_tol = `blk_tol_default_`,
		const MagnitudeType	dep_tol = `dep_tol_default_`,
		const MagnitudeType	sing_tol = `sing_tol_default_`
	)

inline

Constructor specifying re-orthogonalization tolerance.

Definition at line 95 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Belos::DGKSOrthoManager< ScalarType, MV, OP >::DGKSOrthoManager	(	const Teuchos::RCP< Teuchos::ParameterList > &	plist,
		const std::string &	label = `"Belos"`,
		Teuchos::RCP< const OP >	Op = `Teuchos::null`
	)

inline

Constructor that takes a list of parameters.

Definition at line 127 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Belos::DGKSOrthoManager< ScalarType, MV, OP >::~DGKSOrthoManager ( )

inline

Destructor.

Definition at line 158 of file BelosDGKSOrthoManager.hpp.

Member Function Documentation

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::setParameterList ( const Teuchos::RCP< Teuchos::ParameterList > & plist )

inlinevirtual

Implements Teuchos::ParameterListAcceptor.

Definition at line 165 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::RCP<const Teuchos::ParameterList> Belos::DGKSOrthoManager< ScalarType, MV, OP >::getValidParameters ( ) const

inlinevirtual

Reimplemented from Teuchos::ParameterListAcceptor.

Definition at line 200 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::setBlkTol ( const MagnitudeType blk_tol )

inline

Set parameter for block re-orthogonalization threshhold.

Definition at line 215 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::setDepTol ( const MagnitudeType dep_tol )

inline

Set parameter for re-orthogonalization threshhold.

Definition at line 229 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::setSingTol ( const MagnitudeType sing_tol )

inline

Set parameter for singular block detection.

Definition at line 239 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::getBlkTol ( ) const

inline

Return parameter for block re-orthogonalization threshhold.

Definition at line 249 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::getDepTol ( ) const

inline

Return parameter for re-orthogonalization threshhold.

Definition at line 252 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::getSingTol ( ) const

inline

Return parameter for singular block detection.

Definition at line 255 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::project	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

virtual

Given a list of (mutually and internally) orthonormal bases Q, this method takes a multivector X and projects it onto the space orthogonal to the individual Q[i], optionally returning the coefficients of X for the individual Q[i]. All of this is done with respect to the inner product innerProd().

After calling this routine, X will be orthogonal to each of the Q[i].

The method uses either one or two steps of classical Gram-Schmidt. The algebraically equivalent projection matrix is $P_Q = I - Q Q^H Op$ , if Op is the matrix specified for use in the inner product. Note, this is not an orthogonal projector.

Parameters

X	[in/out] The multivector to be modified. On output, `X` will be orthogonal to `Q[i]` with respect to innerProd().
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
C	[out] The coefficients of `X` in the `Q`[i], with respect to innerProd(). If `C[i]` is a non-null pointer and `C`[i] matches the dimensions of `X` and `Q`[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix `C`[i]. If `C[i]` is a non-null pointer whose size does not match the dimensions of `X` and `*Q`[i], then a std::invalid_argument std::exception will be thrown. Otherwise, if `C.size() < i` or `C[i]` is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.
Q	[in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each `Q[i]` is assumed to have orthonormal columns, and the `Q[i]` are assumed to be mutually orthogonal.

Implements Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 839 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::project	(	MV &	X,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

inlinevirtual

This method calls project(X,Teuchos::null,C,Q); see documentation for that function.

Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 297 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::normalize	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B
	)		const

virtual

This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$ , with respect to innerProd().

The method uses classical Gram-Schmidt, so that the coefficient matrix B is upper triangular.

This routine returns an integer rank stating the rank of the computed basis. If X does not have full rank and the normalize() routine does not attempt to augment the subspace, then rank may be smaller than the number of columns in X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors in X with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters

X	[in/out] The multivector to the modified. On output, `X` will have some number of orthonormal columns (with respect to innerProd()).
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
B	[out] The coefficients of the original `X` with respect to the computed basis. The first rows in `B` corresponding to the valid columns in `X` will be upper triangular.

Returns: Rank of the basis computed by this method.

Implements Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 822 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::normalize	(	MV &	X,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B
	)		const

inlinevirtual

This method calls normalize(X,Teuchos::null,B); see documentation for that function.

Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 335 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::projectAndNormalizeWithMxImpl	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

protectedvirtual

Given a set of bases Q[i] and a multivector X, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ .

This routine returns an integer rank stating the rank of the computed basis. If the subspace $colspan(X) - \sum_i colspan(Q[i])$ does not have dimension as large as the number of columns of X and the orthogonalization manager doe not attempt to augment the subspace, then rank may be smaller than the number of columns of X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters

X	[in/out] The multivector to the modified. On output, the relevant rows of `X` will be orthogonal to the `Q[i]` and will have orthonormal columns (with respect to innerProd()).
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
C	[out] The coefficients of the original `X` in the `Q`[i], with respect to innerProd(). If `C[i]` is a non-null pointer and `C`[i] matches the dimensions of `X` and `Q`[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix `C`[i]. If `C[i]` is a non-null pointer whose size does not match the dimensions of `X` and `Q`[i], then C[i] will first be resized to the correct size. This will destroy the original contents of the matrix. (This is a change from previous behavior, in which a std::invalid_argument exception was thrown if *C[i] was of the wrong size.) Otherwise, if `C.size() < i<> or C[i] is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.`
B	`[out] The coefficients of the original X with respect to the computed basis. The first rows in B corresponding to the valid columns in X will be upper triangular.`
Q	`[in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each Q[i] is assumed to have orthonormal columns, and the Q[i] are assumed to be mutually orthogonal.`

Returns: Rank of the basis computed by this method.

Implements Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 642 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::ScalarTraits<ScalarType>::magnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::orthonormError ( const MV & X ) const

inlinevirtual

This method computes the error in orthonormality of a multivector.

Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 414 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::ScalarTraits< ScalarType >::magnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::orthonormError	(	const MV &	X,
		Teuchos::RCP< const MV >	MX
	)		const

virtual

This method computes the error in orthonormality of a multivector. The method has the option of exploiting a caller-provided MX.

Implements Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 604 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::ScalarTraits<ScalarType>::magnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::orthogError	(	const MV &	X1,
		const MV &	X2
	)		const

inlinevirtual

This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y).

Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 431 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::ScalarTraits< ScalarType >::magnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::orthogError	(	const MV &	X1,
		Teuchos::RCP< const MV >	MX1,
		const MV &	X2
	)		const

virtual

This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y). The method has the option of exploiting a caller-provided MX.

Implements Belos::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 624 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

void Belos::DGKSOrthoManager< ScalarType, MV, OP >::setLabel ( const std::string & label )

virtual

This method sets the label used by the timers in the orthogonalization manager.

Implements Belos::OrthoManager< ScalarType, MV >.

Definition at line 577 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const std::string& Belos::DGKSOrthoManager< ScalarType, MV, OP >::getLabel ( ) const

inlinevirtual

This method returns the label being used by the timers in the orthogonalization manager.

Implements Belos::OrthoManager< ScalarType, MV >.

Definition at line 453 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::findBasis	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	C,
		bool	completeBasis,
		int	howMany = `-1`
	)		const

private

Routine to find an orthonormal basis for X.

Definition at line 926 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

bool Belos::DGKSOrthoManager< ScalarType, MV, OP >::blkOrtho1	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

private

Routine to compute the block orthogonalization.

Definition at line 1246 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

bool Belos::DGKSOrthoManager< ScalarType, MV, OP >::blkOrtho	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

private

Routine to compute the block orthogonalization.

Definition at line 1369 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::blkOrthoSing	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	QQ
	)		const

private

Project X against QQ and normalize X, one vector at a time.

Note: QQ is called QQ, rather than Q, because we convert it internally from an ArrayView to an Array (named Q inside). This is because the C++ compiler doesn't know how to do type inference (Array has a constructor that takes an ArrayView input). This routine wants an Array rather than an ArrayView internally, because it likes to add (via push_back()) and remove (via resize()) elements to the Q array. Remember that Arrays can be passed by value, just like std::vector objects, so this routine can add whatever it likes to the Q array without changing it from the caller's perspective.

Definition at line 1493 of file BelosDGKSOrthoManager.hpp.

Member Data Documentation

template<class ScalarType , class MV , class OP >

const int Belos::DGKSOrthoManager< ScalarType, MV, OP >::max_blk_ortho_default_ = 2

static

Max number of (re)orthogonalization steps, including the first (default).

Definition at line 461 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::blk_tol_default_

static

Initial value:

= 10*Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::squareroot(

Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::eps() )

Block reorthogonalization threshold (default).

Definition at line 463 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::dep_tol_default_

static

Initial value:

= Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::one()
      / Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::squareroot( 
      2*Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::one() )

(Non-block) reorthogonalization threshold (default).

Definition at line 465 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::sing_tol_default_ = 10*Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::eps()

static

Singular block detection threshold (default).

Definition at line 467 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const int Belos::DGKSOrthoManager< ScalarType, MV, OP >::max_blk_ortho_fast_ = 1

static

Max number of (re)orthogonalization steps, including the first (fast).

Definition at line 470 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::blk_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()

static

Block reorthogonalization threshold (fast).

Definition at line 472 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::dep_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()

static

(Non-block) reorthogonalization threshold (fast).

Definition at line 474 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

const DGKSOrthoManager< ScalarType, MV, OP >::MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::sing_tol_fast_ = Teuchos::ScalarTraits<typename DGKSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero()

static

Singular block detection threshold (fast).

Definition at line 476 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

int Belos::DGKSOrthoManager< ScalarType, MV, OP >::max_blk_ortho_

private

Max number of (re)orthogonalization steps, including the first.

Definition at line 483 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::blk_tol_

private

Block reorthogonalization threshold.

Definition at line 485 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::dep_tol_

private

(Non-block) reorthogonalization threshold.

Definition at line 487 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

MagnitudeType Belos::DGKSOrthoManager< ScalarType, MV, OP >::sing_tol_

private

Singular block detection threshold.

Definition at line 489 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

std::string Belos::DGKSOrthoManager< ScalarType, MV, OP >::label_

private

Label for timer(s).

Definition at line 492 of file BelosDGKSOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

Teuchos::RCP<Teuchos::ParameterList> Belos::DGKSOrthoManager< ScalarType, MV, OP >::defaultParams_

mutableprivate

Default parameter list.

Definition at line 498 of file BelosDGKSOrthoManager.hpp.

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

BelosDGKSOrthoManager.hpp

Private Types

Private Member Functions

Private Attributes

Constructor/Destructor

Implementation of Teuchos::ParameterListAcceptorDefaultBase interface

Accessor routines

Orthogonalization methods

Error methods

Label methods

Default orthogonalization constants

Additional Inherited Members

Detailed Description

template<class ScalarType, class MV, class OP> class Belos::DGKSOrthoManager< ScalarType, MV, OP >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class ScalarType, class MV, class OP>
class Belos::DGKSOrthoManager< ScalarType, MV, OP >